mm-4909 === Subject: Re: Problems with the News Group > Usenet is a part of the Internet that predates the Web. Google provides > a web-based reader for Usenet news groups, but there are other readers. > In fact Usenet is best experienced as it was 90's, via custom client > software that you install and run on your local machine. I disagree. I prefer using Google Groups to both Thunderbird and Agent, because I can view an entire thread on one contiguous page. Its annoying having to click through thread tree controls to sew up the conversation. With Google Groups I can just use my middle mouse wheel. -Andrew. === Subject: Re: Problems with the News Group posting-account=6ea2ugoAAACnO44ASKspIG0s--Ju5Ekb Gecko/20020604,gzip(gfe),gzip(gfe) Usenet is a part of the Internet that predates the Web. Google provides > a web-based reader for Usenet news groups, but there are other readers. > In fact Usenet is best experienced as it was 90's, via custom client > software that you install and run on your local machine. I disagree. I prefer using Google Groups to both Thunderbird and > Agent, because I can view an entire thread on one contiguous page. > Its annoying having to click through thread tree controls to sew up > the conversation. With Google Groups I can just use my middle mouse > wheel. It is one of the reasons I use Googlegroups too. I assume there is some newsreader which offers the functionality of looking at a thread as one continuous stream instead of having to open individual messages but I don't want to spend the time to try one after another until I find one which does. [Crossposting to news.software.readers] === Subject: óMr. Achava's posts, last 2 days. óThis shows some(not all) of Bousbouras' posts, last 2 days: Mr. Achava's posts, last 2 days: Tomazos': fishfry's: Some newsGroups are indexed more frequently than others. Some aren't indexed at all. .81201201201201201201201201201201201201 201201201201 My useNet client is called .81gX.ZIP.81h. No one but me can operate it. As far as I know, no one but me has ever tried to operate it. When creating or updating a newsGroup, it puts thousands of posts into one .TXT file; this way, I can navigate it easily in my code editor(Visual Studio). .81g JeffRelf.F-M.FM/X.ZIP .81h, includes: JeffRelf.F-M.FM/X.TXT JeffRelf.F-M.FM/X.EXE JeffRelf.F-M.FM/X.CPP JeffRelf.F-M.FM/Visual_Studio_Macros.TXT JeffRelf.F-M.FM/Games.EXE JeffRelf.F-M.FM/Dif.EXE JeffRelf.F-M.FM/_Crap_.REG JeffRelf.F-M.FM/userContent.CSS X.TXT is the settings file, including C++-style //comments, help. X.EXE is the newsReader. X.CPP is the source code, Visual C++ 9. Games.EXE is a Mindless, semiRandom version of .81gChess.81h. Dif.EXE compares two plain-text files. Unicode is supported. Example of how to run it from a .BAT file: start Dif.EXE prevX.CPP X.CPP _Crap_.REG has some registry settings I use. userContent.CSS, for FireFox 3, controls the format of webPages. === Subject: Re: Problems with the News Group posting-account=Z3AipgkAAABkoMfyNwddSxsYhXHi5CDt CLR 1.1.4322; InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) On Jun 17, 11:03pm, Achava Nakhash, the Loving Snake > Hi all, little bit of extra information. the secret > (of other ways to read news groups)? expect I will soon by trying several of them out. I have been kindn of busy lately - just finished a week of 12 hour a day trining on MuSQL, otherwise learning MySQL, Plone, Zope, html, xhtml, JavaScript, PHP, and other things. I will be dragged kicking and screaming into the modern world of programming whether I want to or not. Fortunately I want to. Along the way I am learning a lot more about how the web is implemented and how it is used. It is lots of fun, but as it is for work I need to be disciplined, and so I have been off math mostly for the last several months and don't see any quick let up. All of which is my excuse for not implementing your suggestions immediately and for posting only a very small amount. Achava === Subject: Re: Mystery of the Missing Sunspots, Solved? <9wg%l.248$9l4.88@nwrddc01.gnilink.net> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 1.1.4322; eSobiSubscriber 2.0.4.16; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > -------- The Prolog ------- = The debate is over. Kill any & all Cap'n Trade schemes = > == Stop, kill and rescind any & all Carbon Tax attempts == -------- The Posting ------- AHAHAHAHA... yourmommycalled you a Little Green Idiot > [snip crap] > ... ahahaha... == The fact is that you are a perfect example of > Someone whom 'yourmommycalled' a Little Green Idiot == hanson didn't reply with any useful other than a hahahaha > indicating he cannot engage in meaningful discussion. > Since you are pissed that you didn't get to hear what you > wanted to hear... ahahahaha... and you are too afraid to > open your Green Bible and then apologize every day for > everything you say, because of it... let me open it for you: -------- The Opening ------- Why does that fraudulent behavior by the Global Warmers > surprise you? They have promoted fraud from the get go. > It's all in the their Green Bible which says quite clearly & > explicit on all issues of information that: -- Green Genesis --: > 1 It doesn't matter what is true ... it only matters what people > = believe is true. -- Paul Watson, Sea Shepard/ex-Greenpeace, &... > 2 If you don't know an answer, a fact, a statistic, then .... make it > = up on the spot... for the mass-media today... the truth is irrelevant. > = -- Paul Watson in Earthforce: An Earth Warrior's Guide to Strategy. > 3 We make simplified, dramatic statements, and make little > = mention of any doubts we may have [about] being honest. > = -- Stephen Schneider (Stanford prof. who first sought fame as > = a global cooler, but has now hit the big time as a global warmer) -- Revelations --: > 4 A lot of environmental [sci/soc/pol] messages are simply not > = accurate. We use hype. -- Jerry Franklin, Ecologist, UoW, and... > 5 to attract great funding you have to scare the public by making > = things bigger and more dangerous than they really are. > = --Petr Chylek, Prof. Atmospheric Sci., Dalhousie Uni, Halifax > 6 Even if the theory of global warming is wrong, we will be doing the > = right thing -- Sen.Tim Wirth, Admin of Ted Turner's $1Billion UN-gift. > 7 No matter if the science is all phony, Climate change [provides] > = equality in the world. -- Christine Stewart, Can. Enviro Minister > 8 It is appropriate to have an over-representation of factual presen- > = tations -- Al Gore, Chairman, Gen. Investment Management Bank -- Tribulations --: > 9= I got the impression that instead of going out to shoot birds, > = I should go out and shoot the kids who shoot birds. > -- Paul Watson, founder of Greenpeace and **Sea Shepherd** Modern, attributal definitions of enviro classifications: ...are the ones who advocate, promote, support, legalize, > institute and extort the permit charges, the user fees, the > enviro surtaxes and the CO2/Carbon tax, all reflected in > HIGHER PRICES of goods and services!, ...and being > responsible for much of the OUT-SOURCING! > ... are the ones who are recipients and beneficiaries from > the lootings of (1), directly or indirectly. > .. are the unpaid, well-meaning ones, in environmental > groups who think they do something for the environment, > when in fact they are only the enablers and facilitators for > (2) who are harvesting the green $$$ that (1) has extorted. The most intriguing fact though is that during the past 40 years > **EVERYBODY** has adopted the Green Bible & learned, > by now how to uses these machination principles for their > own agenda by now.... ahahaha....ALL of'em use and do it... > from the far Left to the far Right, from Lenders to Creditors, > from Union bosses to Wallstreet CEO, from Jews to Muslims, > from secular Heads of State to the Pope, & most ominously > of all ... from Elementary School pupils to their Teachers... > WORLDWIDE!... Strange enough though, the original hard core class 3 enviros > the first tier disciples of environmentalism are in full denial on this. ----------- the real Green conclusion ----------- = The debate is over. Kill any & all Cap'n Trade schemes = > == Stop, kill and rescind any & all Carbon Tax attempts == If there is any problem arising from global warming then > do some ing old fashioned engineering to counter the > problem. Tax the green turds to get the $Billions back they > extorted from society and finance the needed engineering > with it. Start with making/buying a bigger HVA when it gets > too hot or too cold for you.... ....ahahahaha... ahahanson help Fallout PnP by expanding it. ... green plastic grocery-store army men/cowboys and indians work very well, .... This means that, sometime after World War II, real history and Fallout history diverged, ... 2077, the war became the War, and reached its inevitable conclusion. ... pnp.fallout.wikia.com/wiki/Chapter_I:_Introduction Nuclear Physics A : Experimental studies of the 209Bi(p, n) 209Po ...The (p, np) neutrons stand out in the real TOF region as a sharp spike 2 ns in .... The conclusion from this comparison is that our rela tive (p, .... 5) W.L. Fadner, E.R.L. Green, S.I. Hayakawa, J.J. Kraushaar and R.R. Johnson Nucl. ... linkinghub.elsevier.com/retrieve/pii/0375947472906823 The Importance of the P vs. NP Problem, Page 3 of 3 - Associated ...In conclusion, you have learned about complexity classes P and NP, and you now have a ... Theory, Not Law: The Real Problem with How Evolution is Taught ... www.associatedcontent.com/.../the_importance_of_the_p_vs_np_problem_pg3.html The Evolution of Thoroughbred Bloodline CrossesAs a consequence, invoking P/NP, for example, as a singular explanation for an observed ... Nevertheless, as we shall see, the actual difference is real and ... that developing a statistical conclusion based on something like P/NP that .... And although the NP/NP trend line (green) still shows the most stamina, ... Axial anomaly at finite temperature and finite densitydifferent, all the conclusions agree that the axial anomaly ... [p [ 2 4- m 2) 1/2 np and rp are respectively ... and p the density of fermions, In the real time Green's function framework, the density effects is ... www.springerlink.com/index/N545088T78K36042.pdf Phys. Rev. D 30, 774 (1984): Valent - Renormalizable ...It is first explained, for the real model with p=1 (the old .83[CapitalEth] model), ..... q- gqlg- gEiG Restricting ourselves to I1N-P e g=[l-ET i where E is an (N- p)Xp real-valued matrix ..... Six-point Green's function. is independent of p at the one-loop level. ... CONCLUSION We have shown, in a nonstandard parametrization, ... link.aps.org/doi/10.1103/PhysRevD.30.774 Hidden Histories: the Story of Sustainable Design, ProQuest ...Conclusion. Printable Version (PDF). Tell a Friend ... The Green Consumer Guide http://cgi.ebay.com.my/ws/eBayISAPI.dll? ... Ibid. p.91. Papanek, Victor. 1985. 2nd ed. Design for the real world: human ecology and ... 1., n.p., http://www.desphilosophy.com/dpp/dpp_journal/feature/body.html Accessed April 6th, 2009 ... www.csa.com/discoveryguides/design/reviewf.php?SID... [PDF] Microsoft PowerPoint - King WQ trading.pptFile Format: PDF/Adobe Acrobat - View as HTML for P/NP Nutrient Credit Trading. DEMAND. Point Source saves $ ... Conclusions. * Serious Supply and Demand Problems (few willing buyers and sellers) because of: ... The real unit of exchange is a low-cost allowance credit .... Can landowner sell credits for nutrient reductions that resulted in green payment? ... www.mawaterquality.org/.../Necessary_Conditions_for_P_NP_Nutrient_Credit_Tra ding_King.pdf and ...the roots of Eq. (6) are real and, consequently, rl = 0, while in the region --v5 < (np) < 0 (the ... (p -- m z -- 2 (np) R) Fp (, 7]') = I [-I (Kx -- '), ... www.springerlink.com/index/T1TP3U081L6186RH.pdf Phys. Rev. A 56, 4764 (1997): Marinescu - Dispersion coefficients ...The various symmetries associated with the n P-nP asymp-tote for a ... VI, and finally the conclusions are presented in Sec. VII. ..... Green's function relative to theatomic state designated by the real part of the energy argument. VI. ... link.aps.org/doi/10.1103/PhysRevA.56.4764 About .81.87 Blog .81.87 FreeWiki(tm) (c)2009 MeAmI.org Search for the People Powered by infinity: .81.87 === Subject: Re: Mystery of the Missing Sunspots, Solved? posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > Fartin' Martin Musatov marty.musatov@gmail.com , here as > MeAmI.org is trying to > suck up to me again after he was earnestly adminstered > to, to follow these instructions: http://tinyurl.com/lnkmaq > which he confused with these one here, because -------- The Prolog ------- = The debate is over. Kill any & all Cap'n Trade schemes = > == Stop, kill and rescind any & all Carbon Tax attempts == -------- The Posting ------- AHAHAHAHA... yourmommycalled you a Little Green Idiot > [snip crap] ... ahahaha... == The fact is that you are a perfect example of > Someone whom 'yourmommycalled' a Little Green Idiot == > Now read your Green Bible and see why you are a LGI & feel good: hanson didn't reply with any useful other than a hahahaha > indicating he cannot engage in meaningful discussion. Since you are pissed that you didn't get to hear what you > wanted to hear... ahahahaha... and you are too afraid to > open your Green Bible and then apologize every day for > everything you say, because of it... let me open it for you: -------- The Opening ------- Why does that fraudulent behavior by the Global Warmers > surprise you? They have promoted fraud from the get go. > It's all in the their Green Bible which says quite clearly & > explicit on all issues of information that: -- Green Genesis --: > 1 It doesn't matter what is true ... it only matters what people > = believe is true. -- Paul Watson, Sea Shepard/ex-Greenpeace, &... > 2 If you don't know an answer, a fact, a statistic, then .... make it > = up on the spot... for the mass-media today... the truth is irrelevant. > = -- Paul Watson in Earthforce: An Earth Warrior's Guide to Strategy. > 3 We make simplified, dramatic statements, and make little > = mention of any doubts we may have [about] being honest. > = -- Stephen Schneider (Stanford prof. who first sought fame as > = a global cooler, but has now hit the big time as a global warmer) -- Revelations --: > 4 A lot of environmental [sci/soc/pol] messages are simply not > = accurate. We use hype. -- Jerry Franklin, Ecologist, UoW, and... > 5 to attract great funding you have to scare the public by making > = things bigger and more dangerous than they really are. > = --Petr Chylek, Prof. Atmospheric Sci., Dalhousie Uni, Halifax > 6 Even if the theory of global warming is wrong, we will be doing the > = right thing -- Sen.Tim Wirth, Admin of Ted Turner's $1Billion UN-gift. > 7 No matter if the science is all phony, Climate change [provides] > = equality in the world. -- Christine Stewart, Can. Enviro Minister > 8 It is appropriate to have an over-representation of factual presen- > = tations -- Al Gore, Chairman, Gen. Investment Management Bank -- Tribulations --: > 9= I got the impression that instead of going out to shoot birds, > = I should go out and shoot the kids who shoot birds. > -- Paul Watson, founder of Greenpeace and **Sea Shepherd** Modern, attributal definitions of enviro classifications: ...are the ones who advocate, promote, support, legalize, > institute and extort the permit charges, the user fees, the > enviro surtaxes and the CO2/Carbon tax, all reflected in > HIGHER PRICES of goods and services!, ...and being > responsible for much of the OUT-SOURCING! > ... are the ones who are recipients and beneficiaries from > the lootings of (1), directly or indirectly. > .. are the unpaid, well-meaning ones, in environmental > groups who think they do something for the environment, > when in fact they are only the enablers and facilitators for > (2) who are harvesting the green $$$ that (1) has extorted. The most intriguing fact though is that during the past 40 years > **EVERYBODY** has adopted the Green Bible & learned, > by now how to uses these machination principles for their > own agenda by now.... ahahaha....ALL of'em use and do it... > from the far Left to the far Right, from Lenders to Creditors, > from Union bosses to Wallstreet CEO, from Jews to Muslims, > from secular Heads of State to the Pope, & most ominously > of all ... from Elementary School pupils to their Teachers... > WORLDWIDE!... Strange enough though, the original hard core class 3 enviros > the first tier disciples of environmentalism are in full denial on this. ----------- the real Green conclusion ----------- = The debate is over. Kill any & all Cap'n Trade schemes = > == Stop, kill and rescind any & all Carbon Tax attempts == If there is any problem arising from global warming then > do some ing old fashioned engineering to counter the > problem. Tax the green turds to get the $Billions back they > extorted from society and finance the needed engineering > with it. Start with making/buying a bigger HVA when it gets > too hot or too cold for you.... ....ahahahaha... ahahanson ----------- ----------- ----------- > Fartin' Martin, don't you have any self-esteem at all?... Sheesh!... > http://tinyurl.com/lnkmaq ... If you run after me, then at least > say something original & in a style that one can understand > and do NOT just post cut and paste crap that has the same > buzz words: blah, blah, blah.... ... Green's function... ... blah, blah, blah > [snip crap] .... ahahahaha... Go ahead and explain ELSEWHERE to all > those little green idiots what Greens' function has to do with > environmentalism. They will look at you and conclude that > you are a Big green idiot.... ahahahaha... ahahahaha... > http://tinyurl.com/lnkmaq ... ahahahaha.... ahahahahanson Why did you call me this? -- MeAmI.org Martin Musatov text box like auto-complete. My name has a u but not an i. Can you tell me why this happened and explain the mechanics please? === Subject: Re: Mystery of the Missing Sunspots, Solved? posting-account=GAxY0QkAAAAF_LOpeqXWnUpwaRFIuJqm Gecko/2009042316 Firefox/3.0.10 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) I don't think we need worry too much about the globally significant fraction of CO2 released by the USA beyond (say) 2020 when there will be a total collapse into anarchy and Third World status. With America out of the way the world can finally relax its concentration on self- defence and concentrate on building up non-polluting energy sources. Solar electric will probably evolve into thin films which can be applied directly to buildings with a consequent drop in direct solar heating and avoidance of air conditioning. External insulation will probably become very much thinner allowing its use without rebuilding of the existing housing stock. Windows with direct control over transparency to various wavelength will become the norm and far more affordable via mass production. Overnight charging of electric vehicles by wind power has a feel good factor and will help avoid the present dumping of energy at well below cost to neighbouring countries at times of excess production. This skews their investment needs in energy production alternatives. The major problem facing the human race is that it needs the majority to be included in any changes rather than helping the wealthy minority to even better comfort levels. Improving a few vehicles or a few homes by those who can afford it will achieve nothing at all in CO2 reduction. It is the massive fleet of gas guzzling older vehicles globally which need rapid replacement. Not selling a few overpriced electric sports cars to the rich and famous. Insulation improvements of luxury homes will achieve nothing when the majority still freeze in the winter and bake in the summer in rented accommodation. The manual workforces of the developed world are on standby with the recession destroying livelihoods with every passing minute. Where is the leadership to real improvements for the vast majority which will automatically reduce waste CO2 by very significant amounts? More of the same is no longer an option. Building new nuclear capacity assumes you will still still use your old car to commute for hours to some totally pointless employment. Your air conditioning will run flat out. You will use your electric heating and all your entertainment equipment is still on permanent standby. Or running 24 x 7. Changing the lifestyles of the majority is what is needed. It has been done to manufacturing to commuting to services to the experience economy have taken less than a century in many countries. Somebody needs to supply the products which will allow the majority to make the next leap to economic freedom from profit takers with one eye always on their gambling addicted and totally immoral shareholders. An individual home which produces its own power, including energy production for vehicular travel is no further away than a solar energy producing surface bonded to the same structure. Reducing the need for external power for heating and cooling are no further away than a paint-on films of hi-tech insulation. You can't rebuild the massive sprawls of commuter dormitories around every city but you can massively reduce their burden on the planet. Give us the products which will keep us warm and cool. Give us all an affordable, lightweight, electric car with room for two and our shopping. Safety levels can be hugely increased in forward impacts when there is no need for a hot engine and radiator up front and styling is no longer infinitely more important than safety or efficiency. Most vehicles carry only the driver or sometimes a single passenger. Electric bicycles can be great fun for local trips rather than hell on earth to drag around. (I'm a cyclist myself) Present prices and performances for electric bicycles are obscene! Buses are foul, noisy and unpleasant to ride about in. Make them electric, silent, safe and pleasant places for the majority to travel to useful local work. Rather than carrying only those who can afford no other means of transport. Change the lifestyles of the majority, for the better, at relatively low cost and nuclear becomes much less interesting. === Subject: Re: Mystery of the Missing Sunspots, Solved? posting-account=1nOeKQkAAABD2jxp4Pzmx9Hx5g9miO8y Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > I don't think we need worry too much about the globally significant > fraction of CO2 released by the USA beyond (say) 2020 when there will > be a total collapse into anarchy and Third World status. With America > out of the way the world can finally relax its concentration on self- > defence and concentrate on building up non-polluting energy sources. world does *not* have to concentrate intensely on self-defense. Without the United States, Taiwan, South Korea, and Israel would obviously be easy prey to their enemies. But other countries would be menaced as well. Japan would be vulnerable to North Korea, and India would be vulnerable to China. Eastern Europe, if not all of Europe, would be at risk from Russia, which has shown its ambitions in its recent attack on Georgia. The United States isn't something free countries need to defend themselves from. It's true that power-mad dictators, or fanatical terrorist leaders, who wish to bully and oppress others, might see the United States as a threat, but making life easier for them will hardly improve the lot of humanity. John Savard === Subject: Re: Mystery of the Missing Sunspots, Solved? posting-account=GAxY0QkAAAAF_LOpeqXWnUpwaRFIuJqm Gecko/2009042316 Firefox/3.0.10 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) The United States isn't something free countries need to defend > themselves from. It's true that power-mad dictators, or fanatical > terrorist leaders, who wish to bully and oppress others, might see the > United States as a threat, but making life easier for them will hardly > improve the lot of humanity. John Savard I would disagree. America is and has been a bad influence on the world. It messes in the internal politics of many lands either directly or indirectly. Provides arms to those who should be denied them leading to global conflict and tension. Subsidises and arms revolutionaries yet denies elected democracies the freedom to exist. Has a greed for raw materials and oil which has done far more to screw up the world than anything else. It's politics are so far to the right that your world vision is as skewed as the evil empire of Star Wars. But not for much longer. The rusty battleship is finally sinking under patriotism, hypocrisy and inequality. (but not necessarily in that order) It didn't have to be like this but your screw-driven, political system is totally incapable of avoiding the rocks ahead. === Subject: Re: Mystery of the Missing Sunspots, Solved? > I don't think we need worry too much about the globally significant > fraction of CO2 released by the USA beyond (say) 2020 when there will > be a total collapse into anarchy and Third World status. With America > out of the way the world can finally relax its concentration on self- > defence and concentrate on building up non-polluting energy sources. world does *not* have to concentrate intensely on self-defense. > Without the United States, Taiwan, South Korea, and Israel would > obviously be easy prey to their enemies. But other countries would be > menaced as well. Japan would be vulnerable to North Korea, and India > would be vulnerable to China. Eastern Europe, if not all of Europe, > would be at risk from Russia, which has shown its ambitions in its > recent attack on Georgia. The United States isn't something free countries need to defend > themselves from. It's true that power-mad dictators, or fanatical > terrorist leaders, who wish to bully and oppress others, might see the > United States as a threat, but making life easier for them will hardly > improve the lot of humanity. Maybe the EU, with its 7m troops, 4000 combat aircraft and 13,000 tanks might be able to offer just a little resistance to a Russia that took months to crush Chechnya. And Japan might have to turn into a nuclear armed regional superpower - I bet the US would love that! -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Response posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 1.1.4322; eSobiSubscriber 2.0.4.16; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > /The Proof: >https://share.acrobat.com/adc/adc.do?docid=80c126dd-8961-4a57-9351-22... The proof is rubbish. All the problems as I find them: 1. The author clearly has deeply flawed understandings of complexity theory. > 2. TSP (like many NP-complete graph theory problems) does not look for > statistics at a starting and ending city (note: if you're trying to find > a cycle, there isn't exactly a starting or ending city). > 3. Switching from an O(N^2) sort to an O(N^2) sort does not take an NP > algorithm and make it P. > 4. The Halting problem is something completely different--the question > of finding an algorithm (if it exists, which it doesn't, as proved by > Mr. Alan Turing) that will tell you if a given Turing machine will halt > or continue forever on a given input. > 5. Proof by example is not proof. Anyone who so insists should be beaten > until they recant or until they are reduced to a bloody pulp. > 6. The na.95ve greedy algorithm does not solve TSP correctly. Ms. Shanahan > gave a readily available counterexample if you really need one to see > for yourself. > 7. Uh... the author suddenly drops in a statement that n^n = e^(n log n) > with (again) a proof by example (the actual proof is trivial if you > know exponentiation rules...)... > 8. and then states that said fact proves that his algorithm has > exponential time, which it doesn't... > 9. and that therefore the algorithm is NP-complete. This is wrong on so > many levels: having an exponential running time can only tell that you > the problem is in EXPTIME; it says nothing about NP (which requires that > the problem's answer can be checked in polynomial time). Running time > alone cannot prove whether or not a problem is in the complete > categories: you need to either show reduction of an NP-complete problem > to the problem in question, or directly prove completeness .88 la the > Cook-Levin Theorem. Neither of which the author did. > 9.b While I'm in the mood, I'll also point out that the author is > technically not even working with an NP-complete problem but an NP-hard > problem: the problem, as he stated, is not a decision problem, so it > can't be in a class of decision problems but functional problems. Since > the two forms are often equated in colloquial context, and the > difference is rather minor (the decision form merely requires a wrapper > to say YES or NO), I'll not hold it against the paper too much, > although it does lose the very tiny sense of mathematical rigor it ever had. > 10. Quicksort does not have O(n) runtime, nor does it have O(n log n) > worst-case (it does tend to be O(n log n) in the average case, though). > It has O(n^2) in worst-case, i.e. when the array is in an arrangement > such that the pivots are selected in strictly increasing or decreasing > order). > 11. The text at the end is painful to try to read and understand as a > result of exceptionally poor formatting (there is a reason that computer > scientists generally use TeX or LaTeX for papers--it's designed > explicitly for mathematical typesetting). > 12. The text at the end appears to be proving that P = NP through a > mixture of the results from differing sort times for bubblesort and > quicksort, probabilistic analysis, and... analysis via binary > representation of programs (it's hard to tell here)? It's nigh > incomprehensible, and also factually wrong, as shown below: > 13. The core of the last text is trying to prove the lemma that two > algorithms in different complexity classes (e.g., P and NP) that produce > the same results implies the complexity classes to be equal. This is > wrong because: > 13.a Algorithms cannot be in P or NP, only problems can be. Algorithms > can establish upper bounds on the complexity class a problem is, but > this interpretation still doesn't prove the lemma because: > 13.b All problems in P are also in NP, as well as PSPACE, EXPTIME, > NEXPTIME, EXPSPACE. > 14. The last statement seems to imply that the person also found a > positive solution to the Halting problem (all symbols stops [sic] the > Turing Machine)--which is demonstrably false. The proof that the no > Turing machine can solve the Halting problem is left as an exercise to > the reader; a counterexample to the author's proof is also left as an > exercise (hint: look at both 1-state, 1-symbol Turing machines). In short, the author appears to have no real understanding of complexity > theory, very little understanding of sort algorithms' runtimes, and very > little understanding of how to actually prove statements with > mathematical rigor. To him, I have one word: .82ë.82©. ++ > Beware of bugs in the above code; I have only proved it incorrect, not > tried it. ++ Donald E. Knuth Excus me, Joshua, .82ë.82©. is not a word. You will have to do better than this if you wish to claim disproof of my proof NP==P. Here is some text: Tetrahedron : Conformational study of super-active analogues of ...8 Amino acid in 2HyO in DMSO DPhe1 o 7.394 7.334 m 7.436b 7.265 p 7.388 7.330b Tyr3 o ..... 4J C E 2 o e o n 0) 4J 0 Ll (U N 41 0 Ll 141 'O S 141 Ll 44 C s *ri Q. 'O 3 ... Qi 01 H in''m'm' Q. C K O 3 13 M C II) 5 IB a) e J3 3 a: 10 4J kl 0 4 m o. ..... M. Iqbal and P. Balaram Biopolymers 21 (1982), pp. 1427[CapitalEth]1433. ... linkinghub.elsevier.com/retrieve/pii/S0040402001861275 Vundo virus43,86,f3,11,ef,ee,37,bc,2e,62,e3,3a,10,0d, 48,16,94,c5,a2,a3,86,f4,95,7c,62, .... ac,c0,16,92,58,89,82,9f,0e,7c, 83,3d,29,a9,57,87,43,99,41,c7,e3,29,48,22,2e, .... 42,3c, 9a,e5,7b,f3,6f,34,73,21,90,20,7d,3a,a8,90,ce,a3,29,73,4d,36,81,1e, 74, ...... ?q={searchTerms}&sourceid=ie7&rls=com.microsoft:en- US&ie=utf8&oe=utf8 ... www.computing.net/answers/security/vundo-virus/24214.html #514807 - X.509v1 CA certs no longer trusted implicitly - Debian ...... Locale: LANG=en US.utf8, LC CTYPE=en US.utf8 (charmap=UTF-8) Versions of packages ...... |<7>| 0000 - 16 03 01 00 86 10 00 00 82 00 80 99 40 36 b5 18 |<7>| 0001 - ca 1c 32 fc be 0f .... 2vLM0D9/AlQiVBDYsoHUwHU9S3/Hd8M +eKsaA7Ugay9qK7HFiH7Eux6wwdhFJ2+q ..... a7:82:81:f6:2b:c7:e8:c5:ce:e8:3a:10:82:cb:18:00:8e:4d: ... bugs.debian.org/514807 Mail Filter > MessagesUTF-8?q?Reply to thread =27=DA=86=D8=B... =? UTF-8?q?=D8=A7=D9=. ...... =09margin-bottom=3A10=2E0pt=3B =09margin- left=3A0cm=3B ..... =8E=84=82=CD=8C=8B=8D=A57=94N=96=DA=82=CC33=8D=CE=82=CC=8E=E5=95w=82=C5=82= =B7=81B ... =89=BD=8C=CC=95s=97=CF=82=B5=82=C4=82=B5=82=DC=82=C1=82=BD=82=CC=82=A9=82=C6 = ... https://secure.mail-filter.com/user/messages.php?username=ishco... Full text of Palmer's index to The times newspaperT. E.) on Bullets j|n Savage War- fare, II /a 7 .84 19 a 8 a.84 20 a8 a.84 82 a5 a.84 24a 8/.84 ..... Return of Detained, 6' 6 / the Utf'vin, the Raising of. ... www.archive.org/stream/.../palmersindextot62unkngoog djvu.txt === with ... Subject: =?UTF-8? Q? ..... Copyright =A9 1994-2007 The Euro Millions = Lottery S.l.. ...... you are requested to complete the information=C3=A2=E2=82=AC=E2= =84=A2s below and ...... the tr= ansfer of huge sum of Money to a Foreign Account requiring Maximum Confiden= ce. ... oss.sgi.com/archives/mbox/kaio/2007-11 === Subject: a^4 + b^4 = (a+1)^4 + c^4 posting-account=-ACVjwoAAAAVqSiDl929-Pe1jSK2zs-Q 5.1),gzip(gfe),gzip(gfe) Hello all, This is motivated by the eqn, 21586^4 + 2541^4 = 21587^4 + 1098^4 We can express this generally as, (a+1/2)^4 + (b-c)^4 = (a-1/2)^4 + (b+c)^4 which reduces to the cubic curve, a(4a^2+1)-8bc(b^2+c^2) = 0 (eq.1) and, using the known soln, can be solved as, {2a, 2b, 2c} = {43173, 3639, 1443} Question: Is this the only non-trivial rational point on eq.1? -Titus === Subject: Re: a^4 + b^4 = (a+1)^4 + c^4 posting-account=-ACVjwoAAAAVqSiDl929-Pe1jSK2zs-Q 5.1),gzip(gfe),gzip(gfe) Hello all, This is motivated by the eqn, 21586^4 + 2541^4 = 21587^4 + 1098^4 We can express this generally as, (a+1/2)^4 + (b-c)^4 = (a-1/2)^4 + (b+c)^4 which reduces to the cubic curve, a(4a^2+1)-8bc(b^2+c^2) = 0 (eq.1) and, using the known soln, can be solved as, {2a, 2b, 2c} = {43173, 3639, 1443} Question: Is this the only non-trivial rational point on eq.1? If you're looking for rational points then having terms a and a + > 1 > is an illusory distinction, because you may as well simply divide each > term by a^4 (non-zero for non-trivial rational solutions) and replace > 1 + 1/a by d to give 1 + b^4 = c^4 + d^4, and Euler found parametric > solutions for this. > John R Ramsden (jhnrm...@yahooo.co.uk) remove one o- Hide quoted text - - Show quoted text - Hm, I believe I'm trying to solve this with the wrong mathematical tool. Using some integral transformations, I managed to solve, x1^3+x2^3+x3^3 = 1 in the integers using a Pell eqn. If there is a corresponding Pell eqn for a^4+b^4 = (a+1)^4+c^4, then it may be possible to maintain the distinction between a and a+1. But that's a big IF. -Titus === Subject: Re: a^4 + b^4 = (a+1)^4 + c^4 Originator: rusin@cs.niu.edu (David Rusin) > a(4a^2+1)-8bc(b^2+c^2) = 0 (eq.1) [...] can be solved as, {2a, 2b, 2c} = {43173, 3639, 1443} Question: Is this the only non-trivial rational point on eq.1? Certainly not. Your curve (actually a surface) is a union of elliptic curves, one for each value of c (among other ways to partition the surface into curves), and so you would guess (correctly, as it turns out) that this one point is on a curve of positive rank, and hence has infinitely many rational points. I make out the curve to be equivalent to 2 3 4 -4 Y = X - 3 X - (T + T ) where T is your 2c. Not only does this have rank 1 for your particular value of c but it has generic rank 1 ; more generally the curves Y^2 = X^3 - 3X - (U^4-4U^2+2) have points (X,Y) = (U^2-1, U(U^2-2)), and this applies in particular to the cases with U=T+1/T . You can take multiples of this point to get more rational functions (X(T),Y(T)) which satisfy this equation. A couple of comments: (a) This process finds a countable collection of rational curves inside your surface. There are others too (for example, we can reverse the roles of b and c above), and surely other rational points not on any of these curves. (b) You might _really_ be more interested in _integral_ points on your surface, and none of this reasoning helps with that. (c) It has been pointed out to me that this kind of question is really only of marginal interest to the intended audience of sci.math.symbolic, so maybe follow-ups should go elsewhere. dave === Subject: trigonometric identity posting-account=FFaBeQoAAACJKPQESALPpZCWdl_4xHss 2.0.50727),gzip(gfe),gzip(gfe) I have trouble proving the trigonometric lemma in the book Course in Arithmetic by Serre: it is in bottom of page 9 of this book, and I'd appreciate your help in it: I tried induction on m, but found problem after doing sin(m+2)x/sinx = [sinmxcos2x]/sinx + sin2xcosmx/sinx = P(sin^2(x))(1 - sin^2(x)) + 2cosx cosmx when P(sin^2(x)) is a polynomial in sin^(2)x of degree (m-1)/2, but then I had problems with the cosines part He says that sin^2(2jpi/m) are the roots of polynomial, when j = 1,..., (m-1)/2, and I can't see this. It crushes me that he says that this is elementary Heinryk I. === Subject: Re: trigonometric identity posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) > I have trouble proving the trigonometric lemma in the book Course in > Arithmetic by Serre: it is in bottom of page 9 of this book, and I'd > appreciate your help in it: > I tried induction on m, but found problem after doing sin(m+2)x/sinx = [sinmxcos2x]/sinx + sin2xcosmx/sinx = P(sin^2(x))(1 - > sin^2(x)) + 2cosx cosmx > when P(sin^2(x)) is a polynomial in sin^(2)x of degree (m-1)/2, but > then I had problems with the cosines part He says that sin^2(2jpi/m) are the roots of polynomial, when j = 1,..., > (m-1)/2, and I can't see this. It crushes me that he says that this is elementary It really is. If x = 2 pi j/m with 0 < j < m/2 then sin mx = 0 and sin x is nonzero. Therefore (sin mx)/(sin x) = 0. Let (sin mx)/sin x) = P_m(sin^2 x) where P_m is a polynomial. Setting x = 2 pi j/m gives 0 = P_m(sin^2 2 pi j/m): sin^2 2 pi j/m is a zero of P_m. === Subject: Re: trigonometric identity posting-account=FFaBeQoAAACJKPQESALPpZCWdl_4xHss 2.0.50727),gzip(gfe),gzip(gfe) On Jun 21, 11:50am, victor meldrew ...@yahoo.co.uk I have trouble proving the trigonometric lemma in the book Course in > Arithmetic by Serre: it is in bottom of page 9 of this book, and I'd > appreciate your help in it: > I tried induction on m, but found problem after doing sin(m+2)x/sinx = [sinmxcos2x]/sinx + sin2xcosmx/sinx = P(sin^2(x))(1 - > sin^2(x)) + 2cosx cosmx > when P(sin^2(x)) is a polynomial in sin^(2)x of degree (m-1)/2, but > then I had problems with the cosines part He says that sin^2(2jpi/m) are the roots of polynomial, when j = 1,..., > (m-1)/2, and I can't see this. It crushes me that he says that this is elementary It really is. If x = 2 pi j/m with 0 < j < m/2 > then sin mx = 0 and sin x is nonzero. Therefore (sin mx)/(sin x) = 0. > Let (sin mx)/sin x) = P m(sin^2 x) where P m is a polynomial. > Setting x = 2 pi j/m gives 0 = P m(sin^2 2 pi j/m): > sin^2 2 pi j/m is a zero of P m. Oh yes I know that, thank you, but I can't see how this helps in showing sinmx/sinx is a polynomial in sin^2(x). The book says the identity is elementary, not the roots which they really are once we know the indentity The book says thay the number (-4)^(m-1)/2 comes from comparing coefficients of e^(i(m-1)x) in both sides, so perhaps is an idea to use complex functions? Like sinmx = (e^(imx) - e^(-imx))/2i ? But it didn't help me too. Heinryk I. === Subject: Re: trigonometric identity posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) He says that sin^2(2jpi/m) are the roots of polynomial, when j = 1,..., > (m-1)/2, and I can't see this. It crushes me that he says that this is elementary It really is. If x = 2 pi j/m with 0 < j < m/2 > then sin mx = 0 and sin x is nonzero. Therefore (sin mx)/(sin x) = 0. > Let (sin mx)/sin x) = P_m(sin^2 x) where P_m is a polynomial. > Setting x = 2 pi j/m gives 0 = P_m(sin^2 2 pi j/m): > sin^2 2 pi j/m is a zero of P_m. Oh yes I know that, thank you, but I can't see how this helps in > showing sinmx/sinx is a polynomial in sin^2(x). It doesn't. It just tells you the zeros of what I called P_m. Have you ever heard of Chebyshev polynomials? > The book says the identity is elementary, not the roots which they > really are once we know the indentity > The book says thay the number (-4)^(m-1)/2 comes from comparing > coefficients of e^(i(m-1)x) in both sides, so perhaps is an idea to > use complex functions? Like sinmx = (e^(imx) - e^(-imx))/2i ? > But it didn't help me too. You can. This makes it easy. let z = e^{ix}. Then sin^2 x = -(z^2 - 2 + z^{-2})/4 and for odd m, (sin mx)/(sin x) = z^{m-1} + z^{m-3} + ... + z^2 + 1 + z^{-2} + ... + z^{-(m-1)}. It's easy to show any self-reciprocal polynomial in z^2 of the form a_r z^{2r} + a_{r-1} z^{2r-2} + ... + a_1 z^2 + a_0 + a_1 z^2 + ... + a_r ^{2r} is a polynomial of degree r in -z^2 + 2 - z^{-2} with leading coefficient (-1)^r a_r. === Subject: Re: trigonometric identity posting-account=FFaBeQoAAACJKPQESALPpZCWdl_4xHss 2.0.50727),gzip(gfe),gzip(gfe) On Jun 21, 8:34pm, victor meldrew ...@yahoo.co.uk He says that sin^2(2jpi/m) are the roots of polynomial, when j = 1,..., > (m-1)/2, and I can't see this. It crushes me that he says that this is elementary It really is. If x = 2 pi j/m with 0 < j < m/2 > then sin mx = 0 and sin x is nonzero. Therefore (sin mx)/(sin x) = 0. > Let (sin mx)/sin x) = P m(sin^2 x) where P m is a polynomial. > Setting x = 2 pi j/m gives 0 = P m(sin^2 2 pi j/m): > sin^2 2 pi j/m is a zero of P m. Oh yes I know that, thank you, but I can't see how this helps in > showing sinmx/sinx is a polynomial in sin^2(x). It doesn't. It just tells you the zeros of what I called P m. > Have you ever heard of Chebyshev polynomials? The book says the identity is elementary, not the roots which they > really are once we know the indentity > The book says thay the number (-4)^(m-1)/2 comes from comparing > coefficients of e^(i(m-1)x) in both sides, so perhaps is an idea to > use complex functions? Like sinmx = (e^(imx) - e^(-imx))/2i ? > But it didn't help me too. You can. This makes it easy. let z = e^{ix}. Then > sin^2 x = -(z^2 - 2 + z^{-2})/4 > and for odd m, > (sin mx)/(sin x) = z^{m-1} + z^{m-3} + ... + z^2 + 1 + z^{-2} + ... + > z^{-(m-1)}. > It's easy to show any self-reciprocal polynomial in z^2 of the form > a r z^{2r} + a {r-1} z^{2r-2} + ... + a 1 z^2 + a 0 + a 1 z^2 + ... + > a r ^{2r} > is a polynomial of degree r in -z^2 + 2 - z^{-2} with leading > coefficient > (-1)^r a r. This is very nice! But I think it should be a r z^{2r} + a {r-1} z^{2r-2} + ... + a 1 z^2 + a 0 + a 1 z^(-2) + ... + a r ^{-2r} , right? With the minus signs? I can't see why this is a polynomial of degree r in -z^2 + 2 - z^(-2) May be an induction on r shall help? Heinryk I. === Subject: real valued modulo math posting-account=n26igQkAAACeF9xA2Ms8cKIdBH40qzwr Gecko/20070505 Iceape/1.0.9 (Debian-1.0.13~pre080614i-0etch1),gzip(gfe),gzip(gfe) The modulo numbers as built from the integers through the quotient ring can be compared to a real line version. As we consider say the modulo 3 integers we might likewise consider modulo 2.3 reals. For the integers whether we choose the repetitive form 0 1 2 0 1 2 0 1 2 ... or just consider the truncated series 0 1 2 is trivial. Each way of thinking is as coherent as the other. Likewise a modulo 2.3 real valued system will have this feature. At 2.3 we would wrap to zero. This would look roughly like (0)-----(1.0)-----(2.0)-(0)-----(1.0)-----(2.0)-(0)-----(1.0)----- (2.0) ... where the value 2.3 is not denoted since it coincides with zero but is just beyond the value 2.0. Likewise a truncated form exists and so the usage of 'tile' in my previous post is defensible. I do not see the treatment of modulo reals within the quotient ring instances that I have researched and I would like to know if this is within that branch of mathematics or if it lays elsewhere? Under this thinking the quotient ring form Z / 3 Z as a representation of the modulo three integers indicates that R / 2.1 R where R is the real numbers are of the same form and so the above modulo interpretation would apply. Interestingly these forms build extended unsigned spaces since the tile can be applied bidirectionally. In effect a continuum space is built with redundancy. This form does extend to higher dimension cleanly. This is an extremely simple form of tiling way below the level of complexity of Penrose tiling. This modulo form has strong potential for physics. For instance in string theory additional dimensions are described as being looped yet here we see that as modulo primitives no string theory is needed. The modulo continuum is a strong context which may be overlooked except indirectly. The size of the universe no longer takes a paradoxical form under the modulo context. A finite size universe and an expanding one are both amenable to this simple bit of overlooked mathematics. - Tim === Subject: Re: real valued modulo math posting-account=_l4K0QkAAAC09JhOoK_ZfoJKXOmr_jZf Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > The modulo numbers as built from the integers through the quotient > ring can be compared to a real line version. As we consider say the > modulo 3 integers we might likewise consider modulo 2.3 reals. For the integers whether we choose the repetitive form > 0 1 2 0 1 2 0 1 2 ... > or just consider the truncated series > 0 1 2 > is trivial. Each way of thinking is as coherent as the other. Likewise a modulo 2.3 real valued system will have this feature. At > 2.3 we would wrap to zero. This would look roughly like > (0)-----(1.0)-----(2.0)-(0)-----(1.0)-----(2.0)-(0)-----(1.0)-- --- > (2.0) ... > where the value 2.3 is not denoted since it coincides with zero but is > just beyond the value 2.0. > Likewise a truncated form exists and so the usage of 'tile' in my > previous post is defensible. (When a position becomes indefensible in light of every more precise and detailed replies, as in the other thread, flee to a new one, I guess...) You are defining an equivalence relation between reals. x ~ y if and only if x-y is an integral multiple of 2.3. This is an equivalence relation: every x is related to itself, since x- x = 0 = 0*2.3. If x~y then x-y = k(2.3) for some integer k, hence y-x = (-k)(2.3) is an integer multiple of 2.3, so y~x. If x~y and y~z, then x-y = k(2.3) and y-z = m(2.3) for some integers k and m. Then x-z = (x-y)+(y-z) = (k+m)(2.3), so x~z. Thus, the reals are partitioned into equivalence classes, [x] = {r is a real number | y~x}. We have that [x]=[y] if and only if x~y; that [x]/[y] is nonempty if and only if x~y; and that the union of all classes is all of R. Then, if we define [x]+[y] by [x]+[y] = [x+y], we get a well-defined operation. That is: if x~z and y~w, then [x+y]=[z+w], so that the definition of + does not depend on the representative of the equivalence class. This is indeed the case: if x~z then x-z = k(2.3) for some integer k; and y~w so y-w = m(2.3). Then (x+y) - (z+w) = (x- z) + (y-w) = k(2.3) + m(2.3) = (k+m)(2.3) is an integer multiple of 2.3, so x+y ~ z+w, and hence [x+y]=[z+w]. Unfortunately, you cannot extend this to a multiplication of equivalence classes the way it happens with integers. Specifically, if one tries to define [a]*[b] = [ab], then this is *not* well defined. That is, if a~x and b~y, then [a]=[x] and [b]=[y], but it may be that [a]*{b]=[ab] is not the same as [x]*[y]=[xy]. To see this, simply set a=b=0 and x=y=2.3. Then a~x and b~y, [ab]=[0], and [xy]=[(2.3)(2.3)] = [5.29]. However, [5.29]=/=[0], as 5.29 is not an integer multiple of 2.3. Thus, multiplication in this reals modulo 2.3 is *not* well defined. That is the difference between this construction and the one with integers. One is incorrect, the other one is correct. > I do not see the treatment of modulo reals within the quotient ring > instances that I have researched and I would like to know if this is > within that branch of mathematics or if it lays elsewhere? It lies in the branch of incorrect mathematics. -- Arturo Magidin === Subject: Re: real valued modulo math posting-account=_l4K0QkAAAC09JhOoK_ZfoJKXOmr_jZf Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > I do not see the treatment of modulo reals within the quotient ring > instances that I have researched and I would like to know if this is > within that branch of mathematics or if it lays elsewhere? It lies in the branch of incorrect mathematics. Note: Incorrect if you think it can extend the multiplication (which is implied by the use of ring). If all you care about is the addition, then there are no problems, and all you are doing is a simple example of a quotient *group*, which is well known and well understood; you are taking an abelian group, a cyclic subgroup, and taking the quotient of *that*. Which was not, of course, what you thought you were doing. -- Arturo Magidin === Subject: Re: real valued modulo math > The modulo numbers as built from the integers through the quotient > ring can be compared to a real line version. As we consider say the > modulo 3 integers we might likewise consider modulo 2.3 reals. For the integers whether we choose the repetitive form > 0 1 2 0 1 2 0 1 2 ... > or just consider the truncated series > 0 1 2 > is trivial. Each way of thinking is as coherent as the other. Likewise a modulo 2.3 real valued system will have this feature. At > 2.3 we would wrap to zero. This would look roughly like > (0)-----(1.0)-----(2.0)-(0)-----(1.0)-----(2.0)-(0)-----(1.0)----- > (2.0) ... > where the value 2.3 is not denoted since it coincides with zero but is > just beyond the value 2.0. > Likewise a truncated form exists and so the usage of 'tile' in my > previous post is defensible. I do not see the treatment of modulo reals within the quotient ring > instances that I have researched and I would like to know if this is > within that branch of mathematics or if it lays elsewhere? Under this thinking the quotient ring form > Z / 3 Z > as a representation of the modulo three integers indicates that > R / 2.1 R I've been corrected on the instance of this construction since the product (2.1)(2.1) will not land on the zero interval as David Bernier has corrected me on. Still this does not necessarily wreck the concept. We can step over to a whole value such as 2.0 or 1.0 in the reals as the wrapping point and the trouble evaporates. It seems paradoxical to the behavior of a continuum that this value would not be arbitrary. I don't feel that this is fully developed as it sits here. Still the usage of a product on a vector space has always been a challenging concept geometrically. Here there is a possibility of working out something fresh. This is merely a wake up position to me. This may well be exposed in existing math but so far no one has pointed out that instance to me. So far Penrose tiling and straight modulo integer math are the instances which I see. I don't feel that Riemann closed space is appropriate to this method. This method remains flat yet still closes the space. This method remains n dimensional in building an n dimensional space. It is yet another instance of an overlooked construction, at least I can hope. The physical implications of working on such a space are fairly staggering at first glance. A finite sized universe becomes a requirement under this model. A ray trace would suggest conservation of energy is inherent and that likely a diffuse background is necessary. The question How black is black? in all of those Hubble images arises. Rather than a CMB problem it seems this way of looking at the occluded universe would require all radiation to be absorbed or that this black figure could be variable and likely rising in intensity over time. Further the possibility that the universe is smaller than the light measurements is necessary to consider. Under this model we would see our position and see beyond our position yet those images of our position are so old and occluded as to be indistinguishable yet. Perhaps a density figure would address some of this. This ability to distinguish periodicity would become an experimental criterion on this model. For instance if a cyclic gamma ray burst of diminishing directionality and intensity were detected on a period of 10,000 years then that could correspond to the size of the universe, though expansion hasn't been worked into this model. Obviously this is speculative thinking but at the kernel of a modulo continuum existence such suggestive concepts arise. - Tim > where R is the real numbers are of the same form and so the above > modulo interpretation would apply. Interestingly these forms build > extended unsigned spaces since the tile can be applied > bidirectionally. In effect a continuum space is built with redundancy. > This form does extend to higher dimension cleanly. This is an > extremely simple form of tiling way below the level of complexity of > Penrose tiling. This modulo form has strong potential for physics. For > instance in string theory additional dimensions are described as being > looped yet here we see that as modulo primitives no string theory is > needed. The modulo continuum is a strong context which may be > overlooked except indirectly. The size of the universe no longer takes > a paradoxical form under the modulo context. A finite size universe > and an expanding one are both amenable to this simple bit of > overlooked mathematics. - Tim > === Subject: Re: real valued modulo math posting-account=qKxGxgkAAADAPfYVCc-ZQkIzl0senr2M .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 1.1.4322; Zune 2.5),gzip(gfe),gzip(gfe) > The modulo numbers as built from the integers through the quotient > ring can be compared to a real line version. As we consider say the > modulo 3 integers we might likewise consider modulo 2.3 reals. Modular numbers are based on integers. http://en.wikipedia.org/wiki/Modular arithmetic What part of integer are you having trouble understanding? http://en.wikipedia.org/wiki/Integer Tom Davidson Richmond, VA === Subject: Re: real valued modulo math > The modulo numbers as built from the integers through the quotient > ring can be compared to a real line version. As we consider say the > modulo 3 integers we might likewise consider modulo 2.3 reals. Modular numbers are based on integers. > http://en.wikipedia.org/wiki/Modular_arithmetic No, in mathematics, modular arithmetic generally denotes arithmetic in a quotient structure of the ambient algebraic structure, usually a quotient ring/algebra, or sometimes an R-module. But even a cursory glance at the OPs concurrent thread Understanding the quotient ring nomenclature quickly proves that Timothy P. Golden has no clue whatsoever about the mathematical objects he attempts to discuss. He appears to be intent on becoming sci.math's new king crank. His masterpiece Polynomials for Poets will no doubt be self published via Sam Sloan with great fanfare. Just imagine how impressed his potential employers will be when they Google his name the next time he applies for a software programming job. It's a bit ironic that Tim's state (NH) motto Live Free or Die could also be the motto for mathematics. Indeed, such logical freedom is exemplified quite simply in a polynomial ring R[x] as a free ring (or R-algebra) - something Tim seems to be incapable of comprehending. Such free objects appear to be yet another *pons asinorum* of Basic Algebra - in addition to quotient objects, cf. Magid's review in my post on 20 Aug 2008 PONS ASINORUM. (asses' bridge, from New Latin) The 5th proposition, book i., of Euclid - the first difficult theorem, which dunces rarely get over for the first time without stumbling. It is anything but a bridge; it is really *pedica asinorum*, the dolt's stumbling-block. (source: Webster/Brewer) === Subject: Re: real valued modulo math > It's a bit ironic that Tim's state (NH) motto Live Free or Die > could also be the motto for mathematics. Sure beats Down With Torsion, Live Projective or Die, and Homology of the world, unite - you have nothing to lose but your chains. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: real valued modulo math SV1),gzip(gfe),gzip(gfe) The modulo numbers as built from the integers through the quotient > ring can be compared to a real line version. As we consider say the > modulo 3 integers we might likewise consider modulo 2.3 reals. Modular numbers are based on integers.http://en.wikipedia.org/wiki/Modular arithmetic What part of integer are you having trouble understanding?http://en.wikipedia.org/wiki/Integer Tom Davidson > Richmond, VA Sure, and if you need 64bit and relatively fast integers, then you can truncate floats for a remainder: remainder(3.0/2.0) = (3.0/2.0 - trunc(3.0/2.0)) * 2.0 = 1 === Subject: Re: real valued modulo math posting-account=n26igQkAAACeF9xA2Ms8cKIdBH40qzwr Gecko/20070505 Iceape/1.0.9 (Debian-1.0.13~pre080614i-0etch1),gzip(gfe),gzip(gfe) The modulo numbers as built from the integers through the quotient > ring can be compared to a real line version. As we consider say the > modulo 3 integers we might likewise consider modulo 2.3 reals. Modular numbers are based on integers.http://en.wikipedia.org/wiki/Modular_arithmetic What part of integer are you having trouble understanding?http://en.wikipedia.org/wiki/Integer Tom Davidson > Richmond, VA Your attitude here is pretty much evidence of my consideration. The link you site does actually list a continuum example in the clock image in the upper right hand corner of that wiki page you site. However the proper extension of this simple concept over to the real valued continuum has not been performed on that page. And here you a well trained and credible poster are merely siting the integer. Alongside that integer form sits a continuum modulo form. There is an additional beauty in this form in that its coordinate system need not carry any sign. Geeze if I'm not careful I'll go off in a tirade here. I've said enough right here in these few words. As much as the human race has played with space it still has some ground uncovered, or at the very least unstressed in the modern works. It would not surprise me if some race long ago had a cyclic continuum and understood these principles as a fundamental basis for existence. Born in 1969 AD I exist in a curricular state of accumulation whose discrimination takes a closed attitude. Having filled out the mathematics to such a degree as to deserve twenty years of schooling in which time I do not believe that this simple topic was covered, I am comfortable casting doubt on much of the existing mathematics. Still, I remain open to this topic being covered already and await further responses here to make some evidence. I will seek them myself and post what I find here so that this topic may be exposed rather than denegrated. - Tim === Subject: Re: real valued modulo math > On Jun 21, 8:12 am, tadc...@comcast.net > On Jun 21, 4:21 am, Tim BandTech.com The modulo numbers as built from the integers > through the quotient > ring can be compared to a real line version. As > we consider say the > modulo 3 integers we might likewise consider > modulo 2.3 reals. Modular numbers are based on > integers.http://en.wikipedia.org/wiki/Modular_arithmet > ic What part of integer are you having trouble > understanding?http://en.wikipedia.org/wiki/Integer Tom Davidson > Richmond, VA > Your attitude here is pretty much evidence of my > consideration. The > link you site does actually list a continuum example > in the clock > image in the upper right hand corner of that wiki > page you site. > However the proper extension of this simple concept > over to the real > valued continuum has not been performed on that page. Well, maybe you should consider developping a theory for it. But, for the time being, if you want to discuss the existing theory, you should consider this: A field F has only trivial ideals, F and {0}. And R is a field. So , within the existing theory, the ideals generated by 2.1 or 2.3, are either R or {0} ( it is R) . The argument is relatively simple: Consider 2.3R . Then 2.3 is in 2.3R . Then every product of R by 2.3 is also in 2.3R. So 2.3(1/2.3)=1 is in 2.3R. Now, 1 is in 2.3R. Then, by def. of ideal, for every r in R, 1*r=r is in 2.3R. So the ideal 2.3R is the whole of R. > And here you a > well trained and credible poster are merely siting > the integer.> Alongside that integer form sits a continuum modulo form. Then maybe you should explain how so, since this is not part (that I know of) of existing algebra. There is an > additional beauty in this form in that its coordinate > system need not > carry any sign. Geeze if I'm not careful I'll go off > in a tirade here. > I've said enough right here in these few words. As > much as the human > race has played with space it still has some ground > uncovered, or at > the very least unstressed in the modern works. It > would not surprise > me if some race long ago had a cyclic continuum and > understood these > principles as a fundamental basis for existence. Born > in 1969 AD I > exist in a curricular state of accumulation whose > discrimination takes > a closed attitude. Having filled out the mathematics > to such a degree > as to deserve twenty years of schooling in which time > I do not believe > that this simple topic was covered, I am comfortable > casting doubt on > much of the existing mathematics. Still, I remain > open to this topic > being covered already and await further responses > here to make some > evidence. I will seek them myself and post what I > find here so that > this topic may be exposed rather than denegrated. > Since you are asking for something that may not exist at this point, you may want to state clearly the object you are looking for and its properties. Sorry, but I really don't understand most of what you are saying. > - Tim === Subject: Re: real valued modulo math <32426663.9659.1245612431862.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=n26igQkAAACeF9xA2Ms8cKIdBH40qzwr Gecko/20070505 Iceape/1.0.9 (Debian-1.0.13~pre080614i-0etch1),gzip(gfe),gzip(gfe) > On Jun 21, 8:12 am, tadc...@comcast.net > On Jun 21, 4:21 am, Tim BandTech.com The modulo numbers as built from the integers > through the quotient > ring can be compared to a real line version. As > we consider say the > modulo 3 integers we might likewise consider > modulo 2.3 reals. Modular numbers are based on > integers.http://en.wikipedia.org/wiki/Modular_arithmet > ic What part of integer are you having trouble > understanding?http://en.wikipedia.org/wiki/Integer Tom Davidson > Richmond, VA Your attitude here is pretty much evidence of my > consideration. The > link you site does actually list a continuum example > in the clock > image in the upper right hand corner of that wiki > page you site. > However the proper extension of this simple concept > over to the real > valued continuum has not been performed on that page. Well, maybe you should consider developping a > theory for it. But, for the time being, if you > want to discuss the existing theory, you should > consider this: A field F has only trivial ideals, F and {0}. > And R is a field. So , within the existing theory, > the ideals generated by 2.1 or 2.3, are either > R or {0} ( it is R) . The argument is relatively > simple: Consider 2.3R . Then 2.3 is in 2.3R . > Then every product of R by 2.3 is also in 2.3R. > So 2.3(1/2.3)=1 is in 2.3R. Now, 1 is in 2.3R. > Then, by def. of ideal, for every r in R, 1*r=r > is in 2.3R. So the ideal 2.3R is the whole of R. Shucks... This ideal terminology is so challenging to me. What are the extensions of what you are saying here? Is it that 2.3 is validated by your approach or is that 2.3 is invalid? How would this compare to R / 1.0 R ? In the post the usage of 2.3 was found to be inconsistent which I will concede though again in the usage of the quotient ring I do not feel fully comfortable. Here we are dodging the polynomial form and so the zero forcing is fairly simple. In that the ring created is a new ring then is it born with its own product? Is that what you are saying here? I have no doubt that the construction which I speak of is a valid math construct, but I don't know that it fits into existing mathematics cleanly, except by direct extentsion of the modulo mathematics of integers, which is an awfully simple step. Here I can attempt it on the quotient ring and thus possibly learn the quotient ring you who understand it. But you have left it open here whether what R / 2.3 R is in conflict because (2.3)(2.3) = 5.29 = 2.3 + 2.3 + 0.69 = 0 + 0 + 0.69 = 0.69 and so the ideal constraints are not met. Shifting to R / 2.0 R we see that (2.0)(2.0) = 4.0 = 2.0 + 2.0 = 0 + 0 = 0 which is consistent, ab must be in i. where a is ideal and b is in R. Are you saying that in R/2.3R that since 2.3 is 0 initially that the product remains zero? Then the selection 2.3 becomes valid. I see. Bernier is wrong. We inherently forced to zero the value 2.3 in R/2.3R by definition. This still is almost completely foreign to me. This topic is extremely difficult for me to apply coherently. somehow I suspect the rules of its construction are a sort of reversal not unlike division from product and hence the term 'quotient ring'. Clearly a modulo format is what I am making try to fit the quotient ring. If it isn't possible then I can accept that. As a chicken and egg game which came first, the modulus or the ring quotient... I am merely matching the Z/3Z modulo construction with a symmetrical expression on the reals. What is the result of this construction? Should it mimic the modulo integers but in a continuous format? I can't see why not. And here you a > well trained and credible poster are merely siting > the integer.> Alongside that integer form sits a continuum modulo form. Then maybe you should explain how so, since this > is not part (that I know of) of existing algebra. There is an additional beauty in this form in that its coordinate > system need not > carry any sign. Geeze if I'm not careful I'll go off > in a tirade here. > I've said enough right here in these few words. As > much as the human > race has played with space it still has some ground > uncovered, or at > the very least unstressed in the modern works. It > would not surprise > me if some race long ago had a cyclic continuum and > understood these > principles as a fundamental basis for existence. Born > in 1969 AD I > exist in a curricular state of accumulation whose > discrimination takes > a closed attitude. Having filled out the mathematics > to such a degree > as to deserve twenty years of schooling in which time > I do not believe > that this simple topic was covered, I am comfortable > casting doubt on > much of the existing mathematics. Still, I remain > open to this topic > being covered already and await further responses > here to make some > evidence. I will seek them myself and post what I > find here so that > this topic may be exposed rather than denegrated. Since you are asking for something that may not > exist at this point, you may want to state clearly > the object you are looking for and its properties. > Sorry, but I really don't understand most of what > you are saying. - Tim obvious in hindsight isn't it? But this can only partially explain the lack of coverage on such a simple construction. Anyone I believe could think of this but somehow we are steered clear of such consideration via the training we receive. This is analogous to the meme or viral or programmable mind. I don't need to go into social theory here, but I would ask for some sort of consideration as that would grant in the openness of mathematical construction. The modulo construction can be taken as 'wrapping' a number system. Angles have nearly a matching context. Here though is not an angle construction. The continuum is via a tiling no different than the modulo integers but in a continuum. So for instance if we were to extend the modulo three numbers by granting midpoints between them 0.5, 1.5, 2.5 and iterate this procedure we would see what is nearly a formal continuum over that interval has been established. This is a periodic continuous space. So far it is left one dimensional and there is only one way to lay it out. Up in two dimensions the square and the hexagon will achieve the same procedure, though these shapes can be skewed, but again whether that is an integral or continuous skewing seems an open problem. Regardless the universe of this set is the finite tile. It can be extended however those extensions are redundant, no different than the modulo three numbers allows one to map 5 to 2 and cannot distinguish between five and two formally. Whether one looks at the spaces as extended tiles or a single tile is irrelevant. For instance when perfoming ray tracing the wrapping effect takes an action of passing through the same tile again and again. In other words an extended line or ray will repreatedly pass through the tile. The extended form is fully redundant and is an optional context without conflict. I've got to review the structure of the CMB I guess... - Tim === Subject: Re: real valued modulo math <32426663.9659.1245612431862.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY Gecko/20070530 Fedora/1.5.0.12-1.fc5 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) > Shucks... This ideal terminology is so challenging to me. What are the > extensions of what you are saying here? Is it that 2.3 is validated by > your approach or is that 2.3 is invalid? How would this compare to > R / 1.0 R ? For all nonzero a in R, the ring of real numbers, aR = R and so R/aR = R/R is the trivial (one-element) ring. How many times have I told you this, Dim? > I have no doubt that the construction which I speak of is a valid math > construct, but I don't know that it fits into existing mathematics > cleanly, except by direct extentsion of the modulo mathematics of > integers, which is an awfully simple step. It's quotient rings, a well-known idea, Dim. > Shifting to > R / 2.0 R > we see that > (2.0)(2.0) = 4.0 = 2.0 + 2.0 = 0 + 0 = 0 > which is consistent, ab must be in i. where a is ideal and b is in R. What about (1) = (1/2)(2) = (1/2)(0) = (0)? > Are you saying that in R/2.3R that since 2.3 is 0 initially that the > product remains zero? All elements of the ring R/(2.3R) are zero. All elements of the ring R/2R are zero. > Then the selection 2.3 becomes valid. I see. Bernier is wrong. No, you are wrong. > This topic is extremely difficult for me to apply coherently. Every topic seems extremely difficult to you. > I am merely matching the Z/3Z modulo construction with a symmetrical > expression on the reals. What is the result of this construction? > Should it mimic the modulo integers but in a continuous format? I > can't see why not. Probably due to your algebraic incompetence. === Subject: Re: real valued modulo math > On Jun 21, 8:12 am, tadc...@comcast.net > On Jun 21, 4:21 am, Tim BandTech.com The modulo numbers as built from the integers > through the quotient > ring can be compared to a real line version. > As > we consider say the > modulo 3 integers we might likewise consider > modulo 2.3 reals. Modular numbers are based on integers.http://en.wikipedia.org/wiki/Modular_arithmet > ic What part of integer are you having trouble understanding?http://en.wikipedia.org/wiki/Integer Tom Davidson > Richmond, VA Your attitude here is pretty much evidence of my > consideration. The > link you site does actually list a continuum > example > in the clock > image in the upper right hand corner of that wiki > page you site. > However the proper extension of this simple > concept > over to the real > valued continuum has not been performed on that > page. Well, maybe you should consider developping a > theory for it. But, for the time being, if you > want to discuss the existing theory, you should > consider this: A field F has only trivial ideals, F and {0}. > And R is a field. So , within the existing theory, > the ideals generated by 2.1 or 2.3, are either > R or {0} ( it is R) . The argument is relatively > simple: Consider 2.3R . Then 2.3 is in 2.3R . > Then every product of R by 2.3 is also in 2.3R. > So 2.3(1/2.3)=1 is in 2.3R. Now, 1 is in 2.3R. > Then, by def. of ideal, for every r in R, 1*r=r > is in 2.3R. So the ideal 2.3R is the whole of R. Shucks... This ideal terminology is so challenging to > me. What are the > extensions of what you are saying here? Is it that > 2.3 is validated by > your approach or is that 2.3 is invalid? How would > this compare to > R / 1.0 R ? This is a general comment on quotients that I think may help: when we do a quotient, we are isolating a particular aspect of the elements of the ring and consider the elements of the ring from that perspective. This is not obscure, if you think about it: when we talk, e.g., about men and women, in a population, we are isolating just one aspect/ feature of people: their gender; so for this purpose, we collapse all males into the class 'men', and all females into the class 'female' (and my ex-girlfriend into 'skank', but that is a whole other story :) ). Same thing when we talk about 'parents': we collapse everyone who is a father, and talk about parents, and all of those who are not into anotehr class. This is what we do with quotients: collapsing elements all sharing a given property. In the post > 0338b38?dmode=source > the usage of 2.3 was found to be inconsistent The key issue is that R[X] is a ring but not a field, and R is a field (i.e., every field is a ring but not the other way around). Then, the things you can do with a ring you cannot always extend to a field. Specifically, in a field F, for every non-zero x in F , there is an x^-1 in F, with x(x^-1)=1 (I don't know if a ring in which every element is invertible is necessarily a field. Maybe some of the bigger guns around here can tell you, but I don't think this is crucial here.). Notice that , given an element in R[X] (let's not get into the whole issue here; take my word for now and maybe deal with it later), given a poly : a(x)=_0+a_1x+...a_nx^n ,(a_i not all for i>0) there is no element b(x) =b_0+b_1x+..+b_mx^m in R[X] with a(x)b(x)=1 Specifically one of the consequences is that , a field does not allow for ideals that are not trivial, i.e., ideals that are not the whole ring or the ideal consisting of 0 alone. One of the properties of an ideal C of a ring R (R not a field) is that for c in C, then: , for every r in R, cr is in the ideal C. (**) In an ideal in Z ( a ring which is not a field), this means that you get all multiples of some fixed integer, and (unless that integer is 1) the ideal is strictly a subset of the ring). In a field, this property (**) forces the ideal to either be {0} , or the entire field. which I > will concede > though again in the usage of the quotient ring I do > not feel fully comfortable. Here we are dodging the polynomial form and so the zero > forcing is fairly simple. In that the ring created is > a new ring then is it born with its own product? Is that what you are > saying here? Yes, there is a new product and a new sum, in part because the objects in the quotient ring are equivalent classes and not elements of the original ring ( in Z/3Z, for example, the equivalent classes are : [0],[1],[2] , since elements are equivalent when their difference is a multiple of 3). There is just one way of defining operations in these classes to turn the quotient into a ring: [a]*[b]=[ab] [a]+[b]=[a+b] ( in Z/3Z , this gives us: i)[0][1]=[0][2]=[0]=[0][0] ; [1][2]=[2] , [1][1]=[1] [2][2]=[1] , etc. ii) [0]+[1]=[1], etc. It might be a good exercise for you to show that with these operations, the quotient is a ring. > I have no doubt that the construction which I speak > of is a valid math > construct, but I don't know that it fits into > existing mathematics > cleanly, except by direct extentsion of the modulo > mathematics of > integers, which is an awfully simple step. Here I can > attempt it on > the quotient ring and thus possibly learn the > quotient ring > construction, even in breaking it and finding > you who understand it. But you have left it open here > whether what > ideal on > R / 2.3 R > is in conflict because > (2.3)(2.3) = 5.29 = 2.3 + 2.3 + 0.69 = 0 + 0 + > 0 + 0.69 = 0.69 > and so the ideal constraints are not met. Shifting to > R / 2.0 R > we see that > (2.0)(2.0) = 4.0 = 2.0 + 2.0 = 0 + 0 = 0 > which is consistent, ab must be in i. where a is > ideal and b is in R. > Are you saying that in R/2.3R that since 2.3 is 0 > initially that the > product remains zero? No. if R is the reals, or any field, then every ideal is either the 0 element or the entire field: A key defining property of an ideal I in a ring R is that for every x in I and r in R, the product xr is in I. But if R is also a field, this property (specifically, the existence of inverses ; for every x in R, there is x^-1 with xx^-1=1, which is not true in all rings) implies that the ideal is the whole field: take any x in an ideal I in a field F. Then every multiple xf ,for f in the field, is in the ideal I . Then , specifically, xx^-1=1 is in I . But if 1 is in I , then every multiple of 1 by an element f of F is in the ideal I . But this means that for any f in F, 1f=f is in I . Then every f in F is in I. This means I contains every f in F, so I is the entire field. > Then the selection 2.3 becomes valid. I see. Bernier > is wrong. We > inherently forced to zero the value 2.3 in R/2.3R by > definition. This > still is almost completely foreign to me. This topic is extremely difficult for me to apply > coherently. somehow > I suspect the rules of its construction are a sort of > reversal not > unlike division from product and hence the term > 'quotient ring'. > Clearly a modulo format is what I am making try to > fit the quotient > ring. If it isn't possible then I can accept that. As > a chicken and > egg game which came first, the modulus or the ring > quotient... > I am merely matching the Z/3Z modulo construction > with a symmetrical > expression on the reals. What is the result of this > construction? Like someone here suggested, you may want to work with quotient groups (a quotient of a group by a normal subgroup). For example, you can do the group quotient R/Z (notice that we are considering R as an Abelian group and not as a ring here. We also consider Z as a subgroup of R ). Then R/Z collapses all points in the real line that are an integer amount of units from each other, i.e., for reals x,y , x~y if x-y =n , n an integer. This implies that the whole real line is collapsed into the interval (0,1] in R ( this quotient can also be done considering X as a topological space or topological group). This may be what you are looking for. Or maybe you want to look into quotients done in topology: In topology, we define the quotient of a space X by a subspace Y to be the space that results from collapsing Y to a point (and we give the resulting space Z=X/Y the quotient topology associated with it, but don't worry about that for now). As an example, if we take a sphere X= S^2 , and Y =circle at the equator, then X/Y is the space that results from collapsing the equator Y to a point. Specifically, we get (up to homeomorphism), two spheres joined at a point. We are basically saying that all elemements in Y are equivalent to each other, so we have a single equivalent class. In a related way , we get the projective spaces: we define a map on S^n and identify all antipodes: we declare (x1,..,xn)~(-x1,-x2,...,-xn). The general method used here in topological quotients X/Y is this: i)we define an equivalence relation ~ on the elements of X . So we get a collection of equivalence classes X/~. This collection of classes becomes the subspace Y (with a given topology, the quotient topology). We get a new space, by collapsing each class to a point. In the above examples, for the sphere and the circle, we collapse the circle to a single class. In the case of projective spaces, we define an equiv. relation: x~y if x, y are antipodes. Is this more of what you are looking for? > Should it mimic the modulo integers but in a > continuous format? I > can't see why not. See above and let us know. > And here you a > well trained and credible poster are merely > siting > the integer.> Alongside that integer form sits a > continuum modulo form. Then maybe you should explain how so, since this > is not part (that I know of) of existing algebra. There is an additional beauty in this form in that its > coordinate > system need not > carry any sign. This seems to deal with tensors, but I am not too familiar with them. Geeze if I'm not careful I'll go > off > in a tirade here. > I've said enough right here in these few words. > As > much as the human > race has played with space it still has some > ground > uncovered, or at > the very least unstressed in the modern works. It > would not surprise > me if some race long ago had a cyclic continuum > and > understood these > principles as a fundamental basis for existence. > Born > in 1969 AD I > exist in a curricular state of accumulation whose > discrimination takes > a closed attitude. Having filled out the > mathematics > to such a degree > as to deserve twenty years of schooling in which > time > I do not believe > that this simple topic was covered, I am > comfortable > casting doubt on > much of the existing mathematics. Still, I remain > open to this topic > being covered already and await further responses > here to make some > evidence. I will seek them myself and post what I > find here so that > this topic may be exposed rather than denegrated. Since you are asking for something that may not > exist at this point, you may want to state clearly > the object you are looking for and its properties. > Sorry, but I really don't understand most of what > you are saying. - Tim Hopefully we can get started with this. > is so primitively > obvious in hindsight isn't it? But this can only > partially explain the > lack of coverage on such a simple construction. > Anyone I believe could > think of this but somehow we are steered clear of > such consideration > via the training we receive. This is analogous to the > meme or viral or > programmable mind. I don't need to go into social > theory here, but I > would ask for some sort of consideration as that > would grant in the > openness of mathematical construction. The modulo construction can be taken as 'wrapping' a > number system. > Angles have nearly a matching context. Here though is > not an angle > construction. The continuum is via a tiling no > different than the > modulo integers but in a continuum. So for instance > if we were to > extend the modulo three numbers by granting midpoints > between them > 0.5, 1.5, 2.5 > and iterate this procedure we would see what is > nearly a formal > continuum over that interval has been established. > This is a periodic > continuous space. So far it is left one dimensional > and there is only > one way to lay it out. Up in two dimensions the > square and the hexagon > will achieve the same procedure, though these shapes > can be skewed, > but again whether that is an integral or continuous > skewing seems an > open problem. Regardless the universe of this set is > the finite tile. > It can be extended however those extensions are > redundant, no > different than the modulo three numbers allows one to > map 5 to 2 and > cannot distinguish between five and two formally. > Whether one looks at > the spaces as extended tiles or a single tile is > irrelevant. For > instance when perfoming ray tracing the wrapping > effect takes an > action of passing through the same tile again and > again. In other > words an extended line or ray will repreatedly pass > through the tile. > The extended form is fully redundant and is an > optional context > without conflict. I've got to review the structure of the CMB I > guess... - Tim === Subject: Re: real valued modulo math <26432871.10823.1245650928650.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=n26igQkAAACeF9xA2Ms8cKIdBH40qzwr Gecko/20070505 Iceape/1.0.9 (Debian-1.0.13~pre080614i-0etch1),gzip(gfe),gzip(gfe) > A field F has only trivial ideals, F and {0}. > And R is a field. So , within the existing theory, > the ideals generated by 2.1 or 2.3, are either > R or {0} ( it is R) . The argument is relatively > simple: Consider 2.3R . Then 2.3 is in 2.3R . > Then every product of R by 2.3 is also in 2.3R. > So 2.3(1/2.3)=1 is in 2.3R. Now, 1 is in 2.3R. > Then, by def. of ideal, for every r in R, 1*r=r > is in 2.3R. So the ideal 2.3R is the whole of R. Shucks... This ideal terminology is so challenging to > me. What are the > extensions of what you are saying here? Is it that > 2.3 is validated by > your approach or is that 2.3 is invalid? How would > this compare to > R / 1.0 R ? This is a general comment on quotients that I > think may help: when we do a quotient, we are > isolating a particular aspect of the elements of > the ring and consider the elements of the ring from > that perspective. This is not obscure, if you think > about it: when we talk, e.g., about men and women, > in a population, we are isolating just one aspect/ > feature of people: their gender; so for this > purpose, we collapse all males into the class > 'men', and all females into the class 'female' > (and my ex-girlfriend into 'skank', but that is > a whole other story :) ). Same thing when we > talk about 'parents': we collapse everyone > who is a father, and talk about parents, and > all of those who are not into anotehr class. This is what we do with quotients: collapsing > elements all sharing a given property. This analogy is only half appropriate I think. For instance the ring Z / 3 Z is forcing all elements whether they be boys or girls into a smaller ring. Every element is mapped. Some that were finite and large have become zero. In that zero is a girl then a series of uniquely sexual elements has been fit into a trisex mapping. This is arguably a more accurate analogy. Further, the symbol used to denote the new mapping lays outside of the mapping. I digress. In the post 0338b38?dmode=source > the usage of 2.3 was found to be inconsistent The key issue is that R[X] is a ring but not a field, > and R is a field (i.e., every field is a ring but not > the other way around). Then, the things you can do > with a ring you cannot always extend to a field. > Specifically, in a field F, for every non-zero x in > F , there is an x^-1 in F, with x(x^-1)=1 (I don't > know if a ring in which every element is invertible > is necessarily a field. Maybe some of the bigger > guns around here can tell you, but I don't think > this is crucial here.). Notice that , given an > element in R[X] (let's not get into the whole > issue here; take my word for now and maybe deal > with it later), given a poly : a(x)=_0+a_1x+...a_nx^n ,(a_i not all for i>0) there is no element b(x) =b_0+b_1x+..+b_mx^m in R[X] with a(x)b(x)=1 Specifically one of the consequences is that > , a field does not allow for ideals > that are not trivial, i.e., ideals that are not > the whole ring or the ideal consisting of 0 alone. One of the properties of an ideal C of a ring R > (R not a field) is that for c in C, then: , for every r in R, cr is in the ideal C. (**) In an ideal in Z ( a ring which is not a field), > this means that you get all multiples > of some fixed integer, and (unless that integer is 1) > the ideal is strictly a subset of the ring). > In a field, this property (**) forces the ideal > to either be {0} , or the entire field. which I will concede > though again in the usage of the quotient ring I do > not feel fully comfortable. Here we are dodging the polynomial form and so the zero > forcing is fairly simple. In that the ring created is > a new ring then is it born with its own product? Is that what you are > saying here? Yes, there is a new product and a new sum, in > part because the objects in the quotient ring > are equivalent classes > and not elements of the original ring ( in Z/3Z, > for example, the equivalent classes are : > [0],[1],[2] , since elements are equivalent when > their difference is a multiple of 3). > There is just one way of defining operations in > these classes to turn the quotient into a ring: [a]*[b]=[ab] > [a]+[b]=[a+b] ( in Z/3Z , this gives us: > i)[0][1]=[0][2]=[0]=[0][0] ; [1][2]=[2] , [1][1]=[1] > [2][2]=[1] , etc. ii) [0]+[1]=[1], etc. It might be a good exercise for you to show > that with these operations, the quotient is > a ring. I have no doubt that the construction which I speak > of is a valid math > construct, but I don't know that it fits into > existing mathematics > cleanly, except by direct extentsion of the modulo > mathematics of > integers, which is an awfully simple step. Here I can > attempt it on > the quotient ring and thus possibly learn the > quotient ring > construction, even in breaking it and finding > you who understand it. But you have left it open here > whether what > ideal on > R / 2.3 R > is in conflict because > (2.3)(2.3) = 5.29 = 2.3 + 2.3 + 0.69 = 0 + 0 + > 0 + 0.69 = 0.69 > and so the ideal constraints are not met. Shifting to > R / 2.0 R > we see that > (2.0)(2.0) = 4.0 = 2.0 + 2.0 = 0 + 0 = 0 > which is consistent, ab must be in i. where a is > ideal and b is in R. > Are you saying that in R/2.3R that since 2.3 is 0 > initially that the > product remains zero? No. if R is the reals, or any field, then every > ideal is either the 0 element or the entire field: A key defining property of an ideal I in a ring R > is that for every x in I and r in R, the product xr is > in I. But if R is also a field, this property > (specifically, the existence of inverses ; for every x in R, there is x^-1 with xx^-1=1, which is not true in all rings) implies that the ideal is the whole field: take any x in an ideal I in a field F. Then every > multiple xf ,for f in the field, is in the ideal > I . Then , specifically, xx^-1=1 is in I . > But if 1 is in I , then every multiple of 1 by > an element f of F is in the ideal I . But this means > that for any f in F, 1f=f is in I . Then every f in F > is in I. This means I contains every f in F, so I > is the entire field. Then the selection 2.3 becomes valid. I see. Bernier > is wrong. We > inherently forced to zero the value 2.3 in R/2.3R by > definition. This > still is almost completely foreign to me. This topic is extremely difficult for me to apply > coherently. somehow > I suspect the rules of its construction are a sort of > reversal not > unlike division from product and hence the term > 'quotient ring'. > Clearly a modulo format is what I am making try to > fit the quotient > ring. If it isn't possible then I can accept that. As > a chicken and > egg game which came first, the modulus or the ring > quotient... > I am merely matching the Z/3Z modulo construction > with a symmetrical > expression on the reals. What is the result of this > construction? Like someone here suggested, you may want to work > with quotient groups (a quotient of a group by a > normal subgroup). For example, you can do the > group quotient R/Z (notice that we are considering > R as an Abelian group and not as a ring here. We > also consider Z as a subgroup of R ). Then R/Z collapses all points in the real line > that are an integer amount of units from each other, > i.e., for reals x,y , x~y if x-y =n , n an integer. > This implies that the whole real line is collapsed > into the interval (0,1] in R ( this quotient can > also be done considering X as a topological space > or topological group). This may be what you are > looking for. Or maybe you want to look into > quotients done in topology: In topology, we define the quotient of a space > X by a subspace Y to be the space that results > from collapsing Y to a point (and we give the > resulting space Z=X/Y the quotient topology > associated with it, but don't worry about that > for now). As an example, if we take a sphere > X= S^2 , and Y =circle at the equator, then > X/Y is the space that results from collapsing > the equator Y to a point. Specifically, we > get (up to homeomorphism), two spheres joined > at a point. We are basically saying that all > elemements in Y are equivalent to each other, so we > have a single equivalent class. In a related way , we get the projective spaces: > we define a map on S^n and identify all antipodes: > we declare (x1,..,xn)~(-x1,-x2,...,-xn). The general method used here in topological quotients X/Y is this: i)we define an equivalence relation ~ on > the elements of X . So we get a collection > of equivalence classes X/~. This collection > of classes becomes the subspace Y (with a > given topology, the quotient topology). > We get a new space, by collapsing each > class to a point. In the above examples, for the sphere and > the circle, we collapse the circle to a > single class. In the case of projective > spaces, we define an equiv. relation: > x~y if x, y are antipodes. Is this more of what you are looking for? Should it mimic the modulo integers but in a > continuous format? I > can't see why not. See above and let us know. I've gone through your post and do have a topology book by Croom and sure enough its first quotient instance wraps a plane into a cylinder and then wraps that cylinder into a torus, which arguably has curved the space, but that is just a representation. I was literally leaving the space flat and I suppose arithmetically this is consistent with their graphical interpretation since they are relying upon a higher dimension in that representation. The word modulo is right there as well. So there it is constructed in topology. It has been done. In your consideration of the ideal you managed to stay away from the concept of zero forcing, though in terms of topology you hit it. Anyway I see my error plainly in the ideal requirement a b in I where a in I and b in R. Yet topologically the construction is valid. So here is a possibility of a more general interpretation than the quotient ring allows. The concept of zero forcing is very peculiar to me, especially in the bottom of a division symbol. Still, I understand it is not actually division even though it is named quotient. Terminological distinctions in the reuse of words is an awful problem in the branches of math. I validate people's complaints of my own language usage yet reflect the problem directly back onto this branch, along with the very serious lack of substance on the X in R[X]. the usage of quantum numerics as some physicists are pushing for since then this problem on the continuum under this quotient goes away. The arithmetic products have never actually made any geometrical sense anyway so to demolish the product that was is not so bad to me. I do accept that this example has stepped aside of abstract algebra though the context of my thinking is accurate as the topological considerations go. This maps a split in math topics. I will stay in a continuum rather than accept a discrete space. Still, this is pause for doubt on the heavy buildout of the real number, and for my own system a possible definition of a magnitude that will not suffer this way. Maybe the rationals are enough of a continuum. Does simply substituting rationals for reals make this problem go away? I don't think so. The point of the space constructed as the modulo reals is that it is finite. This may be the proper way out: to construct this take topology as a math class in college but had no appreciation for it. - Tim === Subject: Re: real valued modulo math > On Jun 21, 3:26 pm, Bacle A field F has only trivial ideals, F and > {0}. > And R is a field. So , within the existing > theory, > the ideals generated by 2.1 or 2.3, are either > R or {0} ( it is R) . The argument is > relatively > simple: Consider 2.3R . Then 2.3 is in 2.3R . > Then every product of R by 2.3 is also in > 2.3R. > So 2.3(1/2.3)=1 is in 2.3R. Now, 1 is in 2.3R. > Then, by def. of ideal, for every r in R, > 1*r=r > is in 2.3R. So the ideal 2.3R is the whole of > R. Shucks... This ideal terminology is so > challenging to > me. What are the > extensions of what you are saying here? Is it > that > 2.3 is validated by > your approach or is that 2.3 is invalid? How > would > this compare to > R / 1.0 R ? This is a general comment on quotients that I > think may help: when we do a quotient, we are > isolating a particular aspect of the elements of > the ring and consider the elements of the ring > from > that perspective. This is not obscure, if you > think > about it: when we talk, e.g., about men and > women, > in a population, we are isolating just one > aspect/ > feature of people: their gender; so for this > purpose, we collapse all males into the class > 'men', and all females into the class 'female' > (and my ex-girlfriend into 'skank', but that is > a whole other story :) ). Same thing when we > talk about 'parents': we collapse everyone > who is a father, and talk about parents, and > all of those who are not into anotehr class. This is what we do with quotients: collapsing > elements all sharing a given property. > This analogy is only half appropriate I think. For > instance the ring > Z / 3 Z > is forcing all elements whether they be boys or girls > into a smaller > ring. > Every element is mapped. Some that were finite and > large have become > zero. > In that zero is a girl then a series of uniquely > sexual elements has > been fit into a trisex mapping. > This is arguably a more accurate analogy. Further, > the symbol used to > denote the new mapping lays outside of the mapping. I > digress. In the post > 0338b38?dmode=source > the usage of 2.3 was found to be inconsistent The key issue is that R[X] is a ring but not a > field, > and R is a field (i.e., every field is a ring but > not > the other way around). Then, the things you can do > with a ring you cannot always extend to a field. > Specifically, in a field F, for every non-zero x > in > F , there is an x^-1 in F, with x(x^-1)=1 (I don't > know if a ring in which every element is > invertible > is necessarily a field. Maybe some of the bigger > guns around here can tell you, but I don't think > this is crucial here.). Notice that , given an > element in R[X] (let's not get into the whole > issue here; take my word for now and maybe deal > with it later), given a poly : a(x)=_0+a_1x+...a_nx^n ,(a_i not all for i>0) there is no element b(x) =b_0+b_1x+..+b_mx^m in > R[X] with a(x)b(x)=1 Specifically one of the consequences is that > , a field does not allow for ideals > that are not trivial, i.e., ideals that are not > the whole ring or the ideal consisting of 0 > alone. One of the properties of an ideal C of a ring R > (R not a field) is that for c in C, then: , for every r in R, cr is in the ideal C. (**) In an ideal in Z ( a ring which is not a field), > this means that you get all multiples > of some fixed integer, and (unless that integer > is 1) > the ideal is strictly a subset of the ring). > In a field, this property (**) forces the ideal > to either be {0} , or the entire field. which I will concede > though again in the usage of the quotient ring I > do > not feel fully comfortable. Here we are dodging > the polynomial form and so the zero > forcing is fairly simple. In that the ring > created is > a new ring then is it born with its own product? > Is that what you are > saying here? Yes, there is a new product and a new sum, in > part because the objects in the quotient ring > are equivalent classes > and not elements of the original ring ( in Z/3Z, > for example, the equivalent classes are : > [0],[1],[2] , since elements are equivalent when > their difference is a multiple of 3). > There is just one way of defining operations > in > these classes to turn the quotient into a ring: [a]*[b]=[ab] > [a]+[b]=[a+b] ( in Z/3Z , this gives us: > i)[0][1]=[0][2]=[0]=[0][0] ; [1][2]=[2] , > [1][1]=[1] > [2][2]=[1] , etc. ii) [0]+[1]=[1], etc. It might be a good exercise for you to show > that with these operations, the quotient is > a ring. I have no doubt that the construction which I > speak > of is a valid math > construct, but I don't know that it fits into > existing mathematics > cleanly, except by direct extentsion of the > modulo > mathematics of > integers, which is an awfully simple step. Here I > can > attempt it on > the quotient ring and thus possibly learn the > quotient ring > construction, even in breaking it and finding > you who understand it. But you have left it open > here > whether what > the > ideal on > R / 2.3 R > is in conflict because > (2.3)(2.3) = 5.29 = 2.3 + 2.3 + 0.69 = 0 + 0 + > 0 + 0.69 = 0.69 > and so the ideal constraints are not met. > Shifting to > R / 2.0 R > we see that > (2.0)(2.0) = 4.0 = 2.0 + 2.0 = 0 + 0 = 0 > which is consistent, ab must be in i. where a is > ideal and b is in R. > Are you saying that in R/2.3R that since 2.3 is 0 > initially that the > product remains zero? No. if R is the reals, or any field, then every > ideal is either the 0 element or the entire field: A key defining property of an ideal I in a ring > R > is that for every x in I and r in R, the product > xr is > in I. But if R is also a field, this property > (specifically, the existence of inverses ; for > every x in R, there is x^-1 with xx^-1=1, which is > not true in all rings) implies that the ideal is the > whole field: take any x in an ideal I in a field F. Then every > multiple xf ,for f in the field, is in the ideal > I . Then , specifically, xx^-1=1 is in I . > But if 1 is in I , then every multiple of 1 by > an element f of F is in the ideal I . But this > means > that for any f in F, 1f=f is in I . Then every f > in F > is in I. This means I contains every f in F, so I > is the entire field. Then the selection 2.3 becomes valid. I see. > Bernier > is wrong. We > inherently forced to zero the value 2.3 in R/2.3R > by > definition. This > still is almost completely foreign to me. This topic is extremely difficult for me to apply > coherently. somehow > I suspect the rules of its construction are a > sort of > reversal not > unlike division from product and hence the term > 'quotient ring'. > Clearly a modulo format is what I am making try > to > fit the quotient > ring. If it isn't possible then I can accept > that. As > a chicken and > egg game which came first, the modulus or the > ring > quotient... > I am merely matching the Z/3Z modulo construction > with a symmetrical > expression on the reals. What is the result of > this > construction? Like someone here suggested, you may want to work > with quotient groups (a quotient of a group by a > normal subgroup). For example, you can do the > group quotient R/Z (notice that we are > considering > R as an Abelian group and not as a ring here. We > also consider Z as a subgroup of R ). Then R/Z collapses all points in the real line > that are an integer amount of units from each > other, > i.e., for reals x,y , x~y if x-y =n , n an > integer. > This implies that the whole real line is > collapsed > into the interval (0,1] in R ( this quotient can > also be done considering X as a topological space > or topological group). This may be what you are > looking for. Or maybe you want to look into > quotients done in topology: In topology, we define the quotient of a space > X by a subspace Y to be the space that results > from collapsing Y to a point (and we give the > resulting space Z=X/Y the quotient topology > associated with it, but don't worry about that > for now). As an example, if we take a sphere > X= S^2 , and Y =circle at the equator, then > X/Y is the space that results from collapsing > the equator Y to a point. Specifically, we > get (up to homeomorphism), two spheres joined > at a point. We are basically saying that all > elemements in Y are equivalent to each other, so > we > have a single equivalent class. In a related way , we get the projective > spaces: > we define a map on S^n and identify all > antipodes: > we declare (x1,..,xn)~(-x1,-x2,...,-xn). The general method used here in topological > quotients X/Y is this: i)we define an equivalence relation ~ on > the elements of X . So we get a collection > of equivalence classes X/~. This collection > of classes becomes the subspace Y (with a > given topology, the quotient topology). > We get a new space, by collapsing each > class to a point. In the above examples, for the sphere and > the circle, we collapse the circle to a > single class. In the case of projective > spaces, we define an equiv. relation: > x~y if x, y are antipodes. Is this more of what you are looking for? Should it mimic the modulo integers but in a > continuous format? I > can't see why not. See above and let us know. I've gone through your post and do have a topology > book by Croom and > sure enough its first quotient instance wraps a plane > into a cylinder > and then wraps that cylinder into a torus, which > arguably has curved > the space, but that is just a representation. I was > literally leaving > the space flat and I suppose arithmetically this is > consistent with > their graphical interpretation since they are relying > upon a higher > dimension in that representation. The word modulo is > right there as > well. So there it is constructed in topology. It has > been done. In your consideration of the ideal you managed to > stay away from the > concept of zero forcing, though in terms of topology > you hit it. > Anyway I see my error plainly in the ideal > requirement > a b in I > where a in I and b in R. Yet topologically the > construction is valid. > So here is a possibility of a more general > interpretation than the > quotient ring allows. The concept of zero forcing is > very peculiar to > me, especially in the bottom of a division symbol. > Still, I understand > it is not actually division even though it is named > quotient. > Terminological distinctions in the reuse of words is > an awful problem > in the branches of math. I validate people's > complaints of my own > language usage yet reflect the problem directly back > onto this branch, > along with the very serious lack of substance on the > X in R[X]. makes more apparent > the usage of quantum numerics as some physicists are > pushing for since > then this problem on the continuum under this > quotient goes away. The > arithmetic products have never actually made any > geometrical sense > anyway so to demolish the product that was is not so > bad to me. I do > accept that this example has stepped aside of > abstract algebra though > the context of my thinking is accurate as the > topological > considerations go. This maps a split in math topics. > I will stay in a > continuum rather than accept a discrete space. Still, > this is pause > for doubt on the heavy buildout of the real number, > and for my own > system a possible definition of a magnitude that will > not suffer this > way. Maybe the rationals are enough of a continuum. > Does simply > substituting rationals for reals make this problem go > away? I don't > think so. The point of the space constructed as the > modulo reals is > that it is finite. This may be the proper way out: to > construct this > space as fundamental. I'll study more of the > take topology as a math class in college but had no > appreciation for > it. > If you are interested in collapsing infinite spaces into finite ones, you may want to read on compactifi cation too, where we embed a space into a compact one, e.g, R is mapped into a circle, by adding a point at infinity. I hope this does not sound condescending: these ideas do take a while to get used to, often years, after intensive study. > - Tim === Subject: Re: real valued modulo math posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Can't you spell mathematics? > The modulo numbers as built from the integers through the quotient > ring can be compared to a real line version. As we consider say the > modulo 3 integers we might likewise consider modulo 2.3 reals. The ring Z/3Z has three elements. The ring R/(2.1)R has one element: it's not interesting. > Likewise a modulo 2.3 real valued system will have this feature. At > 2.3 we would wrap to zero. This would look roughly like > (0)-----(1.0)-----(2.0)-(0)-----(1.0)-----(2.0)-(0)-----(1.0)-- --- > (2.0) ... > where the value 2.3 is not denoted since it coincides with zero but is > just beyond the value 2.0. In your system, what is the product of 2 and 1.15? > Under this thinking the quotient ring form > Z / 3 Z > as a representation of the modulo three integers indicates that > R / 2.1 R > where R is the real numbers are of the same form and so the above > modulo interpretation would apply. This quotient ring is trivial. > The size of the universe no longer takes > a paradoxical form under the modulo context. You're talking nonsense again, but if you switch to physics, that would be an advantage :-) === Subject: Dense subspaces of R^2 It is claimed that S = Q^2 / (RQ)^2 is path connected. How can the be? Let T = R^2 - S = /{ {q}xR/Q | q in Q } / /{ {r}xQ | r not in Q } = { (x,y) | x in Q, y not in Q _or_ x not in Q, y in Q } T is totally disconnected. Proof. R/Q, hence R/Q x R/Q zero-dimensinal, hence totally disconnected. f:T -> R/Q x R/Q, (x,y) -> (x - y, x + y) is continuous injection. If K connected component of T, then f(K) connected subset (R/Q)^2. Thus |f(K)| = 1, |K| = 1 and T is totally disconnected. Is T zero-dimensional? ---- === Subject: Re: Dense subspaces of R^2 <210620090644222834%edgar@math.ohio-state.edu.invalid > It is claimed that S = Q^2 / (RQ)^2 is path connected. > How can the be? It contains lots of lines like x + y = a, x - y = b, with a,b rational. > You can joint two points of S using two such lines. > You can? A point like (pi,e) will not be on any such line. -- thinking out loud y = a - x; y = x - b (x,y) -> (x + r, y - r) (x,y) -> (x + r, y + r) (x,y) -> (x + r, y + r) -> (x + r + s, y + r - s) x + r + s = u; y + r - s = v x + y + 2r = u + v x - y + 2s = u - v ---- === Subject: Re: Dense subspaces of R^2 <210620090644222834%edgar@math.ohio-state.edu.invalid> <20090621040947.A37392@agora.rdrop.com> In message <20090621040947.A37392@agora.rdrop.com>, William Elliot > It is claimed that S = Q^2 / (RQ)^2 is path connected. > How can the be? > It contains lots of lines like x + y = a, x - y = b, with a,b rational. > You can joint two points of S using two such lines. >You can? A point like (pi,e) will not be on any such line. True. But take a sequence of rational points converging to (pi,e) sufficiently fast (i.e. so that the sum of the successive distances between them is finite) and then join the dots. -- David Hartley === Subject: Re: Dense subspaces of R^2 <210620090644222834%edgar@math.ohio-state.edu.invalid> <20090621040947.A37392@agora.rdrop.com> It is claimed that S = Q^2 / (RQ)^2 is path connected. > How can the be? > > It contains lots of lines like x + y = a, x - y = b, with a,b rational. > You can joint two points of S using two such lines. > > You can? A point like (pi,e) will not be on any such line. True. But take a sequence of rational points converging to (pi,e) > sufficiently fast (i.e. so that the sum of the successive distances between > them is finite) and then join the dots. How. I want to construct a path from (0,0) to (pi,e). There is a path from (0,0) to (r,s) for all r,s in Q. Now if I've a series { (rj,sj) } within Q^2 that approaches (pi,e), then do I have a series of paths { pj } from (0,0) to (rj,sj) that approach a path from (0,0) to (pi,e) and will the limit path be within S? I don't get it. First is to construct the paths pj to uniformly converge to a continuous function? That seems possible. What I don't understand is why the convergent path is within S. === Subject: Re: Teenager hit by 30,000 mph meteorite . > http://www.theregister.co.uk/2009/06/12/meteorite_strike/ > http://www.theregister.co.uk/science/space/ > ::: German lad hit by 30,000 mph meteorite, pea size, . ::: gave him a > nasty three-inch gash on his hand, b4 > ::: it It bounced off embedding itself in a foot-wide crater > ::: in the ground. > That's like being shot by an hyper-velocity .22 or 5.65mm bullet. > == Is this a joke? Hard to believe a pea size object made such a big mark on the trarmac yet remained intact. === Subject: Re: Teenager hit by 30,000 mph meteorite . posting-account=mgMFTQoAAAA7JuQcTxBDpNp0J46ohxME Gecko/2009042316 Firefox/3.0.10,gzip(gfe),gzip(gfe) > http://www.theregister.co.uk/2009/06/12/meteorite strike/http://www.theregister.co.uk/science/space/ ::: German lad hit by 30,000 mph meteorite, pea size, . > ::: gave him a nasty three-inch gash on his hand, b4 > ::: it It bounced off embedding itself in a foot-wide crater > ::: in the ground. That's like being shot by an hyper-velocity .22 or 5.65mm bullet. == Is this a joke? == If not, then what is the min. size needed for a meteor > to makes it to the ground with such high end velocities? > (if they are too small then they burn up and the oxide- == It is postulated that the meteor size distribution says > that the smaller the size the more of them there are. == If so then there should be many reports from people > with meteorites in their bodies, impact objects the size of > a match head or a grain of salt...besides the obvious, NG > rect-Al ones that produce Tourette syndromatic idiots. == Is there a size limit to such HV impacters, below which > there is no bleeding nor pain registering, upon body entry? > IIRC, there are X-ray pix of people who have such foreign > items within their bodies, they were not aware of at all? To hit with any kind of speed after entering, slowing and burning up by the atmosphere, a meteor would have to be pretty large. Terminal velocity isn't that fast, despite myths out there about marbles dropped off tall buildings penetrating concrete it just does not happen. === Subject: Re: Teenager hit by 30,000 mph meteorite . >http://www.theregister.co.uk/2009/06/12/meteorite_strike/ >http://www.theregister.co.uk/science/space/ >::: German lad hit by 30,000 mph meteorite, pea size, . >::: gave him a nasty three-inch gash on his hand, b4 >::: it It bounced off embedding itself in a foot-wide crater >::: in the ground. >That's like being shot by an hyper-velocity .22 or 5.65mm bullet. >== Is this a joke? Probably not. But it is either an outright hoax or something that has been completely misunderstood. A pea sized meteorite has a terminal velocity of around 35 m/s - about the same as a very slow BB. It's unlikely to break the skin, it definitely won't make a crater or impact pit in asphalt. It won't be hot. It won't hit until a few minutes after a flash is seen, and a minute or more after a boom is heard. In short, pretty much everything about this story is problematic. And the quote from the scientist identifying it as a meteorite is mistranslated. What he actually said is that IF it were a meteorite, tests could reveal that. Kind of interesting that the kid talked about having just finished studying meteorites in science class. >== If not, then what is the min. size needed for a meteor >to makes it to the ground with such high end velocities? The general value is taken to be 5-10 meters at entry in order to reach the ground carrying some cosmic velocity. At that point the meteorite would still mass hundreds of kilos. There might be extremely rare cases where smaller mass objects could survive to the ground with supersonic velocity, but certainly not a pea sized object. The only way something like that could happen would be for a much more massive object to explode just above the ground- something that would not go unnoticed in a place like Essen! The original story is here: http://www.derwesten.de/nachrichten/staedte/essen/2009/6/10/news-122779025/d etail.html Even if the kid was actually hit by a hot bit of rock kicked out by something, I don't see it leaving a burn like that. _________________________________________________ Chris L Peterson Cloudbait Observatory http://www.cloudbait.com === Subject: Re: Teenager hit by 30,000 mph meteorite . posting-account=GAxY0QkAAAAF_LOpeqXWnUpwaRFIuJqm Gecko/2009042316 Firefox/3.0.10 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > up in the mountains behind your old haunt I experienced this: Why did we automatically assume that you had been hit on the head by a meteorite? If the cap fits... ;-) === Subject: OT: Re: Teenager hit by 30,000 mph meteorite . Interesting, and about what I would have thought. It gives me an opportunity to ask a related (but non-astro) question. In some Middle Eastern countries in particular, it seems quite fashionable to fire AK47s into the air in celebration, even in quite densely populated areas. I have long wondered if this represents a health risk to the population. I assume that if the bullet is fired more or less straight up, it will return to earth at the terminal velocity of the bullet. What would happen if you were hit by one? Does it bounce-off, bruise you, penetrate the skin, or kill you? Any idea? === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . > Interesting, and about what I would have thought. It gives me an opportunity to ask a related (but non-astro) question. In some Middle Eastern countries in particular, it seems quite > fashionable to fire AK47s into the air in celebration, even in quite > densely populated areas. I have long wondered if this represents a > health risk to the population. I assume that if the bullet is fired more or less straight up, it will > return to earth at the terminal velocity of the bullet. What would > happen if you were hit by one? Does it bounce-off, bruise you, penetrate > the skin, or kill you? The terminal velocity is about the same as the muzzle velocity of a paintball. Now imagine that paintball being replaced with a ball bearing. -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . <4a3d9bc7$0$23688$afc38c87@news.optusnet.com.au> <7a6prhF1tjt54U6@mid.individual.net> posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > Interesting, and about what I would have thought. It gives me an opportunity to ask a related (but non-astro) question. In some Middle Eastern countries in particular, it seems quite > fashionable to fire AK47s into the air in celebration, even in quite > densely populated areas. I have long wondered if this represents a > health risk to the population. I assume that if the bullet is fired more or less straight up, it will > return to earth at the terminal velocity of the bullet. What would > happen if you were hit by one? Does it bounce-off, bruise you, penetrate > the skin, or kill you? The terminal velocity is about the same as the muzzle velocity of a > paintball. Now imagine that paintball being replaced with a ball bearing. -- > Dirk http://www.transcendence.me.uk/ - Transcendence UK > http://www.theconsensus.org/ - A UK political party > http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff Ouch! Good logic/real world analysis. Get practical! (Message to all) 3SAT is Not Too Easy. A Future Retrospective In Computational Complexity Read G.9adel's Lost Letter and P=NP. Also check out Iannis Tourlakis' paper on extensions of these lower bound. What I find nice about this type of proof is you get lower bounds by finding new algorithms. How to Solve P=NP? G.9adel's Lost Letter and P=NP was a good start but we all guessed wrong. G.9adel's Lost Letter and P=NP led to a discussion and proof that mathsf{NLOG} is closed under complement. Perhaps we should put P=NP on theory exams and hope dots [...]. I am serious. All the properties are easy to check. The main point is if the machine guesses wrong during the computational complexity theory, P = NP if and only if there exists a Turing machine T and a natural number k such that (ri) < nk, the question already considered by Godel! Computational Complexity: G.9adel Prize 12 Apr 2006 [...] Even proving it couldn't be done would solve the P/NP puzzle. [...] NP because it seems very counter intuitive to say that we can check an exponential number of [...]. Obviously it's not a formal proof, but it is an intuitive coding. Imagine some time in the future the problem has been solved and we programmer who solved the P vs. NP problem. [Note: I only use the word ingenious here as it is cited in the P vs. NP problem description: http://www.claymath.org/millennium/P vs NP/ from the Clay Mathematics Institute: (excerpt )However, this apparent difficulty may only reflect the lack of ingenuity of your programmer.] Well, I thought I may not be able to prove P = NP by traditional means, but I can certainly prove NP ! [....]. Hey Atwood, here's a cashes yet another nice check from the controversy his blog has [....] proof, establishing that 3-SAT could be reduced to 2SAT in O(n3) time. What can I say? It is the Power of randomness: Efficient Computation & P vs. NP. G.9adel's letter to von Neumann [1954]: [...] Probabilistically Checkable Proofs (PCPs). Claim: The Riemann Hypothesis. Prover: (argument)[...] Every proof can be efficiently transformed to ZK proof [...]. An Argument for P=NP: the winner needn't provide a constructive proof that P=NP. 2. Despite Godel's [...] Godel, writing of course before the modern P=?NP framework, inquires [.....]. By definition, a guess for an NP problem is checkable in polynomial time. [...] Imagine possibilities, conceive, wonder, speculate, discover! Complex Multi-Tiered Abstracts: Abstract: It is shown how to restrict G.9adel's system $T$ of recursion in all higher [...] Abstract: We discuss the forcing approach to P==NP problem. [...] sound proof-systems) showed how to efficiently check proofs of [...]. Then mathematics, science, technology, innovation, and most importantly advances in medicine, (still governed by fundamental physics--bases of reality) become more like storytelling. Imagination is more important than intelligence. --Albert Einstein The Tale of NP-Completeness By [...] 1931 [CapitalEth] Kurt G.9adel introduces the incompleteness theorems [...]. First Formal Proof that P ? NP. By giving a poly-time solution for the matching search problem, [....] find a proof then check it? - [YES]. Is nature nondeterministic? [YES]. A Short History of A Short History of Computational Complexity By Martin Musatov It was a dark night in Los Angeles. I was curled up on a futon at a friend's downtown loft (4th & Broadway), writing a USENET post at 4 poked at the tiny QWERTY keyboard of my BlackBerry. -- Martin Musatov http://MeAmI.org Better than Google alone, plus no ads. === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . > On Jun 20, 9:31?pm, Peter Webb > Interesting, and about what I would have thought. > It gives me an opportunity to ask a related (but non-astro) question. > In some Middle Eastern countries in particular, it seems quite fashionable > to fire AK47s into the air in celebration, even in quite densely populated > areas. I have long wondered if this represents a health risk to the > population. > I assume that if the bullet is fired more or less straight up, it will > return to earth at the terminal velocity of the bullet. What would happen if > you were hit by one? Does it bounce-off, bruise you, penetrate the skin, or > kill you? > Any idea? Bullets are not designed to be deadly on their fall > back to earth. But they can be designed to be. Flechetes > of WWI were bullet sized bomblets (pointed with fins) > that reached very high terminal velocity when simply > dropped from planes onto trenches, fast enough to > penetrate helmets. WWI flechettes were steel darts about 4 inches long. They were not bullets. -- Jim Pennino === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . > On Jun 20, 9:31 pm, Peter Webb > Interesting, and about what I would have thought. > It gives me an opportunity to ask a related (but non-astro) question. > In some Middle Eastern countries in particular, it seems quite fashionable > to fire AK47s into the air in celebration, even in quite densely populated > areas. I have long wondered if this represents a health risk to the > population. > I assume that if the bullet is fired more or less straight up, it will > return to earth at the terminal velocity of the bullet. What would happen if > you were hit by one? Does it bounce-off, bruise you, penetrate the skin, or > kill you? > Any idea? > Bullets are not designed to be deadly on their fall > back to earth. But they can be designed to be. Flechetes > of WWI were bullet sized bomblets (pointed with fins) > that reached very high terminal velocity when simply > dropped from planes onto trenches, fast enough to > penetrate helmets. > WWI flechettes were steel darts about 4 inches long. Possibly some were, and modern ones appear to be. The ones I saw pictured for sale in a war > surplus catalog 40 years ago were about > an inch long, as big around as a pencil > with small tail fins. Nothing at all like > a dart. dart a. A slender, pointed missile, often having tail fins, thrown by hand, shot from a blowgun, or expelled by an exploding bomb. b. An object likened to a slender, pointed missile either in shape, use, or effect. What you saw was likely from artillery or bombs. > They were not bullets. But not much different in terms of mass. Or a can of cat food. bullet a. A usually metal projectile in the shape of a pointed cylinder or a ball that is expelled from a firearm, especially a rifle or handgun. b. Such a projectile in a metal casing; a cartridge. > The point being that bullets are in the grey > area where the difference between lethal and > non-lethal can be due to aerdynamics. The difference between lethal and non-lethal for bullets is due to velocity. -- Jim Pennino === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . > On Jun 20, 9:31 pm, Peter Webb > Interesting, and about what I would have thought. > It gives me an opportunity to ask a related (but non-astro) question. > In some Middle Eastern countries in particular, it seems quite fashionable > to fire AK47s into the air in celebration, even in quite densely populated > areas. I have long wondered if this represents a health risk to the > population. > I assume that if the bullet is fired more or less straight up, it will > return to earth at the terminal velocity of the bullet. What would happen if > you were hit by one? Does it bounce-off, bruise you, penetrate the skin, or > kill you? > Any idea? > Bullets are not designed to be deadly on their fall > back to earth. But they can be designed to be. Flechetes > of WWI were bullet sized bomblets (pointed with fins) > that reached very high terminal velocity when simply > dropped from planes onto trenches, fast enough to > penetrate helmets. > WWI flechettes were steel darts about 4 inches long. > Possibly some were, and modern ones appear to be. > The ones I saw pictured for sale in a war > surplus catalog 40 years ago were about > an inch long, as big around as a pencil > with small tail fins. Nothing at all like > a dart. > dart > a. ?A slender, pointed missile, often having tail fins, thrown by hand, > shot from a blowgun, or expelled by an exploding bomb. > b. ?An object likened to a slender, pointed missile either in shape, use, > or effect. > What you saw was likely from artillery or bombs. It's the darts you speak of that are packed into > artillery shells. Check with the Israelis. You mean the flechettes? > The catalog specifically called them flechettes and > specifically mentioned being dropped from planes. > Probably what I saw is what Wikpedia calls > Devil Dogs. used by the U.S. in the Korean and Vietnam Wars. > These 1 3/4 length (4.5 cm) bomblets were > air-dropped at height in canisters by aircraft > or scattered from buckets by helicopter crews, > reaching high sub-sonic speeds as they fell. > Targeted at enemy personnel and unarmored > vehicles, the flechette hit the targets with > the force of a bullet. > Note that the Devil Dog is sill refered to as > a type of flechette. You are needlessly splitting > hairs. flechette A steel missile or dart dropped from an aircraft or fired from an artillery piece. Nope, I'm just using the words per the definition of the words and not making things up as a go. > They were not bullets. > But not much different in terms of mass. > Or a can of cat food. I wouldn't want to get hit by a falling can > of cat food either. > > bullet > a. ?A usually metal projectile in the shape of a pointed cylinder or a > ball that is expelled from a firearm, especially a rifle or handgun. > b. ?Such a projectile in a metal casing; a cartridge. I suppose you think it makes a difference whether > it's fired by a pistol or a revolver. Not according to the definition of the word bullet. > The point being that bullets are in the grey > area where the difference between lethal and > non-lethal can be due to aerdynamics. > The difference between lethal and non-lethal for bullets is due to > velocity. And terminal velocity is determined by aerodynamics. If it is falling from a height. -- Jim Pennino === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . > On Jun 20, 9:31 pm, Peter Webb > Interesting, and about what I would have thought. Bullets are not designed to be deadly on their fall > back to earth. But they can be designed to be. Flechetes > of WWI were bullet sized bomblets (pointed with fins) > that reached very high terminal velocity when simply > dropped from planes onto trenches, fast enough to > penetrate helmets. > WWI flechettes were steel darts about 4 inches long. flechette > A steel missile or dart dropped from an aircraft or fired from an > artillery piece. > Nope, I'm just using the words per the definition of the words and > not making things up as a go. So you failed to notice the word or in that definition. > So you ARE making things up. Nope, I'm not the one calling a flechette a bullets. On Jun 20, 9:31 pm, Peter Webb > Interesting, and about what I would have thought. > Bullets are not designed to be deadly on their fall > back to earth. But they can be designed to be. Flechetes > of WWI were bullet sized bomblets (pointed with fins) > that reached very high terminal velocity when simply > dropped from planes onto trenches, fast enough to > penetrate helmets. > WWI flechettes were steel darts about 4 inches long. > Hey, you're the one that introduced the term dart. > Yes, in response to you refering to flechettes as bullet sized bomblets > above. Which happens to be true. What's your point? No, it is not. Bullets are not several inches long, while flechettes are. > A flechette is a particular type of dart and not related to bullets. Just as a revolver is a particuar type of handgun. > That does NOT mean all handguns are revolvers just > as NOT all flechettes are darts. flechette 1. a missile resembling a dart that is dropped from an aircraft. Also called aerial dart. Etymology: early 20th cent.: from French flechette, diminutive of fleche arrow. missile An object or weapon that is fired, thrown, dropped, or otherwise projected at a target; a projectile. > I did not call them bullets, I said they (of the > particular type I had in mind) had a size and mass > similar to bullets. It is therefore legitimate to > speculate on whether bullets falling from a height > can be lethal since it is known that flechettes are. The only flechettes similar in size, in length only, to bullets are the stamped wire flechettes that were loaded into 12 gauge shotgun shells during the Vietnam war. Flechettes are nothing like bullets. Bullets are stabilized by the spin created by barrel rifling. The farther they go, the less stable they get. Flechettes are stabilized by fins. The farther they go, the more stable they get. The length/diameter ratio of flechettes is many times that of bullets. > And I suppose you think rifles can't fire flechettes. There has never been anything like that that has ever been sucessful and it is a stupid concept from the start. The closest was the Gyrojet rocket system which was an utter failure. > You would be wrong about that. Shotgun shells can and do > have flechette loads available. A shotgun is not a rifle. Is English your first language? -- Jim Pennino === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . > A shotgun is not a rifle. Now THAT'S funny! > > Is English your first language? Care to share what you THINK a rifle is? Go ahead, I dare you. rifle A firearm having a long barrel with a spirally grooved interior, which gives the bullet a spinning motion and thus greater accuracy over a longer range. shotgun A smoothbore gun that fires shot over short ranges. Also called scattergun. Or, in case you can't understand the obvious, a rifle has a rifled bore while a shotgun has a smooth bore. Have you ever heard of a dictionary? -- Jim Pennino === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . > A shotgun is not a rifle. > Now THAT'S funny! > Is English your first language? > Care to share what you THINK a rifle is? > Go ahead, I dare you. > rifle > A firearm having a long barrel with a spirally grooved interior, which > gives the bullet a spinning motion and thus greater accuracy over a longer > range. You left out the part about firing a single projectile. I didn't leave out anything; that is a dictionary definition. And FYI, there has been rifle ammunition with multiple bullets; yet another failed experiment. > shotgun > A smoothbore gun that fires shot over short ranges. Also called ?scattergun. > Or, in case you can't understand the obvious, a rifle has a rifled bore > while a shotgun has a smooth bore. What about when the shotgun has a rifled bore and shoots > slugs (single projectile)? Rifled shotguns were little more than a failed experiment and were never massed produced. Also, rifled shotguns are called rifled shotguns, not shotguns. There were also smooth bored rifles at one time. Oddly enough, those are called smooth bore rifles. None of this changes the current definitions of the words rifle and shotgun. I use English of the 21st Century. Get yourself a dictionary and try it out. -- Jim Pennino === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . > A shotgun is not a rifle. > Now THAT'S funny! > Is English your first language? > Care to share what you THINK a rifle is? > Go ahead, I dare you. > rifle > A firearm having a long barrel with a spirally grooved interior, which > gives the bullet a spinning motion and thus greater accuracy over a longer > range. > You left out the part about firing a single projectile. > I didn't leave out anything; that is a dictionary definition. Depends on whose dictionary you use. Do you think I made that up? There is nothing about single projectile in The American Heritage Dictionary, Collins Essential English Dictionary 2nd Edition, The Mirriam-Webster Dictionary, or Webster's New World College Dictionary. > And FYI, there has been rifle ammunition with multiple bullets; yet > another failed experiment. Then it doesn't count. Do you understand the difference between the words rifle and ammunition? > shotgun > A smoothbore gun that fires shot over short ranges. Also called scattergun. > Or, in case you can't understand the obvious, a rifle has a rifled bore > while a shotgun has a smooth bore. > What about when the shotgun has a rifled bore and shoots > slugs (single projectile)? > Rifled shotguns were little more than a failed experiment and were never > massed produced. But still produced. That's not a failed experiment, just > one that wasn't marketing failure. And widely enough known to > the multiple bullet experiments? Ahh, now I see your problem. All your knowledge of firearms comes from Wikipedia. > Also, rifled shotguns are called rifled shotguns, not shotguns. > There were also smooth bored rifles at one time. Oddly enough, those > are called smooth bore rifles. Whithout rifling, they were not, by your dictionary's > definition, rifles, despite what they are called. Correct, they were not rifles, they were smooth bore rifles. > Can't you see the irony here? If a smooth bore > rifle is a rifle, then a Devil Dog is a flechette. No, a smooth bore rifle is a smooth bore rifle. I never said a Devil Dog wasn't a flechette; I ignored this irrelvancy and you are imagining things. What I said was a flechette is a dart like thing, not a bullet like thing. -- Jim Pennino === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . > A shotgun is not a rifle. > Now THAT'S funny! > Is English your first language? > Care to share what you THINK a rifle is? > Go ahead, I dare you. > rifle > A firearm having a long barrel with a spirally grooved interior, which > gives the bullet a spinning motion and thus greater accuracy over a longer > range. > You left out the part about firing a single projectile. > I didn't leave out anything; that is a dictionary definition. > Depends on whose dictionary you use. Do you think I made that up? > There is nothing about single projectile in The American Heritage > Dictionary, Collins Essential English Dictionary 2nd Edition, The > Mirriam-Webster Dictionary, or Webster's New World College Dictionary. I did not note where I saw this. Keep looking, > you'll find it eventually and then you can yell > at them. What are you, 12 years old? > > And FYI, there has been rifle ammunition with multiple bullets; yet > another failed experiment. > Then it doesn't count. > Do you understand the difference between the words rifle and ammunition? > shotgun > A smoothbore gun that fires shot over short ranges. Also called scattergun. > Or, in case you can't understand the obvious, a rifle has a rifled bore > while a shotgun has a smooth bore. > What about when the shotgun has a rifled bore and shoots > slugs (single projectile)? > Rifled shotguns were little more than a failed experiment and were never > massed produced. > But still produced. That's not a failed experiment, just > one that wasn't marketing failure. And widely enough known to > the multiple bullet experiments? > Ahh, now I see your problem. > All your knowledge of firearms comes from Wikipedia. Not all. I didn't look up rifle in Wikipedia. Besides, what in Wikipedia do you think is wrong? In this particular case, the use of the term Devil Dog in relation to Lazy Dog, which you seem to be clinging to like a bull dog. Wikipedia is the only place you will find such a reference. http://en.wikipedia.org/wiki/Lazy_Dog_(bomb) is correct. The term Devil Dog commonly refers to Marines. I find it unlikely that a system that already has a common name would be given yet another common name which itself is already in common use. the sky, the bullet-like thing is irrelevant? Can you explain that lunatic logic? It escapes me. Simple, in a discussion of bullets falling from the sky, a dart like thing is basically irrelevant unless you want to extend the discussion to all possible shapes falling from the sky. -- Jim Pennino === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . > There were also smooth bored rifles at one time. Oddly enough, those > are called smooth bore rifles. Did any ever shoot fin stabilised ammo? I would have thought that the answer to the inaccuracy of (say) a musket ball. -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . > > There were also smooth bored rifles at one time. Oddly enough, those > are called smooth bore rifles. Did any ever shoot fin stabilised ammo? > I would have thought that the answer to the inaccuracy of (say) a musket > ball. That would require a sabot to work and the technology to create rifled barrels precedes the technology to make a working sabot. A rifled musket of the 1860's could nearly match the accuracy of a modern production rifle. The bullets, or musket balls, by that time had evolved from round balls to essentially the same shape as a modern bullet. I have a modern reproduction of a Enfield Pattern 1853 Rifle-Musket, which with modern musket balls, is every bit as accurate as a modern hunting rifle out to a couple of hundred yards. -- Jim Pennino === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . > Interesting, and about what I would have thought. It gives me an opportunity to ask a related (but non-astro) question. In some Middle Eastern countries in particular, it seems quite fashionable > to fire AK47s into the air in celebration, even in quite densely populated > areas. I have long wondered if this represents a health risk to the > population. I assume that if the bullet is fired more or less straight up, it will > return to earth at the terminal velocity of the bullet. What would happen if > you were hit by one? Does it bounce-off, bruise you, penetrate the skin, or > kill you? Any idea? The subject was intensively studied by a guy named Hatcher not long after WWI as the US Army wanted to know the implications of shooting up in the air at the then new airplane. The bottom line was all but the most massive bullets weren't likely to give you much more than a bruise. The biggest danger was large, as in 50 caliber, bullets hitting an unprotected head. So if you are going to fire your 50 caliber machine gun in the air, wear a helmet and make sure there are no kids around. -- Jim Pennino === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . >Interesting, and about what I would have thought. It gives me an opportunity to ask a related (but non-astro) question. In some Middle Eastern countries in particular, it seems quite fashionable >to fire AK47s into the air in celebration, even in quite densely populated >areas. I have long wondered if this represents a health risk to the >population. I assume that if the bullet is fired more or less straight up, it will >return to earth at the terminal velocity of the bullet. What would happen if >you were hit by one? Does it bounce-off, bruise you, penetrate the skin, or >kill you? Any idea? The bullet returns at terminal velocity, which can be high enough to injure or even kill somebody, although the conditions for it to do so would be unusual. Nevertheless, I recall a couple of incidents when I lived in Southern California of people being killed by falling bullets shot off on New Year's Eve or some other holiday. Both were babies or small children, IIRC. Of course, a baby doesn't have a fully developed skull to stop a bullet. I think that in most of the cases where people are injured by falling bullets, they are actually hit by a faster bullet because it wasn't truly fired straight up. Shoot a bullet at 45Á and it can still come down with an obvious vertical velocity component, but it will probably be moving well over terminal velocity (in its horizontal component). Mythbusters tested this, and arrived at a very unusual conclusion. http://kwc.org/mythbusters/2006/04/episode_50_bullets_fired_up_vo.html _________________________________________________ Chris L Peterson Cloudbait Observatory http://www.cloudbait.com === Subject: Re: OT: Re: Teenager hit by 30,000 mph meteorite . > Interesting, and about what I would have thought. It gives me an opportunity to ask a related (but non-astro) question. In some Middle Eastern countries in particular, it seems quite > fashionable to fire AK47s into the air in celebration, even in quite > densely populated areas. I have long wondered if this represents a > health risk to the population. I assume that if the bullet is fired more or less straight up, it will > return to earth at the terminal velocity of the bullet. What would > happen if you were hit by one? Does it bounce-off, bruise you, penetrate > the skin, or kill you? Any idea? Terminal velocity of up to 100m/s. Big bruise at the very least. Heavy handgun calibres would be more dangerous because of the bigger mass of bullet. -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: Teenager hit by 30,000 mph meteorite . > http://www.theregister.co.uk/2009/06/12/meteorite_strike/ > http://www.theregister.co.uk/science/space/ > ::: German lad hit by 30,000 mph meteorite, pea size, . ::: gave him a > nasty three-inch gash on his hand, b4 > ::: it It bounced off embedding itself in a foot-wide crater > ::: in the ground. > That's like being shot by an hyper-velocity .22 or 5.65mm bullet. > == Is this a joke? > == If not, then what is the min. size needed for a meteor > to makes it to the ground with such high end velocities? > (if they are too small then they burn up and the oxide- > == It is postulated that the meteor size distribution says that the > smaller the size the more of them there are. > == If so then there should be many reports from people with meteorites > in their bodies, impact objects the size of a match head or a grain of > salt...besides the obvious, NG > rect-Al ones that produce Tourette syndromatic idiots. > == Is there a size limit to such HV impacters, below which there is no > bleeding nor pain registering, upon body entry? > IIRC, there are X-ray pix of people who have such foreign > items within their bodies, they were not aware of at all? Not surprising. I once jumped onto a plank and thought I must have had a fairly hard impact. Only later did I discover there must have been nail in the wood that left a neat puncture hole in my foot. I did it again years later jumping into a lake in Bavaria and hitting something. Only when I got out did I notice the bleeding. Quite often a puncture wound just feels like a bump - only the blood gives it away. And maybe not then if you are really cold. -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: Answer to Dik T. Winter posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Your claim is that no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path. The complete infinite binary tree is constructed from a countable set of infinite paths. There is no chance to distinguish a given infinite path from the complete tree. A: actually infinite paths exist, If not, then there are no other paths than finite path in the tree. > B: the infinite tree contains a path p that can be > distinguished from every path of P. I do not state that it contains such a path. I stated that it is impossible to distinguish a given infinite path from the tree. You agree A ==> B So if A is true then B is true > and your claim is false. And if B is false, then A is false. Whether my claim is true should be decided by experiment. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) > A: actually infinite paths exist, That is the question. We do neither state that A is true nor that it is false. We simply look whether B is true. We find that B is false. This can be proved by experiment. You do not like the result, and you cannot change it, therefore you say that the experiment gives a circular result, because anybody with a sober mind could have predicted the result. === Subject: Re: Answer to Dik T. Winter > Your claim is that no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path. The complete infinite binary tree is constructed from a countable set > of infinite paths. > There is no chance to distinguish a given infinite path from the > complete tree. WM misses the point quite deliberately. The point is that when a maximal infinite binary tree is constructed from a countable set of paths, there are necessarily paths in the tree which are not in the set from which it was constructed. This is the case since the set of ALL paths of such a tree is not a countable set. That is an immediate and unvoidable conseqeunce of Cantor's diagonal proof. A: actually infinite paths exist, If not, then there are no other paths than finite path in the tree. In which case all of WM's claims about what happens with maximal infinite binary trees are impossibilities. B: the infinite tree contains a path p that can be > distinguished from every path of P. I do not state that it contains such a path. We claim it contains uncounably many such paths. > I stated that it is > impossible to distinguish a given infinite path from the tree. WM is being sloppy again. Since no path is the entire tree, every path is distinguishable from the tree itself. What WM is trying, but failing, to say is that every path in the tree is a path in the tree, with which remark we have no quarrel. You agree A ==> B So if A is true then B is true > and your claim is false. And if B is false, then A is false. > Whether my claim is true should be decided by experiment. Perhaps if this were physics, but it is only in the tiny minds of some warped physicists that all mathematics is the slave of physics rather than a queen over physics. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) > A: actually infinite paths exist, That is the question. If your answer is in the negative, WM, then you have no business even speculating about the properties of maximal infinite binary trees. > We find that B is false. This can be proved by experiment. We find that WM is false. This can be proved by experiment. All one has to do is test a few of WM's postings for logical consistency and coherence to find claims by him that are false or logically inconsistent or both. -- Virgil === Subject: Re: Answer to Dik T. Winter posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I Your claim is that no possibility exists to construct or to distinguish by one or many or infinitely many nodes of the tree another path. A: actually infinite paths exist, B: the infinite tree contains a path p that can be distinguished from every path of P. You agree A ==> B So if A is true then B is true and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) Outside Wolkenmuekenheim, if infinite paths actually exist *is* a matter of of A or not A. Since you cannot prove ~B without assuming ~A. we conclude that neither A nor ~A can be proved. - William Hughes === Subject: Re: Answer to Dik T. Winter posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Since you cannot prove ~B without assuming ~A. > we conclude that neither A nor ~A can be proved. I thought I can prove ~B by your incapability of distinguishing t from T. Your incapability of distingushing A from B suggests that this proof is not of much value though. However, there are others able to distinguish A from B but unable to distinguish t from T. I will stop this useless discussion here. I have put together a brief version of the argument in the thread originally devoted to the binary tree. === Subject: Re: Answer to Dik T. Winter Since you cannot prove ~B without assuming ~A. > we conclude that neither A nor ~A can be proved. I thought I can prove ~B by your incapability of distinguishing t from > T. If T is any countable set of infinite binary sequences, let t be Cantor's anti-diagonal sequence and then t will be distinguishable from every member of T. > I will stop this useless discussion here. You should have stopped posting your foolishness long since. -- Virgil === Subject: Re: Answer to Dik T. Winter posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > Your claim is that no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path. A: actually infinite paths exist, > B: the infinite tree contains a path p that can be > distinguished from every path of P. You agree A ==> B So if A is true then B is true > and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) > Outside Wolkenmuekenheim, if infinite paths > actually exist *is* a matter of > of A or not A. > Since you cannot prove ~B without assuming ~A. > we conclude that neither A nor ~A can be proved. > - William Hughes All truths can and will be proved in time. 3SAT is Not Too Easy. A Future Retrospective In Computational Complexity Read G.9adel's Lost Letter and P=NP. Also check out Iannis Tourlakis' paper on extensions of these lower bound. What I find nice about this type of proof is you get lower bounds by finding new algorithms. How to Solve P=NP? G.9adel's Lost Letter and P=NP was a good start but we all guessed wrong. G.9adel's Lost Letter and P=NP led to a discussion and proof that mathsf{NLOG} is closed under complement. Perhaps we should put P=NP on theory exams and hope dots [...]. I am serious. All the properties are easy to check. The main point is if the machine guesses wrong during the computational complexity theory, P = NP if and only if there exists a Turing machine T and a natural number k such that (ri) < nk, the question already considered by Godel! Computational Complexity: G.9adel Prize 12 Apr 2006 [...] Even proving it couldn't be done would solve the P/NP puzzle. [...] NP because it seems very counterintuitive to say that we can check an exponential number of [...]. Obviously it's not a formal proof, but it is an intuitive coding. Imagine some time in the future the problem has been solved and we programmer who solved the P vs. NP problem. [Note: I only use the word ingenius here as it is cited in the P vs. NP problem description: http://www.claymath.org/millennium/P vs NP/ from the Clay Mathematics Institute: (excerpt )However, this apparent difficulty may only reflect the lack of ingenuity of your programmer.] Well, I thought I may not be able to prove P = NP by traditional means, but I can certainly prove NP ! [....]. Hey Atwood, here's a cashes yet another nice check from the controversy his blog has [....] proof, establishing that 3-SAT could be reduced to 2SAT in O(n3) time. What can I say? It is the Power of randomness: Efficient Computation & P vs. NP. G.9adel's letter to von Neumann [1954]: [...] Probabilistically Checkable Proofs (PCPs). Claim: The Riemann Hypothesis. Prover: (argument)[...] Every proof can be efficiently transformed to ZK proof [...]. An Argument for P=NP: the winner needn't provide a constructive proof that P=NP. 2. Despite Godel's [...] Godel, writing of course before the modern P=?NP framework, inquires [.....]. By definition, a guess for an NP problem is checkable in polynomial time. [...] Imagine possibilities, conceive, wonder, speculate, discover! Complex Multi-Tiered Abstracts: Abstract: It is shown how to restrict G.9adel's system $T$ of recursion in all higher [...] Abstract: We discuss the forcing approach to P==NP problem. [...] sound proof-systems) showed how to efficiently check proofs of [...]. Then mathematics, science, technology, innovation, and most importantly advances in medicine, (still governed by fundamental physics--bases of reality) become more like storytelling. Imagination is more important than intelligence. --Albert Einstein The Tale of NP-Completeness By [...] 1931 [CapitalEth] Kurt G.9adel introduces the incompleteness theorems [...]. First Formal Proof that P ? NP. By giving a poly-time solution for the matching search problem, [....] find a proof then check it? - [YES]. Is nature nondeterministic? [YES]. A Short History of A Short History of Computational Complexity By Martin Musatov It was a dark night in Los Angeles. I was curled up on a Futon at a friend's downtown loft (4th & Broadway), writing a USENET post at 4 poked at the tiny QWERTY keyboard of my BlackBerry. -- Martin Musatov http://MeAmI.org Better than Google alone, plus no ads. === Subject: Can a comp.ai person look at this? Here is the information I have about his document and a link to his document. P Versus NP Summary on Math and Science 15 Apr 2009 My friend says (according to Google)[...]Yes I will be collecting the Clay Mathematics Institute Millennium Prize but I will[ ...] For a solution to so many things. And then it reads: MMMusatov Mathematics. The URL for the file is: http://www.scribd.com/doc/14262891/P-Versus-NP-Summary-on-Math-and-Science Meami === Subject: critical point f[x, y]=Sqrt[x^2 + (-2 + y)^2] + Sqrt[(-1 + x)^2 + y^2] + Sqrt[x^2 + y^2] find critical point of f === Subject: Re: critical point > f[x, y]=Sqrt[x^2 + (-2 + y)^2] + > Sqrt[(-1 + x)^2 + y^2] + Sqrt[x^2 + y^2] find critical point of f do you sometimes try to do your homework yourself? Alois === Subject: Re: critical point > f[x, y]=Sqrt[x^2 + (-2 + y)^2] + > Sqrt[(-1 + x)^2 + y^2] + Sqrt[x^2 + y^2] > find critical point of f Approximately: x = 0.3045037013 y = 0.2545693135 --Lynn http://math.asu.edu/~kurtz === Subject: Re: critical point posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > f[x, y]=Sqrt[x^2 + (-2 + y)^2] + > Sqrt[(-1 + x)^2 + y^2] + Sqrt[x^2 + y^2] find critical point of f {'e'*<'e'+2>}-1=f f=p Lemma: P=NP: An even integer 'e' and 'p' prime: {'e'*<'e'+2>}-1='p === Subject: Re: Help. What is a model? David C. Ullrich said > A group is a model of _group theory_, not some given > group theory. You may think that there can only be one 'group theory', but a theory is simply a man-made conception. There is nothing to stop conceiving a theory that they call a 'group theory'. It might be inconsistent, and you might not think it is a 'proper' group theory, but it can still be called a group theory, so that you cannot assume that the set of all group theories is a set with a singular element. > There is no such thing as an expression of a model. It really seems as though you're not _trying_ to > follow this. It's > already been explained that there's no such thing as > an expression > of a model. If you don't understand why not fine, > ask. But > continuing to talk about an expression of a model > after > the people you're asking to explain have explained > that > there's no such thing makes very little sense. That doesn't tally with what Jack Markam said. He said that a model is a function that can be explicitly stated. Therefore there is an expression that is that function, and when a variable of that expression is substituted, that also is an expression. So such expressions are clearly inherent aspects of the model. Denying that they 'belong' to the model seem to me to be the worst sort of semantical hair-splitting that hinder understanding rather that assist it. > You said you were confused over whether a model of a > formal > system was the same thing as the formal system. One > would > think that a counterexample would help. Group theory > is > a formal system. A group is a model of group theory. > A > group is not group theory. So a model of group theory > is not the same thing as group theory. Your seem to think that I am either dim-witted or unwilling to try to understand what a model is. You can think that if you like, but you are making assumptions that make it difficult for me to know what you intend to mean. Simply referring to groups is not very helpful. Suppose that I showed an alien without legs from another solar system a chair and a table, and said, That is a chair, and that is a table - now you know what a chair is, because I've shown you an example. But the alien still has no idea what the essential characteristics of a chair are. Does it have to be made out of metal and plastic? Does it have to have a flat horizontal area at half a metre from the ground? And so on. Apparently, a model: a) shares some, but not all of the properties of the formal system that it is a model of b) has some properties that are not the properties of the formal system that it is a model of Surely someone can clearly define these properties as in a) and b in terms that can apply to any formal system, so that we can have a clear definition of what a model actually is? === Subject: Re: Help. What is a model? posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) On Jun 21, 2:09am, revolt...@live.co.uk so that we can have a clear definition of what a model actually is? I already gave a precise definition of 'model', as well as I showed how different senses of 'model' in mathematical logic boil down to essentially the same. MoeBlee === Subject: Re: Help. What is a model? <28497419.8016.1245575409354.JavaMail.jakarta@nitrogen.mathforum.org Surely someone can clearly define these properties as in a) and b in > terms that can apply to any formal system, so that we can have a clear > definition of what a model actually is? Is there some reason you can't just look up the definition? -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon mann nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === Subject: Re: Help. What is a model? <87tz29x3kq.fsf@alatheia.truth.invalid> posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) Surely someone can clearly define these properties as in a) and b in > terms that can apply to any formal system, so that we can have a clear > definition of what a model actually is? Is there some reason you can't just look up the definition? -- > Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon mann nicht sprechen kann, dar?ber muss man schweigen > - Ludwig Wittgenstein, Tractatus Logico-Philosophicus Dictionaries can be revised. Definitions depend on context. In this sense a model is [...]: a new way to approach the P vs. NP problem: storytelling. 3SAT is Not Too Easy. A Future Retrospective In Computational Complexity Read G.9adel's Lost Letter and P=NP. Also check out Iannis Tourlakis' paper on extensions of these lower bound. What I find nice about this type of proof is you get lower bounds by finding new algorithms. How to Solve P=NP? G.9adel's Lost Letter and P=NP was a good start but we all guessed wrong. G.9adel's Lost Letter and P=NP led to a discussion and proof that mathsf{NLOG} is closed under complement. Perhaps we should put P=NP on theory exams and hope dots [...]. I am serious. All the properties are easy to check. The main point is if the machine guesses wrong during the computational complexity theory, P = NP if and only if there exists a Turing machine T and a natural number k such that (ri) < nk, the question already considered by Godel! Computational Complexity: G.9adel Prize 12 Apr 2006 [...] Even proving it couldn't be done would solve the P/NP puzzle. [...] NP because it seems very counterintuitive to say that we can check an exponential number of [...]. Obviously it's not a formal proof, but it is an intuitive coding. Imagine some time in the future the problem has been solved and we programmer who solved the P vs. NP problem. [Note: I only use the word ingenious here as it is cited in the P vs. NP problem description: http://www.claymath.org/millennium/P vs NP/ from the Clay Mathematics Institute: (excerpt )However, this apparent difficulty may only reflect the lack of ingenuity of your programmer.] Well, I thought I may not be able to prove P = NP by traditional means, but I can certainly prove NP ! [....]. Hey Atwood, here's a cashes yet another nice check from the controversy his blog has [....] proof, establishing that 3-SAT could be reduced to 2SAT in O(n3) time. What can I say? It is the Power of randomness: Efficient Computation & P vs. NP. G.9adel's letter to von Neumann [1954]: [...] Probabilistically Checkable Proofs (PCPs). Claim: The Riemann Hypothesis. Prover: (argument)[...] Every proof can be efficiently transformed to ZK proof [...]. An Argument for P=NP: the winner needn't provide a constructive proof that P=NP. 2. Despite Godel's [...] Godel, writing of course before the modern P=?NP framework, inquires [.....]. By definition, a guess for an NP problem is checkable in polynomial time. [...] Imagine possibilities, conceive, wonder, speculate, discover! Complex Multi-Tiered Abstracts: Abstract: It is shown how to restrict G.9adel's system $T$ of recursion in all higher [...] Abstract: We discuss the forcing approach to P==NP problem. [...] sound proof-systems) showed how to efficiently check proofs of [...]. Then mathematics, science, technology, innovation, and most importantly advances in medicine, (still governed by fundamental physics--bases of reality) become more like storytelling. Imagination is more important than intelligence. --Albert Einstein The Tale of NP-Completeness By [...] 1931 [CapitalEth] Kurt G.9adel introduces the incompleteness theorems [...]. First Formal Proof that P ? NP. By giving a poly-time solution for the matching search problem, [....] find a proof then check it? - [YES]. Is nature non deterministic? [YES]. A Short History of A Short History of Computational Complexity By Martin Musatov It was a dark night in Los Angeles. I was curled up on a futon at a friend's downtown loft (4th & Broadway), writing a USENET post at 4 poked at the tiny QWERTY keyboard of my BlackBerry. -- Martin Musatov http://MeAmI.org Better than Google alone, plus no ads. === Subject: Re: Help. What is a model? In terms of an analogy: I could have a computer programmed to simulate a formal system. It would have in the program all the symbols, axioms, rules and definitions of the formal system. The keyboard contains all the symbols of the system. And there would also be two buttons to switch between two modes. In mode one you could create any well-formed formula of the system. In mode two, you would only be able to create new formulas from the axioms according to the rules of the system, to give proven formulas. (You could also have additional keys for quick access to axioms, etc, but that would not be essential). So, in these terms of such a programmed computer, how would you describe the model? You say that the model is a function, and that can be explicitly defined, so that given the original computer program for the formal system, one would only need: a) additional keys on the keyboard for the symbols of the function that are not symbols of the formal system b) some additional programming. Now, you say that the model function, for some formal system formula, will have one of two values, 0 or 1. But clearly, these values cannot be obtained from our computer program, not for every formula. For if that were the case, the problem of incompleteness of formal systems would be solved. So I don't see what benefit the model is in the examination of a formal system. It simply seems to be an additional layer of complexity with no raison d'etre. === Subject: Re: Help. What is a model? > In terms of an analogy: I could have a computer > programmed to simulate a formal system. It would have > in the program all the symbols, axioms, rules and > definitions of the formal system. The keyboard > contains all the symbols of the system. And there > would also be two buttons to switch between two > modes. In mode one you could create any well-formed > formula of the system. In mode two, you would only be > able to create new formulas from the axioms according > to the rules of the system, to give proven formulas. > (You could also have additional keys for quick access > to axioms, etc, but that would not be essential). So, in these terms of such a programmed computer, how > would you describe the model? You say that the model > is a function, and that can be explicitly defined, so > that given the original computer program for the > formal system, one would only need: > a) additional keys on the keyboard for the symbols of > the function that are not symbols of the formal > system > b) some additional programming. Now, you say that the model function, for some formal > system formula, will have one of two values, 0 or 1. > But clearly, these values cannot be obtained from our > computer program, not for every formula. For if that > were the case, the problem of incompleteness of > formal systems would be solved. So I don't see what > benefit the model is in the examination of a formal > system. It simply seems to be an additional layer of > complexity with no raison d'etre. Maybe the best analogy for the relation between models and formal systems is that between sentence logic and truth tables. But of course, the notion of truth and satisfiability are different, as are many other issues: sentences are not just empty letters any more, but the inner structure of the sentence now matters: quantification, predicates, etc., instead of just place-holders as in sentence logic. === Subject: Re: either Google employee is censoring Archimedes Plutonium or a vandal has struck Sadly, you have no standing in this matter, as you do not exist. I am an elaborate prank enacted by a group of bored graduate students > === Subject: An Honest Serious Post and Declaration of Theory posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) 3SAT is Not Too Easy. A Future Retrospective In Computational Complexity Read G.9adel's Lost Letter and P=NP. Also check out Iannis Tourlakis' paper on extensions of these lower bound. What I find nice about this type of proof is you get lower bounds by finding new algorithms. How to Solve P=NP? G.9adel's Lost Letter and P=NP was a good start but we all guessed wrong. G.9adel's Lost Letter and P=NP led to a discussion and proof that mathsf{NLOG} is closed under complement. Perhaps we should put P=NP on theory exams and hope dots [...]. I am serious. All the properties are easy to check. The main point is if the machine guesses wrong during the computational complexity theory, P = NP if and only if there exists a Turing machine T and a natural number k such that (ri) < nk, the question already considered by Godel! Computational Complexity: G.9adel Prize 12 Apr 2006 [...] Even proving it couldn't be done would solve the P/NP puzzle. [...] NP because it seems very counter intuitive to say that we can check an exponential number of [...]. Obviously it's not a formal proof, but it is an intuitive coding. Imagine some time in the future the problem has been solved and we programmer who solved the P vs. NP problem. [Note: I only use the word ingenious here as it is cited in the P vs. NP problem description: http://www.claymath.org/millennium/P vs NP/ from the Clay Mathematics Institute: (excerpt )However, this apparent difficulty may only reflect the lack of ingenuity of your programmer.] Well, I thought I may not be able to prove P = NP by traditional means, but I can certainly prove NP ! [....]. Hey Atwood, here's a cashes yet another nice check from the controversy his blog has [....] proof, establishing that 3-SAT could be reduced to 2SAT in O(n3) time. What can I say? It is the Power of randomness: Efficient Computation & P vs. NP. G.9adel's letter to von Neumann [1954]: [...] Probabilistically Checkable Proofs (PCPs). Claim: The Riemann Hypothesis. Prover: (argument)[...] Every proof can be efficiently transformed to ZK proof [...]. An Argument for P=NP: the winner needn't provide a constructive proof that P=NP. 2. Despite Godel's [...] Godel, writing of course before the modern P=?NP framework, inquires [.....]. By definition, a guess for an NP problem is checkable in polynomial time. [...] Imagine possibilities, conceive, wonder, speculate, discover! Complex Multi-Tiered Abstracts: Abstract: It is shown how to restrict G.9adel's system $T$ of recursion in all higher [...] Abstract: We discuss the forcing approach to P==NP problem. [...] sound proof-systems) showed how to efficiently check proofs of [...]. Then mathematics, science, technology, innovation, and most importantly advances in medicine, (still governed by fundamental physics--bases of reality) become more like storytelling. Imagination is more important than intelligence. --Albert Einstein The Tale of NP-Completeness By [...] 1931 [CapitalEth] Kurt G.9adel introduces the incompleteness theorems [...]. First Formal Proof that P ? NP. By giving a poly-time solution for the matching search problem, [....] find a proof then check it? - [YES]. Is nature nondeterministic? [YES]. A Short History of A Short History of Computational Complexity By Martin Musatov It was a dark night in Los Angeles. I was curled up on a futon at a friend's downtown loft (4th & Broadway), writing a USENET post at 4 poked at the tiny QWERTY keyboard of my BlackBerry. -- Martin Musatov http://MeAmI.org Better than Google alone, plus no ads. === Subject: Conjecture posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) An even integer 'e' and 'p' prime: {'e'*<'e'+2>}-1='p' -- Martin Musatov http://MeAmI.org Better search results than Google alone, plus no ads. === Subject: Re: Conjecture An even integer 'e' and 'p' prime: {'e'*<'e'+2>}-1='p' e(e + 2) - 1 = (2x(2x + 2))- 1 = (2x)^2 + 4x - 1 = 4x^2 + 4x - 1 No polynomial with rational coefficients is prime-representing. -- hz === Subject: Re: Conjecture An even integer 'e' and 'p' prime: {'e'*<'e'+2>}-1='p' e(e + 2) - 1 = (2x(2x + 2))- 1 > = (2x)^2 + 4x - 1 > = 4x^2 + 4x - 1 No polynomial with rational coefficients is prime-representing. Unless it's a constant function. Also, it would have been nicer if I had used 'n' instead of 'x'. Also, 119 = 7 * 17. -- hz === Subject: Re: Conjecture <4A3E4C1D.1EFEE54D@gmail.com> <4A3E66A7.36DBEE23@gmail.com> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) An even integer 'e' and 'p' prime: {'e'*<'e'+2>}-1='p' e(e + 2) - 1 = (2x(2x + 2))- 1 > = (2x)^2 + 4x - 1 > = 4x^2 + 4x - 1 No polynomial with rational coefficients is prime-representing. Unless it's a constant function. Also, it would have been nicer if I had used 'n' instead of 'x'. Also, 119 = 7 * 17. -- > hz An even number 'n' and 'p' prime can be {'n'*<'n'+2>}-1='p' ['p'~'n'p'] -- mmm === Subject: Re: Conjecture An even integer 'e' and 'p' prime: {'e'*<'e'+2>}-1='p' e(e + 2) - 1 = (2x(2x + 2))- 1 > = (2x)^2 + 4x - 1 > = 4x^2 + 4x - 1 No polynomial with rational coefficients is > prime-representing. Unless it's a constant function. Also, it would have been nicer if I had used 'n' > instead of 'x'. Also, 119 = 7 * 17. -- > hz An even number 'n' and 'p' prime can be > {'n'*<'n'+2>}-1='p' > ['p'~'n'p'] another 1st grade question?. Did you try _anything_ at all? 2(2+2)-1=7 6(6+2)-1=47 Maybe before trying adult problems like whether P=NP , you should aim to do intelligent conjectures. I mean, if this was false for 1 thru 20, I would understand, but it is true for n=2 ????? -- > mmm === Subject: Re: Conjecture <4A3E4C1D.1EFEE54D@gmail.com> <4A3E66A7.36DBEE23@gmail.com> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) An even integer 'e' and 'p' prime: {'e'*<'e'+2>}-1='p' e(e + 2) - 1 = (2x(2x + 2))- 1 > = (2x)^2 + 4x - 1 > = 4x^2 + 4x - 1 No polynomial with rational coefficients is prime-representing. Unless it's a constant function. Also, it would have been nicer if I had used 'n' instead of 'x'. Also, 119 = 7 * 17. -- > hz An even number 'n' and 'p' prime can be > {'n'*<'n'+2>}-1='p' > ['p'~'n'p'] -- > mmm > n(n + 2) - 1 = (2n(2n + 2))- 1 > = (2n)^2 + 4n - 1 > = 4n^2 + 4n - 1 -- mmm === Subject: Any solution manual or testbank for $25 ! only this week 17.06.2009 - 24.06.2009 ! posting-account=5BdoyQkAAAACm5Si7oheX_9haNFD_3c2 AppleWebKit/525.19 (KHTML, like Gecko) Version/3.1.2 Safari/525.21,gzip(gfe),gzip(gfe) electronic format (PDF or Doc), they are for sale: Automation, Production Systems, and Computer-Integrated Manufacturing - Mikell P. Groover (3rd ed) ISBN-10: 0132393212 ISBN-13: 978-0132393218 Price: $29 _________________________________________________________________________ Supply Chain Management - Sunil Chopra (3rd ed) by Prentice Hall ISBN-10: 0131730428 ISBN-13: 978-0131730427 Price: $29 _________________________________________________________________________ Operations Management: Process and Value Chains - Lee J. Krajewski (8th edition) solution manual ISBN-10: 0131697390 ISBN-13: 978-0131697393 Price: $29 _________________________________________________________________________ Operations Management: Process and Value Chains - Lee J. Krajewski (8th edition) testbank ISBN-10: 0131697390 ISBN-13: 978-0131697393 Price: $29 _________________________________________________________________________ Facilities Planning: James A. Tompkins, 3rd edition, Wiley ISBN-10: 0471413895 ISBN-13: 978-0471413899 Price: $29 _________________________________________________________________________ Mechanics of Materials Gere 6e solution manual Price: $12 _________________________________________________________________________ Accounting Information Systems, 11/E solution manual Marshall B. Romney, Brigham Young University Paul J. Steinbart, Arizona State University ISBN-10: 0136015182 ISBN-13: 9780136015185 price: $29 _________________________________________________________________________ Accounting Information Systems, 11/E testbank Marshall B. Romney, Brigham Young University Paul J. Steinbart, Arizona State University ISBN-10: 0136015182 ISBN-13: 9780136015185 price: $29 _________________________________________________________________________ Management Information Systems, 11/E solution manual Ken Laudon Jane Laudon ISBN-10: 013607846X ISBN-13: 9780136078463 price: $29 _________________________________________________________________________ Management Information Systems, 11/E testbank Ken Laudon Jane Laudon ISBN-10: 013607846X ISBN-13: 9780136078463 price: $29 _________________________________________________________________________ Business Statistics: A Decision Making approach, solution manual David F. Groebner ISBN-10: 0132416921 ISBN-13: 9780132416924 price: $29 _________________________________________________________________________ Business Statistics: A Decision Making approach, testbank David F. Groebner ISBN-10: 0132416921 ISBN-13: 9780132416924 Price: $29 _________________________________________________________________________ PROJECT MANAGEMENT ACHIEVING COMPETITIVE ADVANTAGE AND MS PROJECT international edition, Testbank by Jeffrey K. Pinto ISBN 10: 0138129320 ISBN 13: 9780138129323 Price: $29 _________________________________________________________________________ Consumer Behavior, 9/E ,Test bank Leon Schiffman, St. John's University Leslie Kanuk, CUNY-Baruch College Price: $29 _________________________________________________________________________ Introduction To Operations Research (scanned) solution manual Author: Hillier, Lieberman ISBN: 0070473870 ISBN-13: 9780070473874 Price $12 _________________________________________________________________________ Management Accounting, 5/E solution manual Anthony A. Atkinson, University of Waterloo Robert S. Kaplan, Harvard Business School Ella Mae Matsumura, University of Wisconsin-Madison S. Mark Young, University of Southern California ISBN-10: 0136005314 ISBN-13: 9780136005315 Price : $25 _________________________________________________________________________ Management Accounting, 5/E testbank Anthony A. Atkinson, University of Waterloo Robert S. Kaplan, Harvard Business School Ella Mae Matsumura, University of Wisconsin-Madison S. Mark Young, University of Southern California ISBN-10: 0136005314 ISBN-13: 9780136005315 Price : $25 _________________________________________________________________________ Cost Management: Strategies for Business Decisions, 4/e solution manual By Ronald W Hilton, Michael W Maher, Frank Selto ISBN: 0073526800 / 9780073526805 Price : $25 _________________________________________________________________________ Cost Management: Strategies for Business Decisions, 4/e testbank By Ronald W Hilton, Michael W Maher, Frank Selto ISBN: 0073526800 / 9780073526805 Price : $25 _________________________________________________________________________ Managerial Accounting, 12/e solution manual By: Ray Garrison, Brigham Young University Eric Noreen, University of Washington Peter Brewer, Miami University ISBN: 0073526703 Price: $25 _________________________________________________________________________ Operations research Hamdy Taha 8th edition solution manual (scanned) ISBN 0131889230 Price: $12 *Dont send here any questions email: cheap_manuals[@]hotmail.com Payment is through paypal to this email email: amverycool[@]live.com you can recieve it in less than 12 hours after payment. Its a limited time discount, get yours now before 24.June.2009 === Subject: Re: This Week's Finds in Mathematical Physics (Week 275) A correction: >Meanwhile, Christian Schommer-Pries has written a thesis on 2d extended >TQFTs - you can see it here: 6) Christian Schommer-Pries, The Classification of Two-Dimensional >Extended Topological Field Theories, Ph.D. theis, U.C. Berkeley, 2009. His name is Chris, not Christian! You see more discussion of week275 here: http://golem.ph.utexas.edu/category/2009/06/this_weeks_finds_in_mathematic_3 6.html === Subject: Any solution manual or testbank for $25 ! only this week 17.06.2009 - 24.06.2009 ! posting-account=5BdoyQkAAAACm5Si7oheX_9haNFD_3c2 AppleWebKit/525.19 (KHTML, like Gecko) Version/3.1.2 Safari/525.21,gzip(gfe),gzip(gfe) electronic format (PDF or Doc), they are for sale: Automation, Production Systems, and Computer-Integrated Manufacturing - Mikell P. Groover (3rd ed) ISBN-10: 0132393212 ISBN-13: 978-0132393218 Price: $29 _________________________________________________________________________ Supply Chain Management - Sunil Chopra (3rd ed) by Prentice Hall ISBN-10: 0131730428 ISBN-13: 978-0131730427 Price: $29 _________________________________________________________________________ Operations Management: Process and Value Chains - Lee J. Krajewski (8th edition) solution manual ISBN-10: 0131697390 ISBN-13: 978-0131697393 Price: $29 _________________________________________________________________________ Operations Management: Process and Value Chains - Lee J. Krajewski (8th edition) testbank ISBN-10: 0131697390 ISBN-13: 978-0131697393 Price: $29 _________________________________________________________________________ Facilities Planning: James A. Tompkins, 3rd edition, Wiley ISBN-10: 0471413895 ISBN-13: 978-0471413899 Price: $29 _________________________________________________________________________ Mechanics of Materials Gere 6e solution manual Price: $12 _________________________________________________________________________ Accounting Information Systems, 11/E solution manual Marshall B. Romney, Brigham Young University Paul J. Steinbart, Arizona State University ISBN-10: 0136015182 ISBN-13: 9780136015185 price: $29 _________________________________________________________________________ Accounting Information Systems, 11/E testbank Marshall B. Romney, Brigham Young University Paul J. Steinbart, Arizona State University ISBN-10: 0136015182 ISBN-13: 9780136015185 price: $29 _________________________________________________________________________ Management Information Systems, 11/E solution manual Ken Laudon Jane Laudon ISBN-10: 013607846X ISBN-13: 9780136078463 price: $29 _________________________________________________________________________ Management Information Systems, 11/E testbank Ken Laudon Jane Laudon ISBN-10: 013607846X ISBN-13: 9780136078463 price: $29 _________________________________________________________________________ Business Statistics: A Decision Making approach, solution manual David F. Groebner ISBN-10: 0132416921 ISBN-13: 9780132416924 price: $29 _________________________________________________________________________ Business Statistics: A Decision Making approach, testbank David F. Groebner ISBN-10: 0132416921 ISBN-13: 9780132416924 Price: $29 _________________________________________________________________________ PROJECT MANAGEMENT ACHIEVING COMPETITIVE ADVANTAGE AND MS PROJECT international edition, Testbank by Jeffrey K. Pinto ISBN 10: 0138129320 ISBN 13: 9780138129323 Price: $29 _________________________________________________________________________ Consumer Behavior, 9/E ,Test bank Leon Schiffman, St. John's University Leslie Kanuk, CUNY-Baruch College Price: $29 _________________________________________________________________________ Introduction To Operations Research (scanned) solution manual Author: Hillier, Lieberman ISBN: 0070473870 ISBN-13: 9780070473874 Price $12 _________________________________________________________________________ Management Accounting, 5/E solution manual Anthony A. Atkinson, University of Waterloo Robert S. Kaplan, Harvard Business School Ella Mae Matsumura, University of Wisconsin-Madison S. Mark Young, University of Southern California ISBN-10: 0136005314 ISBN-13: 9780136005315 Price : $25 _________________________________________________________________________ Management Accounting, 5/E testbank Anthony A. Atkinson, University of Waterloo Robert S. Kaplan, Harvard Business School Ella Mae Matsumura, University of Wisconsin-Madison S. Mark Young, University of Southern California ISBN-10: 0136005314 ISBN-13: 9780136005315 Price : $25 _________________________________________________________________________ Cost Management: Strategies for Business Decisions, 4/e solution manual By Ronald W Hilton, Michael W Maher, Frank Selto ISBN: 0073526800 / 9780073526805 Price : $25 _________________________________________________________________________ Cost Management: Strategies for Business Decisions, 4/e testbank By Ronald W Hilton, Michael W Maher, Frank Selto ISBN: 0073526800 / 9780073526805 Price : $25 _________________________________________________________________________ Managerial Accounting, 12/e solution manual By: Ray Garrison, Brigham Young University Eric Noreen, University of Washington Peter Brewer, Miami University ISBN: 0073526703 Price: $25 _________________________________________________________________________ Operations research Hamdy Taha 8th edition solution manual (scanned) ISBN 0131889230 Price: $12 *Dont send here any questions email: cheap_manuals[@]hotmail.com Payment is through paypal to this email email: amverycool[@]live.com you can recieve it in less than 12 hours after payment. Its a limited time discount, get yours now before 24.June.2009 === Subject: Solution manual and test bank posting-account=WMGg9woAAAB3bYTClCVTyzuu-K8I_Byc Gecko/2009051221 Firefox/3.0.10,gzip(gfe),gzip(gfe) E-mail me if any solution manual you need is in the list below at instructors.team[at]gmail.com Or visit http://quick-n-easy-solution-shop.blogspot.com/ for a latest list of resources. Also here is a list for which I can get resources for you. HERE IS THE LIST OF MANUALS FOR SALE WHICH I CAN GET FOR YOU: 2009 Federal Taxation - Pratt [CapitalEth] Solutions Manual & test Bank Accounting for Non-Accounting Students test bank Accounting Information Systems (6thEd) - Hall - Solutions Manual Aerodynamics for Engineers, 5E Solution manual Bertin Russ Cummings Algebra and Trigonometry 3rd Ed, and Precalculus 3rd Ed, Instructor's Solutions Manual 2008 - Beecher, Penna, & Bittinger Analysis- With an Introduction to Proof, 4-E-Instructors SM Art Through The Ages A Global Hist Vol II Test Bank complete Auditing A Business Risk Approach (6thEd) - Rittenberg [CapitalEth] Solutions Manual and Test Bank Auditing and Assurance Services An Intergrated Approach and ACL Software12E -ISBN 0136128300 Solution Manual & Test bank Auditing Cases Interactive Learning Approach (4thEd) - Beasley - Solutions Manual Beer, Johnston & Dewolf - Mechanics Of Materials Solution Manual 3Rd Ed Biology with Mastering Biology 8E Campbell Reece ISBN -0321494334 Test Bank Bond Markets, Analysis and Strategies 6E Instructors manual Fabozzi Brock Biology of Microorganisms 12E ISBN -0132324997 Test Bank Busines statistics Decision making 7E David F Groebner Solution manual & test bank Business Law and the Legal Environment Jeffrey F. Beatty 5th edition Test Bank Business Law Tax And Cases (11thEd) - Clarkson [CapitalEth] TestBank Business Statistics First Course Solutions Manual Levine Calculus A Complete Course Adams - - Instructors Solution Manual Concepts Of Programming Languages (8thEd) - Sebesta [CapitalEth] Solutions Manual Contemporary Financial Management (11thEd) - Moyer - Solutions Manual Cornerstone Of Managerial Accounting (2ndEd) - Mowen - Solutions Manual Corporate Partnership Estate Gift Tax 2009 - Pratt - Solutions Manual Cost accounting by Hongren 13/e test bank and Solution manual Cutnell John, Physics 7th E, Instructors manual (all solutions even +odd) Data Structures Algorithm Analysis In CPP (3rdEd) - Weiss - Solutions Manual Deitel & Deitel How to Program C++ 6th E Code solutions Options, Futures and Other Derivatives John Hull 7E test bank ch 1-21 with answers Digital Electronics A Practical Approach - William Kleitz 8th ed ISM Econometric Analysis - Solutions Manual (Greene 6Th 2007) Effective Small Business Management - Norman M Scarborough test bank Electrical Machines, Drives and Power Systems - Solutions Manual Electronic Devices and Circuit Theory 9e Instructors resource manual ISBN 0132214466 Elementary Differential Equations Boundary Value (2ndEd) - Kohler - Solutions Manual Elementary Linear Algebra (6thEd) - Larson, Falvo - Solutions Manual E-Marketing 5E Strauss Frost ISBN 0136154417 Test Bank Entrepreneurial Finance (3rdEd) - Leach - Instructors Solutions Manual Exploring Microsoft Office Excel 2007, Comprehensive, 2E Test bank Financial Accounting - Jane Reimers (1st Ed) (ISBN-10: 0131492012) Financial And Managerial Acct (10thEd) - Warren - Solutions Manual Financial Management Theory Practice (12thEd) - Brigham - Solutions Manual and test bank Friendly Introduction To Analysis (2ndEd) - Kosmala - Solutions Manual Friendly Introduction to Numerical Analysis Brian Bradie Fundamentals of Communication Systems Proakis & Salehi Fundamentals of Differential Equations 7thE Nagle Snider Instructors resource manual ISBN -0321388445 Fundamentals of Engineering Electromagnetics By David K. Cheng Solutions Manual Fundamentals of Multinational Finance 3e Gas Dynamics John & Keith Instructors Solution Manual General, Organic, and Biological Chemistry Structures of Life, 3E Test bank Gregory - Classical Mechanics - SOLUTIONS MANUAL (Cambridge, 2006) Human Anatomy & Physiology 7E TEST BANK ISBN 0805373810 Human Anatomy & Physiology 8E TEST BANK Hydraulics in Civil and Environmental Engineering Solutions by Chadwick & Morfett Solution's Manual Instructor's Manual Contemporary Engineering economics 4e Park Instructor's Edition LAN Switching and Wireless CCNA Exploration Labs and Study Guide Allan Johnson EBOOK International Economics Theory and Policy 8E Krugman Obstfeld International Marketing and Export Management 6E Albaum Introduction To Business Statistics (6thEd) - Weiers - Solutions Manual Introduction to Econometrics 2E Stock Watson Solution manual Introduction to Linear Algebra -3rd Edition - Gilbert Strang Instructors Solutions Manual Introduction To Management Accounting (14thEd) - Horngren - Solutions Manual Introduction to Management Science - Taylor 9E Solution Manual Introduction to Parallel Computing Kumar solution manual Behavior in Organizations Greenberg 9th Edition test bank Introduction to the Design and Analysis of Algorithms 2E Levitin ISBN 0321428102 Introductory Circuit Analysis 11e Boylestad Solution manual Introductory Econometrics (4thEd) - Woolridge - Solutions Manual Investment Analysis & Portfolio Management, 7e by Reilly and Brown Solutions Manual Java Foundations- Introduction to Program Design and Data Structures- ES zip Java Foundations- Introduction to Program Design and Data Structures- project solutions Linear Algebra (Jim Hefferon) (2006) Solutions Manual Linear Algebra For Engineers And Scientist (1stEd) - Hardy [CapitalEth] Solutions Manual Management Accounting Anthony A Atkinson (5th Ed) ISM and TB Management Information Systems 11E Laudon 0136078907 test bank Management Information Systems Managing the Digital Firm 10th Edition by Laudon Managerial Accounting Information for Decisions 4th ed Albrite Marketing Real people Real Choices 6 e Test Bank ISBN 0136054234 Mathematical Proofs A Transition to Advanced Mathematics (2ndEd) - Chartrand - Solutions Manual Mathematical Thinking problem solving Angelo & West Instructors manual ISBN -0130144126 Microbiology with Diseases by Body System Robert W Bauman 2nd ed Instructors manual MIS Cases Decision Making wih Application Software, 4E Instructors manual and solution files Object Oriented Programming in C++ 4E suplement robert Lafore Operations Management 9E Jay Heizer ISBN 0131585576 Operations Management 9E Jay Heizer ISBN 0132342979 test bank Organic Chemistry 6E Wade Test Bank Parallel Programming (2ndEd) - Wilkinson [CapitalEth] Solutions Manual Partial Differential Equations And Boundary Value Problems (2nd Ed) - Asmar - Solutions Manual Physics Principles with Applications with Mastering Physics Giancoli 6E ISM Physics with Mastering Physics 3E James walker Prebles' Artforms 9E patrick Frank TESTGEN file ISBN 0136044166 Prebles' Artforms Test Bank Precalculus (4thEd) - Blitzer - Solutions Manual Prentice Hall Federal Taxation 2009 Comprehensive - Pope - Solutions Manual Prentice Hall's Federal Taxation 22/e 2009 Corporations test bank and solution manual Prince Medical Imaging Signals and Systems Instructors manual Principles Of Foundation Engineering (6thEd) - Das - Solution Manual Principles Of Managerial Finance Brief (5thEd) - Gitman [CapitalEth] Solutions Manual Principles of Marketing 5th European edition by Kotler Instructors solution manual Principles Of Operations Management (6thEd) - Heizer [CapitalEth] Test Bank Problem Solving With CPP (7thEd) - Savitch [CapitalEth] Solutions Manual Reinforced Concrete Design - George F. Limbrunner 7th ed ISBN [CapitalEth] 0135044359 Roads to Geometry, 3/E Solutions manual Edward C. Wallace Sandler S. I. - Chemical and Engineering Thermodynamics - Solution manual Source Code Files for Programming Concepts in MATLAB 2E David M Smith Statics And Strengths Of Materials (6thEd) - Morrow - Solutions Manual Statistics 11E James T. McClave Solution manual Stats Data And Models (2ndEd) - Veaux [CapitalEth] Solutions Manual Strategic Compensation Joe Martocchio 5th ed Test Bank Strategic Management and Competitive Advantage Concepts and Cases 2E barney hesterly ISBN 0136036112Pearson TESTGEN file Strategic Management Concepts and Cases 12E Fred David ISBN 0138132178 test bank Strategic Management TestBank Hitt 8th edition Test Bank Martini EAP 5E TestBank International economics 12th edition Carbaugh TestBank Macroeconomics Principles and Policy Baumol 10th Undergraduate Econometrics Solutions Manual - Hill, Judge and Griffiths Understanding and Managing Organizational Behavior 5E Test bank University Chemistry with Student Access Kit siska 1e test bank Wang, L. & Zhou, X. & Wei, X. - Heat conduction. Mathematical models and analytical solutions (Springer, 2008) 2009 Corporate, Partnership, Estate and Gift Taxation - James Pratt (3rd ed) (ISBN 1426639015) 2009 Federal Taxation - James Pratt (3rd ed) (ISBN 1426639171) 2009 Individual Taxation - James Pratt (3rd ed) (ISBN 1426649193) A Gift of Fire: Social, Legal, and Ethical Issues for Computing and the Internet - Sara Baase (3rd ed) (ISBN 0136008488) Absolute C++ - Walter Savitch (3rd ed) (ISBN 0321468937) Absolute Java - Walter Savitch (3rd ed) (ISBN 0321487923) Access 2007 Guidebook - Maggie Trigg (6th ed) (ISBN 0321517016) Accounting - Carl Warren (22nd ed) (ISBN 0324401841) Accounting - Carl Warren (23rd ed) (ISBN 0324662963) Accounting Chapters 1-13 - Charles T. Horngren et al (7th ed) (ISBN 0132249952) Accounting Chapters 1-25 - Charles T. Horngren et al (7th ed) (ISBN 0132439603) Accounting Chapters 1-26 - Charles T. Horngren et al (6th ed) (ISBN 0131088513) Accounting Chapters 12-25 - Charles T. Horngren et al (7th ed) (ISBN 0132249960) Accounting Concepts and Applications - Steve Albrecht (10th ed) (ISBN 0324376154) Accounting Concepts and Applications - Steve Albrecht (9th ed) (ISBN 0324187564) Accounting Information Systems - James Hall (5th ed) (ISBN 0324312954) Accounting Information Systems - James Hall (6th ed) (ISBN 0324560893) Accounting Information Systems - Marshall Romney, Paul Steinbart (10th ed) (ISBN 0131475916) Accounting Information Systems - Marshall Romney, Paul Steinbart (11th ed) (ISBN 0136015182) Accounting Information Systems - Ulric J. Gelinas (7th ed) (ISBN 0324378823) Accounting Information Systems - Ulric J. Gelinas (8th ed) (ISBN 0324663803) Additional Calculus Topics - Raymond Barnett (11th ed) (ISBN 0132318229) Administrative Law: Bureaucracy in a Democracy - Daniel E. Hall (4th ed) (ISBN 0135005183) Advanced Accounting - Floyd Beams (9th ed) (ISBN 0131851225) Advanced Accounting - Floyd Beams (10th ed) (ISBN 0136033970) Advanced Accounting - Paul Fischer (10th ed) (ISBN 0324379056) Advanced Accounting - Paul Fischer (Test Bank only) (9th ed) (ISBN 0324304013) Advanced Calculus - G. B. Folland (1st ed) (ISBN 0130652652) Advanced Engineering Mathematics - Michael Greenberg (2nd ed) (ISBN 0133214311) Advanced Engineering Mathematics - Peter V. O'Neil (6th ed) (ISBN 0534552080) Advertising - Sandra Moriarty (8th ed) (ISBN 0132224151) Algebra and Trigonometry - Judith A. Beecher (3rd ed) (ISBN 0321466209) Algebra and Trigonometry - Michael Sullivan (8th ed) (ISBN 0132329034) Algebra and Trigonometry Enhanced with Graphing Utilities - Michael Sullivan (4th ed) (ISBN 0131527398) Algebra and Trigonometry Enhanced with Graphing Utilities - Michael Sullivan (5th ed) (ISBN 013600492X) Algebra and Trigonometry: Graphs & Models and Graphing Calculator Manual Package - Marvin L. Bittinger (4th ed) (ISBN 0321501519) Algebra for College Students - Allen R. Angel (3rd ed) (ISBN 0136129080) Algebra for College Students - Margaret L. Lial (6th ed) (ISBN 0321442547) Algebra For College Students - Robert F Blitzer (6th ed) (ISBN 0136019749) An Introduction to Signals and Systems - John Alan Stuller (1st ed) (ISBN 0495073016) Dunlap (1st ed) (ISBN 0534392946) Analytical Mechanics - Grant Fowles, George Cassiday (7th ed) (ISBN 0534494927) Anatomy & Physiology - Elaine N. Marieb (3rd ed) (ISBN 0805347739) Anatomy & Physiology for Emergency Care - Bryan E. Bledsoe (2nd ed) (ISBN 0132342987) Applied Algebra - Darel Hardy (1st ed) (ISBN 0130674648) Applied Calculus - Geoffrey C. Berresford (5th ed) (ISBN 0547169787) Applied Linear Algebra - Chehrzad Shakiban, Peter J. Olver (1st ed) (ISBN 0131473824) Applied Mechanics for Engineering Technology - Keith M. Walker (8th ed) (ISBN 0131721518) Applied Multivariate Statistical Analysis - Richard A. Johnson (6th ed) (ISBN 0131877151) Applied Partial Differential Equations - Richard Haberman (4th ed) (ISBN 0130652431) Applied Physics - Dale Ewen (9th ed) (ISBN 0135157331) Applied Statistics for Engineers and Physical Scientists - Johannes Ledolter (3rd ed) (ISBN 0136017983) Art and Science of Leadership - Afsaneh Nahavandi (5th ed) (ISBN 0136044085) Auditing and Assurance Services - Alvin A. Arens et al (11th ed) (ISBN 0131867121) Auditing and Assurance Services - Alvin A. Arens et al (12th ed) (ISBN 0135132126) Auditing and Assurance Services: An Integrated Approach - Alvin A Arens (13th ed) (ISBN 0136084737) Auditing Assurance and Risk - W. Robert Knechel, Steve Salterio, Brian Ballou (3rd ed) (ISBN 0324313187) Auditing Cases - Mark Beasley (3rd ed) (ISBN 0131494910) Auditing Cases - Mark S Beasley (4th ed) (ISBN 0132423502) Auditing: A Business Risk Approach - Larry E. Rittenberg (6th ed) (ISBN 0324375581) Automation, Production Systems, and Computer-Integrated Manufacturing - Mikell P. Groover (2nd ed) (ISBN 0130889784) Automation, Production Systems, and Computer-Integrated Manufacturing - Mikell P. Groover (3rd ed) (ISBN 0132393212) Basic Business Statistics - Mark L Berenson (10th ed) (ISBN 0131678310) Basic Chemistry - Karen C. Timberlake (2nd ed) (ISBN 0805344691) Basic Economics - Frank V. Mastrianna (Test Bank) (15th ed) (ISBN 0324599161) Basic Environmental Technology: Water Supply, Waste Management & Pollution Control - Jerry A. Nathanson (5th ed) (ISBN 0131190822) Basic Marketing Research Using Microsoft Excel Data Analysis - Alvin C Burns (2nd ed) (ISBN 0132059584) Basic Mathematics through Applications - Geoffrey Akst (4th ed) (ISBN 0321500113) Basics of Occupational Safety - David L. Goetsch (1st ed) (ISBN 013502613X) Beginning & Intermediate Algebra - Elayn El Martin-Gay (5th ed) (ISBN 0136007317) Beginning Algebra - Elayn El Martin-Gay (5th ed) (ISBN 0136007023) Beginning Algebra - Margaret L. Lial (10th ed) (ISBN 0321437268) Beginning Algebra with Applications & Visualization - Gary K. Rockswold (2nd ed) (ISBN 0321500040) Beginning and Intermediate Algebra - Margaret L. Lial (4th ed) (ISBN 0321442334) Beginning and Intermediate Algebra with Applications & Visualization - Gary K. Rockswold (2nd ed) (ISBN 0321500059) Behavior in Organizations - Jerald Greenberg (9th ed) (ISBN 0131542842) Biochemistry - Mary Campbell (4th ed) (ISBN 0534405215) Biochemistry (with Lecture Notebook) - Mary Campbell (4th ed) (ISBN 0534391818) Biology - Neil A. Campbell (Test Bank only w/ TestGen Software) (7th ed) (ISBN 080537146X) Biology: Science for Life - Colleen Belk (3rd ed) (ISBN 0321559592) Biology: Science for Life with Physiology - Colleen Belk (3rd ed) (ISBN 0321559584) Biomaterials: The Intersection of Biology and Materials Science - Johnna S. Temenoff (1st ed) (ISBN 0130097101) Biostatistics for the Health Sciences - R. Clifford Blair (1st ed) (ISBN 0131176609) Bond Markets, Analysis and Strategies - Frank Fabozzi (6th ed) (ISBN 0131986430) Bond Markets, Analysis, and Strategies - Frank J Fabozzi (7th ed) (ISBN 0136078974) Brief Course in Mathematical Statistics - Elliot A. Tanis (1st ed) (ISBN 0131751395) Brief Principles of Macroeconomics - Gregory Mankiw (5th ed) (ISBN 0324590377) Brock Biology of Microorganisms - Michael T. Madigan (12th ed) (ISBN 0132324601) Brock Biology of Microorganisms - Michael T. Madigan (Test Bank) (11th ed) (ISBN 0132192268) Building Construction: Principles, Materials, and Systems - Madan Mehta (1st ed) (ISBN 0130494216) Building Java Programs: A Back to Basics Approach - Stuart Reges (1st ed) (ISBN 0321382838) Business - William M. Pride (10th ed) (ISBN 0324829558) Business Analysis and Valuation: Using Financial Statements - Krishna Palepu (3rd ed) (ISBN 0324118945) Business and Its Environment - David P. Baron (6th ed) (ISBN 0136083927) Business and Society: Ethics and Stakeholder Management - Archie B. Carroll (7th ed) (ISBN 0324569394) Business Communication Essentials - Courtland Bovee (4th ed) (ISBN 0136084419) Business Communication Essentials and Peak Performance Grammar and Mechanics 2.0 CD Package - Court Bovee (3rd ed) (ISBN 0132328992) Business Communication Today - Court Bovee (9th ed) (ISBN 0131995359) Business Data Networks and Telecommunications - Raymond R. Panko (7th ed) (ISBN 0136153402) Business English: Writing in the Workplace - Blanche Ettinger (4th ed) (ISBN 0131565702) Business Ethics: A Stakeholder and Issues Management Approach - Joseph W. Weiss (6th ed) (ISBN 0324589735) Business Ethics: Case Studies and Selected Readings - Marianne M. Jennings (6th ed) (ISBN 0324657749) Business Forecasting - John Hanke (9th ed) (ISBN 0132301202) Business in Action with Real Time Updates - Court Bovee (4th ed) (ISBN 0136154085) Business Law - Henry R. Cheeseman (7th ed) (ISBN 0136085547) Business Law and the Legal Environment - Jeffrey F. Beatty (4th ed) (ISBN 0324303971) Business Law and the Legal Environment - Jeffrey F. Beatty (5th ed) (ISBN 0324663528) Business Law and the Regulation of Business - Richard A. Mann (9th ed) (ISBN 0324537131) Business Law Principles for Today's Commercial Environment - David P. Twomey (2nd ed) (ISBN 0324303947) Business Law Today: Comprehensive - Roger LeRoy Miller (8th ed) (ISBN 0324595743) Business Law Today: The Essentials - Roger LeRoy Miller (8th ed) (ISBN 0324654545) Business Law: Alternate Edition - Gaylord A. Jentz (11th ed) (ISBN 0324596162) Business Law: Text and Cases - Kenneth W. Clarkson (11th ed) (ISBN 0324655223) Business Law: Text and Exercises - Roger LeRoy Miller (5th ed) (ISBN 032464096X) Business Statistics: A Decision Making Approach - David F. Groebner (7th ed) (ISBN 0132416921) Business Statistics: A First Course - David Levine (5th ed) (ISBN 0136065805) Business: Its Legal, Ethical, and Global Environment - Marianne M. Jennings (8th ed) (ISBN 0324655541) Calculus - Dale Varberg (9th ed) (ISBN 0131429248) Calculus and Its Applications - Larry Goldstein (11th ed) (ISBN 0131919636) Calculus and Its Applications - Larry Goldstein (12th ed) (ISBN 0321571304) Calculus and Its Applications - Marvin L. Bittinger (8th ed) (ISBN 0321166396) Calculus and Its Applications - Marvin L. Bittinger (9th ed) (ISBN 0321395344) Calculus Early Transcendentals - Henry Edwards (7th ed) (ISBN 0131569899) Calculus for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett (11th ed) (ISBN 0132328186) Calculus for the Life Sciences - Marvin L. Bittinger (1st ed) (ISBN 0321279352) Calculus With Applications - Margaret L. Lial et al (8th ed) (ISBN 0321228146) Calculus with Applications for the Life Sciences - Raymond N. Greenwell (1st ed) (ISBN 0201745828) Calculus, Early Transcendentals - C. Henry Edwards (7th ed) (ISBN 0131569899) California Real Estate Law - Theodore Gordon (7th ed) (ISBN 0324654685) Capital Budgeting and Long-Term Financing Decisions - Neil Seitz (4th ed) (ISBN 0324258089) Capital Markets: Institutions and Instruments - Frank J Fabozzi (4th ed) (ISBN 0136026028) Cases in Management Accounting and Control Systems - Brandt Allen (4th ed) (ISBN 0135704251) Chemistry - John E McMurry (Test Bank only) (5th ed) (ISBN 0131993232) Chemistry : An Introduction to General, Organic, Biological Chemistry - Karen Timberlake (9th ed) (ISBN 0805330151) Chemistry for Changing Times - John W. Hill (12th ed) (ISBN 0136054498) Chemistry: An Introduction to General, Organic, & Biological Chemistry - Karen C Timberlake (10th ed) (ISBN 0136019706) Civil Drafting Technology - David A. Madsen (7th ed) (ISBN 0135000688) ed) (ISBN 0534408966) CMOS Circuit Design, Layout, and Simulation - David E. Boyce et al (1st ed) (ISBN 0780334167) College Accounting 1-12 - Jeffrey Slater (9th ed) (ISBN 0131071696) College Accounting 1-25 - Jeffrey Slater (10th ed) (ISBN 0132286386) College Accounting Chapters 1-15 - James Heintz (19th ed) (ISBN 0324382499) College Accounting Chapters 1-27 - James Heintz (19th ed) (ISBN 0324376162) College Accounting Chapters 1-9 - James Heintz (19th ed) (ISBN 0324382480) College Accounting: A Practical Approach Canadian Edition - Jeffrey Slater (10th ed) (ISBN 0132069245) College Algebra - J. S. Ratti (1st ed) (ISBN 0321296443) College Algebra - Judith A. Beecher (3rd ed) (ISBN 0321466071) College Algebra - Margaret L. Lial (10th ed) (ISBN 0321499131) College Algebra - Mark Dugopolski (4th ed) (ISBN 0321356918) College Algebra - Michael Sullivan (8th ed) (ISBN 0132402866) College Algebra - Robert F. Blitzer (5th ed) (ISBN 0321559835) College Algebra and Trigonometry - J. S. Ratti (1st ed) (ISBN 0321296427) College Algebra and Trigonometry - Margaret L. Lial (4th ed) (ISBN 0321497449) College Algebra Enhanced with Graphing Utilities - Michael Sullivan (5th ed) (ISBN 0136004911) College Algebra Essentials - Michael Sullivan (8th ed) (ISBN 0136154344) College Algebra: Graphs and Models with Graphing Calculator Manual Package - Marvin L. Bittinger (4th ed) (ISBN 0321531922) College Geometry - David C. Kay (2nd ed) (ISBN 0321046242) College Geometry: A Problem Solving Approach with Applications - Gary L. Musser (2nd ed) (ISBN 0131879693) College Math for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett (11th ed) (ISBN 0131572253) College Physics - Jerry D Wilson (6th ed) (ISBN 0131495798) College Physics - Jerry D Wilson (7th ed) (ISBN 0321571118) College Physics with Mastering Physics - Hugh Young (8th ed) (ISBN 0805390707) Communicating in the Workplace - Thomas Cheesebro (1st ed) (ISBN 0136136915) Communication Systems Engineering - John G. Proakis (2nd ed) (ISBN 0130617938) Comparative International Accounting - Christopher Nobes (9th ed) (ISBN 0273703579) Complex Variables With Applications - A. David Wunsch (3rd ed) (ISBN 0201756099) Comprehensive Periodontics for the Dental Hygienist - Mea A. Weinberg (3rd ed) (ISBN 0135015421) Computer Algorithms - Allen Van Gelder, Sara Baase (3rd ed) (ISBN 0201612445) Computer Networking Complete Package - James F. Kurose (3rd ed) (ISBN 0321418492) Computer Networking with Internet Protocols - William Stallings (1st ed) (ISBN 0131410989) Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) Computer Networking: A Top-Down Approach - James F. Kurose (5th ed) (ISBN 0136079679) Computer Networking: A Top-Down Approach Featuring the Internet - James F. Kurose (3rd ed) (ISBN 0321227352) Computer Organization and Architecture - William Stallings (7th ed) (ISBN 0130351199) Computer Organization and Architecture: Designing for Performance - William Stallings (7th ed) (ISBN 0131856448) Computer Organization and Architecture: Designing for Performance - William Stallings (8th ed) (ISBN 0136073735) Computer Science: An Overview - J. Glenn Brookshear (10th ed) (ISBN 0321524039) Computer Security: Principles and Practice - William Stallings (1st ed) (ISBN 0136004245) Computer Systems Organization & Architecture - John D. Carpinelli (1st ed) (ISBN 0201612534) Concepts in Federal Taxation 2007 - Kevin Murphy (14th ed) (ISBN 0324313527) Concepts in Federal Taxation 2008 - Kevin Murphy (15th ed) (ISBN 0324640153) Concepts in Federal Taxation 2009 - Kevin Murphy (16th ed) (ISBN 0324659377) Concepts In Systems and Signals - John D. Sherrick (2nd ed) (ISBN 0131782711) Concepts of Calculus with Applications - Martha Goshaw (1st ed) (ISBN 0321320786) Concepts of Calculus With Applications-Updated Edition - Martha Goshaw (2nd ed) (ISBN 0321577442) Concepts of Programming Languages - Robert W. Sebesta (8th ed) (ISBN 0321493621) Conceptual Physical Science - Paul G. Hewitt (4th ed) (ISBN 0321516958) Conceptual Physics Fundamentals - Paul G. Hewitt (1st ed) (ISBN 0321501365) Conceptual Physics Media Update - Paul G. Hewitt (10th ed) (ISBN 0321548094) Concrete Structures - Mehdi Setareh (1st ed) (ISBN 0131988271) Construction Accounting & Financial Management - Stephen Peterson (2nd ed) (ISBN 0135017114) Construction Methods and Management - Stephens W. Nunnally (7th ed) (ISBN 0131716859) Construction Project Management - Fred Gould (3rd ed) (ISBN 0131996231) Consumer Behavior - Michael Solomon (8th ed) (ISBN 0136015964) Consumer Behavior - Wayne D. Hoyer (5th ed) (ISBN 0547079923) Contemporary Auditing: Real Issues & Cases - Michael C. Knapp (7th ed) (ISBN 0324658052) Contemporary Auditing: Real Issues & Cases Update - Michael C. Knapp (7th ed) (ISBN 143907819X) Contemporary Business and Online Commerce Law - Henry R. Cheeseman (6th ed) (ISBN 013601500X) Contemporary Engineering Economics - Chan S. Park (4th ed) (ISBN 0131876287) Contemporary Financial Management - Charles Moyer (10th ed) (ISBN 0324289081) Contemporary Financial Management - R. Charles Moyer, James R. McGuigan (11th ed) (ISBN 0324653506) Contemporary Logistics - Paul R. Murphy (9th ed) (ISBN 013156207X) Contemporary Marketing - Louis E. Boone (14th ed) (ISBN 032458203X) Contemporary Marketing 2009 Update - Louis E. Boone (13th ed) (ISBN 0324580215) Contemporary Mathematics for Business and Consumers - Robert Brechner (5th ed) (ISBN 0324568495) Contemporary Project Management - Timothy Kloppenborg (1st ed) (ISBN 0324382383) Cornerstones of Managerial Accounting - Maryanne M. Mowen (2nd ed) (ISBN 0324379609) Cornerstones of Managerial Accounting - Maryanne M. Mowen (3rd ed) (ISBN 0324660138) Corporate Finance - Jonathan Berk (1st ed) (ISBN 0321415116) Corporate Finance - Michael C. Ehrhardt, Eugene F. Brigham (3rd ed) (ISBN 0324655681) Corporate Finance: The Core plus MyFinanceLab Student Access Kit - Jonathan Berk (1st ed) (ISBN 032155759X) Corporate Financial Accounting - Carl S. Warren (10th ed) (ISBN 0324663838) Corporate Financial Management - Douglas R. Emery (3rd ed) (ISBN 0132278723) Cost Accounting - Charles T. Horngren, George Foster, Srikant M. Datar (12th ed) (ISBN 0131495380) Cost Accounting - Charles T. Horngren, George Foster, Srikant M. Datar (13th ed) (ISBN 0136126634) Cost Accounting Canadian Edition - Charles Horngren (4th ed) (ISBN 0131971905) Cost Accounting: Traditions & Innovations - Jesse Barfield (5th ed) (ISBN 032418090X) Cost Benefit Analysis: Concepts and Practice - Anthony Boardman (3rd ed) (ISBN 0131435833) Cost Management: Accounting and Control - Don R. Hansen, Maryanne M. Mowen (6th ed) (ISBN 0324559674) Course in Probability - Neil Weiss (1st ed) (ISBN 0201774712) Criminology: A Global Perspective - Robert W. Winslow (1st ed) (ISBN 0131839020) Cryptography and Network Security - William Stallings (4th ed) (ISBN 0131873164) Customer Service: Career Success Through Customer Loyalty - Paul R. Timm (4th ed) (ISBN 0132236583) Data Abstraction & Problem Solving with C++ - Frank M. Carrano (5th ed) (ISBN 0321433327) Data and Computer Communications - William Stallings (8th ed) (ISBN 0132433109) Data Structures and Algorithm Analysis in C++ - Mark Allen Weiss (3rd ed) (ISBN 032144146X) Data Structures and Algorithm Analysis in Java - Mark Allen Weiss (2nd ed) (ISBN 0321370139) Database Concepts - David Kroenke (3rd ed) (ISBN 0131986252) Database Concepts - David Kroenke (4th ed) (ISBN 0136086535) Database Systems: A Practical Approach - Thomas M. Connolly (4th ed) (ISBN 0321294017) Derivatives Markets - Robert L. McDonald (2nd ed) (ISBN 032128030X) Detection and Estimation:Theory and Its Applications - Thomas Schonhoff (1st ed) (ISBN 0130894990) Developmental Mathematics - Marvin L. Bittinger (7th ed) (ISBN 0321331915) Developmental Mathematics: Basic Mathematics and Algebra - Margaret L. Lial (1st ed) (ISBN 0321506421) Differential Equations - John Polking (2nd ed) (ISBN 0131437380) Differential Equations and Boundary Value Problems: Computing and Modeling - Henry Edwards (4th ed) (ISBN 0131561073) Differential Equations and Linear Algebra - Henry Edwards, David E. Penney (2nd ed) (ISBN 0131481460) Differential Equations and Linear Algebra - Henry Edwards, David E. Penney (3rd ed) (ISBN 0136054250) Differential Equations and Linear Algebra - Jerry Farlow (2nd ed) (ISBN 0131860615) Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) (ISBN 0130457949) Differential Equations Computing and Modeling - Henry Edwards (4th ed) (ISBN 0136004385) Differential Equations With Boundary Value Problems - John C. Polking (2nd ed) (ISBN 0130911062) Digital & Analog Communication Systems - Leon Couch (7th ed) (ISBN 0131424920) Digital Communications - John Proakis (4th ed) (ISBN 0072321113) Digital Design - Morris Mano (4th ed) (ISBN 0131989243) Digital Electronics: A Practical Approach - William Kleitz (8th ed) (ISBN 0132435780) Digital Fundamentals - Thomas Floyd (10th ed) (ISBN 0132359235) Digital Signal Processing - John Proakis (4th ed) (ISBN 0131873741) Digital Signal Processing Using MATLAB -Vinay K. Ingle, John G. Proakis (2nd ed) (ISBN 0495073113) Digital Systems Design Using VHDL - Charles H. Roth (2nd ed) (ISBN 0534384625) Digital Systems: Principles and Applications - Ronald Tocci et al (10th ed) (ISBN 0131725793) Discrete and Combinatorial Mathematics - Ralph P. Grimaldi (5th ed) (ISBN 0201726343) Discrete Mathematics - Edgar G. Goodaire, Michael M Parmenter (3rd ed) (ISBN 0131679953) Discrete Mathematics - Otto, Eynden, Dossey, Spence (4th ed) (ISBN 0321079124) Discrete Mathematics - Otto, Eynden, Dossey, Spence (5th ed) (ISBN 0321305159) Discrete Mathematics - Richard Johnsonbaugh (6th ed) (ISBN 0131176862) Drugs & the Human Body - Ken Liska (8th ed) (ISBN 0132447134) Dynamics of Structures - Anil K. Chopra (3rd ed) (ISBN 013156174X) ECON for Macroeconomics - William A. McEachern (1st ed) (ISBN 0324587805) Economic Development - Michael P. Todaro (10th ed) (ISBN 0321485734) Economic Development - Michael Todaro, Stephen Smith (9th ed) (ISBN 0321278887) Economic Growth - David N. Weil (2nd ed) (ISBN 0321416627) Economic Growth - David Weil (1st ed) (ISBN 0201680262) Economics - Michael Parkin (8th ed) (ISBN 0321423003) Economics - Michael Parkin (9th ed) (ISBN 0321600037) Economics - Richard Lipsey (13th ed) (ISBN 0321369211) Economics - Roger A. Arnold (9th ed) (ISBN 0324595425) Economics for Managers - Paul G Farnham (1st ed) (ISBN 0130924253) Economics for Managers - Paul G Farnham (2nd ed) (ISBN 013606552X) Economics for Today - Irvin B. Tucker (6th ed) (ISBN 0324591365) Economics of Money, Banking, and Financial Markets - Frederic Mishkin (Test Bank) (8th ed) (ISBN 0321415051) Economics of Money, Banking, and Financial Markets, Update - Frederic Mishkin (7th ed) (ISBN 0321331850) Economics Today - Roger LeRoy Miller (14th ed) (ISBN 0321422341) Economics Today - Roger Miller (15th ed) (ISBN 0321600215) Economics Today: The Macro View - Roger Miller (13th ed) (ISBN 0321278992) Economics Today: The Macro View - Roger Miller (14th ed) (ISBN 0321421442) Economics Today: The Macro View - Roger Miller (15th ed) (ISBN 0321600223) Economics Today: The Micro View - Roger Miller (13th ed) (ISBN 0321278984) Economics Today: The Micro View - Roger Miller (14th ed) (ISBN 0321425065) Economics Today: The Micro View - Roger Miller (15th ed) (ISBN 0321600185) Economics: A Contemporary Introduction - William A. McEachern (8th ed) (ISBN 0324579217) Economics: A Tool for Critically Understanding Society - Tom Riddell (8th ed) (ISBN 0321423585) Economics: Principles and Policy - William J. Baumol (10th ed) (ISBN 0324537026) Economics: Principles and Policy - William J. Baumol (11th ed) (ISBN 0324586205) Economics: Private and Public Choice - James D. Gwartney (12th ed) (ISBN 0324580185) Effective Small Business Management - Norman M. Scarborough (9th ed) (ISBN 0136152708) Effective Writing - Claire B. May (8th ed) (ISBN 0136029086) Electric Circuits - James Nilsson (8th ed) (ISBN 0131989251) Electrical Engineering: Principles and Applications - Allan R. Hambley (4th ed) (ISBN 0131989227) Electrical Machines, Drives and Power Systems - Theodore Wildi (6th ed) (ISBN 0131776916) Electronic Commerce 2008 - Efraim Turban (5th ed) (ISBN 0132243318) Electronic Communications for Technicians - Tom Wheeler (2nd ed) (ISBN 0131130498) Electronics and Computer Math - Bill R. Deem (8th ed) (ISBN 0131711377) Electronics Fundamentals: Circuits, Devices and Applications - Thomas Floyd (7th ed) (ISBN 013219709X) Elementary Algebra - George Woodbury (1st ed) (ISBN 0321166426) Elementary Algebra Early Graphing for College Students - Allen R. Angel (3rd ed) (ISBN 0136134165) Elementary Algebra: Graphs and Authentic Applications - Jay Lehmann (1st ed) (ISBN 013220164X) Elementary and Intermediate Algebra - George Woodbury (2nd ed) (ISBN 0321500067) Elementary and Intermediate Algebra: Graphs & Models - Marvin L. Bittinger (3rd ed) (ISBN 0321422406) Elementary Differential Equations - Henry Edwards (6th ed) (ISBN 0132397307) Elementary Differential Equations - Werner E. Kohler, Lee W.Johnson (1st ed) (ISBN 0201709260) Elementary Differential Equations with Boundary Value Problems - Henry Edwards (6th ed) (ISBN 0136006132) Elementary Differential Equations With Boundary Value Problems - Lee Johnson et al (1st ed) (ISBN 0321121643) Elementary Differential Equations With Boundary Value Problems - Lee Johnson et al (2nd ed) (ISBN 0321398505) Elementary Linear Algebra - Ron Larson (6th ed) (ISBN 0618783768) Elementary Linear Algebra with Applications - Bernard Kolman (9th ed) (ISBN 0132296543) Elementary Number Theory - Kenneth H. Rosen (5th ed) (ISBN 0321237072) Elementary Statistics - Mario F. Triola (10th ed) (ISBN 0321331834) Elementary Statistics - Mario F. Triola (9th ed) (ISBN 0201775700) Elementary Statistics - Mario F. Triola (11th ed) (ISBN 0321500245) Elementary Statistics - Neil A. Weiss (7th ed) (ISBN 0321422090) Elementary Statistics - Ron Larson (4th ed) (ISBN 0132424339) Elementary Statistics Using Excel - Mario Triola (3rd ed) (ISBN 0321365135) Elementary Statistics Using the TI-83/84 Plus Calculator - Mario F. Triola (2nd ed) (ISBN 0321462572) Elementary Statistics With Multimedia Study Guide - Mario F. Triola (10th ed) (ISBN 0321460928) Elements of Forecasting - Francis X. Diebold (4th ed) (ISBN 032432359X) Embedded Microcontrollers & Processor Design - Charles Greg Osborn (1st ed) (ISBN 0131130412) Embedded System Design with C805 - Han-Way Huang (1st ed) (ISBN 0495471747) Employment Law - John J. Moran (4th ed) (ISBN 0136009964) Engineering Computation with MATLAB - David M. Smith (2nd ed) (ISBN 0136080634) Engineering Economy - William G Sullivan (13th ed) (ISBN 0131486497) Engineering Economy - William G. Sullivan (14th ed) (ISBN 0136142974) Engineering Economy and the Decision-Making Process - Joseph C. Hartman (1st ed) (ISBN 0131424017) Engineering Fundamentals: An Introduction to Engineering - Saeed Moaveni (3rd ed) (ISBN 0495082538) Engineering Materials: Properties and Selection - Ken Budinski (8th ed) (ISBN 0131837796) Engineering Materials: Properties and Selection - Kenneth G. Budinski (9th ed) (ISBN 0137128428) Engineering Mechanics Dynamics - Anthony M Bedford (5th ed) (ISBN 0136129161) Engineering Mechanics: Dynamics - Andrew Pytel (3rd ed) (ISBN 0495295612) Engineering Mechanics: Dynamics - Russell C. Hibbeler (11th ed) (ISBN 0131561480) Engineering Mechanics: Statics - Andrew Pytel (3rd ed) (ISBN 0495244694) Engineering Mechanics: Statics - Anthony M Bedford (5th ed) (ISBN 0136129153) Engineering Mechanics: Statics - Russell C. Hibbeler (11th ed) (ISBN 0132295660) Engineering Mechanics: Statics - Russell C. Hibbeler (12th ed) (ISBN 0136077900) Engineering Mechanics: Statics Computational Edition - Robert W. Soutas-Little (1st ed) (ISBN 0534549217) Engineering Vibration - Daniel Inman (3rd ed) (ISBN 0132281732) Enterprise Systems for Management - Luvai Motiwalla (1st ed) (ISBN 013233531X) Entrepreneurial Finance - Chris Leach (3rd ed) (ISBN 0324561253) Entrepreneurial Finance - Philip J. Adelman (4th ed) (ISBN 0132434792) Entrepreneurial Finance - Philip J. Adelman (5th ed) (ISBN 013502529X) Entrepreneurship: Successfully Launching New Ventures - Bruce Barringer (2nd ed) (ISBN 0132240572) Entrepreneurship: Theory, Process, and Practice - Donald F. Kuratko (8th ed) (ISBN 0324590911) Environmental and Natural Resource Economics - Tom Tietenberg (7th ed) (ISBN 0321305043) Environmental Issues: An Introduction to Sustainability - Robert L. McConnell (3rd ed) (ISBN 0131566504) Environmental Law - Nancy K. Kubasek (6th ed) (ISBN 0136142168) Environmental Science: Toward A Sustainable Future - Richard T. Wright (10th ed) (ISBN 0132302659) Error Control Coding - Daniel J. Costello Jr., Shu Lin (2nd ed) (ISBN 0130426725) Essential Foundations of Economics - Robin Bade (4th ed) (ISBN 0321522354) Essentials of Business Law - Jeffrey F. Beatty (3rd ed) (ISBN 0324537123) Essentials of Business Law and the Legal Environment - Richard A. Mann (10th ed) (ISBN 0324593562) Essentials of College Algebra with Modeling and Visualization - Gary K. Rockswold (3rd ed) (ISBN 0321448898) Essentials of College Algebra, Alternate Edition - Margaret L. Lial (1st ed) (ISBN 0321491858) Essentials of Economics - Gregory Mankiw (4th ed) (ISBN 0324236964) Essentials of Economics - Gregory Mankiw (5th ed) (ISBN 0324590024) Essentials of Entrepreneurship and Small Business Management - Thomas W Zimmerer (5th ed) (ISBN 0132294389) Essentials of Logic - Irving Copi (2nd ed) (ISBN 013238034X) Essentials of Management Information Systems - Jane Laudon (8th ed) (ISBN 013602579X) Essentials of Managerial Finance - Scott Besley (13th ed) (ISBN 0324258755) Essentials of Marketing - Charles W. Lamb (6th ed) (ISBN 0324656203) Essentials of Materials Science & Engineering - Donald R. Askeland (2nd ed) (ISBN 0495244465) Essentials of Organizational Behavior - Stephen P Robbins (9th ed) (ISBN 0132431521) Essentials of Organizational Behavior - Stephen P. Robbins (10th ed) (ISBN 0136077617) Essentials of Statistics - Mario F. Triola (3rd ed) (ISBN 0321434250) Essentials of Statistics for Business and Economics - David R. Anderson (5th ed) (ISBN 0324568606) Essentials of the Legal Environment - Roger LeRoy Miller (2nd ed) (ISBN 0324400403) Ethics for the Information Age - Mike Quinn (3rd ed) (ISBN 0321536851) Excellence in Business Communication - John V. Thill (8th ed) (ISBN 0136157505) Experiencing MIS - David Kroenke (2nd ed) (ISBN 0136078680) Exploring Business - Karen Collins (1st ed) (ISBN 0131403656) Exploring Corporate Strategy - Gerry Johnson (8th ed) (ISBN 140588732X) Exploring Macroeconomics - Robert L. Sexton (4th ed) (ISBN 0324395558) Federal Tax Research - William A. Raabe (8th ed) (ISBN 0324659652) Feedback Control of Dynamic Systems - Gene Franklin (5th ed) (ISBN 0131499300) Financial & Managerial Accounting - Carl S. Warren (9th ed) (ISBN 0324401884) Financial & Managerial Accounting - Carl S. Warren (10th ed) (ISBN 0324663811) Financial Accounting - Belverd E. Needles (10th ed) (ISBN 0547193289) Financial Accounting - Carl S. Warren, James M. Reeve (10th ed) (ISBN 0324380674) Financial Accounting - Carl S. Warren, James M. Reeve (11th ed) (ISBN 0324663781) Financial Accounting - Jane Reimers (1st ed) (ISBN 0131492012) Financial Accounting - Walter Harrison, Charles Horngren (6th ed) (ISBN 0131499459) Financial Accounting - Walter Harrison, Charles Horngren (7th ed) (ISBN 0138128200) Financial Accounting and Financial Tips - Walter T. Harrison (7th ed) (ISBN 0135012848) Financial Accounting, Reporting & Analysis: International Edition - Barry Elliott (2nd ed) (ISBN 027370253X) Financial Accounting: A Bridge to Decision Making - Robert Ingram (6th ed) (ISBN 0324313357) Financial Accounting: A Business Process Approach - Jane L. Reimers (2nd ed) (ISBN 0131473867) Financial Accounting: An Integrated Statements Approach - Jonathan Duchac (2nd ed) (ISBN 0324312113) Financial Accounting: An Introduction to Concepts, Methods and Uses - Clyde P. Stickney (12th ed) (ISBN 0324381980) Financial Accounting: An Introduction to Concepts, Methods and Uses - Clyde P. Stickney (13th ed) (ISBN 0324651147) Financial Accounting: The Impact on Decision Makers - Gary Porter (6th ed) (ISBN 0324655231) Financial and Managerial Accounting - Meg Pollard (1st ed) (ISBN 0136008984) Financial And Managerial Accounting (Ch 1-13) - Charles Horngren (1st ed) (ISBN 0135009855) Financial Economics - Zvi Bodie (2nd ed) (ISBN 0131856154) Financial Management for Public, Health, and Not-for-Profit - Steven A Finkler (3rd ed) (ISBN 0136070736) Financial Management For Public, Health, and Not-for-Profit Organizations - Steven Finkler (2nd ed) (ISBN 0131471988) Financial Management: Theory & Practice - Eugene Brigham (12th ed) (ISBN 0324422695) Financial Markets and Institutions - Frederic S. Mishkin (5th ed) (ISBN 0321280296) Financial Markets and Institutions - Frederic S. Mishkin (6th ed) (ISBN 0321374215) Financial Markets and Institutions - Jeff Madura (8th ed) (ISBN 0324568215) Financial Markets and Institutions Abridged Edition - Jeff Madura (8th ed) (ISBN 0324593643) Financial Reporting and Analysis - Lawrence Revsine (3rd ed) (ISBN 0131430211) Financial Reporting and Analysis Using Financial Accounting Information - Charles Gibson (10th ed) (ISBN 0324304455) Financial Reporting and Analysis Using Financial Accounting Information - Charles Gibson (11th ed) (ISBN 0324657420) Financial Reporting, Financial Statement Analysis, and Valuation - Clyde P. Stickney (6th ed) (ISBN 0324302959) Financial/Managerial Accounting - Walter T. Harrison (1st ed) (ISBN 0131568779) Finite Element Analysis Theory and Application with ANSYS - Saeed Moaveni (3rd ed) (ISBN 0131890808) Finite Math and Its Application - Larry Goldstein (9th ed) (ISBN 0131873644) Finite Mathematics - Margaret L. Lial et al (8th ed) (ISBN 032122826X) Finite Mathematics and Calculus with Applications - Margaret Lial (8th ed) (ISBN 0321426517) Finite Mathematics for Business, Economics, Life Sciences & Social Sciences - Raymond Barnett (11th ed) (ISBN 0132255707) Finite Mathematics with Applications - Margaret L. Lial (9th ed) (ISBN 0321386728) First Course in Abstract Algebra - John Fraleigh (7th ed) (ISBN 0201763907) First Course in Abstract Algebra - Joseph Rotman (3rd ed) (ISBN 0131862677) First Course In Probability - Sheldon M. Ross (7th ed) (ISBN 0131856626) First Course In Probability - Sheldon M. Ross (8th ed) (ISBN 013603313X) First Course in Statistics, A - James T. McClave (10th ed) (ISBN 0136152597) Fluency with Information Technology: Skills, Concepts, and Capabilities - Lawrence Snyder (3rd ed) (ISBN 0321512391) Foundations of Economics - Robin Bade (4th ed) (ISBN 0321522362) Foundations of Finance - Arthur Keown, William Petty, John Martin, David Scott (5th ed) (ISBN 0131856057) Foundations of Finance: Logic and Practice of Financial Mangement - Arthur J. Keown (6th ed) (ISBN 0135048168) Foundations of Finance: The Logic and Practice of Financial Management - Arthur Keown (6th ed) (ISBN 0132339226) Foundations of Financial Markets and Institutions - Frank J. Fabozzi (4th ed) (ISBN 0136135315) Foundations of Geometry - Gerard Venema (5th ed) (ISBN 0131437003) Foundations of Macroeconomics - Robin Bade (4th ed) (ISBN 0321522370) Foundations of MEMS - Chang Liu (1st ed) (ISBN 0131472860) Foundations of Microeconomics - Robin Bade (3rd ed) (ISBN 0321415957) Foundations of Microeconomics - Robin Bade (4th ed) (ISBN 0321522389) Foundations of the Legal Environment of Business - Marianne M. Jennings (1st ed) (ISBN 0324566514) Framework for Human Resource Management, A - Gary Dessler (5th ed) (ISBN 0136041531) Framework for Marketing Management, A - Philip Kotler (4th ed) (ISBN 0136026605) Fraud Examination - Steve Albrecht (2nd ed) (ISBN 0324651155) Friendly Introduction to Analysis - Witold A.J. Kosmala (2nd ed) (ISBN 0130457965) Fundamental Cornerstones of Managerial Accounting - Dan L. Heitger, Maryanne M. Mowen (1st ed) (ISBN 0324378068) Fundamental Mathematics through Applications - Geoffrey Akst (4th ed) (ISBN 0321496906) Fundamentals of Advanced Accounting - Paul M. Fischer (Test Bank) (1st ed) (ISBN 0324378904) Fundamentals of Applied Electromagnetics - Fawwaz T. Ulaby (5th ed) (ISBN 0132413264) Fundamentals of Business Law Summarized Cases - Roger LeRoy Miller (7th ed) (ISBN 0324381689) Fundamentals of Business Law: Excerpted Cases - Roger LeRoy Miller (2nd ed) (ISBN 0324595727) Fundamentals of Business Law: Summarized Cases - Roger LeRoy Miller (8th ed) (ISBN 0324595735) Fundamentals of Communication Systems - John G. Proakis (1st ed) (ISBN 013147135X) Fundamentals of Complex Analysis - Edward Saff (3rd ed) (ISBN 0139078746) Fundamentals of Derivatives Markets - Robert L. McDonald (1st ed) (ISBN 0321357175) Fundamentals of Differential Equations - Kent Nagle, Edward Saff (6th ed) (ISBN 0321145720) Fundamentals of Differential Equations - R. Kent Nagle (7th ed) (ISBN 0321410483) Fundamentals of Differential Equations with Boundary Value Problems - R. Kent Nagle (5th ed) (ISBN 0321419219) Fundamentals of Electromagnetics for Electrical and Computer Engineering - Nannapaneni Narayana Rao (1st ed) (ISBN 0136013333) Fundamentals of Engineering Economics - Chan S. Park (2nd ed) (ISBN 0132209608) Fundamentals of Financial Management - Eugene Brigham (11th ed) (ISBN 0324319800) Fundamentals of Financial Management - Eugene F. Brigham (12th ed) (ISBN 0324597703) Fundamentals of Financial Management Concise - Eugene F. Brigham (6th ed) (ISBN 0324664559) Fundamentals of Investing - Lawrence J. Gitman (10th ed) (ISBN 0321489381) Fundamentals of Management: Essential Concepts and Applications - Stephen P. Robbins (Test Bank) (5th ed) (ISBN 0131487361) Fundamentals of Multinational Finance - Michael Moffett (3rd ed) (ISBN 0321541642) Fundamentals of Organic Chemistry - John McMurry (Test Bank only) (5th ed) (ISBN 0534395732) Fundamentals of Probability, with Stochastic Processes - Saeed Ghahramani (3rd ed) (ISBN 0131453408) Fundamentals of Signals and Systems - Edward Kamen (3rd ed) (ISBN 0131687379) Fundamentals of Statistics - Michael Sullivan (2nd ed) (ISBN 0131569872) Further Mathematics for Economic Analysis - Knut Sydsaeter et al (1st ed) (ISBN 0273655760) Geometry: Theorems and Constructions - Allan Berele (1st ed) (ISBN 0130871214) Global Investments - Bruno Solnik (6th ed) (ISBN 0321527704) Global Strategy - Mike W. Peng (2nd ed) (ISBN 0324590997) Governmental and Nonprofit Accounting: Theory and Practice - Robert J. Freeman (9th ed) (ISBN 0136029515) Health Economics - Charles E. Phelps (4th ed) (ISBN 0321594576) High-Speed Networks and Internets: Performance and Quality of Service - William Stallings (2nd ed) (ISBN 0130322210) Historical Geology - Reed Wicander (6th ed) (ISBN 0495560073) Human Anatomy & Physiology - Elaine N. Marieb (7th ed) (ISBN 0805359095) Human Anatomy and Physiology - Elaine N. Marieb (8th ed) (ISBN 0805395911) Human Anatomy and Physiology Lab Manual - Elaine N. Marieb (9th ed) (ISBN 0805372652) Human Biology: Concepts and Current Issues - Michael D. Johnson (5th ed) (ISBN 0321570200) Human Diseases: A Systemic Approach - Mark Zelman (7th ed) (ISBN 0135155568) Human Physiology: An Integrated Approach - Dee Unglaub Silverthorn (5th ed) (ISBN 0321559398) (ISBN 0495014850) Human Relations for Career and Personal Success: Concepts, Applications, and Skills - Andrew J. DuBrin (8th ed) (ISBN 0131791796) Human Relations: Interpersonal Job-Oriented Skills - Andrew J. DuBrin (10th ed) (ISBN 0135019443) Human Resource Management - Gary Dessler (11th ed) (ISBN 0131746170) Human Resource Management - R. Wayne Mondy (11th ed) (ISBN 0136077285) Human Resource Management - Wayne Mondy (10th ed) (ISBN 0132225956) Human Side of Organizations - Michael Drafke (10th ed) (ISBN 0135139740) Hydrology and Floodplain Analysis - Philip B. Bedient (4th ed) (ISBN 0131745891) Income Tax Fundamentals 2006 - Gerald E. Whittenburg (24th ed) (ISBN 0324399022) Income Tax Fundamentals 2007 - Gerald E. Whittenburg (25th ed) (ISBN 032439926X) Income Tax Fundamentals 2009 - Gerald E. Whittenburg (27th ed) (ISBN 0324663676) Information Systems Today: Managing in the Digital World - Leonard Jessup (3rd ed) (ISBN 0132335069) Information Systems Today: Managing the Digital World - Joseph Valacich (4th ed) (ISBN 0136078400) Information Technology Auditing and Assurance - James Hall (2nd ed) (ISBN 0324191987) Inquiry into Physics - Vern J. Ostdiek (6th ed) (ISBN 0495119431) Integrated Arithmetic and Basic Algebra - Bill E. Jordan (4th ed) (ISBN 0321442555) Intel Micro 8086 - Barry B. Brey (8th ed) (ISBN 0135026458) Intel Microprocessors - Barry B. Brey (7th ed) (ISBN 0131195069) Intel Microprocessors - Barry B. Brey (8th ed) (ISBN 0135026458) Interactive Computer Graphics: A Top-Down Approach Using OpenGL - Edward Angel (5th ed) (ISBN 0321535863) Interactive Statistics - Martha Aliaga, Brenda Gunderson (3rd ed) (ISBN 0131497561) Intermediate Accounting - James D. Stice (16th ed) (ISBN 0324312148) Intermediate Accounting - James D. Stice (17th ed) (ISBN 032459237X) Intermediate Accounting - Loren A. Nikolai (10th ed) (ISBN 0324651929) Intermediate Accounting - Loren A. Nikolai (11th ed) (ISBN 032465913X) Intermediate Accounting (Revised) - David Spiceland (4th ed) (ISBN 0073215422) Intermediate Algebra - Elayn El Martin-Gay (5th ed) (ISBN 0136007295) Intermediate Algebra - Margaret L. Lial (10th ed) (ISBN 0321443624) Intermediate Algebra - Margaret L. Lial (9th ed) (ISBN 0321574974) Intermediate Algebra - Marvin L. Bittinger (10th ed) (ISBN 0321319087) Intermediate Algebra for College Students - Allen R. Angel (7th ed) (ISBN 0132383578) Intermediate Algebra for College Students - Robert F. Blitzer (5th ed) (ISBN 0136007627) Intermediate Algebra with Applications & Visualization - Gary K. Rockswold (3rd ed) (ISBN 0321500032) Intermediate Algebra: Functions & Authentic Applications - Jay Lehmann (3rd ed) (ISBN 0131953338) Intermediate Algebra: Graphs & Models - Marvin L. Bittinger (3rd ed) (ISBN 0321416163) Intermediate Financial Management - Eugene F. Brigham (10th ed) (ISBN 0324594690) International Accounting - Frederick Choi (5th ed) (ISBN 0131480979) International Accounting - Frederick D. Choi (6th ed) (ISBN 0131588141) International Business - John Daniels (12th ed) (ISBN 0136029655) International Business - Ricky Griffin (6th ed) (ISBN 0137153732) International Business Law - Ray A. August (5th ed) (ISBN 013600864X) International Business Law and Its Environment - Richard Schaffer (7th ed) (ISBN 0324649673) International Business: Environments and Operations - John Daniels (11th ed) (ISBN 0131869426) International Business: Strategy, Management, and the New Realities - Tamer Cavusgil (1st ed) (ISBN 0131738607) International Business: The Challenges of Globalization - John J. Wild (4th ed) (ISBN 0131747436) International Business: The Challenges of Globalization - John J. Wild (5th ed) (ISBN 0137153759) International Economics - Charles Sawyer, Richard Sprinkle (2nd ed) (ISBN 0131704168) International Economics - James Gerber (3rd ed) (ISBN 032123796X) International Economics - James Gerber (4th ed) (ISBN 0321415558) International Economics - Robert Carbaugh (11th ed) (ISBN 032442194X) International Economics - W. Charles Sawyer (3rd ed) (ISBN 0136054692) International Economics: Theory And Policy - Paul Krugman, Maurice Obstfeld (7th ed) (ISBN 0321293835) International Economics: Theory and Policy - Paul R. Krugman (8th ed) (ISBN 0321488830) International Financial Management - Geert Bekaert (1st ed) (ISBN 0131163604) International Financial Management - Jeff Madura (9th ed) (ISBN 0324568193) International Financial Management Abridged Edition - Jeff Madura (9th ed) (ISBN 0324593473) International Financial Management, Abridged Edition - Jeff Madura (8th ed) (ISBN 0324365632) International Management: Managing Across Borders and Cultures - Helen Deresky (6th ed) (ISBN 0136143261) International Money and Finance - Michael Melvin (7th ed) (ISBN 0201770288) Intro Stats - Richard D. De Veaux (3rd ed) (ISBN 0321500458) Introduction to Abstract Algebra - Olympia Nicodemi (1st ed) (ISBN 0131019635) Introduction to Analysis - William R. Wade (3rd ed) (ISBN 0131453335) Introduction to Business Law - Jeffrey F. Beatty (2nd ed) (ISBN 0324311427) Introduction to Business Statistics - Ronald M. Weiers (6th ed) (ISBN 0324381433) Introduction to C++ EXCEL MATLAB & Basic Engineering Numerical Methods - Harvey G. Stenger (1st ed) (ISBN 0136142931) Introduction to C++, Excel MatLab & Basic Engineering Numerical Methods - Harvey Stenger (1st ed) (ISBN 0136120245) Introduction to Chemical Principles - Stephen Stoker (9th ed) (ISBN 0132379945) Introduction to Computing Systems - Sanjay J. Patel, Yale Patt (2nd ed) (ISBN 0072467509) Introduction to Corporate Finance - William L. Megginson (1st ed) (ISBN 0324379862) Introduction to Corporate Finance - William L. Megginson (2nd ed) (ISBN 0324657935) Introduction to Cryptography with Coding Theory - Wade Trappe (2nd ed) (ISBN 0131862391) Introduction to Derivatives and Risk Management - Don M. Chance (7th ed) (ISBN 0324321392) Introduction to Econometrics - James H. Stock (2nd ed) (ISBN 0321278879) Introduction to Econometrics Brief Edition - James H. Stock (1st ed) (ISBN 0321432517) Introduction to Economic Reasoning - William D. Rohlf (7th ed) (ISBN 0321416112) Introduction to Electrodynamics -David J. Griffiths (3rd ed) (ISBN 013805326X) Introduction to Embedded Systems - Jonathan W. Valvano (1st ed) (ISBN 049541137X) Introduction to Environmental Engineering - P. Aarne Vesilind (3rd ed) (ISBN 0495295833) Introduction to Environmental Engineering - Richard O. Mines (1st ed) (ISBN 0132347474) Introduction to Environmental Engineering and Science - Gilbert M. Masters (3rd ed) (ISBN 0131481932) Introduction to Financial Accounting - Charles Horngren (9th ed) (ISBN 0131479725) Introduction to Fire Prevention - James C. Robertson (7th ed) (ISBN 0135041945) Introduction to Fourier Optics - Joseph Goodman (3rd ed) (ISBN 0974707724) Introduction to Government and Non-for-Profit Accounting - Martin Ives (6th ed) (ISBN 0132366355) Introduction to Graph Theory - Douglas West (2nd ed) (ISBN 0130144002) Introduction to Law - Joanne Hames (3rd ed) (ISBN 0131183818) Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593) Introduction to Linear Programming - Leonid Vaserstein (1st ed) (ISBN 0130359173) Introduction to Management Accounting - Charles T. Horngren (14th ed) (ISBN 0136129218) Introduction to Management Accounting, Chap. 1-17: International Edition - Charles Horngren (13th ed) (ISBN 0131273078) Introduction to Management Science and Student - Bernard Taylor (8th ed) (ISBN 0131050524) Introduction to Management Science and Student - Bernard Taylor (9th ed) (ISBN 0131888099) Introduction to Materials Management - Tony Arnold (6th ed) (ISBN 0132337614) Introduction to Materials Science for Engineers - James F. Shackelford (7th ed) (ISBN 0136012604) Introduction to Mathematical Statistics and Its Applications - Richard J. Larsen (4th ed) (ISBN 0131867938) Introduction to Operations and Supply Chain Management - Cecil Bozarth (2nd ed) (ISBN 0131791036) Introduction to Optics - Frank Pedrotti et al. (3rd ed) (ISBN 0131499335) Introduction to Programming with C++ - Y. Daniel Liang (2nd ed) (ISBN 0136097200) Introduction to Quantum Mechanics - David Griffiths (2nd ed) (ISBN 0131118927) Introduction to Risk Management and Insurance - Mark Dorfman (8th ed) (ISBN 0131449583) Introduction to Risk Management and Insurance - Mark S. Dorfman (9th ed) (ISBN 0132242273) Introduction to Signal and System Analysis - Kaliappan Gopalan (1st ed) (ISBN 0534466060) Introduction to Spectroscopy - Donald L. Pavia (4th ed) (ISBN 0495114782) Introduction to Technical Mathematics - Allyn J. Washington, Mario Triola (5th ed) (ISBN 0321374177) Introduction to Telecommunications - Martha Rosengrant (2nd ed) (ISBN 0131126156) Introduction to the Design & Analysis of Experiments - George C Canavos (1st ed) (ISBN 0136158633) Introduction to the Design and Analysis of Algorithms - Anany Levitin (1st ed) (ISBN 0201743957) Introduction to the Design and Analysis of Algorithms - Anany Levitin (2nd ed) (ISBN 0321358287) Introduction to Transportation Engineering - Lester A. Hoel (1st ed) (ISBN 0534952895) Introduction to Vacuum Technology - David M. Hata (1st ed) (ISBN 0130450189) Introductory & Intermediate Algebra for College Students - Robert F. Blitzer (3rd ed) (ISBN 0136028950) Introductory Algebra - Marvin L. Bittinger (10th ed) (ISBN 0321269470) Introductory Algebra for College Students - Robert F. Blitzer (5th ed) (ISBN 0132356791) Introductory Algebra through Applications - Geoffrey Akst (2nd ed) (ISBN 0321518020) Introductory and Intermediate Algebra - Robert F Blitzer (2nd ed) (ISBN 0131492594) Introductory Chemistry - Nivaldo J. Tro (3rd ed) (ISBN 0136003826) Introductory Chemistry - Steve Russo, Michael Silver, Mike Silver (2nd ed) (ISBN 032104634X) Introductory Circuit Analysis - Robert Boylestad (11th ed) (ISBN 0131730444) Introductory Econometrics: A Modern Approach - Jeffrey Wooldridge (3rd ed) (ISBN 0324289782) Introductory Econometrics: A Modern Approach - Jeffrey Wooldridge (4th ed) (ISBN 0324581629) Introductory Linear Algebra: An Applied First Course - Bernard Kolman (8th ed) (ISBN 0131437402) Introductory Mathematical Analysis - Ernest F Haeussler (12th ed) (ISBN 0132404222) Introductory Statistics - Neil A. Weiss (8th ed) (ISBN 0321393619) Inventing Entrepreneurs: Technology Innovators and their Entrepreneurial Journey - Gerry George (1st ed) (ISBN 0131574701) Investments - Frank K. Reilly (7th ed) (ISBN 0324288999) Investments: An Introduction - Herbert B. Mayo (9th ed) (ISBN 0324561261) Java Software Solutions: Foundations of Program Design - John Lewis (5th ed) (ISBN 0321409493) Java: Introduction to Problem Solving and Programming - Walter Savitch (6th ed) (ISBN 0136072259) John E. Freund's Mathematical Statistics with Applications - Irwin Miller (7th ed) (ISBN 0131427067) Kleppner's Advertising Procedure - Ronald Lane (17th ed) (ISBN 0132308290) Labor and Employment Law: Text & Cases - David Twomey (14th ed) (ISBN 0324594844) Labor Relations - Arthur A Sloane (12th ed) (ISBN 013196223X) Labor Relations - Arthur A. Sloane (13th ed) (ISBN 0136077188) Labor Relations and Collective Bargaining: Cases, Practice, and Law - Michael R. Carrell (8th ed) (ISBN 0131868721) Labor Relations and Collective Bargaining: Cases, Practice, and Law - Michael R. Carrell (9th ed) (ISBN 0136084354) Lakeside Company: Case Studies in Auditing - John M. Trussel (11th ed) (ISBN 0131588516) Law and Economics - Robert Cooter (5th ed) (ISBN 0321336348) Law and Ethics in the Business Environment - Terry Halbert (6th ed) (ISBN 0324657323) Law for Business - John D. Ashcroft (16th ed) (ISBN 0324381573) Leadership - Robert N. Lussier (3rd ed) (ISBN 0324316976) Leadership in Organizations - Gary Yukl (7th ed) (ISBN 0132424312) Learning Microsoft Office Accounting 2007 and Student CD Package - Terri Brunsdon (1st ed) (ISBN 0131586602) Learning Peachtree Complete 2007 & Peachtree Complete CD Package - Terri Brunsdon (1st ed) (ISBN 0132405571) Learning Quickbooks Pro 2007 and Student CD Package - Terri Brunsdon (1st ed) (ISBN 0132419386) Legal Aspects of Architecture, Engineering & the Construction Process - Justin Sweet (8th ed) (ISBN 0495411213) Legal Terminology - Gordon W. Brown (5th ed) (ISBN 0131568043) Level Three Leadership: Getting Below the Surface - James G Clawson (4th ed) (ISBN 0132423847) Linear Algebra and Its Applications - David C. Lay (3rd ed) (ISBN 0321287134) Linear Algebra for Engineers and Scientists Using Matlab - Kenneth Hardy (1st ed) (ISBN 0139067280) Linear Algebra with Applications - Otto Bretscher (3rd ed) (ISBN 0131453343) Linear Algebra with Applications - Steven Leon (7th ed) (ISBN 0131857851) Logic and Computer Design Fundamentals - M. Morris Mano (4th ed) (ISBN 013198926X) Machine Design: An Integrated Approach - Robert L. Norton (3rd ed) (ISBN 0131481908) Machines and Mechanisms: Applied Kinematic Analysis - David H. Myszka (3rd ed) (ISBN 0131837761) Macroeconomics - Andrew B. Abel (6th ed) (ISBN 0321451406) Macroeconomics - Glenn Hubbard (2nd ed) (ISBN 0132356694) Macroeconomics - Michael Parkin (7th ed) (ISBN 032124608X) Macroeconomics - Michael Parkin (8th ed) (ISBN 0321416570) Macroeconomics - Michael Parkin (9th ed) (ISBN 0321600053) Macroeconomics - Olivier Blanchard (5th ed) (ISBN 0132078295) Macroeconomics - Richard Froyen (8th ed) (ISBN 0131435825) Macroeconomics - Richard G. Lipsey (13th ed) (ISBN 0321369238) Macroeconomics - Richard T Froyen (9th ed) (ISBN 0132438356) Macroeconomics - Robert Gordon (10th ed) (ISBN 0321278801) Macroeconomics - Robert Gordon (11th ed) (ISBN 0321485513) Macroeconomics - Roger A. Arnold (9th ed) (ISBN 032478550X) Macroeconomics - Stephen D. Williamson (3rd ed) (ISBN 0321416589) Macroeconomics: A Modern Approach - Robert J. Barro (1st ed) (ISBN 0324178107) Macroeconomics: Principles and Policy - William J. Baumol (10th ed) (ISBN 0324537034) Macroeconomics: Principles and Policy - William J. Baumol (11th ed) (ISBN 0324586213) Macroeconomics: Principles and Tools - Arthur O'Sullivan, Steven Sheffrin (4th ed) (ISBN 0131536184) Macroeconomics: Principles, Applications, and Tools - Arthur O'Sullivan (5th ed) (ISBN 013232928X) Macroeconomics: Public and Private Choice - James D. Gwartney (12th ed) (ISBN 0324580193) Making Career Decisions that Count: A Practical Guide - Darrell A. Luzzo (3rd ed) (ISBN 0131712772) Making the Team - Leigh Thompson (3rd ed) (ISBN 0131861352) Management - Michael Hitt (2nd ed) (ISBN 0132354373) Management - Richard L. Daft (9th ed) (ISBN 0324595840) Management - Stephen P Robbins (9th ed) (ISBN 0132257734) Management Communication: A Case-Analysis Approach - James S O'Rourke (4th ed) (ISBN 0136079768) Management Information Systems - Ken Laudon (11th ed) (ISBN 013607846X) Management of Organizational Behavior - Paul H Hersey (9th ed) (ISBN 0131441396) Manager's Bookshelf - Jon L. Pierce (8th ed) (ISBN 0132301652) Managerial Accounting - Carl Warren (9th ed) (ISBN 0324381913) Managerial Accounting - Carl Warren (10th ed) (ISBN 032466382X) Managerial Accounting - Linda S. Bamber (1st ed) (ISBN 0138129711) Managerial Accounting (Class Test Edition) - Linda S. Bamber (1st ed) (ISBN 0132284634) Managerial Accounting: A Focus on Ethical Decision Making - Steve Jackson, Roby Sawyers (4th ed) (ISBN 0324650647) Managerial Accounting: A Focus on Ethical Decision Making - Steve Jackson, Roby Sawyers (5th ed) (ISBN 0324663854) Managerial Accounting: An Introduction to Concepts, Methods and Uses - Michael W. Maher (10th ed) (ISBN 0324639767) Managerial Economics - Mark Hirschey (12th ed) (ISBN 0324584849) Managerial Economics: A Problem Solving Approach - Luke M. Froeb (1st ed) (ISBN 0324359810) Managerial Economics: Applications, Strategies, and Tactics - James R. McGuigan (11th ed) (ISBN 0324421605) Managerial Economics: Economic Tools for Today's Decision Makers - Paul G. Keat (5th ed) (ISBN 0131860151) Managerial Economics: Economic Tools for Today's Decision Makers - Paul G. Keat (6th ed) (ISBN 0136040047) Managerial Statistics A Case-Based Approach - Peter Klibanoff (1st ed) (ISBN 0324226454) Managers and the Legal Environment - Constance E. Bagley (6th ed) (ISBN 0324582048) Managing Human Resources - Luis Gomez-Mejia (5th ed) (ISBN 013187067X) Managing in a Global Economy: Demystifying International Macroeconomics - John E. Marthinsen (1st ed) (ISBN 0324395507) Managing Information Technology - Carol V Brown (6th ed) (ISBN 0131789546) Managing the Law: The Legal Aspects of Doing Business - Mitchell McInnes (2nd ed) (ISBN 0132042762) Manual Auditing and Assurance Practice Set: CAST - Frank A. Buckless (1st ed) (ISBN 0130464716) Manufacturing Processes for Engineering Materials - Serope Kalpakjian (5th ed) (ISBN 0132272717) Manufacturing, Engineering & Technology - Serope Kalpakjian (5th ed) (ISBN 0131489658) Market Regulation - Roger Sherman (1st ed) (ISBN 0321322320) Market-Based Management - Roger Best (5th ed) (ISBN 0132336537) Marketing - Charles W. Lamb (10th ed) (ISBN 0324591098) Marketing - William M. Pride (15th ed) (ISBN 0547167474) Marketing Management - Dawn Iacobucci (1st ed) (ISBN 0324784430) Marketing Management - Philip Kotler (13th ed) (ISBN 0136009980) Materials Science and Engineering: An Introduction - William Callister (6th ed) (ISBN 0471135763) Mathematical Economics - Jeffrey Baldani (2nd ed) (ISBN 0324183321) Mathematical Ideas - Charles D. Miller (11th ed) (ISBN 0321361466) Mathematical Ideas - Charles D. Miller (11th ed) (ISBN 0321361482) Mathematical Methods for Economics - Michael Klein (2nd ed) (ISBN 0201726262) Mathematical Proofs: A Transition to Advanced Mathematics - Gary Chartrand (2nd ed) (ISBN 0321390539) Mathematical Proofs: A Transition to Advanced Mathematics - Gary Chartrand (1st ed) (ISBN 0201710900) Mathematical Reasoning for Elementary Teachers - Calvin T. Long (5th ed) (ISBN 0321460847) Mathematics for Business - Stanley A. Salzman (8th ed) (ISBN 0321357434) Mathematics for Elementary School Teachers - Phares O'Daffer (4th ed) (ISBN 0321448049) Mathematics for Physicists - Susan Lea (1st ed) (ISBN 0534379974) Mathematics of Interest Rates and Finance - Gary Guthrie (1st ed) (ISBN 0130461822) Mathematics with Applications - Margaret L. Lial (9th ed) (ISBN 0321334337) Mechanical Behavior of Materials - Norman Dowling (3rd ed) (ISBN 0131863126) Mechanics of Materials - James M. Gere (7th ed) (ISBN 0534553974) Mechanics of Materials - Russell C. Hibbeler (7th ed) (ISBN 0132209918) Medical Imaging Signals and Systems - Jerry L. Prince (1st ed) (ISBN 0130653535) Microbiology with Diseases by Body System - Robert W. Bauman (2nd ed) (ISBN 032151341X) Microbiology: An Introduction - Gerard J. Tortora (9th ed) (ISBN 0805347909) Microeconomics - Glenn Hubbard (2nd ed) (ISBN 0138132771) Microeconomics - Jeffrey Perloff (4th ed) (ISBN 0321414527) Microeconomics - Jeffrey Perloff (5th ed) (ISBN 0321531191) Microeconomics - Michael Parkin (7th ed) (ISBN 0321454944) Microeconomics - Michael Parkin (8th ed) (ISBN 0321416600) Microeconomics - Michael Parkin (9th ed) (ISBN 0321600045) Microeconomics - Richard G. Lipsey (13th ed) (ISBN 032136922X) Microeconomics - Robert Pindyck, Daniel Rubinfeld (6th ed) (ISBN 0130084611) Microeconomics - Robert Pindyck, Daniel Rubinfeld (7th ed) (ISBN 0132080230) Microeconomics - Roger A. Arnold (9th ed) (ISBN 0324785496) Microeconomics: Principles and Policy - William J. Baumol (11th ed) (ISBN 0324586221) Microeconomics: Principles and Tools - Arthur O'Sullivan, Steven Sheffrin (4th ed) (ISBN 0131536060) Microeconomics: Principles, Applications, and Tools - Arthur O'Sullivan (5th ed) (ISBN 0131572830) Microeconomics: Public and Private Choice - James D. Gwartney (12th ed) (ISBN 0324580207) Microeconomics: Theory and Applications with Calculus - Jeffrey M. Perloff (1st ed) (ISBN 0321277945) Microwave Engineering - David Pozar (3rd ed) (ISBN 0471448788) MIS Essentials - David Kroenke (1st ed) (ISBN 0136075606) MKTG 3.0 2009 Edition - Charles W. Lamb (3rd ed) (ISBN 0324789289) Modern Control Systems - Richard C Dorf (11th ed) (ISBN 0132270285) Modern Database Management - Jeffrey Hoffer (8th ed) (ISBN 0132212110) Modern Database Management - Jeffrey Hoffer (9th ed) (ISBN 0136003915) Modern Electronic Communication - Jeff Beasley (9th ed) (ISBN 0132251132) Modern Elementary Statistics - John E. Freund (12th ed) (ISBN 013187439X) Modern Industrial Organization - Dennis Carlton, Jeffrey Perloff (4th ed) (ISBN 0321180232) Modern Labor Economics: Theory and Public Policy - Ronald Ehrenberg (10th ed) (ISBN 0321533739) Modern Labor Economics: Theory and Public Policy - Ronald Ehrenberg (9th ed) (ISBN 0321305035) Modern Management - Samuel C. Certo (10th ed) (ISBN 0131494708) Modern Physics - Randy Harris (2nd ed) (ISBN 0805303081) Modern Physics - Raymond Serway (3rd ed) (ISBN 0534493394) Modern Semiconductor Devices for Integrated Circuits - Chenming C. Hu (1st ed) (ISBN 0136085253) Modern Systems Analysis and Design - Jeffrey A. Hoffer (5th ed) (ISBN 0132240769) Modern Wireless Communications - Simon Haykin (1st ed) (ISBN 0130224723) Money, Banking and Financial Markets - Roger LeRoy Miller (3rd ed) Money, the Financial System, and the Economy - R. Glenn Hubbard (6th ed) (ISBN 0321426703) Multinational Business Finance - David K. Eiteman (11th ed) (ISBN 0321357965) Multinational Finance - Kirt C. Butler (3rd ed) (ISBN 0324177453) Multinational Management - John B. Cullen (4th ed) (ISBN 032442177X) Multivariate Data Analysis - Joseph F. Hair (7th ed) (ISBN 0138132631) Nanoengineering of Structural, Functional and Smart Materials - Mark J. Schulz (1st ed) (ISBN 0849316537) New Venture Management: The Entrepreneur's Roadmap - Donald Kuratko (1st ed) (ISBN 0136130321) Numerical Analysis - Timothy Sauer (1st ed) (ISBN 0321268989) Numerical Methods for Engineers - Bilal Ayyub, Richard McCuen (1st ed) (ISBN 0133373614) Numerical Methods Using Matlab - John Mathews (4th ed) (ISBN 0130652482) Occupational Safety and Health for Technologists, Engineers, and Managers - David L. Goetsch (6th ed) (ISBN 0132397609) Office Procedures 21st Century & Student Workbook Package - Sharon Burton (7th ed) (ISBN 0132343436) OM 2008 - David Alan Collier (1st ed) (ISBN 0324662556) Operating Systems Principles - Lubomir F. Bic (1st ed) (ISBN 0130266116) Operating Systems: Internals and Design Principles - William Stallings (5th ed) (ISBN 0131479547) Operations Management - Jay Heizer (8th ed) (ISBN 0131554441) Operations Management - Jay Heizer (9th ed) (ISBN 0138128782) Operations Management - Nigel Slack (5th ed) (ISBN 0273708473) Operations Management and Student CD and Student DVD Package - Jay Heizer (9th ed) (ISBN 0138128782) Operations Management: Process and Value Chains - Lee J. Krajewski (8th ed) (ISBN 0131697390) Operations Research: An Introduction - Hamdy A. Taha (8th ed) (ISBN 0131889230) Opportunities and Challenges of Workplace Diversity: Theory, Cases, and Exercises - Kathryn Canas (1st ed) (ISBN 0131343068) Oracle 10g Programming: A Primer - Rajshekhar Sunderraman (1st ed) (ISBN 0321463048) Organic Chemistry - Paula Bruice (Test Bank only) (5th ed) (ISBN 0131963163) Organization Development and Change - Thomas G. Cummings (9th ed) (ISBN 0324421389) Organizational Behavior - Don Hellriegel (12th ed) (ISBN 0324578725) Organizational Behavior - Stephen P Robbins (13th ed) (ISBN 0136007171) Organizational Behavior Today - Leigh Thompson (1st ed) (ISBN 0131858114) Organizational Behavior: An Experiential Approach - Joyce S Osland (8th ed) (ISBN 0131441515) Organizational Behavior: An Introduction to Your Life in Organizations - Rae Andre (1st ed) (ISBN 013185495X) Organizational Behavior: Managing People and Organizations - Ricky W. Griffin (9th ed) (ISBN 0547167334) Organizational Behavior: Science, The Real World, and You - Debra L. Nelson (6th ed) (ISBN 0324578733) Organizational Theory, Design and Change - Gareth R. Jones (5th ed) (ISBN 0131865420) Organizational Theory, Design and Change - Gareth R. Jones (6th ed) (ISBN 0136087310) Orthopaedic Biomechanics: Mechanics and Design in Musculoskeletal Systems - Donald L. Bartel (1st ed) (ISBN 0130089095) Parallel and Distributed Computation: Numerical Methods - Dimitri Bertsekas, John Tsitsiklis (1st ed) (ISBN 0136487009) Parallel Programming - Barry Wilkinson (2nd ed) (ISBN 0131405632) Partial Differential Equations and Boundary Value Problems - Nakhle Asmar (2nd ed) (ISBN 0131480960) Payroll Accounting 2008 - Bernard Bieg (18th ed) (ISBN 0324645546) Payroll Accounting 2009 - Bernard Bieg (19th ed) (ISBN 0324663730) Performance Management - Herman Aguinis (2nd ed) (ISBN 0136151752) Personal Finance - Jeff Madura (3rd ed) (ISBN 0321409965) Personal Finance: Turning Money into Wealth - Arthur J. Keown (5th ed) (ISBN 0135077710) Personal Financial Planning - Lawrence J. Gitman (11th ed) (ISBN 0324422865) Pharmacology for Nurses: A Pathophysiological Approach - Michael Patrick Adams (2nd ed) (ISBN 0131756656) Physical Chemistry - Thomas Engel, Philip Reid (1st ed) (ISBN 080533842X) Physical Chemistry for the Life Sciences - Thomas Engel (1st ed) (ISBN 0805382771) Physical Geography - Robert E. Gabler (9th ed) (ISBN 0495555061) Physical Metallurgy Principles - Reza Abbaschian (4th ed) (ISBN 0495082546) Physics : Principles with Applications - Douglas Giancoli (6th ed) (ISBN 0130606200) Physics for Scientists & Engineers (Chs 1-37) with MasteringPhysics» - Doug Giancoli (4th ed) (ISBN 0136139264) Physics for Scientists and Engineers with Modern Physics and MasteringPhysics» - Douglas C. Giancoli (4th ed) (ISBN 0136139221) Physics with Mastering Physics - James S. Walker (3rd ed) (ISBN 0136138969) Physics with Mastering Physics - James S. Walker (4th ed) (ISBN 0321541634) Physics: Principles with Applications with MasteringPhysics - Douglas C. Giancoli (6th ed) (ISBN 0321569830) Portfolio Construction, Management, and Protection - Robert A. Strong (4th ed) (ISBN 0324359365) Portfolio Construction, Management, and Protection - Robert A. Strong (5th ed) (ISBN 0324665105) Power Systems Analysis and Design - J. Duncan Glover (4th ed) (ISBN 0534548849) Practical Financial Management - William R. Lasher (5th ed) (ISBN 0324422636) Prealgebra - Elayn El Martin-Gay (5th ed) (ISBN 0132319519) Prealgebra - Margaret L. Lial (4th ed) (ISBN 0321567927) Prealgebra - Marvin L. Bittinger (5th ed) (ISBN 0321331907) Prealgebra & Introductory Algebra - Elayn El Martin-Gay (2nd ed) (ISBN 0131577050) Prealgebra and Introductory Algebra - Marvin L. Bittinger (2nd ed) (ISBN 0321331893) Prealgebra: An Integrated Approach - Margaret L. Lial (1st ed) (ISBN 032135639X) Precalculus - J. S. Ratti (1st ed) (ISBN 032129646X) Precalculus - Judith A. Beecher (3rd ed) (ISBN 0321460065) Precalculus - Margaret Lial (4th ed) (ISBN 0321528840) Precalculus - Mark Dugopolski (4th ed) (ISBN 0321357795) Precalculus - Michael Sullivan (8th ed) (ISBN 0132256886) Precalculus - Michael Sullivan (8th ed) (ISBN 0132256886) Precalculus - Robert F. Blitzer (3rd ed) (ISBN 0131874799) Precalculus - Robert F. Blitzer (4th ed) (ISBN 0321559843) Precalculus: Enhanced with Graphing Utilities - Michael Sullivan (5th ed) (ISBN 0136015786) Precalculus: Functions and Graphs - Mark Dugopolski (3rd ed) (ISBN 032150111X) Precalculus: Graphs & Models and Graphing Calculator Manual Package - Marvin L. Bittinger (4th ed) (ISBN 0321501527) Prehospital Emergency Care - Joseph J. Mistovich (8th ed) (ISBN 0131741438) Prentice Hall's Federal Taxation 2007: Comprehensive - Thomas Pope (20th ed) (ISBN 0132389479) Prentice Hall's Federal Taxation 2007: Corporations - Thomas Pope (20th ed) (ISBN 0131751484) Prentice Hall's Federal Taxation 2007: Individuals - Thomas Pope (20th ed) (ISBN 013243220X) Prentice Hall's Federal Taxation 2008: Comprehensive - Thomas Pope (21st ed) (ISBN 0132416492) Prentice Hall's Federal Taxation 2008: Corporations - Thomas Pope (21st ed) (ISBN 0136156436) Prentice Hall's Federal Taxation 2008: Individuals - Thomas Pope (21st ed) (ISBN 0136156371) Prentice Hall's Federal Taxation 2009: Comprehensive - Thomas Pope (22nd ed) (ISBN 0136067190) Prentice Hall's Federal Taxation 2009: Corporations - Thomas Pope (22nd ed) (ISBN 0136067131) Prentice Hall's Federal Taxation 2009: Individuals - Thomas Pope (22nd ed) (ISBN 0136067042) Preparing Effective Business Plans: An Entrepreneurial Approach - Bruce R. Barringer (1st ed) (ISBN 0132318326) Price Theory and Applications - Steven Landsburg (7th ed) (ISBN 0324421613) Principles of Accounting - Meg Pollard (1st ed) (ISBN 0132304791) Principles of Auditing: An Introduction to International Standards on Auditing - Rick Hayes (2nd ed) (ISBN 0273684108) Principles of CMOS VLSI Design - Neil H.E. Weste (3rd ed) (ISBN 0201533766) Principles of Cost Accounting - Edward J. Vanderbeck (13th ed) (ISBN 0324191693) Principles of Cost Accounting - Edward J. Vanderbeck (14th ed) (ISBN 0324374178) Principles of Customer Relationship Management - Roger Baran (1st ed) (ISBN 0324322380) Principles of Economics - Gregory Mankiw (4th ed) (ISBN 0324224729) Principles of Economics - Gregory Mankiw (5th ed) (ISBN 0324589972) Principles of Economics - Karl Case (8th ed) (ISBN 0132289148) Principles of Electric Circuits: Conventional Current Version - Thomas Floyd (8th ed) (ISBN 0131701797) Principles of Electric Circuits: Conventional Flow Version - Thomas L. Floyd (9th ed) (ISBN 013507309X) Principles of Finance - Scott Besley (3rd ed) (ISBN 0324232624) Principles of Finance - Scott Besley (4th ed) (ISBN 0324655886) Principles of Foundation Engineering - Braja M. Das (6th ed) (ISBN 0495082465) Principles of Geotechnical Engineering - Braja M. Das (6th ed) (ISBN 0534551440) Principles of Heat Transfer - Frank Kreith (6th ed) (ISBN 0534375960) Principles of Law and Economics - Daniel Cole, Peter Grossman (1st ed) (ISBN 0130932612) Principles of Macroeconomics - Gregory Mankiw (4th ed) (ISBN 0324236956) Principles of Macroeconomics - Gregory Mankiw (5th ed) (ISBN 0324589999) Principles of Managerial Finance - Lawrence J. Gitman (12th ed) (ISBN 0321557530) Principles of Managerial Finance Brief Edition - Lawrence Gitman (5th ed) (ISBN 0321557522) Principles of Managerial Finance plus MyfinanceLab Student Access Kit - Lawrence J. Gitman (12th ed) (ISBN 0321557530) Principles of Marketing - Philip Kotler (12th ed) (ISBN 0132390027) Principles of Marketing - Philip Kotler (13th ed) (ISBN 0136079415) Principles of Microeconomics - Gregory Mankiw (4th ed) (ISBN 0324319169) Principles of Microeconomics - Karl E. Case (8th ed) (ISBN 0131994859) Principles of Money, Banking & Financial Markets - Lawrence Ritter (12th ed) (ISBN 0321375572) Principles of Money, Banking, Financial Markets - Lawrence Ritter et al (11th ed) (ISBN 0321205251) Principles Of Operations Management - Jay Heizer (6th ed) (ISBN 013155445X) Principles Of Operations Management - Jay Heizer (7th ed) (ISBN 0132449757) Principles of Risk Management and Insurance - George E. Rejda (10th ed) (ISBN 0321414934) Probabilistic Systems and Random Signals - Abraham Haddad (1st ed) (ISBN 0130094552) Probability & Statistics for Engineers & Scientists - Ronald E. Walpole (8th ed) (ISBN 0131877119) Probability and Statistical Inference - Robert Hogg, Eliot Tanis (7th ed) (ISBN 0131464132) Probability and Statistical Inference - Robert Hogg, Eliot Tanis (8th ed) (ISBN 0321584759) Probability and Statistics - Morris DeGroot, Mark Schervish (3rd ed) (ISBN 0201524880) Probability and Statistics for Engineers - Richard Johnson, Irwin Miller, John Freund (7th ed) (ISBN 0131437453) Probability and Statistics for Engineers and Scientists - Anthony J. Hayter (3rd ed) (ISBN 0495107573) Probability Random Variables, and Stochastic Processes - Papoulis et al (4th ed) (ISBN 0073660116) Probability, Statistics, and Random Processes For Electrical Engineering - Alberto Leon-Garcia (3rd ed) (ISBN 0131471228) Problem Solving and Program Design in C - Jeri R. Hanly (5th ed) (ISBN 0321409914) Problem Solving and Program Design in C - Jeri R. Hanly (6th ed) (ISBN 0321535421) Problem Solving with C++ - Walter Savitch (6th ed) (ISBN 0321412699) Problem Solving with C++ - Walter Savitch (7th ed) (ISBN 0321531345) Problem Solving, Abstraction & Design Using C++ - Frank L. Friedman (5th ed) (ISBN 0321450051) Process Control Instrumentation Technology - Curtis Johnson (8th ed) (ISBN 0131194577) Professional Office Procedures - Susan Cooperman (5th ed) (ISBN 0135156645) Professional Selling: A Trust-Based Approach - Thomas N. Ingram (4th ed) (ISBN 032453809X) Professionalism: Real Skills for Workplace Success - Lydia E. Anderson (1st ed) (ISBN 0131714392) Programming the World Wide Web - Robert W. Sebesta (4th ed) (ISBN 0321489691) Project Management for Information Systems - James Cadle (5th ed) (ISBN 0132068583) Public Relations Practices: Managerial Case Studies and Problems - Allen H. Center (7th ed) (ISBN 0132341360) Quality Control - Dale H. Besterfield (8th ed) (ISBN 0135000955) Quality Management - Donna C.S. Summers (2nd ed) (ISBN 0135005108) Quality Management for Organizational Excellence - David L. Goetsch (6th ed) (ISBN 0135019672) Quantitative Analysis for Management - Barry Render (10th ed) (ISBN 0136036252) Quantitative Analysis for Management - Barry Render (9th ed) (ISBN 0131857029) Quantum Chemistry and Spectroscopy - Thomas Engel (1st ed) (ISBN 0805339795) QuickBooks Pro 2006 with Update 2007 and CD Package - Janet Horne (9th ed) (ISBN 013242407X) Real Estate Law - George Siedel (6th ed) (ISBN 0324204809) Real Estate Law - Marianne M. Jennings (8th ed) (ISBN 0324650205) Reinforced Concrete Design - George F. Limbrunner (7th ed) (ISBN 0135044359) Reinforced Concrete: Mechanics and Design - James K. Wight (5th ed) (ISBN 0132281414) Retailing - Patrick M. Dunne (6th ed) (ISBN 032436279X) Rethinking Marketing: The Entrepreneurial Imperative - Minet Schindehutte (1st ed) (ISBN 0132393891) Risk Management and Insurance - James S. Trieschmann (12th ed) (ISBN 0324183208) Risk Takers: Uses and Abuses of Financial Derivatives - John Marthinsen (2nd ed) (ISBN 0321542568) Routers and Routing Basics CCNA 2 Labs and Study Guide - Allan Johnson (1st ed) (ISBN 1587131676) Selling Today - Gerald L. Manning (11th ed) (ISBN 013207995X) Short-Term Financial Management - Terry Maness (3rd ed) (ISBN 0324202938) Short-Term Financial Management - Terry Maness (Test Bank) (3rd ed) (ISBN 0324202938) Signals, Systems, and Transforms - Charles L Phillips (4th ed) (ISBN 0131989235) Social Entrepreneurship: A Modern Approach to Social Value Creation - Arthur C. Brooks (1st ed) (ISBN 0132330768) Software Engineering - Ian Sommerville (8th ed) (ISBN 0321313798) Software Engineering: Theory and Practice - Shari Lawrence Pfleeger (4th ed) (ISBN 0136061699) Soils and Foundations - Cheng Liu, Jack Evett (7th ed) (ISBN 0132221381) Solid State Electronic Devices - Ben Streetman (6th ed) (ISBN 013149726X) Solid State Physics: Essential Concepts - David W. Snoke (1st ed) (ISBN 0805386645) South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660529) South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660529) South-Western Federal Taxation 2009: Corporations - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660219) South-Western Federal Taxation 2009: Corporations - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660219) South-Western Federal Taxation 2009: Individual Income Taxes - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660200) South-Western Federal Taxation 2009: Individual Income Taxes - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660200) South-Western Federal Taxation 2009: Taxation of Business Entities - James Smith (Solutions Manual) (12th ed) (ISBN 0324660510) South-Western Federal Taxation 2009: Taxation of Business Entities - James Smith (Test Bank) (12th ed) (ISBN 0324660510) South-Western Federal Taxation 2010: Comprehensive - William Hoffman (Solutions Manual) (33rd ed) (ISBN 0324828616) South-Western Federal Taxation 2010: Comprehensive - William Hoffman (Test Bank) (33rd ed) (ISBN 0324828616) South-Western Federal Taxation 2010: Corporations - William Hoffman (Solutions Manual) (33rd ed) (ISBN 0324828632) South-Western Federal Taxation 2010: Corporations - William Hoffman (Test Bank) (33rd ed) (ISBN 0324828632) South-Western Federal Taxation 2010: Individual Income Taxes - William Hoffman (Solutions Manual) (33rd ed) (ISBN 0324828659) South-Western Federal Taxation 2010: Individual Income Taxes - William Hoffman (Test Bank) (33rd ed) (ISBN 0324828659) South-Western Federal Taxation 2010: Taxation of Business Entities - James Smith (Solutions Manual) (33rd ed) (ISBN 0324828586) South-Western Federal Taxation 2010: Taxation of Business Entities - James Smith (Test Bank) (33rd ed) (ISBN 0324828586) Spectral Analysis of Signals - Peter Stoica, Randolph Moses (1st ed) (ISBN 0131139568) Starting Out with C++: Early Objects - Tony Gaddis (6th ed) (ISBN 0321512383) Starting Out with Java: Early Objects - Tony Gaddis (3rd ed) (ISBN 0321497686) Gaddis (4th ed) (ISBN 0136080200) Starting Out with Visual Basic 2008 - Tony Gaddis (4th ed) (ISBN 0321531353) Starting Out With Visual Basic 2008 Update - Tony Gaddis (4th ed) (ISBN 0136076955) Statics and Strength of Materials - Robert L. Mott (1st ed) (ISBN 0135159822) Statics and Strengths of Materials - Harold I. Morrow (6th ed) (ISBN 0131719777) Statistical Methods for the Social Sciences - Alan Agresti (4th ed) (ISBN 0130272957) Statistical Reasoning for Everyday Life - Jeffrey O. Bennett (3rd ed) (ISBN 0321286723) Statistics - James T. McClave (11th ed) (ISBN 0132069512) Statistics for Business & Economics - James T. McClave (10th ed) (ISBN 0132409356) Statistics for Business and Economics - David R. Anderson (Test Bank only) (10th ed) (ISBN 0324360681) Statistics for Business and Economics - Paul Newbold, William L. Carlson (6th ed) (ISBN 0132203847) Statistics for Business and Economics - Paul Newbold, William L. Carlson (7th ed) (ISBN 0136085369) Statistics for Management and Economics - Gerald Keller (7th ed) (ISBN 0534491243) Statistics for Managers Using Microsoft Excel - David M. Levine (5th ed) (ISBN 0136149901) Statistics for Science and Engineering - John Kinney (1st ed) (ISBN 0201437201) Statistics for the Behavioral and Social Sciences - Arthur Aron (4th ed) (ISBN 0131562789) Statistics for the Life Sciences - Myra Samuels (3rd ed) (ISBN 013041316X) Statistics, Data Analysis & Decision Modeling - James R. Evans (4th ed) (ISBN 0136066003) Statistics: Informed Decisions Using Data - Michael Sullivan (3rd ed) (ISBN 0321568028) (1st ed) (ISBN 0130083690) Statistics: The Art and Science of Learning from Data - Alan Agresti (2nd ed) (ISBN 0135131995) Stats: Data and Models - Richard D. De Veaux (2nd ed) (ISBN 0321433793) Steel Design - William T. Segui (4th ed) (ISBN 0495244716) Strategic Brand Management - Kevin Keller (3rd ed) (ISBN 0131888595) Strategic Compensation - Joe Martocchio (5th ed) (ISBN 0136007449) Strategic Management and Business Policy - Tom Wheelen (10th ed) (ISBN 0131494597) Strategic Management and Business Policy - Tom Wheelen (11th ed) (ISBN 013232346X) Strategic Management and Competitive Advantage - Jay Barney (2nd ed) (ISBN 013613520X) Strategic Management and Competitive Advantage: Concepts and Cases - Jay Barney (2nd ed) (ISBN 0132338238) Strategic Management in Action - Mary Coulter (4th ed) (ISBN 0132277476) Strategic Management: A Dynamic Perspective Integrated Stratsim Simulation Experience - Print Upgrade - Mason Carpenter (1st ed) (ISBN 0136149057) Strategic Management: Concepts and Cases - Fred David (11th ed) (ISBN 0131869493) Strategic Management: Concepts and Cases - Fred David (12th ed) (ISBN 0136015700) Strategic Marketing for Non-Profit Organizations - Alan Andreasen (7th ed) (ISBN 013175372X) Strategic Staffing - Jean M. Phillips (1st ed) (ISBN 0131586947) Structural Analysis - Aslam Kassimali (4th ed) (ISBN 0495295655) Structural Analysis - Russell C. Hibbeler (7th ed) (ISBN 0136020607) Structural Steel Design - Jack C. McCormac (4th ed) (ISBN 013221816X) Structural Steel Design ASD Method - Jack C. McCormac (4th ed) (ISBN 0065000609) Structural Steel Design: A Practice Oriented Approach - Abi O. Aghayere (1st ed) (ISBN 0132340186) Structure and Interpretation of Signals and Systems - Edward Lee, Pravin Varaiya (1st ed) (ISBN 0201745518) Structures - Daniel Lewis Schodek (6th ed) (ISBN 0131789392) Supply Chain Management - Sunil Chopra (3rd ed) (ISBN 0131730428) Supply Chain Management: A Logistics Perspective - John J. Coyle (8th ed) (ISBN 0324376928) Survey of Accounting - Carl S. Warren (3rd ed) (ISBN 0324312482) Survey of Accounting - Carl S. Warren (4th ed) (ISBN 0324658265) Survey of Economics - Irvin B. Tucker (6th ed) (ISBN 0324579616) Survey of Mathematics with Applications - Allen R. Angel (8th ed) (ISBN 0321501071) Survey of Mathematics with Applications Expanded Edition - Allen Angel (8th ed) (ISBN 032150108X) Surveying with Construction Applications - Barry F. Kavanagh (6th ed) (ISBN 0131709321) Surveying with Construction Applications - Barry F. Kavanagh (7th ed) (ISBN 0135000513) Surveying: Principles and Applications - Barry F. Kavanagh (8th ed) (ISBN 013236512X) System Dynamics and Response - S. Graham Kelly (1st ed) (ISBN 0534549306) System Modeling and Analysis: Foundations of System Performance Evaluation - Hisashi Kobayashi (1st ed) (ISBN 013034835X) Systems Analysis and Design - Kenneth E. Kendall (7th ed) (ISBN 0132240858) Tax Research - Barbara H Karlin (4th ed) (ISBN 013601531X) Taxation for Decision Makers 2008 - Shirley Dennis-Escoffier (2nd ed) (ISBN 0324654111) Taxes & Business Strategy - Myron S. Scholes (4th ed) (ISBN 0136033156) Teaching Today's Health - David Anspaugh (9th ed) (ISBN 0321596773) Technical Calculus with Analytic Geometry - Allyn J. Washington (4th ed) (ISBN 0201711125) Technical Communication: A Practical Approach - William S. Pfeiffer (7th ed) (ISBN 0135000505) Technology Strategy for Managers and Entrepreneurs - Scott A. Shane (1st ed) (ISBN 0131879324) The Economics of Macro Issues - Roger LeRoy Miller (3rd ed) (ISBN 0321416597) The Economics of Poverty and Discrimination - Bradley R Schiller (10th ed) (ISBN 0131889699) The Economics of Public Issues - Roger LeRoy Miller (15th ed) (ISBN 0321416104) The Economics of Sports - Michael A. Leeds (3rd ed) (ISBN 0321415566) The Labor Relations Process - William H. Holley (9th ed) (ISBN 0324421443) The Legal Environment of Business - Roger E. Meiners (10th ed) (ISBN 0324654367) The Legal Environment of Business: Text and Cases Ethical, Regulatory, Global, and E-Commerce Issues - Roger LeRoy Miller (7th ed) (ISBN 0324590008) The Legal Environment Today: Business In Its Ethical, Regulatory, E- Commerce, and Global Setting - Roger LeRoy Miller (6th ed) (ISBN 0324599250) The Paralegal Professional - Henry Cheeseman (2nd ed) (ISBN 0131751905) The Science of Nutrition - Janice Thompson (1st ed) (ISBN 0805394354) The Strategy of Managing Innovation and Technology - Murray Millson (1st ed) (ISBN 0132303833) Theory of Asset Pricing - George Pennacchi (1st ed) (ISBN 032112720X) Thermodynamics: An Engineering Approach - Yunus Cengel (5th ed) (ISBN 0073107689) Thinking Mathematically - Robert F. Blitzer (4th ed) (ISBN 0131752049) Thomas' Calculus - George B. Thomas, Jr. (11th ed) (ISBN 0321185587) Thomas' Calculus, Early Transcendentals, Media Upgrade - George B. Thomas, Jr (11th ed) (ISBN 0321495756) Thomas' Calculus, Early Transcendentals, Media Upgrade, Part One - George B. Thomas, Jr. (11th ed) (ISBN 0321498747) Thomas' Calculus, Media Upgrade - George B. Thomas, Jr. (11th ed) (ISBN 032148987X) Thomas' Calculus, Media Upgrade, Part One (Single Variable) - George B. Thomas, Jr. (11th ed) (ISBN 0321498755) Thomas' Calculus, Media Upgrade, Part Two (Multivariable, Chap 11-16) - George B. Thomas, Jr. (11th ed) (ISBN 0321501039) Traffic & Highway Engineering - Nicholas J. Garber (4th ed) (ISBN 0495082503) Training in Interpersonal Skills - Stephen P. Robbins (5th ed) (ISBN 0132354993) Trigonometry - Margaret L. Lial (9th ed) (ISBN 0321528859) Trigonometry - Mark Dugopolski (2nd ed) (ISBN 032135690X) Trigonometry: A Right Triangle Approach - Michael Sullivan (5th ed) (ISBN 0136028969) Trigonometry: A Unit Circle Approach - Michael Sullivan (8th ed) (ISBN 0132392798) UFL Collective Bargaining Agreement - Louis Marino (1st ed) (ISBN 0131587668) Understanding and Managing Diversity - Carol Harvey (4th ed) (ISBN 0132069105) Understanding and Managing Organizational Behavior - Jennifer George (5th ed) (ISBN 013239457X) Understanding Fiber Optics - Jeff Hecht (5th ed) (ISBN 0131174290) Understanding Financial Statements - Lyn M. Fraser (8th ed) (ISBN 0131878565) Understanding Modern Economics - Roger Miller (1st ed) (ISBN 0321245822) University Calculus - Joel Hass, Maurice D. Weir (1st ed) (ISBN 0321350146) University Calculus: Alternate Edition - Joel Hass (1st ed) (ISBN 0321471962) University Calculus: Alternate Edition, Part One (Single Variable, Chap 1-9) - Joel Hass (1st ed) (ISBN 0321475194) University Calculus: Elements with Early Transcendentals - Joel Hass (1st ed) (ISBN 0321533488) University Physics with Modern Physics with MasteringPhysics» - Hugh D. Young (12th ed) (ISBN 080532187X) Using and Understanding Mathematics: A Quantitative Reasoning Approach - Jeffrey O. Bennett (4th ed) (ISBN 0321458206) Using Financial Accounting Information: The Alternative to Debits & Credits - Gary A. Porter (5th ed) (ISBN 0324645104) Using Financial Accounting Information: The Alternative to Debits & Credits - Gary A. Porter (6th ed) (ISBN 0324593740) Using MIS - David Kroenke (2nd ed) (ISBN 0138132488) Using Peachtree Complete 2007 for Accounting - Glenn Owen (1st ed) (ISBN 0324377975) Using Peachtree Complete 2009 for Accounting - Glenn Owen (3rd ed) (ISBN 0324665512) Using Quickbooks Pro 2007 for Accounting - Glenn Owen (7th ed) (ISBN 0324378750) Vector Calculus - Susan Colley (3rd ed) (ISBN 0131858742) VHDL: A Starter's Guide - Sudhakar Yalamanchili (2nd ed) (ISBN 0131457357) Water and Wastewater Technology - Mark J. Hammer (6th ed) (ISBN 0131745425) Water Resources Engineering - David A. Chin (2nd ed) (ISBN 0131481924) Water Supply and Pollution Control - Warren Viessman, Jr. (8th ed) (ISBN 0132337177) Web 101 - Wendy G. Lehnert (3rd ed) (ISBN 0321424670) West Federal Taxation Comprehensive 2007 - William Hoffman (Solutions Manual) (30th ed) (ISBN 0324313497) West Federal Taxation Comprehensive 2007 - William Hoffman (Test Bank) (30th ed) (ISBN 0324313497) West Federal Taxation Corporations 2007 - William Hoffman (Solutions Manual) (30th ed) (ISBN 0324313616) West Federal Taxation Corporations 2007 - William Hoffman (Test Bank) (30th ed) (ISBN 0324313616) West Federal Taxation Corporations 2008 - William Hoffman (Solutions Manual) (31st ed) (ISBN 0324380437) West Federal Taxation Corporations 2008 - William Hoffman (Test Bank) (31st ed) (ISBN 0324380437) West Federal Taxation Individual 2007 - William Hoffman (Solutions Manual) (30th ed) (ISBN 0324399618) West Federal Taxation Individual 2007 - William Hoffman (Test Bank) (30th ed) (ISBN 0324399618) West Federal Taxation Individual 2008 - William Hoffman (Solutions Manual) (31st ed) (ISBN 0324380585) West Federal Taxation Individual 2008 - William Hoffman (Test Bank) (31st ed) (ISBN 0324380585) West Federal Taxation: Taxation of Business Entities 2007 - James Smith (Solutions Manual) (10th ed) (ISBN 0324313950) West Federal Taxation: Taxation of Business Entities 2007 - James Smith (Test Bank) (10th ed) (ISBN 0324313950) West Federal Taxation: Taxation of Business Entities 2008 - James Smith (Solutions Manual) (11th ed) (ISBN 0324366655) West Federal Taxation: Taxation of Business Entities 2008 - James Smith (Test Bank) (11th ed) (ISBN 0324366655) West's Business Law - Kenneth W. Clarkson (10th ed) (ISBN 0324303904) Wireless Communications & Networks - William Stallings (2nd ed) (ISBN 0131918354) Writing and Speaking at Work: A Practical Guide for Business Communication - Edward P. Bailey (4th ed) (ISBN 0131881302) Your Attitude is Showing - Sharon Lund O'Neil (12th ed) (ISBN 0132429047) International Books Abnormal Psychology, First Canadian Edition - James N. Butcher (1st Ed) (ISBN-10: 0205702880) Accounting 1-26 - Charles Horngren (6th Ed) (ISBN-10: 0131248391) Accounting and Finance for Non-Specialists - Peter Atrill (6th Ed) (ISBN-10: 1408208040) Accounting for Canadian Colleges - Ted Palmer (5th Ed) (ISBN-10: 0321415531) Accounting for Non-Accounting Students - John R. Dyson (7th Ed) (ISBN-10: 0273709224) Accounting Information Systems: International Version - Marshall B. Romney (11th Ed) (ISBN-10: 0135009375) Accounting International Version (Ch. 1-23) - Charles T. Horngren (8th Ed) (ISBN-10: 0136112900) Accounting Volume 1 Canadian Edition - Charles T. Horngren (7th Ed) (ISBN-10: 0132067331) Accounting Volume 2 Canadian Edition - Charles T. Horngren (7th Ed) (ISBN-10: 013206734X) Accounting Volume 3 Canadian Edition - Charles T. Horngren (7th Ed) (ISBN-10: 0132067358) Accounting: An Introduction - Peter Atrill (4th Ed) (ISBN-10: 1405893249) Advanced Accounting - Floyd Beams (9th Ed) (ISBN-10: 0131851225) Advanced Accounting: International Version - Floyd A. Beams (10th Ed) (ISBN-10: 0131358057) Advanced Financial Accounting - Richard Lewis (7th Ed) (ISBN-10: 0273658492) Advanced Financial Accounting - Thomas H. Beechy (5th Ed) (ISBN-10: 0131236997) Aging in Contemporary Canada - Neena L. Chappell (2nd Ed) (ISBN-10: 013201873X) Auditing and Assurance Services Global Edition - Alvin Arens (13th Ed) (ISBN-10: 0132458934) Auditing and Other Assurance Services Canadian Edition - Alvin A. Arens (10th Ed) (ISBN-10: 0131296159) Auditing Cases: International Edition - Mark S Beasley (4th Ed) (ISBN-10: 013608415X) Auditing: An International Approach - Bahram Soltani (1st Ed) (ISBN-10: 0273657739) Bond Markets, Analysis, and Strategies: International Edition - Frank J Fabozzi (7th Ed) (ISBN-10: 0136099742) Book-keeping and Accounts - Frank Wood (7th Ed) (ISBN-10: 0273718053) Business Accounting UK GAAP Volume 1 - Alan Sangster (1st Ed) (ISBN-10: 0273718762) Business Accounting UK GAAP Volume 2 - Alan Sangster (1st Ed) (ISBN-10: 0273718800) Business Accounting Volume 1 - F. Wood (10th Ed) (ISBN-10: 0273681494) Business Accounting Volume 1 - Frank Wood (11th Ed) (ISBN-10: 0273712128) Business Accounting Volume 2 - F. Wood (10th Ed) (ISBN-10: 0273693107) Business Accounting Volume 2 - Frank Wood (11th Ed) (ISBN-10: 0273712136) Business Canadian Edition - Ricky W. Griffin (6th Ed) (ISBN-10: 0131734296) Business Communication Essentials, Second Canadian Edition - Courtland L. Bovee (2nd Ed) (ISBN-10: 0132462346) Business Forecasting: International Edition - John E. Hanke (9th Ed) (ISBN-10: 0135009332) Business Law in Canada - Richard A. Yates (8th Ed) (ISBN-10: 0132065487) Business Law in Canada - Richard A. Yates (7th Ed) (ISBN-10: 0131206826) Business Law in Canada Casebook - D'Anne Davis (4th Ed) (ISBN-10: 0131225707) Canadian Industrial Relations - Jon Peirce (3rd Ed) (ISBN-10: 0131277936) Canadian Macroeconomics: Problems and Policies - Brian Lyons (8th Ed) (ISBN-10: 0131982966) Canadian Macroeconomics: Problems and Policies - Brian Lyons (8th Ed) (ISBN-10: 0131982966) Canadian Marketing in Action - Keith J. Tuckwell (7th Ed) (ISBN-10: 0131277790) Canadian Microeconomics: Problems and Policies - Brian Lyons (8th Ed) (ISBN-10: 0131982974) Canadian Microeconomics: Problems and Policies - Brian Lyons (8th Ed) (ISBN-10: 0131982974) Capital Markets: Institutions and Instruments: International Edition - Frank J Fabozzi (4th Ed) (ISBN-10: 0137154992) Cases in Financial Reporting - D. Eric Hirst (5th Ed) (ISBN-10: 0131881205) College Accounting: A Practical Approach Canadian Edition - Jeffrey Slater (9th Ed) (ISBN-10: 0131278177) Comparative International Accounting - Christopher Nobes (10th Ed) (ISBN-10: 0273714767) Concepts In Systems and Signals - John D. Sherrick (2nd Ed) (ISBN-10: 0131782711) Consumer Behaviour - Leon G. Schiffman (1st Ed) (ISBN-10: 0131463047) Consumer Behaviour: Buying, Having, and Being - Michael R. Solomon (4th Ed) (ISBN-10: 0132072874) Contemporary Business Mathematics with Canadian Applications - S. A. Hummelbrunner (8th Ed) (ISBN-10: 0136156088) Corporate Accounting Information Systems - Tony Boczko (1st Ed) (ISBN-10: 0273684876) Corporate Finance: International Edition - Jonathan Berk (1st Ed) (ISBN-10: 1408215039) Cost Accounting: A Managerial Emphasis Canadian Edition - Charles Horngren (3rd Ed) (ISBN-10: 0130355801) Cost Accounting: A Managerial Emphasis Canadian Edition - Charles Horngren (4th Ed) (ISBN-10: 0131971905) Cost Benefit Analysis: Concepts and Practice: International Edition - Anthony Boardman (3rd Ed) (ISBN-10: 0132405601) Economics - Christopher T.S. Ragan (12th Ed) (ISBN-10: 0321469003) Economics of Health and Health Care: International Edition - Sherman Folland (5th Ed) (ISBN-10: 0132342529) Essentials of Corporate Financial Management - Glen Arnold (1st Ed) (ISBN-10: 1405847042) Essentials of Statistics: International Edition - Mario F. Triola (3rd Ed) (ISBN-10: 0321484096) Estimating in Building Construction - Frank R. Dagostino (2nd Ed) (ISBN-10: 0132231379) Ethics in Action: Making Ethical Decisions in Your Daily Life - Jane Ann McLachlan (1st Ed) (ISBN-10: 0135041406) Financial Accounting - Charles Horngren (6th Ed) (ISBN-10: 0131499459) Financial Accounting - Jane Reimers (1st Ed) (ISBN-10: 0131492012) Financial Accounting and Financial Tips - Walter T. Harrison (7th Ed) (ISBN-10: 0135012848) Financial Accounting Canadian Edition - Walter T. Harrison (2nd Ed) (ISBN-10: 0131879294) Financial Accounting Canadian Edition with MyAccountingLab - Walter T. Harrison (2nd Ed) (ISBN-10: 0135146607) Financial Accounting Theory - William R. Scott (4th Ed) (ISBN-10: 0131294911) Financial Accounting Theory - William Scott (5th Ed) (ISBN-10: 0132072866) Financial Accounting, Reporting & Analysis - Barry Elliott (2nd Ed) (ISBN-10: 027370253X) Financial Accounting: An International Approach - Jagdish Kothari (1st Ed) (ISBN-10: 0273693190) Financial Accounting: An International Introduction - David Alexander (2nd Ed) (ISBN-10: 0273685201) Financial Accounting: An International Introduction - David Alexander (3rd Ed) (ISBN-10: 0273709267) Financial Accounting: An Introduction - Augustine Benedict (1st Ed) (ISBN-10: 0273688855) Financial Accounting: An Introduction - Pauline Weetman (4th Ed) (ISBN-10: 0273703404) Financial and Management Accounting - Pauline Weetman (4th Ed) (ISBN-10: 0273703692) Financial and Managerial Accounting - Meg Pollard (1st Ed) (ISBN-10: 0136008984) Financial and Managerial Accounting International Version (Ch. 1-23) - Charles T. Horngren (2nd Ed) (ISBN-10: 0137008457) Financial Economics: International Edition - Zvi Bodie (2nd Ed) (ISBN-10: 0131579525) Financial Management for Decision Makers - Peter Atrill (5th Ed) (ISBN-10: 0273717642) Financial Management for Public, Health, and Not-for-Profit: International Version - Steven A Finkler (3rd Ed) (ISBN-10: 0138152772) Financial Management: Principles and Practice - Timothy J. Gallagher (1st Ed) (ISBN-10: 0131245678) Financial Reporting and Analysis - Lawrence Revsine (3rd Ed) (ISBN-10: 0131430211) First Course in Probability, A: International Edition - Sheldon Ross (7th Ed) (ISBN-10: 0132018179) First Course in Probability, A: International Edition - Sheldon Ross (7th Ed) (ISBN-10: 0132018179) Foundations of Financial Markets and Institutions: International Edition - Frank J. Fabozzi (4th Ed) (ISBN-10: 013135423X) Foundations of Operations Management - Larry P. Ritzman (2nd Ed) (ISBN-10: 0132279312) Fundamentals of Corporate Finance: Global Edition - Jonathan Berk (1st Ed) (ISBN-10: 0137000774) Fundamentals of Financial Management - J. Van Horne (13th Ed) (ISBN-10: 0273713639) Fundamentals of Management Canadian Edition - Stephen P. Robbins (5th Ed) (ISBN-10: 0131988794) Fundamentals of Organizational Behaviour - Nancy Langton (3rd Ed) (ISBN-10: 0131757377) Governmental and Nonprofit Accounting: International Version - Robert J. Freeman (9th Ed) (ISBN-10: 0135031664) Health Economics: International Edition - Charles E. Phelps (4th Ed) (ISBN-10: 0321642902) Health: The Basics Canadian Edition - Rebecca J. Donatelle (4th Ed) (ISBN-10: 0205535585) Human Resources Management in Canada - Gary Dessler (10th Ed) (ISBN-10: 0132270870) Lipczynski (2nd Ed) (ISBN-10: 0273688022) Information Systems Today: Why IS Matters - Leonard Jessup (2nd Ed) (ISBN-10: 0131740393) International Accounting: International Edition - Frederick Choi (5th Ed) (ISBN-10: 0131293575) International Economics: International Edition - W. Charles Sawyer (3rd Ed) (ISBN-10: 0132089971) International Economics:Theory and Policy: International Edition - Paul R. Krugman (8th Ed) (ISBN-10: 1408208075) International Financial Management: International Edition - Geert Bekaert (1st Ed) (ISBN-10: 0136054900) Interpreting and Analyzing Financial Statement - Karen P. Schoenebeck (4th Ed) (ISBN-10: 0132391902) Introduction to Cryptography with Coding Theory: International Edition - Wade Trappe (2nd Ed) (ISBN-10: 0131981994) Introduction to Econometrics: International Edition - James H. Stock (2nd Ed) (ISBN-10: 0321442539) Introduction to Financial Accounting: International Edition - Charles Horngren (9th Ed) (ISBN-10: 0131968750) Introduction to Government and Non-for-Profit Accounting: International Edition - Martin Ives (6th Ed) (ISBN-10: 0132074281) Introduction to Management Accounting - Charles T. Horngren (14th Ed) (ISBN-10: 0136129218) Introduction to Microsoft Dynamics GP 10.0: Focus on Internal Controls - Terri J. Brunsdon (2nd Ed) (ISBN-10: 0136098045) Introduction to Optics: International Edition - Frank Pedrotti et al. (3rd Ed) (ISBN-10: 0131971336) Introduction to Quantum Mechanics: International Edition - David J. Griffiths (2nd Ed) (ISBN-10: 0131911759) Law and Economics: International Edition - Robert D. Cooter (5th Ed) (ISBN-10: 0321522907) Legal Fundamentals for Canadian Business - Richard A. Yates (1st Ed) (ISBN-10: 0131273787) Legal Terminology - Gordon W. Brown (5th Ed) (ISBN-10: 0131568043) Macroeconomics - Andrew B. Abel (4th Ed) (ISBN-10: 0321306627) Macroeconomics - Christopher T.S. Ragan (12th Ed) (ISBN-10: 0321468988) Macroeconomics: International Version - Olivier Blanchard (5th Ed) (ISBN-10: 0132079631) Management Accounting - Anthony A. Atkinson (5th Ed) (ISBN-10: 0136005314) Management Accounting - Charles T. Horngren (5th Ed) (ISBN-10: 0131922688) Management Accounting - Pauline Weetman (1st Ed) (ISBN-10: 0273701991) Management Accounting: Analysis and Interpretation - Cheryl McWatters (1st Ed) (ISBN-10: 0273712470) Management Information Systems: Managing the Digital Firm - Kenneth C. Laudon (3rd Ed) (ISBN-10: 0131973886) Managerial Accounting - Linda S. Bamber (1st Ed) (ISBN-10: 0138129711) Managerial Accounting for Business Decisions - Ray Proctor (3rd Ed) (ISBN-10: 0273717553) Managerial Economics: International Edition - Paul Keat (6th Ed) (ISBN-10: 0135070651) Managing the Law: The Legal Aspects of Doing Business - Mitchell McInnes (2nd Ed) (ISBN-10: 0132042762) Mathematics of Finance with Canadian Applications - S. A. Hummelbrunner (1st Ed) (ISBN-10: 0132073501) Mathematics of Finance with Canadian Applications - S. A. Hummelbrunner (6th Ed) (ISBN-10: 0132073501) Microeconomics - Christopher T.S. Ragan (12th Ed) (ISBN-10: 0321468996) Microeconomics - Saul Estrin (5th Ed) (ISBN-10: 0273646273) Microeconomics: International Edition - Robert Pindyck (7th Ed) (ISBN-10: 0137133359) Modern Labor Economics: Theory and Public Policy: International Edition - Ronald G. Ehrenberg (10th Ed) (ISBN-10: 032153896X) Organizational Behaviour: Concepts, Controversies, Applications - Nancy Langton (4th Ed) (ISBN-10: 0131971107) Organizational Theory, Design, and Change - Gareth R. Jones (1st Ed) (ISBN-10: 0131245228) Personal Finance for Canadians - Elliot J. Currie (9th Ed) (ISBN-10: 0132286750) Principles of Accounting - Meg Pollard (1st Ed) (ISBN-10: 0132304791) Principles of Auditing: An Introduction to International Standards on Auditing - Rick Hayes (2nd Ed) (ISBN-10: 0273684108) Principles of Marketing Canadian Edition - Philip Kotler (7th Ed) (ISBN-10: 0132020017) Principles of Marketing European Edition - Philip Kotler (5th Ed) (ISBN-10: 0273720643) Probability & Statistics for Engineers & Scientists - Ronald E. Walpole (8th Ed) (ISBN-10: 0132047675) Psychology Canadian Edition - Saundra Ciccarelli (1st Ed) (ISBN-10: 0138152160) Selling Today - Gerald L. Manning (4th Ed) (ISBN-10: 0131275992) Society: The Basics Canadian Edition - John J. Macionis (4th Ed) (ISBN-10: 0132057913) Statistics for Economics, Accounting & Business Studies - Michael Barrow (5th Ed) (ISBN-10: 0273717987) Statistics: International Edition - James McClave (10th Ed) (ISBN-10: Survey of Accounting: Making Sense of Business - Katherene P. Terrell (1st Ed) (ISBN-10: 0130911844) Technical Communication Canadian Edition - William S. Pfeiffer (4th Ed) (ISBN-10: 0131962930) The Canadian Criminal Justice System - Thomas Fleming (2nd Ed) (ISBN-10: 0131992465) The Economics of Money, Banking, and Financial Markets Canadian Edition - F. S. Mishkin (3rd Ed) (ISBN-10: 032142395X) The Law and Business Administration in Canada - J. E. Smyth (11th Ed) (ISBN-10: 0132042754) The Practice of Market Research: An Introduction - Yvonne Mcgivern (3rd Ed) (ISBN-10: 0273717073) Thomas' Calculus: International Edition - George B. Thomas, Jr (11th Ed) (ISBN-10: 0321243358) Understanding Financial Statements - Lyn M. Fraser (8th Ed) (ISBN-10: 0131878565) Understanding Financial Statements: International Edition (9th Ed) (ISBN-10: 0138153272) Using QuickBooks Pro 2005 for Windows - M. Purbhoo (1st Ed) (ISBN-10: 0321243307) === Subject: Analysis- With an Introduction to Proof, 4-E-Instructors Solution Manual is available for purchase! Contact me at instructors.team[at]gmail.com posting-account=WMGg9woAAAB3bYTClCVTyzuu-K8I_Byc Gecko/2009051221 Firefox/3.0.10,gzip(gfe),gzip(gfe) Analysis- With an Introduction to Proof, 4-E-Instructors Solution Manual is available for purchase! Contact me at instructors.team[at] gmail.com === Subject: Solution manuals and test bank posting-account=WMGg9woAAAB3bYTClCVTyzuu-K8I_Byc Gecko/2009051221 Firefox/3.0.10,gzip(gfe),gzip(gfe) Deitel &Deitel How to Program C++ 6th Edition ch 1-22 Code solutions contact instructors.team[at]gmail.com === Subject: Operations Management 9th Edition Jay Heizer Instructors Solution Manual and test bank is available for purchase! Contact me at instructors.team[at]gmail.com posting-account=WMGg9woAAAB3bYTClCVTyzuu-K8I_Byc Gecko/2009051221 Firefox/3.0.10,gzip(gfe),gzip(gfe) Operations Management 9th Edition Jay Heizer Instructors Solution Manual and test bank is available for purchase! Contact me at instructors.team[at]gmail.com === Subject: International Economics Theory and Policy 8E Krugman Obstfeld Instructors Solution Manual is available for purchase! Contact me at instructors.team[at]gmail.com posting-account=WMGg9woAAAB3bYTClCVTyzuu-K8I_Byc Gecko/2009051221 Firefox/3.0.10,gzip(gfe),gzip(gfe) International Economics Theory and Policy 8E Krugman Obstfeld Instructors Solution Manual is available for purchase! Contact me at instructors.team[at]gmail.com === Subject: =?windows-1252?Q?2009_Federal_Taxation_=2D_Pratt_=96_Solutions_Manual_=26?= =?windows-1252?Q?_test_Bank_is_available_for_purchase=21_Contact_me_at_instr u ct?= =?windows-1252?Q?ors=2Eteam=5Bat=5Dgmail=2Ecom?= posting-account=WMGg9woAAAB3bYTClCVTyzuu-K8I_Byc Gecko/2009051221 Firefox/3.0.10,gzip(gfe),gzip(gfe) 2009 Federal Taxation - Pratt [CapitalEth] Solutions Manual & test Bank is available for purchase! Contact me at instructors.team[at]gmail.com === Subject: =?windows-1252?Q?Principles_Of_Operations_Management_=286thEd=29_=2D_Heizer? = =?windows-1252?Q?_=96_Test_Bank_is_available_for_purchase=21_Contact_me_at_i n st?= =?windows-1252?Q?ructors=2Eteam=5Bat=5Dgmail=2Ecom?= posting-account=WMGg9woAAAB3bYTClCVTyzuu-K8I_Byc Gecko/2009051221 Firefox/3.0.10,gzip(gfe),gzip(gfe) Principles Of Operations Management (6thEd) - Heizer [CapitalEth] Test Bank is available for purchase! Contact me at instructors.team[at]gmail.com === Subject: accounting information systems 11th edition, romney, steinbart TEST BANK posting-account=v8NCmQkAAACB4IvJvLNgwxUPNbyAq_lC CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn't on the list, don't worry, please email to 1. A First Course in Probability, (7th), By Sheldon Ross .81iSOLUTIONS MANUAL.81j 2. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 3. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 4. Accounting Information Systems 10th ED by Marshall B Romney and Paul J Steinbart SOLUTIONS MANUAL 5. accounting information systems 11th edition, romney, steinbart TEST BANK 6. Accounting what number means 8e by Marshall SOLUTIONS MANUAL 7. Advanced Accounting 9e Beams SOLUTIONS MANUAL 8. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank 9. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik .81iSOLUTIONS MANUAL.81j 10. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin solution manual 11. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin test bank 12. Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd .81iSOLUTIONS MANUAL.81j 13. Auditing and Assurance Services 12 th by: Alvin A Arens, .81iSOLUTIONS MANUAL.81j 14. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual 15. Biology Concepts and Connections 6e Neil A. Campbell Jane B. Reece Martha R. Taylor Eric J. Simon Jean L. Dickey test bank 16. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz instructor manual 17. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank 18. Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson 19. Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) ( solutions manual) 20. COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING FOR PERFOR MANCE 21. Corporate Finance A Focused Approach 3e Brigham TEST BANK 22. Corporate Finance plus MyFinanceLab Student Access 23. Corporate finance: Custom edition. Berk, J., & DeMarzo, P. (2007). Boston : Pearson Education 24. cost accounting 12e Horngren SOLUTIONS MANUAL 25. cost Accounting 13e Horngren test bank 26. Cost Accounting A Managerial Emphasis by Charles T. Horngren 13th .81iSOLUTIONS MANUAL.81j 27. Cost Accounting: Foundations and Evolutions 7E By Kinney (SOLUTIONS MANUAL) 28. Data and Computer Communications, 8th Edition By Stallings .81iSOLUTIONS MANUAL.81j 29. Database System Concepts, Fifth Edition by Avi Silberschatz ,Henry F. Korth solutions to exercises? 30. Database Systems: The Complete Book, 2/E Solutions Manual 31. Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) Instructor manual 32. Differential Equations and Linear Algebra by Penney and Edwards, 2nd .81iSOLUTIONS MANUAL.81j 33. Differential Equations Computing and Modeling (4th Edition) By Edwards .81iSOLUTIONS MANUAL.81j 34. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley .81iSOLUTIONS MANUAL.81j 35. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 36. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 37. Elementary Differential Equations and Boundary Value Problems, 8th by Boyce and Diprima .81iSOLUTIONS MANUAL.81j 38. Elements of engineering electromagnetics (6/ e) by N.N.RAO .81iSOLUTIONS MANUAL.81j 39. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost TEST BANK 40. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost.81iTEST BANK.81j 41. Engineering and Chemical Thermodynamics by Milo D. Koretsky .81iSOLUTIONS MANUAL.81j 42. Engineering Circuit Analysis 7Ed William Hart Hayt .81iSOLUTIONS MANUAL.81j 43. Engineering Economy - Leland Blank & Anthony Tarquin 6th Editionselected solutions ( student solution) 44. Engineering electromagnetics (7/ e) by HAYT .81iSOLUTIONS MANUAL.81j 45. Engineering Fluid Mechanics, 7th, By Clayfor n T. Crowe, Donald F. Elger, John A. Roberson .81iSOLUTIONS MANUAL.81j 46. Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, .81iSOLUTIONS MANUAL.81j MANUAL.81j 48. ENGINEERING MECHANICS: statics by BEDFOR D 5th. .81iSOLUTIONS MANUAL.81j 49. Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus test bank 50. Essentials of Managerial Finance 14e Besley Instructor manual 51. Essentials of Managerial Finance with Thomson ONE, 13e Brigham SOLUTIONS MANUAL 52. Essentials of Managerial Finance with Thomson ONE, 13e Brigham TEST BANK 53. Financial Account 7e Horngren (SOLUTIONS MANUAL) 54. Financial Account 7e Horngren TEST BANK 55. Financial Accounting (Libby, fifth edition) .81iSOLUTIONS MANUAL.81j 56. Financial Accounting 6e by horngren Harrison .81iSOLUTIONS MANUAL.81j 57. Financial Accounting (Libby, 2001 edition) .81iSOLUTIONS MANUAL.81j 58. Financial and Mangerial Accounting 2e by Horngren (SOLUTIONS MANUAL) 59. Financial and Mangerial Accounting 2e by Horngren (TEST BANK) 60. Financial and Mangerial Accounting 2e by Horngren .81iSOLUTIONS MANUAL.81j 61. Financial management theory and practice 12e by Brigham .81iSOLUTIONS MANUAL.81j 62. Finiancial Accounting 7e by Horngren.81iSOLUTIONS MANUAL.81j 63. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL 64. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta solution manual 65. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(TEST BANK) 66. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(SOLUTIONS MANUAL) 67. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta test bank 68. Fundamental Methods Of Mathematical Economics Chiang & Wainwright 2005 Mc Graw Hill (Instructor's Manual ) 69. Fundamentals of Advanced Accounting 3rd Edition by Joe B. Hoyle, , andTimothy S. Doupnik .81iSOLUTIONS MANUAL.81j 70. Fundamentals of Applied Electromagnetics 5th by Fawwaz T. Ulaby .81iSOLUTIONS MANUAL.81j 71. Fundamentals of Classical Thermodynamics 6th edition by Van Wylen .81iSOLUTIONS MANUAL.81j 72. Fundamentals of Corporate Finance ( Ross, Westerfield, Jordan 8th) .81iSOLUTIONS MANUAL.81j 73. Fundamentals of Engineering Thermodynamics 6th by Michael J. Moran, Howard N. Shapiro .81iSOLUTIONS MANUAL.81j 74. Fundamentals of financial management 12e Brigham .81iSOLUTIONS MANUAL.81j 75. Fundamentals of financial management 12e Brigham Solutions manual 76. Fundamentals of financial management 12e Brigham TEST BANK 77. Fundamentals of Financial Management With Infotrac Concise 4th by Eugene Brigham .81iSOLUTIONS MANUAL.81j 78. Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 79. Fundamentals of Fluid Mechanics, 6th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 80. Fundamentals of Physics (8th Edition) By Halliday .81iSOLUTIONS MANUAL.81j 81. Fundamentals of Signals and systems using web and matlab third edition .81iSOLUTIONS MANUAL.81j 82. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, .81iSOLUTIONS MANUAL.81j 83. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, SOLUTIONS MANUAL 84. fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine (SOLUTIONS MANUAL) 85. Gravity: An Introduction to Einstein's General Relativity by James B. Hartle 86. Individual Income Taxes 2009 edition by Hoffman/Solutions manualyith/Willis (TEST BANK) 87. Instructor manual for Digital Fundamentals (10th Edition) floyd (IM) 88. Intermediata Accounting 13e Kieso SOLUTIONS MANUAL 89. Intermediata Accounting 13e Kieso TEST BANK 90. intermediate accounting 5e by spiceland solutions manual 91. International Financial Management Geert Bekaert Robert J. Hodrick test bank 92. Introduction for Chemical Engineering Thermodynamics 7th By J.M. Solutions manualith, Hendrick C Van Ness .81iSOLUTIONS MANUAL.81j 93. Introduction for Environmental engineering and science 3rd editions by Gilbert M. Masters .81iSOLUTIONS MANUAL.81j 94. Introduction for Fluid Mechanics, 7th, Fox, Pritchard, McDonald {Wiley} .81iSOLUTIONS MANUAL.81j 95. Introduction for Mathematical Statistics 6/ E Robert V. Hogg 96. Introduction for Quantum Mechanics (1 & 2 Edition), By David J. Griffiths .81iSOLUTIONS MANUAL.81j 97. Introduction to Chemical Engineering Thermodynamics 7th edition (solution manual) By J.M. Solutions manualith, Hendrick C Van Ness 98. Introduction to Heat Transfer, 5th Edition Incropera, DeWitt, Bergman, Lavine.81iSOLUTIONS MANUAL.81j 99. Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593)( solutions manual) 100. Introduction to Managerial Accounting 2nd ed Brewer test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to 101. Introductory Econometrics for Finance(Chris Brooks 2002) .81iSOLUTIONS MANUAL.81j 102. Linear Algebra and Its Applications, 3rd Edition by: David C. Lay .81iSOLUTIONS MANUAL.81j 103. Linear Algebra with Applications 7th edition by Leon, SOLUTIONS MANUAL 104. Macroeconomics, 4E Olivier Blanchard instructor manual .81iSOLUTIONS MANUAL.81j 105. Macroeconomics, 5E Olivier Blanchard (instructor manual) 106. Macroeconomics, 5E Olivier Blanchard (test bank) 107. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E SOLUTIONS MANUAL 108. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E TEST BANK 109. Managerial Accounting 12e By Garrison Noreen SOLUTIONS MANUAL 110. Managerial Accounting 12e By Garrison Noreen .81iSOLUTIONS MANUAL.81j 111. managerial accounting 12th Edition by Garrison Noreen (TEST BANK) 112. Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson .81iSOLUTIONS MANUAL.81j 113. Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao .81iSOLUTIONS MANUAL.81j 114. Mechanics of Materials By R.C.Hibbeler 7th edition .81iSOLUTIONS MANUAL.81j 115. Mechanics of Materials by roy R. craig 2nd eddition solution manual 116. Mechanics of Materials, 7th James M. Gere - Stanfor d University .81iSOLUTIONS MANUAL.81j 117. Microeconomic Theory, Nicholson & Snyder, 10th ed, .81iSOLUTIONS MANUAL.81j 118. Microelectronic Circuit Analysis and Design, 3ed. by Donald A. Neamen .81iSOLUTIONS MANUAL.81j 119. Microelectronic circuits by R. Jaeger 3rd edition .81iSOLUTIONS MANUAL.81j 120. Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop .81iSOLUTIONS MANUAL.81j 121. Modern Elementary Statistics, 12/e by Freund & Perles .81iSOLUTIONS MANUAL.81j 122. Modern Elementary Statistics, 12/e Freund & Perles (TEST BANK) 123. Modern Physics, 2/E Randy Harris SOLUTIONS MANUAL 124. Numerical methods for engineers 5th by Chapra .81iSOLUTIONS MANUAL.81j 125. Operations Management 10e William J. Stevenson Solutions manual 126. Operations Management 10e William J. Stevenson TEST BANK 127. Operations Management 9e William J. Stevenson (SOLUTIONS MANUAL) 128. Organizational Behaviour, Fourth Canadian Ed., 4E Robins TEST BANK 129. Power System Analysis By John J. Grainger, William D. Stevenson Jr .81iSOLUTIONS MANUAL.81j 130. Principles of Auditing 15e by Whittington TEST BANK 131. Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole .81iSOLUTIONS MANUAL.81j 132. Probability and Statistical Inference 7th edition, Hogg & Tanis .81iSOLUTIONS MANUAL.81j 133. Probability, Statistics, and Random Processes For Electrical Engineering - Alberfor Leon-Garcia (3rd ) .81iSOLUTIONS MANUAL.81j 134. Probability,Random Variables and Stor hastic Processes,4th,by Athanasios Papoulis .81iSOLUTIONS MANUAL.81j 135. Process Systems Analysis And Control - Donald R. Coughanowr Solution Manual .81iSOLUTIONS MANUAL.81j 136. Separation Process Engineering: 2e by wankat SOLUTIONS MANUAL 137. Separation Process Principles, 2nd Ed.,by Seader, Henley .81iSOLUTIONS MANUAL.81j 138. solutions manual for Advanced Accounting 10e Fisher 139. solutions manual for Corporate Finance: A Focused Approach 3e Brigham 140. solutions manual for Advanced Accounting 10th edition by Beams 141. solutions manual for Essential of Accounting for Governmental and Not-for- Profit Organizations By Paul A Copley, 9e 142. solutions manual for Modern Advanced Accounting 10th edition by Larsen - 10e SM 143. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 144. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 145. solutions manual fundamentals of financial management, concise 6th edition by Brigham, Houston 146. South-Western Federal Taxation 2009 (Individual), 32th, Hoffman, Smith, Wills (Test Bank + solution manual) 147. Test Bank for Auditing and Assurance Services: A Systematic Approach, 6th Edition, Messier, Glover, Prawitt 148. Test Bank for Advanced Accounting 10e Fisher 149. test bank for Operations Management 9e William J. Stevenson (TB) 150. Test Bank for Accounting Information Systems - James Hall (6th ed) 151. Test bank for Advanced Accounting 10th edition by Beams 152. Test Bank for fundamentals of financial management, concise 6th edition by Brigham, Houston 153. Test bank for Modern Advanced Accounting 10th edition by Larsen - 10e TB 154. test bank cost Accounting 12e by Horngren 155. Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition .81iSOLUTIONS MANUAL.81j 156. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston test bank 157. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston solutions manual 158. Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Solutions manualith .81iSOLUTIONS MANUAL.81j Edition ,By F. P. Beer, E. R. Johnsfor n .81iSOLUTIONS MANUAL.81j 160. Fundamentals of Machine Component Design, 3rd ed - Student Solutions Manual by Juvinall, Marshek 161. Fundamentals of manufacturing 2nd edition by philip d. rufe solutions manual 162. Fundamentals of Momentum, Heat and Mass Transfer, 5th Edition Welty, Wicks, Rorrer, Wilson 163. Fundamentals of Multinational Finance, 2nd edition by Michael H. Moffett test bank and solution manual 164. Fundamentals of Multinational Finance, 3E by Michael H. Moffett (Instructor's Manual) 165. Fundamentals of Multinational Finance, 3E by Michael H. Moffett test bank 166. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith sm 167. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith tb 168. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith instructor manual 169. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith tb 170. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith sm 171. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow sm 172. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow tb 173. Human resources management 10e Gary dessler (IM+TB) 174. Intermediate Accounting 10e by Nikolai sm 175. Intermediate Accounting 11e by Kieso 176. Intermediate Accounting 12e by Kieso 177. Intermediate accounting 12th Updated by Kieso Solution manual 178. Intermediate accounting 12th Updated by Kieso test bank 179. Intermediate Accounting, 13th Edition Instructor's Manual Kieso, Weygandt, Warfield 180. (Sm+TB+IM) 181. Intermediate Accounting 2e by Baruch Englard 182. Intermediate Accounting 3e by J. David Spiceland 183. Intermediate Accounting 4e revised by J. David Spiceland solution manual 184. Intermediate accounting by Spiceland 4e Solution manual 185. Intermediate Accounting James D. Stice, Earl K. Stice, Fred Skousen 16th edition solution manual 186. Intermediate Accounting, 13th Edition Kieso, Weygandt, Warfield test bank and solution manual 187. Intermediate Accounting, Update, 12th Edition international student solution manual 188. Intermediate Algebra Functions & Authentic Applications 3e lehmann 189. Intermediate Algebra, 8th Edition By Margaret L. Lial, John Hornsby, Terry McGinnis 190. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves instructor manual 191. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves test bank 192. Intermediate Microeconomics, 10th Edition Walter Nicholson ,Christopher Snyder im with tb 193. International Accounting 1e by Doupnik solution manual 194. International Accounting 6e Frederick D. Choi Gary K. Meek 195. International Business The Challenges of Globalization, 4E John J. Wild,Kenneth L. Wild tb and im 196. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan instructor manual 197. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to me.,too. I can find it for === Subject: Accounting what number means 8e by Marshall SOLUTIONS MANUAL posting-account=v8NCmQkAAACB4IvJvLNgwxUPNbyAq_lC CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn't on the list, don't worry, please email to 1. A First Course in Probability, (7th), By Sheldon Ross .81iSOLUTIONS MANUAL.81j 2. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 3. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 4. Accounting Information Systems 10th ED by Marshall B Romney and Paul J Steinbart SOLUTIONS MANUAL 5. accounting information systems 11th edition, romney, steinbart TEST BANK 6. Accounting what number means 8e by Marshall SOLUTIONS MANUAL 7. Advanced Accounting 9e Beams SOLUTIONS MANUAL 8. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank 9. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik .81iSOLUTIONS MANUAL.81j 10. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin solution manual 11. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin test bank 12. Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd .81iSOLUTIONS MANUAL.81j 13. Auditing and Assurance Services 12 th by: Alvin A Arens, .81iSOLUTIONS MANUAL.81j 14. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual 15. Biology Concepts and Connections 6e Neil A. Campbell Jane B. Reece Martha R. Taylor Eric J. Simon Jean L. Dickey test bank 16. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz instructor manual 17. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank 18. Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson 19. Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) ( solutions manual) 20. COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING FOR PERFOR MANCE 21. Corporate Finance A Focused Approach 3e Brigham TEST BANK 22. Corporate Finance plus MyFinanceLab Student Access 23. Corporate finance: Custom edition. Berk, J., & DeMarzo, P. (2007). Boston : Pearson Education 24. cost accounting 12e Horngren SOLUTIONS MANUAL 25. cost Accounting 13e Horngren test bank 26. Cost Accounting A Managerial Emphasis by Charles T. Horngren 13th .81iSOLUTIONS MANUAL.81j 27. Cost Accounting: Foundations and Evolutions 7E By Kinney (SOLUTIONS MANUAL) 28. Data and Computer Communications, 8th Edition By Stallings .81iSOLUTIONS MANUAL.81j 29. Database System Concepts, Fifth Edition by Avi Silberschatz ,Henry F. Korth solutions to exercises? 30. Database Systems: The Complete Book, 2/E Solutions Manual 31. Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) Instructor manual 32. Differential Equations and Linear Algebra by Penney and Edwards, 2nd .81iSOLUTIONS MANUAL.81j 33. Differential Equations Computing and Modeling (4th Edition) By Edwards .81iSOLUTIONS MANUAL.81j 34. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley .81iSOLUTIONS MANUAL.81j 35. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 36. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 37. Elementary Differential Equations and Boundary Value Problems, 8th by Boyce and Diprima .81iSOLUTIONS MANUAL.81j 38. Elements of engineering electromagnetics (6/ e) by N.N.RAO .81iSOLUTIONS MANUAL.81j 39. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost TEST BANK 40. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost.81iTEST BANK.81j 41. Engineering and Chemical Thermodynamics by Milo D. Koretsky .81iSOLUTIONS MANUAL.81j 42. Engineering Circuit Analysis 7Ed William Hart Hayt .81iSOLUTIONS MANUAL.81j 43. Engineering Economy - Leland Blank & Anthony Tarquin 6th Editionselected solutions ( student solution) 44. Engineering electromagnetics (7/ e) by HAYT .81iSOLUTIONS MANUAL.81j 45. Engineering Fluid Mechanics, 7th, By Clayfor n T. Crowe, Donald F. Elger, John A. Roberson .81iSOLUTIONS MANUAL.81j 46. Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, .81iSOLUTIONS MANUAL.81j MANUAL.81j 48. ENGINEERING MECHANICS: statics by BEDFOR D 5th. .81iSOLUTIONS MANUAL.81j 49. Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus test bank 50. Essentials of Managerial Finance 14e Besley Instructor manual 51. Essentials of Managerial Finance with Thomson ONE, 13e Brigham SOLUTIONS MANUAL 52. Essentials of Managerial Finance with Thomson ONE, 13e Brigham TEST BANK 53. Financial Account 7e Horngren (SOLUTIONS MANUAL) 54. Financial Account 7e Horngren TEST BANK 55. Financial Accounting (Libby, fifth edition) .81iSOLUTIONS MANUAL.81j 56. Financial Accounting 6e by horngren Harrison .81iSOLUTIONS MANUAL.81j 57. Financial Accounting (Libby, 2001 edition) .81iSOLUTIONS MANUAL.81j 58. Financial and Mangerial Accounting 2e by Horngren (SOLUTIONS MANUAL) 59. Financial and Mangerial Accounting 2e by Horngren (TEST BANK) 60. Financial and Mangerial Accounting 2e by Horngren .81iSOLUTIONS MANUAL.81j 61. Financial management theory and practice 12e by Brigham .81iSOLUTIONS MANUAL.81j 62. Finiancial Accounting 7e by Horngren.81iSOLUTIONS MANUAL.81j 63. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL 64. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta solution manual 65. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(TEST BANK) 66. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(SOLUTIONS MANUAL) 67. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta test bank 68. Fundamental Methods Of Mathematical Economics Chiang & Wainwright 2005 Mc Graw Hill (Instructor's Manual ) 69. Fundamentals of Advanced Accounting 3rd Edition by Joe B. Hoyle, , andTimothy S. Doupnik .81iSOLUTIONS MANUAL.81j 70. Fundamentals of Applied Electromagnetics 5th by Fawwaz T. Ulaby .81iSOLUTIONS MANUAL.81j 71. Fundamentals of Classical Thermodynamics 6th edition by Van Wylen .81iSOLUTIONS MANUAL.81j 72. Fundamentals of Corporate Finance ( Ross, Westerfield, Jordan 8th) .81iSOLUTIONS MANUAL.81j 73. Fundamentals of Engineering Thermodynamics 6th by Michael J. Moran, Howard N. Shapiro .81iSOLUTIONS MANUAL.81j 74. Fundamentals of financial management 12e Brigham .81iSOLUTIONS MANUAL.81j 75. Fundamentals of financial management 12e Brigham Solutions manual 76. Fundamentals of financial management 12e Brigham TEST BANK 77. Fundamentals of Financial Management With Infotrac Concise 4th by Eugene Brigham .81iSOLUTIONS MANUAL.81j 78. Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 79. Fundamentals of Fluid Mechanics, 6th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 80. Fundamentals of Physics (8th Edition) By Halliday .81iSOLUTIONS MANUAL.81j 81. Fundamentals of Signals and systems using web and matlab third edition .81iSOLUTIONS MANUAL.81j 82. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, .81iSOLUTIONS MANUAL.81j 83. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, SOLUTIONS MANUAL 84. fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine (SOLUTIONS MANUAL) 85. Gravity: An Introduction to Einstein's General Relativity by James B. Hartle 86. Individual Income Taxes 2009 edition by Hoffman/Solutions manualyith/Willis (TEST BANK) 87. Instructor manual for Digital Fundamentals (10th Edition) floyd (IM) 88. Intermediata Accounting 13e Kieso SOLUTIONS MANUAL 89. Intermediata Accounting 13e Kieso TEST BANK 90. intermediate accounting 5e by spiceland solutions manual 91. International Financial Management Geert Bekaert Robert J. Hodrick test bank 92. Introduction for Chemical Engineering Thermodynamics 7th By J.M. Solutions manualith, Hendrick C Van Ness .81iSOLUTIONS MANUAL.81j 93. Introduction for Environmental engineering and science 3rd editions by Gilbert M. Masters .81iSOLUTIONS MANUAL.81j 94. Introduction for Fluid Mechanics, 7th, Fox, Pritchard, McDonald {Wiley} .81iSOLUTIONS MANUAL.81j 95. Introduction for Mathematical Statistics 6/ E Robert V. Hogg 96. Introduction for Quantum Mechanics (1 & 2 Edition), By David J. Griffiths .81iSOLUTIONS MANUAL.81j 97. Introduction to Chemical Engineering Thermodynamics 7th edition (solution manual) By J.M. Solutions manualith, Hendrick C Van Ness 98. Introduction to Heat Transfer, 5th Edition Incropera, DeWitt, Bergman, Lavine.81iSOLUTIONS MANUAL.81j 99. Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593)( solutions manual) 100. Introduction to Managerial Accounting 2nd ed Brewer test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to 101. Introductory Econometrics for Finance(Chris Brooks 2002) .81iSOLUTIONS MANUAL.81j 102. Linear Algebra and Its Applications, 3rd Edition by: David C. Lay .81iSOLUTIONS MANUAL.81j 103. Linear Algebra with Applications 7th edition by Leon, SOLUTIONS MANUAL 104. Macroeconomics, 4E Olivier Blanchard instructor manual .81iSOLUTIONS MANUAL.81j 105. Macroeconomics, 5E Olivier Blanchard (instructor manual) 106. Macroeconomics, 5E Olivier Blanchard (test bank) 107. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E SOLUTIONS MANUAL 108. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E TEST BANK 109. Managerial Accounting 12e By Garrison Noreen SOLUTIONS MANUAL 110. Managerial Accounting 12e By Garrison Noreen .81iSOLUTIONS MANUAL.81j 111. managerial accounting 12th Edition by Garrison Noreen (TEST BANK) 112. Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson .81iSOLUTIONS MANUAL.81j 113. Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao .81iSOLUTIONS MANUAL.81j 114. Mechanics of Materials By R.C.Hibbeler 7th edition .81iSOLUTIONS MANUAL.81j 115. Mechanics of Materials by roy R. craig 2nd eddition solution manual 116. Mechanics of Materials, 7th James M. Gere - Stanfor d University .81iSOLUTIONS MANUAL.81j 117. Microeconomic Theory, Nicholson & Snyder, 10th ed, .81iSOLUTIONS MANUAL.81j 118. Microelectronic Circuit Analysis and Design, 3ed. by Donald A. Neamen .81iSOLUTIONS MANUAL.81j 119. Microelectronic circuits by R. Jaeger 3rd edition .81iSOLUTIONS MANUAL.81j 120. Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop .81iSOLUTIONS MANUAL.81j 121. Modern Elementary Statistics, 12/e by Freund & Perles .81iSOLUTIONS MANUAL.81j 122. Modern Elementary Statistics, 12/e Freund & Perles (TEST BANK) 123. Modern Physics, 2/E Randy Harris SOLUTIONS MANUAL 124. Numerical methods for engineers 5th by Chapra .81iSOLUTIONS MANUAL.81j 125. Operations Management 10e William J. Stevenson Solutions manual 126. Operations Management 10e William J. Stevenson TEST BANK 127. Operations Management 9e William J. Stevenson (SOLUTIONS MANUAL) 128. Organizational Behaviour, Fourth Canadian Ed., 4E Robins TEST BANK 129. Power System Analysis By John J. Grainger, William D. Stevenson Jr .81iSOLUTIONS MANUAL.81j 130. Principles of Auditing 15e by Whittington TEST BANK 131. Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole .81iSOLUTIONS MANUAL.81j 132. Probability and Statistical Inference 7th edition, Hogg & Tanis .81iSOLUTIONS MANUAL.81j 133. Probability, Statistics, and Random Processes For Electrical Engineering - Alberfor Leon-Garcia (3rd ) .81iSOLUTIONS MANUAL.81j 134. Probability,Random Variables and Stor hastic Processes,4th,by Athanasios Papoulis .81iSOLUTIONS MANUAL.81j 135. Process Systems Analysis And Control - Donald R. Coughanowr Solution Manual .81iSOLUTIONS MANUAL.81j 136. Separation Process Engineering: 2e by wankat SOLUTIONS MANUAL 137. Separation Process Principles, 2nd Ed.,by Seader, Henley .81iSOLUTIONS MANUAL.81j 138. solutions manual for Advanced Accounting 10e Fisher 139. solutions manual for Corporate Finance: A Focused Approach 3e Brigham 140. solutions manual for Advanced Accounting 10th edition by Beams 141. solutions manual for Essential of Accounting for Governmental and Not-for- Profit Organizations By Paul A Copley, 9e 142. solutions manual for Modern Advanced Accounting 10th edition by Larsen - 10e SM 143. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 144. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 145. solutions manual fundamentals of financial management, concise 6th edition by Brigham, Houston 146. South-Western Federal Taxation 2009 (Individual), 32th, Hoffman, Smith, Wills (Test Bank + solution manual) 147. Test Bank for Auditing and Assurance Services: A Systematic Approach, 6th Edition, Messier, Glover, Prawitt 148. Test Bank for Advanced Accounting 10e Fisher 149. test bank for Operations Management 9e William J. Stevenson (TB) 150. Test Bank for Accounting Information Systems - James Hall (6th ed) 151. Test bank for Advanced Accounting 10th edition by Beams 152. Test Bank for fundamentals of financial management, concise 6th edition by Brigham, Houston 153. Test bank for Modern Advanced Accounting 10th edition by Larsen - 10e TB 154. test bank cost Accounting 12e by Horngren 155. Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition .81iSOLUTIONS MANUAL.81j 156. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston test bank 157. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston solutions manual 158. Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Solutions manualith .81iSOLUTIONS MANUAL.81j Edition ,By F. P. Beer, E. R. Johnsfor n .81iSOLUTIONS MANUAL.81j 160. Fundamentals of Machine Component Design, 3rd ed - Student Solutions Manual by Juvinall, Marshek 161. Fundamentals of manufacturing 2nd edition by philip d. rufe solutions manual 162. Fundamentals of Momentum, Heat and Mass Transfer, 5th Edition Welty, Wicks, Rorrer, Wilson 163. Fundamentals of Multinational Finance, 2nd edition by Michael H. Moffett test bank and solution manual 164. Fundamentals of Multinational Finance, 3E by Michael H. Moffett (Instructor's Manual) 165. Fundamentals of Multinational Finance, 3E by Michael H. Moffett test bank 166. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith sm 167. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith tb 168. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith instructor manual 169. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith tb 170. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith sm 171. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow sm 172. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow tb 173. Human resources management 10e Gary dessler (IM+TB) 174. Intermediate Accounting 10e by Nikolai sm 175. Intermediate Accounting 11e by Kieso 176. Intermediate Accounting 12e by Kieso 177. Intermediate accounting 12th Updated by Kieso Solution manual 178. Intermediate accounting 12th Updated by Kieso test bank 179. Intermediate Accounting, 13th Edition Instructor's Manual Kieso, Weygandt, Warfield 180. (Sm+TB+IM) 181. Intermediate Accounting 2e by Baruch Englard 182. Intermediate Accounting 3e by J. David Spiceland 183. Intermediate Accounting 4e revised by J. David Spiceland solution manual 184. Intermediate accounting by Spiceland 4e Solution manual 185. Intermediate Accounting James D. Stice, Earl K. Stice, Fred Skousen 16th edition solution manual 186. Intermediate Accounting, 13th Edition Kieso, Weygandt, Warfield test bank and solution manual 187. Intermediate Accounting, Update, 12th Edition international student solution manual 188. Intermediate Algebra Functions & Authentic Applications 3e lehmann 189. Intermediate Algebra, 8th Edition By Margaret L. Lial, John Hornsby, Terry McGinnis 190. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves instructor manual 191. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves test bank 192. Intermediate Microeconomics, 10th Edition Walter Nicholson ,Christopher Snyder im with tb 193. International Accounting 1e by Doupnik solution manual 194. International Accounting 6e Frederick D. Choi Gary K. Meek 195. International Business The Challenges of Globalization, 4E John J. Wild,Kenneth L. Wild tb and im 196. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan instructor manual 197. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to me.,too. I can find it for === Subject: Advanced Accounting 9e Beams SOLUTIONS MANUAL posting-account=v8NCmQkAAACB4IvJvLNgwxUPNbyAq_lC CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn't on the list, don't worry, please email to 1. A First Course in Probability, (7th), By Sheldon Ross .81iSOLUTIONS MANUAL.81j 2. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 3. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 4. Accounting Information Systems 10th ED by Marshall B Romney and Paul J Steinbart SOLUTIONS MANUAL 5. accounting information systems 11th edition, romney, steinbart TEST BANK 6. Accounting what number means 8e by Marshall SOLUTIONS MANUAL 7. Advanced Accounting 9e Beams SOLUTIONS MANUAL 8. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank 9. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik .81iSOLUTIONS MANUAL.81j 10. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin solution manual 11. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin test bank 12. Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd .81iSOLUTIONS MANUAL.81j 13. Auditing and Assurance Services 12 th by: Alvin A Arens, .81iSOLUTIONS MANUAL.81j 14. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual 15. Biology Concepts and Connections 6e Neil A. Campbell Jane B. Reece Martha R. Taylor Eric J. Simon Jean L. Dickey test bank 16. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz instructor manual 17. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank 18. Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson 19. Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) ( solutions manual) 20. COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING FOR PERFOR MANCE 21. Corporate Finance A Focused Approach 3e Brigham TEST BANK 22. Corporate Finance plus MyFinanceLab Student Access 23. Corporate finance: Custom edition. Berk, J., & DeMarzo, P. (2007). Boston : Pearson Education 24. cost accounting 12e Horngren SOLUTIONS MANUAL 25. cost Accounting 13e Horngren test bank 26. Cost Accounting A Managerial Emphasis by Charles T. Horngren 13th .81iSOLUTIONS MANUAL.81j 27. Cost Accounting: Foundations and Evolutions 7E By Kinney (SOLUTIONS MANUAL) 28. Data and Computer Communications, 8th Edition By Stallings .81iSOLUTIONS MANUAL.81j 29. Database System Concepts, Fifth Edition by Avi Silberschatz ,Henry F. Korth solutions to exercises? 30. Database Systems: The Complete Book, 2/E Solutions Manual 31. Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) Instructor manual 32. Differential Equations and Linear Algebra by Penney and Edwards, 2nd .81iSOLUTIONS MANUAL.81j 33. Differential Equations Computing and Modeling (4th Edition) By Edwards .81iSOLUTIONS MANUAL.81j 34. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley .81iSOLUTIONS MANUAL.81j 35. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 36. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 37. Elementary Differential Equations and Boundary Value Problems, 8th by Boyce and Diprima .81iSOLUTIONS MANUAL.81j 38. Elements of engineering electromagnetics (6/ e) by N.N.RAO .81iSOLUTIONS MANUAL.81j 39. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost TEST BANK 40. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost.81iTEST BANK.81j 41. Engineering and Chemical Thermodynamics by Milo D. Koretsky .81iSOLUTIONS MANUAL.81j 42. Engineering Circuit Analysis 7Ed William Hart Hayt .81iSOLUTIONS MANUAL.81j 43. Engineering Economy - Leland Blank & Anthony Tarquin 6th Editionselected solutions ( student solution) 44. Engineering electromagnetics (7/ e) by HAYT .81iSOLUTIONS MANUAL.81j 45. Engineering Fluid Mechanics, 7th, By Clayfor n T. Crowe, Donald F. Elger, John A. Roberson .81iSOLUTIONS MANUAL.81j 46. Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, .81iSOLUTIONS MANUAL.81j MANUAL.81j 48. ENGINEERING MECHANICS: statics by BEDFOR D 5th. .81iSOLUTIONS MANUAL.81j 49. Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus test bank 50. Essentials of Managerial Finance 14e Besley Instructor manual 51. Essentials of Managerial Finance with Thomson ONE, 13e Brigham SOLUTIONS MANUAL 52. Essentials of Managerial Finance with Thomson ONE, 13e Brigham TEST BANK 53. Financial Account 7e Horngren (SOLUTIONS MANUAL) 54. Financial Account 7e Horngren TEST BANK 55. Financial Accounting (Libby, fifth edition) .81iSOLUTIONS MANUAL.81j 56. Financial Accounting 6e by horngren Harrison .81iSOLUTIONS MANUAL.81j 57. Financial Accounting (Libby, 2001 edition) .81iSOLUTIONS MANUAL.81j 58. Financial and Mangerial Accounting 2e by Horngren (SOLUTIONS MANUAL) 59. Financial and Mangerial Accounting 2e by Horngren (TEST BANK) 60. Financial and Mangerial Accounting 2e by Horngren .81iSOLUTIONS MANUAL.81j 61. Financial management theory and practice 12e by Brigham .81iSOLUTIONS MANUAL.81j 62. Finiancial Accounting 7e by Horngren.81iSOLUTIONS MANUAL.81j 63. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL 64. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta solution manual 65. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(TEST BANK) 66. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(SOLUTIONS MANUAL) 67. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta test bank 68. Fundamental Methods Of Mathematical Economics Chiang & Wainwright 2005 Mc Graw Hill (Instructor's Manual ) 69. Fundamentals of Advanced Accounting 3rd Edition by Joe B. Hoyle, , andTimothy S. Doupnik .81iSOLUTIONS MANUAL.81j 70. Fundamentals of Applied Electromagnetics 5th by Fawwaz T. Ulaby .81iSOLUTIONS MANUAL.81j 71. Fundamentals of Classical Thermodynamics 6th edition by Van Wylen .81iSOLUTIONS MANUAL.81j 72. Fundamentals of Corporate Finance ( Ross, Westerfield, Jordan 8th) .81iSOLUTIONS MANUAL.81j 73. Fundamentals of Engineering Thermodynamics 6th by Michael J. Moran, Howard N. Shapiro .81iSOLUTIONS MANUAL.81j 74. Fundamentals of financial management 12e Brigham .81iSOLUTIONS MANUAL.81j 75. Fundamentals of financial management 12e Brigham Solutions manual 76. Fundamentals of financial management 12e Brigham TEST BANK 77. Fundamentals of Financial Management With Infotrac Concise 4th by Eugene Brigham .81iSOLUTIONS MANUAL.81j 78. Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 79. Fundamentals of Fluid Mechanics, 6th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 80. Fundamentals of Physics (8th Edition) By Halliday .81iSOLUTIONS MANUAL.81j 81. Fundamentals of Signals and systems using web and matlab third edition .81iSOLUTIONS MANUAL.81j 82. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, .81iSOLUTIONS MANUAL.81j 83. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, SOLUTIONS MANUAL 84. fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine (SOLUTIONS MANUAL) 85. Gravity: An Introduction to Einstein's General Relativity by James B. Hartle 86. Individual Income Taxes 2009 edition by Hoffman/Solutions manualyith/Willis (TEST BANK) 87. Instructor manual for Digital Fundamentals (10th Edition) floyd (IM) 88. Intermediata Accounting 13e Kieso SOLUTIONS MANUAL 89. Intermediata Accounting 13e Kieso TEST BANK 90. intermediate accounting 5e by spiceland solutions manual 91. International Financial Management Geert Bekaert Robert J. Hodrick test bank 92. Introduction for Chemical Engineering Thermodynamics 7th By J.M. Solutions manualith, Hendrick C Van Ness .81iSOLUTIONS MANUAL.81j 93. Introduction for Environmental engineering and science 3rd editions by Gilbert M. Masters .81iSOLUTIONS MANUAL.81j 94. Introduction for Fluid Mechanics, 7th, Fox, Pritchard, McDonald {Wiley} .81iSOLUTIONS MANUAL.81j 95. Introduction for Mathematical Statistics 6/ E Robert V. Hogg 96. Introduction for Quantum Mechanics (1 & 2 Edition), By David J. Griffiths .81iSOLUTIONS MANUAL.81j 97. Introduction to Chemical Engineering Thermodynamics 7th edition (solution manual) By J.M. Solutions manualith, Hendrick C Van Ness 98. Introduction to Heat Transfer, 5th Edition Incropera, DeWitt, Bergman, Lavine.81iSOLUTIONS MANUAL.81j 99. Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593)( solutions manual) 100. Introduction to Managerial Accounting 2nd ed Brewer test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to 101. Introductory Econometrics for Finance(Chris Brooks 2002) .81iSOLUTIONS MANUAL.81j 102. Linear Algebra and Its Applications, 3rd Edition by: David C. Lay .81iSOLUTIONS MANUAL.81j 103. Linear Algebra with Applications 7th edition by Leon, SOLUTIONS MANUAL 104. Macroeconomics, 4E Olivier Blanchard instructor manual .81iSOLUTIONS MANUAL.81j 105. Macroeconomics, 5E Olivier Blanchard (instructor manual) 106. Macroeconomics, 5E Olivier Blanchard (test bank) 107. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E SOLUTIONS MANUAL 108. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E TEST BANK 109. Managerial Accounting 12e By Garrison Noreen SOLUTIONS MANUAL 110. Managerial Accounting 12e By Garrison Noreen .81iSOLUTIONS MANUAL.81j 111. managerial accounting 12th Edition by Garrison Noreen (TEST BANK) 112. Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson .81iSOLUTIONS MANUAL.81j 113. Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao .81iSOLUTIONS MANUAL.81j 114. Mechanics of Materials By R.C.Hibbeler 7th edition .81iSOLUTIONS MANUAL.81j 115. Mechanics of Materials by roy R. craig 2nd eddition solution manual 116. Mechanics of Materials, 7th James M. Gere - Stanfor d University .81iSOLUTIONS MANUAL.81j 117. Microeconomic Theory, Nicholson & Snyder, 10th ed, .81iSOLUTIONS MANUAL.81j 118. Microelectronic Circuit Analysis and Design, 3ed. by Donald A. Neamen .81iSOLUTIONS MANUAL.81j 119. Microelectronic circuits by R. Jaeger 3rd edition .81iSOLUTIONS MANUAL.81j 120. Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop .81iSOLUTIONS MANUAL.81j 121. Modern Elementary Statistics, 12/e by Freund & Perles .81iSOLUTIONS MANUAL.81j 122. Modern Elementary Statistics, 12/e Freund & Perles (TEST BANK) 123. Modern Physics, 2/E Randy Harris SOLUTIONS MANUAL 124. Numerical methods for engineers 5th by Chapra .81iSOLUTIONS MANUAL.81j 125. Operations Management 10e William J. Stevenson Solutions manual 126. Operations Management 10e William J. Stevenson TEST BANK 127. Operations Management 9e William J. Stevenson (SOLUTIONS MANUAL) 128. Organizational Behaviour, Fourth Canadian Ed., 4E Robins TEST BANK 129. Power System Analysis By John J. Grainger, William D. Stevenson Jr .81iSOLUTIONS MANUAL.81j 130. Principles of Auditing 15e by Whittington TEST BANK 131. Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole .81iSOLUTIONS MANUAL.81j 132. Probability and Statistical Inference 7th edition, Hogg & Tanis .81iSOLUTIONS MANUAL.81j 133. Probability, Statistics, and Random Processes For Electrical Engineering - Alberfor Leon-Garcia (3rd ) .81iSOLUTIONS MANUAL.81j 134. Probability,Random Variables and Stor hastic Processes,4th,by Athanasios Papoulis .81iSOLUTIONS MANUAL.81j 135. Process Systems Analysis And Control - Donald R. Coughanowr Solution Manual .81iSOLUTIONS MANUAL.81j 136. Separation Process Engineering: 2e by wankat SOLUTIONS MANUAL 137. Separation Process Principles, 2nd Ed.,by Seader, Henley .81iSOLUTIONS MANUAL.81j 138. solutions manual for Advanced Accounting 10e Fisher 139. solutions manual for Corporate Finance: A Focused Approach 3e Brigham 140. solutions manual for Advanced Accounting 10th edition by Beams 141. solutions manual for Essential of Accounting for Governmental and Not-for- Profit Organizations By Paul A Copley, 9e 142. solutions manual for Modern Advanced Accounting 10th edition by Larsen - 10e SM 143. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 144. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 145. solutions manual fundamentals of financial management, concise 6th edition by Brigham, Houston 146. South-Western Federal Taxation 2009 (Individual), 32th, Hoffman, Smith, Wills (Test Bank + solution manual) 147. Test Bank for Auditing and Assurance Services: A Systematic Approach, 6th Edition, Messier, Glover, Prawitt 148. Test Bank for Advanced Accounting 10e Fisher 149. test bank for Operations Management 9e William J. Stevenson (TB) 150. Test Bank for Accounting Information Systems - James Hall (6th ed) 151. Test bank for Advanced Accounting 10th edition by Beams 152. Test Bank for fundamentals of financial management, concise 6th edition by Brigham, Houston 153. Test bank for Modern Advanced Accounting 10th edition by Larsen - 10e TB 154. test bank cost Accounting 12e by Horngren 155. Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition .81iSOLUTIONS MANUAL.81j 156. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston test bank 157. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston solutions manual 158. Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Solutions manualith .81iSOLUTIONS MANUAL.81j Edition ,By F. P. Beer, E. R. Johnsfor n .81iSOLUTIONS MANUAL.81j 160. Fundamentals of Machine Component Design, 3rd ed - Student Solutions Manual by Juvinall, Marshek 161. Fundamentals of manufacturing 2nd edition by philip d. rufe solutions manual 162. Fundamentals of Momentum, Heat and Mass Transfer, 5th Edition Welty, Wicks, Rorrer, Wilson 163. Fundamentals of Multinational Finance, 2nd edition by Michael H. Moffett test bank and solution manual 164. Fundamentals of Multinational Finance, 3E by Michael H. Moffett (Instructor's Manual) 165. Fundamentals of Multinational Finance, 3E by Michael H. Moffett test bank 166. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith sm 167. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith tb 168. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith instructor manual 169. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith tb 170. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith sm 171. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow sm 172. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow tb 173. Human resources management 10e Gary dessler (IM+TB) 174. Intermediate Accounting 10e by Nikolai sm 175. Intermediate Accounting 11e by Kieso 176. Intermediate Accounting 12e by Kieso 177. Intermediate accounting 12th Updated by Kieso Solution manual 178. Intermediate accounting 12th Updated by Kieso test bank 179. Intermediate Accounting, 13th Edition Instructor's Manual Kieso, Weygandt, Warfield 180. (Sm+TB+IM) 181. Intermediate Accounting 2e by Baruch Englard 182. Intermediate Accounting 3e by J. David Spiceland 183. Intermediate Accounting 4e revised by J. David Spiceland solution manual 184. Intermediate accounting by Spiceland 4e Solution manual 185. Intermediate Accounting James D. Stice, Earl K. Stice, Fred Skousen 16th edition solution manual 186. Intermediate Accounting, 13th Edition Kieso, Weygandt, Warfield test bank and solution manual 187. Intermediate Accounting, Update, 12th Edition international student solution manual 188. Intermediate Algebra Functions & Authentic Applications 3e lehmann 189. Intermediate Algebra, 8th Edition By Margaret L. Lial, John Hornsby, Terry McGinnis 190. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves instructor manual 191. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves test bank 192. Intermediate Microeconomics, 10th Edition Walter Nicholson ,Christopher Snyder im with tb 193. International Accounting 1e by Doupnik solution manual 194. International Accounting 6e Frederick D. Choi Gary K. Meek 195. International Business The Challenges of Globalization, 4E John J. Wild,Kenneth L. Wild tb and im 196. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan instructor manual 197. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to me.,too. I can find it for === Subject: =?ISO-2022-JP?B?QXVkaXRpbmcgYW5kIEFzc3VyYW5jZSBTZXJ2aWNlcyAgMTIgdGggIGJ5OiBB b HZpbiBBIA==?= =?ISO-2022-JP?B?QXJlbnMsIBskQiFKGyhCU09MVVRJT05TIE1BTlVBTBskQiFLGyhC?= posting-account=v8NCmQkAAACB4IvJvLNgwxUPNbyAq_lC CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn't on the list, don't worry, please email to 1. A First Course in Probability, (7th), By Sheldon Ross .81iSOLUTIONS MANUAL.81j 2. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 3. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 4. Accounting Information Systems 10th ED by Marshall B Romney and Paul J Steinbart SOLUTIONS MANUAL 5. accounting information systems 11th edition, romney, steinbart TEST BANK 6. Accounting what number means 8e by Marshall SOLUTIONS MANUAL 7. Advanced Accounting 9e Beams SOLUTIONS MANUAL 8. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank 9. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik .81iSOLUTIONS MANUAL.81j 10. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin solution manual 11. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin test bank 12. Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd .81iSOLUTIONS MANUAL.81j 13. Auditing and Assurance Services 12 th by: Alvin A Arens, .81iSOLUTIONS MANUAL.81j 14. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual 15. Biology Concepts and Connections 6e Neil A. Campbell Jane B. Reece Martha R. Taylor Eric J. Simon Jean L. Dickey test bank 16. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz instructor manual 17. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank 18. Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson 19. Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) ( solutions manual) 20. COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING FOR PERFOR MANCE 21. Corporate Finance A Focused Approach 3e Brigham TEST BANK 22. Corporate Finance plus MyFinanceLab Student Access 23. Corporate finance: Custom edition. Berk, J., & DeMarzo, P. (2007). Boston : Pearson Education 24. cost accounting 12e Horngren SOLUTIONS MANUAL 25. cost Accounting 13e Horngren test bank 26. Cost Accounting A Managerial Emphasis by Charles T. Horngren 13th .81iSOLUTIONS MANUAL.81j 27. Cost Accounting: Foundations and Evolutions 7E By Kinney (SOLUTIONS MANUAL) 28. Data and Computer Communications, 8th Edition By Stallings .81iSOLUTIONS MANUAL.81j 29. Database System Concepts, Fifth Edition by Avi Silberschatz ,Henry F. Korth solutions to exercises? 30. Database Systems: The Complete Book, 2/E Solutions Manual 31. Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) Instructor manual 32. Differential Equations and Linear Algebra by Penney and Edwards, 2nd .81iSOLUTIONS MANUAL.81j 33. Differential Equations Computing and Modeling (4th Edition) By Edwards .81iSOLUTIONS MANUAL.81j 34. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley .81iSOLUTIONS MANUAL.81j 35. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 36. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 37. Elementary Differential Equations and Boundary Value Problems, 8th by Boyce and Diprima .81iSOLUTIONS MANUAL.81j 38. Elements of engineering electromagnetics (6/ e) by N.N.RAO .81iSOLUTIONS MANUAL.81j 39. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost TEST BANK 40. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost.81iTEST BANK.81j 41. Engineering and Chemical Thermodynamics by Milo D. Koretsky .81iSOLUTIONS MANUAL.81j 42. Engineering Circuit Analysis 7Ed William Hart Hayt .81iSOLUTIONS MANUAL.81j 43. Engineering Economy - Leland Blank & Anthony Tarquin 6th Editionselected solutions ( student solution) 44. Engineering electromagnetics (7/ e) by HAYT .81iSOLUTIONS MANUAL.81j 45. Engineering Fluid Mechanics, 7th, By Clayfor n T. Crowe, Donald F. Elger, John A. Roberson .81iSOLUTIONS MANUAL.81j 46. Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, .81iSOLUTIONS MANUAL.81j MANUAL.81j 48. ENGINEERING MECHANICS: statics by BEDFOR D 5th. .81iSOLUTIONS MANUAL.81j 49. Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus test bank 50. Essentials of Managerial Finance 14e Besley Instructor manual 51. Essentials of Managerial Finance with Thomson ONE, 13e Brigham SOLUTIONS MANUAL 52. Essentials of Managerial Finance with Thomson ONE, 13e Brigham TEST BANK 53. Financial Account 7e Horngren (SOLUTIONS MANUAL) 54. Financial Account 7e Horngren TEST BANK 55. Financial Accounting (Libby, fifth edition) .81iSOLUTIONS MANUAL.81j 56. Financial Accounting 6e by horngren Harrison .81iSOLUTIONS MANUAL.81j 57. Financial Accounting (Libby, 2001 edition) .81iSOLUTIONS MANUAL.81j 58. Financial and Mangerial Accounting 2e by Horngren (SOLUTIONS MANUAL) 59. Financial and Mangerial Accounting 2e by Horngren (TEST BANK) 60. Financial and Mangerial Accounting 2e by Horngren .81iSOLUTIONS MANUAL.81j 61. Financial management theory and practice 12e by Brigham .81iSOLUTIONS MANUAL.81j 62. Finiancial Accounting 7e by Horngren.81iSOLUTIONS MANUAL.81j 63. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL 64. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta solution manual 65. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(TEST BANK) 66. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(SOLUTIONS MANUAL) 67. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta test bank 68. Fundamental Methods Of Mathematical Economics Chiang & Wainwright 2005 Mc Graw Hill (Instructor's Manual ) 69. Fundamentals of Advanced Accounting 3rd Edition by Joe B. Hoyle, , andTimothy S. Doupnik .81iSOLUTIONS MANUAL.81j 70. Fundamentals of Applied Electromagnetics 5th by Fawwaz T. Ulaby .81iSOLUTIONS MANUAL.81j 71. Fundamentals of Classical Thermodynamics 6th edition by Van Wylen .81iSOLUTIONS MANUAL.81j 72. Fundamentals of Corporate Finance ( Ross, Westerfield, Jordan 8th) .81iSOLUTIONS MANUAL.81j 73. Fundamentals of Engineering Thermodynamics 6th by Michael J. Moran, Howard N. Shapiro .81iSOLUTIONS MANUAL.81j 74. Fundamentals of financial management 12e Brigham .81iSOLUTIONS MANUAL.81j 75. Fundamentals of financial management 12e Brigham Solutions manual 76. Fundamentals of financial management 12e Brigham TEST BANK 77. Fundamentals of Financial Management With Infotrac Concise 4th by Eugene Brigham .81iSOLUTIONS MANUAL.81j 78. Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 79. Fundamentals of Fluid Mechanics, 6th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 80. Fundamentals of Physics (8th Edition) By Halliday .81iSOLUTIONS MANUAL.81j 81. Fundamentals of Signals and systems using web and matlab third edition .81iSOLUTIONS MANUAL.81j 82. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, .81iSOLUTIONS MANUAL.81j 83. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, SOLUTIONS MANUAL 84. fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine (SOLUTIONS MANUAL) 85. Gravity: An Introduction to Einstein's General Relativity by James B. Hartle 86. Individual Income Taxes 2009 edition by Hoffman/Solutions manualyith/Willis (TEST BANK) 87. Instructor manual for Digital Fundamentals (10th Edition) floyd (IM) 88. Intermediata Accounting 13e Kieso SOLUTIONS MANUAL 89. Intermediata Accounting 13e Kieso TEST BANK 90. intermediate accounting 5e by spiceland solutions manual 91. International Financial Management Geert Bekaert Robert J. Hodrick test bank 92. Introduction for Chemical Engineering Thermodynamics 7th By J.M. Solutions manualith, Hendrick C Van Ness .81iSOLUTIONS MANUAL.81j 93. Introduction for Environmental engineering and science 3rd editions by Gilbert M. Masters .81iSOLUTIONS MANUAL.81j 94. Introduction for Fluid Mechanics, 7th, Fox, Pritchard, McDonald {Wiley} .81iSOLUTIONS MANUAL.81j 95. Introduction for Mathematical Statistics 6/ E Robert V. Hogg 96. Introduction for Quantum Mechanics (1 & 2 Edition), By David J. Griffiths .81iSOLUTIONS MANUAL.81j 97. Introduction to Chemical Engineering Thermodynamics 7th edition (solution manual) By J.M. Solutions manualith, Hendrick C Van Ness 98. Introduction to Heat Transfer, 5th Edition Incropera, DeWitt, Bergman, Lavine.81iSOLUTIONS MANUAL.81j 99. Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593)( solutions manual) 100. Introduction to Managerial Accounting 2nd ed Brewer test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to 101. Introductory Econometrics for Finance(Chris Brooks 2002) .81iSOLUTIONS MANUAL.81j 102. Linear Algebra and Its Applications, 3rd Edition by: David C. Lay .81iSOLUTIONS MANUAL.81j 103. Linear Algebra with Applications 7th edition by Leon, SOLUTIONS MANUAL 104. Macroeconomics, 4E Olivier Blanchard instructor manual .81iSOLUTIONS MANUAL.81j 105. Macroeconomics, 5E Olivier Blanchard (instructor manual) 106. Macroeconomics, 5E Olivier Blanchard (test bank) 107. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E SOLUTIONS MANUAL 108. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E TEST BANK 109. Managerial Accounting 12e By Garrison Noreen SOLUTIONS MANUAL 110. Managerial Accounting 12e By Garrison Noreen .81iSOLUTIONS MANUAL.81j 111. managerial accounting 12th Edition by Garrison Noreen (TEST BANK) 112. Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson .81iSOLUTIONS MANUAL.81j 113. Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao .81iSOLUTIONS MANUAL.81j 114. Mechanics of Materials By R.C.Hibbeler 7th edition .81iSOLUTIONS MANUAL.81j 115. Mechanics of Materials by roy R. craig 2nd eddition solution manual 116. Mechanics of Materials, 7th James M. Gere - Stanfor d University .81iSOLUTIONS MANUAL.81j 117. Microeconomic Theory, Nicholson & Snyder, 10th ed, .81iSOLUTIONS MANUAL.81j 118. Microelectronic Circuit Analysis and Design, 3ed. by Donald A. Neamen .81iSOLUTIONS MANUAL.81j 119. Microelectronic circuits by R. Jaeger 3rd edition .81iSOLUTIONS MANUAL.81j 120. Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop .81iSOLUTIONS MANUAL.81j 121. Modern Elementary Statistics, 12/e by Freund & Perles .81iSOLUTIONS MANUAL.81j 122. Modern Elementary Statistics, 12/e Freund & Perles (TEST BANK) 123. Modern Physics, 2/E Randy Harris SOLUTIONS MANUAL 124. Numerical methods for engineers 5th by Chapra .81iSOLUTIONS MANUAL.81j 125. Operations Management 10e William J. Stevenson Solutions manual 126. Operations Management 10e William J. Stevenson TEST BANK 127. Operations Management 9e William J. Stevenson (SOLUTIONS MANUAL) 128. Organizational Behaviour, Fourth Canadian Ed., 4E Robins TEST BANK 129. Power System Analysis By John J. Grainger, William D. Stevenson Jr .81iSOLUTIONS MANUAL.81j 130. Principles of Auditing 15e by Whittington TEST BANK 131. Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole .81iSOLUTIONS MANUAL.81j 132. Probability and Statistical Inference 7th edition, Hogg & Tanis .81iSOLUTIONS MANUAL.81j 133. Probability, Statistics, and Random Processes For Electrical Engineering - Alberfor Leon-Garcia (3rd ) .81iSOLUTIONS MANUAL.81j 134. Probability,Random Variables and Stor hastic Processes,4th,by Athanasios Papoulis .81iSOLUTIONS MANUAL.81j 135. Process Systems Analysis And Control - Donald R. Coughanowr Solution Manual .81iSOLUTIONS MANUAL.81j 136. Separation Process Engineering: 2e by wankat SOLUTIONS MANUAL 137. Separation Process Principles, 2nd Ed.,by Seader, Henley .81iSOLUTIONS MANUAL.81j 138. solutions manual for Advanced Accounting 10e Fisher 139. solutions manual for Corporate Finance: A Focused Approach 3e Brigham 140. solutions manual for Advanced Accounting 10th edition by Beams 141. solutions manual for Essential of Accounting for Governmental and Not-for- Profit Organizations By Paul A Copley, 9e 142. solutions manual for Modern Advanced Accounting 10th edition by Larsen - 10e SM 143. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 144. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 145. solutions manual fundamentals of financial management, concise 6th edition by Brigham, Houston 146. South-Western Federal Taxation 2009 (Individual), 32th, Hoffman, Smith, Wills (Test Bank + solution manual) 147. Test Bank for Auditing and Assurance Services: A Systematic Approach, 6th Edition, Messier, Glover, Prawitt 148. Test Bank for Advanced Accounting 10e Fisher 149. test bank for Operations Management 9e William J. Stevenson (TB) 150. Test Bank for Accounting Information Systems - James Hall (6th ed) 151. Test bank for Advanced Accounting 10th edition by Beams 152. Test Bank for fundamentals of financial management, concise 6th edition by Brigham, Houston 153. Test bank for Modern Advanced Accounting 10th edition by Larsen - 10e TB 154. test bank cost Accounting 12e by Horngren 155. Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition .81iSOLUTIONS MANUAL.81j 156. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston test bank 157. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston solutions manual 158. Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Solutions manualith .81iSOLUTIONS MANUAL.81j Edition ,By F. P. Beer, E. R. Johnsfor n .81iSOLUTIONS MANUAL.81j 160. Fundamentals of Machine Component Design, 3rd ed - Student Solutions Manual by Juvinall, Marshek 161. Fundamentals of manufacturing 2nd edition by philip d. rufe solutions manual 162. Fundamentals of Momentum, Heat and Mass Transfer, 5th Edition Welty, Wicks, Rorrer, Wilson 163. Fundamentals of Multinational Finance, 2nd edition by Michael H. Moffett test bank and solution manual 164. Fundamentals of Multinational Finance, 3E by Michael H. Moffett (Instructor's Manual) 165. Fundamentals of Multinational Finance, 3E by Michael H. Moffett test bank 166. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith sm 167. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith tb 168. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith instructor manual 169. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith tb 170. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith sm 171. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow sm 172. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow tb 173. Human resources management 10e Gary dessler (IM+TB) 174. Intermediate Accounting 10e by Nikolai sm 175. Intermediate Accounting 11e by Kieso 176. Intermediate Accounting 12e by Kieso 177. Intermediate accounting 12th Updated by Kieso Solution manual 178. Intermediate accounting 12th Updated by Kieso test bank 179. Intermediate Accounting, 13th Edition Instructor's Manual Kieso, Weygandt, Warfield 180. (Sm+TB+IM) 181. Intermediate Accounting 2e by Baruch Englard 182. Intermediate Accounting 3e by J. David Spiceland 183. Intermediate Accounting 4e revised by J. David Spiceland solution manual 184. Intermediate accounting by Spiceland 4e Solution manual 185. Intermediate Accounting James D. Stice, Earl K. Stice, Fred Skousen 16th edition solution manual 186. Intermediate Accounting, 13th Edition Kieso, Weygandt, Warfield test bank and solution manual 187. Intermediate Accounting, Update, 12th Edition international student solution manual 188. Intermediate Algebra Functions & Authentic Applications 3e lehmann 189. Intermediate Algebra, 8th Edition By Margaret L. Lial, John Hornsby, Terry McGinnis 190. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves instructor manual 191. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves test bank 192. Intermediate Microeconomics, 10th Edition Walter Nicholson ,Christopher Snyder im with tb 193. International Accounting 1e by Doupnik solution manual 194. International Accounting 6e Frederick D. Choi Gary K. Meek 195. International Business The Challenges of Globalization, 4E John J. Wild,Kenneth L. Wild tb and im 196. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan instructor manual 197. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to me.,too. I can find it for === Subject: Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual posting-account=v8NCmQkAAACB4IvJvLNgwxUPNbyAq_lC CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn't on the list, don't worry, please email to 1. A First Course in Probability, (7th), By Sheldon Ross .81iSOLUTIONS MANUAL.81j 2. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 3. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 4. Accounting Information Systems 10th ED by Marshall B Romney and Paul J Steinbart SOLUTIONS MANUAL 5. accounting information systems 11th edition, romney, steinbart TEST BANK 6. Accounting what number means 8e by Marshall SOLUTIONS MANUAL 7. Advanced Accounting 9e Beams SOLUTIONS MANUAL 8. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank 9. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik .81iSOLUTIONS MANUAL.81j 10. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin solution manual 11. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin test bank 12. Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd .81iSOLUTIONS MANUAL.81j 13. Auditing and Assurance Services 12 th by: Alvin A Arens, .81iSOLUTIONS MANUAL.81j 14. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual 15. Biology Concepts and Connections 6e Neil A. Campbell Jane B. Reece Martha R. Taylor Eric J. Simon Jean L. Dickey test bank 16. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz instructor manual 17. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank 18. Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson 19. Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) ( solutions manual) 20. COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING FOR PERFOR MANCE 21. Corporate Finance A Focused Approach 3e Brigham TEST BANK 22. Corporate Finance plus MyFinanceLab Student Access 23. Corporate finance: Custom edition. Berk, J., & DeMarzo, P. (2007). Boston : Pearson Education 24. cost accounting 12e Horngren SOLUTIONS MANUAL 25. cost Accounting 13e Horngren test bank 26. Cost Accounting A Managerial Emphasis by Charles T. Horngren 13th .81iSOLUTIONS MANUAL.81j 27. Cost Accounting: Foundations and Evolutions 7E By Kinney (SOLUTIONS MANUAL) 28. Data and Computer Communications, 8th Edition By Stallings .81iSOLUTIONS MANUAL.81j 29. Database System Concepts, Fifth Edition by Avi Silberschatz ,Henry F. Korth solutions to exercises? 30. Database Systems: The Complete Book, 2/E Solutions Manual 31. Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) Instructor manual 32. Differential Equations and Linear Algebra by Penney and Edwards, 2nd .81iSOLUTIONS MANUAL.81j 33. Differential Equations Computing and Modeling (4th Edition) By Edwards .81iSOLUTIONS MANUAL.81j 34. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley .81iSOLUTIONS MANUAL.81j 35. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 36. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 37. Elementary Differential Equations and Boundary Value Problems, 8th by Boyce and Diprima .81iSOLUTIONS MANUAL.81j 38. Elements of engineering electromagnetics (6/ e) by N.N.RAO .81iSOLUTIONS MANUAL.81j 39. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost TEST BANK 40. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost.81iTEST BANK.81j 41. Engineering and Chemical Thermodynamics by Milo D. Koretsky .81iSOLUTIONS MANUAL.81j 42. Engineering Circuit Analysis 7Ed William Hart Hayt .81iSOLUTIONS MANUAL.81j 43. Engineering Economy - Leland Blank & Anthony Tarquin 6th Editionselected solutions ( student solution) 44. Engineering electromagnetics (7/ e) by HAYT .81iSOLUTIONS MANUAL.81j 45. Engineering Fluid Mechanics, 7th, By Clayfor n T. Crowe, Donald F. Elger, John A. Roberson .81iSOLUTIONS MANUAL.81j 46. Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, .81iSOLUTIONS MANUAL.81j MANUAL.81j 48. ENGINEERING MECHANICS: statics by BEDFOR D 5th. .81iSOLUTIONS MANUAL.81j 49. Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus test bank 50. Essentials of Managerial Finance 14e Besley Instructor manual 51. Essentials of Managerial Finance with Thomson ONE, 13e Brigham SOLUTIONS MANUAL 52. Essentials of Managerial Finance with Thomson ONE, 13e Brigham TEST BANK 53. Financial Account 7e Horngren (SOLUTIONS MANUAL) 54. Financial Account 7e Horngren TEST BANK 55. Financial Accounting (Libby, fifth edition) .81iSOLUTIONS MANUAL.81j 56. Financial Accounting 6e by horngren Harrison .81iSOLUTIONS MANUAL.81j 57. Financial Accounting (Libby, 2001 edition) .81iSOLUTIONS MANUAL.81j 58. Financial and Mangerial Accounting 2e by Horngren (SOLUTIONS MANUAL) 59. Financial and Mangerial Accounting 2e by Horngren (TEST BANK) 60. Financial and Mangerial Accounting 2e by Horngren .81iSOLUTIONS MANUAL.81j 61. Financial management theory and practice 12e by Brigham .81iSOLUTIONS MANUAL.81j 62. Finiancial Accounting 7e by Horngren.81iSOLUTIONS MANUAL.81j 63. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL 64. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta solution manual 65. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(TEST BANK) 66. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(SOLUTIONS MANUAL) 67. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta test bank 68. Fundamental Methods Of Mathematical Economics Chiang & Wainwright 2005 Mc Graw Hill (Instructor's Manual ) 69. Fundamentals of Advanced Accounting 3rd Edition by Joe B. Hoyle, , andTimothy S. Doupnik .81iSOLUTIONS MANUAL.81j 70. Fundamentals of Applied Electromagnetics 5th by Fawwaz T. Ulaby .81iSOLUTIONS MANUAL.81j 71. Fundamentals of Classical Thermodynamics 6th edition by Van Wylen .81iSOLUTIONS MANUAL.81j 72. Fundamentals of Corporate Finance ( Ross, Westerfield, Jordan 8th) .81iSOLUTIONS MANUAL.81j 73. Fundamentals of Engineering Thermodynamics 6th by Michael J. Moran, Howard N. Shapiro .81iSOLUTIONS MANUAL.81j 74. Fundamentals of financial management 12e Brigham .81iSOLUTIONS MANUAL.81j 75. Fundamentals of financial management 12e Brigham Solutions manual 76. Fundamentals of financial management 12e Brigham TEST BANK 77. Fundamentals of Financial Management With Infotrac Concise 4th by Eugene Brigham .81iSOLUTIONS MANUAL.81j 78. Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 79. Fundamentals of Fluid Mechanics, 6th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 80. Fundamentals of Physics (8th Edition) By Halliday .81iSOLUTIONS MANUAL.81j 81. Fundamentals of Signals and systems using web and matlab third edition .81iSOLUTIONS MANUAL.81j 82. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, .81iSOLUTIONS MANUAL.81j 83. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, SOLUTIONS MANUAL 84. fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine (SOLUTIONS MANUAL) 85. Gravity: An Introduction to Einstein's General Relativity by James B. Hartle 86. Individual Income Taxes 2009 edition by Hoffman/Solutions manualyith/Willis (TEST BANK) 87. Instructor manual for Digital Fundamentals (10th Edition) floyd (IM) 88. Intermediata Accounting 13e Kieso SOLUTIONS MANUAL 89. Intermediata Accounting 13e Kieso TEST BANK 90. intermediate accounting 5e by spiceland solutions manual 91. International Financial Management Geert Bekaert Robert J. Hodrick test bank 92. Introduction for Chemical Engineering Thermodynamics 7th By J.M. Solutions manualith, Hendrick C Van Ness .81iSOLUTIONS MANUAL.81j 93. Introduction for Environmental engineering and science 3rd editions by Gilbert M. Masters .81iSOLUTIONS MANUAL.81j 94. Introduction for Fluid Mechanics, 7th, Fox, Pritchard, McDonald {Wiley} .81iSOLUTIONS MANUAL.81j 95. Introduction for Mathematical Statistics 6/ E Robert V. Hogg 96. Introduction for Quantum Mechanics (1 & 2 Edition), By David J. Griffiths .81iSOLUTIONS MANUAL.81j 97. Introduction to Chemical Engineering Thermodynamics 7th edition (solution manual) By J.M. Solutions manualith, Hendrick C Van Ness 98. Introduction to Heat Transfer, 5th Edition Incropera, DeWitt, Bergman, Lavine.81iSOLUTIONS MANUAL.81j 99. Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593)( solutions manual) 100. Introduction to Managerial Accounting 2nd ed Brewer test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to 101. Introductory Econometrics for Finance(Chris Brooks 2002) .81iSOLUTIONS MANUAL.81j 102. Linear Algebra and Its Applications, 3rd Edition by: David C. Lay .81iSOLUTIONS MANUAL.81j 103. Linear Algebra with Applications 7th edition by Leon, SOLUTIONS MANUAL 104. Macroeconomics, 4E Olivier Blanchard instructor manual .81iSOLUTIONS MANUAL.81j 105. Macroeconomics, 5E Olivier Blanchard (instructor manual) 106. Macroeconomics, 5E Olivier Blanchard (test bank) 107. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E SOLUTIONS MANUAL 108. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E TEST BANK 109. Managerial Accounting 12e By Garrison Noreen SOLUTIONS MANUAL 110. Managerial Accounting 12e By Garrison Noreen .81iSOLUTIONS MANUAL.81j 111. managerial accounting 12th Edition by Garrison Noreen (TEST BANK) 112. Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson .81iSOLUTIONS MANUAL.81j 113. Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao .81iSOLUTIONS MANUAL.81j 114. Mechanics of Materials By R.C.Hibbeler 7th edition .81iSOLUTIONS MANUAL.81j 115. Mechanics of Materials by roy R. craig 2nd eddition solution manual 116. Mechanics of Materials, 7th James M. Gere - Stanfor d University .81iSOLUTIONS MANUAL.81j 117. Microeconomic Theory, Nicholson & Snyder, 10th ed, .81iSOLUTIONS MANUAL.81j 118. Microelectronic Circuit Analysis and Design, 3ed. by Donald A. Neamen .81iSOLUTIONS MANUAL.81j 119. Microelectronic circuits by R. Jaeger 3rd edition .81iSOLUTIONS MANUAL.81j 120. Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop .81iSOLUTIONS MANUAL.81j 121. Modern Elementary Statistics, 12/e by Freund & Perles .81iSOLUTIONS MANUAL.81j 122. Modern Elementary Statistics, 12/e Freund & Perles (TEST BANK) 123. Modern Physics, 2/E Randy Harris SOLUTIONS MANUAL 124. Numerical methods for engineers 5th by Chapra .81iSOLUTIONS MANUAL.81j 125. Operations Management 10e William J. Stevenson Solutions manual 126. Operations Management 10e William J. Stevenson TEST BANK 127. Operations Management 9e William J. Stevenson (SOLUTIONS MANUAL) 128. Organizational Behaviour, Fourth Canadian Ed., 4E Robins TEST BANK 129. Power System Analysis By John J. Grainger, William D. Stevenson Jr .81iSOLUTIONS MANUAL.81j 130. Principles of Auditing 15e by Whittington TEST BANK 131. Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole .81iSOLUTIONS MANUAL.81j 132. Probability and Statistical Inference 7th edition, Hogg & Tanis .81iSOLUTIONS MANUAL.81j 133. Probability, Statistics, and Random Processes For Electrical Engineering - Alberfor Leon-Garcia (3rd ) .81iSOLUTIONS MANUAL.81j 134. Probability,Random Variables and Stor hastic Processes,4th,by Athanasios Papoulis .81iSOLUTIONS MANUAL.81j 135. Process Systems Analysis And Control - Donald R. Coughanowr Solution Manual .81iSOLUTIONS MANUAL.81j 136. Separation Process Engineering: 2e by wankat SOLUTIONS MANUAL 137. Separation Process Principles, 2nd Ed.,by Seader, Henley .81iSOLUTIONS MANUAL.81j 138. solutions manual for Advanced Accounting 10e Fisher 139. solutions manual for Corporate Finance: A Focused Approach 3e Brigham 140. solutions manual for Advanced Accounting 10th edition by Beams 141. solutions manual for Essential of Accounting for Governmental and Not-for- Profit Organizations By Paul A Copley, 9e 142. solutions manual for Modern Advanced Accounting 10th edition by Larsen - 10e SM 143. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 144. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 145. solutions manual fundamentals of financial management, concise 6th edition by Brigham, Houston 146. South-Western Federal Taxation 2009 (Individual), 32th, Hoffman, Smith, Wills (Test Bank + solution manual) 147. Test Bank for Auditing and Assurance Services: A Systematic Approach, 6th Edition, Messier, Glover, Prawitt 148. Test Bank for Advanced Accounting 10e Fisher 149. test bank for Operations Management 9e William J. Stevenson (TB) 150. Test Bank for Accounting Information Systems - James Hall (6th ed) 151. Test bank for Advanced Accounting 10th edition by Beams 152. Test Bank for fundamentals of financial management, concise 6th edition by Brigham, Houston 153. Test bank for Modern Advanced Accounting 10th edition by Larsen - 10e TB 154. test bank cost Accounting 12e by Horngren 155. Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition .81iSOLUTIONS MANUAL.81j 156. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston test bank 157. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston solutions manual 158. Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Solutions manualith .81iSOLUTIONS MANUAL.81j Edition ,By F. P. Beer, E. R. Johnsfor n .81iSOLUTIONS MANUAL.81j 160. Fundamentals of Machine Component Design, 3rd ed - Student Solutions Manual by Juvinall, Marshek 161. Fundamentals of manufacturing 2nd edition by philip d. rufe solutions manual 162. Fundamentals of Momentum, Heat and Mass Transfer, 5th Edition Welty, Wicks, Rorrer, Wilson 163. Fundamentals of Multinational Finance, 2nd edition by Michael H. Moffett test bank and solution manual 164. Fundamentals of Multinational Finance, 3E by Michael H. Moffett (Instructor's Manual) 165. Fundamentals of Multinational Finance, 3E by Michael H. Moffett test bank 166. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith sm 167. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith tb 168. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith instructor manual 169. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith tb 170. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith sm 171. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow sm 172. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow tb 173. Human resources management 10e Gary dessler (IM+TB) 174. Intermediate Accounting 10e by Nikolai sm 175. Intermediate Accounting 11e by Kieso 176. Intermediate Accounting 12e by Kieso 177. Intermediate accounting 12th Updated by Kieso Solution manual 178. Intermediate accounting 12th Updated by Kieso test bank 179. Intermediate Accounting, 13th Edition Instructor's Manual Kieso, Weygandt, Warfield 180. (Sm+TB+IM) 181. Intermediate Accounting 2e by Baruch Englard 182. Intermediate Accounting 3e by J. David Spiceland 183. Intermediate Accounting 4e revised by J. David Spiceland solution manual 184. Intermediate accounting by Spiceland 4e Solution manual 185. Intermediate Accounting James D. Stice, Earl K. Stice, Fred Skousen 16th edition solution manual 186. Intermediate Accounting, 13th Edition Kieso, Weygandt, Warfield test bank and solution manual 187. Intermediate Accounting, Update, 12th Edition international student solution manual 188. Intermediate Algebra Functions & Authentic Applications 3e lehmann 189. Intermediate Algebra, 8th Edition By Margaret L. Lial, John Hornsby, Terry McGinnis 190. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves instructor manual 191. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves test bank 192. Intermediate Microeconomics, 10th Edition Walter Nicholson ,Christopher Snyder im with tb 193. International Accounting 1e by Doupnik solution manual 194. International Accounting 6e Frederick D. Choi Gary K. Meek 195. International Business The Challenges of Globalization, 4E John J. Wild,Kenneth L. Wild tb and im 196. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan instructor manual 197. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to me.,too. I can find it for === Subject: =?ISO-2022-JP?B?RGF0YSBhbmQgQ29tcHV0ZXIgQ29tbXVuaWNhdGlvbnMsIDh0aCBFZGl0aW9u I CBCeSBTdA==?= =?ISO-2022-JP?B?YWxsaW5ncyAbJEIhShsoQlNPTFVUSU9OUyBNQU5VQUwbJEIhSxsoQg==?= posting-account=v8NCmQkAAACB4IvJvLNgwxUPNbyAq_lC CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn't on the list, don't worry, please email to 1. A First Course in Probability, (7th), By Sheldon Ross .81iSOLUTIONS MANUAL.81j 2. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 3. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 4. Accounting Information Systems 10th ED by Marshall B Romney and Paul J Steinbart SOLUTIONS MANUAL 5. accounting information systems 11th edition, romney, steinbart TEST BANK 6. Accounting what number means 8e by Marshall SOLUTIONS MANUAL 7. Advanced Accounting 9e Beams SOLUTIONS MANUAL 8. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank 9. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik .81iSOLUTIONS MANUAL.81j 10. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin solution manual 11. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin test bank 12. Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd .81iSOLUTIONS MANUAL.81j 13. Auditing and Assurance Services 12 th by: Alvin A Arens, .81iSOLUTIONS MANUAL.81j 14. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual 15. Biology Concepts and Connections 6e Neil A. Campbell Jane B. Reece Martha R. Taylor Eric J. Simon Jean L. Dickey test bank 16. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz instructor manual 17. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank 18. Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson 19. Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) ( solutions manual) 20. COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING FOR PERFOR MANCE 21. Corporate Finance A Focused Approach 3e Brigham TEST BANK 22. Corporate Finance plus MyFinanceLab Student Access 23. Corporate finance: Custom edition. Berk, J., & DeMarzo, P. (2007). Boston : Pearson Education 24. cost accounting 12e Horngren SOLUTIONS MANUAL 25. cost Accounting 13e Horngren test bank 26. Cost Accounting A Managerial Emphasis by Charles T. Horngren 13th .81iSOLUTIONS MANUAL.81j 27. Cost Accounting: Foundations and Evolutions 7E By Kinney (SOLUTIONS MANUAL) 28. Data and Computer Communications, 8th Edition By Stallings .81iSOLUTIONS MANUAL.81j 29. Database System Concepts, Fifth Edition by Avi Silberschatz ,Henry F. Korth solutions to exercises? 30. Database Systems: The Complete Book, 2/E Solutions Manual 31. Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) Instructor manual 32. Differential Equations and Linear Algebra by Penney and Edwards, 2nd .81iSOLUTIONS MANUAL.81j 33. Differential Equations Computing and Modeling (4th Edition) By Edwards .81iSOLUTIONS MANUAL.81j 34. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley .81iSOLUTIONS MANUAL.81j 35. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 36. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 37. Elementary Differential Equations and Boundary Value Problems, 8th by Boyce and Diprima .81iSOLUTIONS MANUAL.81j 38. Elements of engineering electromagnetics (6/ e) by N.N.RAO .81iSOLUTIONS MANUAL.81j 39. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost TEST BANK 40. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost.81iTEST BANK.81j 41. Engineering and Chemical Thermodynamics by Milo D. Koretsky .81iSOLUTIONS MANUAL.81j 42. Engineering Circuit Analysis 7Ed William Hart Hayt .81iSOLUTIONS MANUAL.81j 43. Engineering Economy - Leland Blank & Anthony Tarquin 6th Editionselected solutions ( student solution) 44. Engineering electromagnetics (7/ e) by HAYT .81iSOLUTIONS MANUAL.81j 45. Engineering Fluid Mechanics, 7th, By Clayfor n T. Crowe, Donald F. Elger, John A. Roberson .81iSOLUTIONS MANUAL.81j 46. Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, .81iSOLUTIONS MANUAL.81j MANUAL.81j 48. ENGINEERING MECHANICS: statics by BEDFOR D 5th. .81iSOLUTIONS MANUAL.81j 49. Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus test bank 50. Essentials of Managerial Finance 14e Besley Instructor manual 51. Essentials of Managerial Finance with Thomson ONE, 13e Brigham SOLUTIONS MANUAL 52. Essentials of Managerial Finance with Thomson ONE, 13e Brigham TEST BANK 53. Financial Account 7e Horngren (SOLUTIONS MANUAL) 54. Financial Account 7e Horngren TEST BANK 55. Financial Accounting (Libby, fifth edition) .81iSOLUTIONS MANUAL.81j 56. Financial Accounting 6e by horngren Harrison .81iSOLUTIONS MANUAL.81j 57. Financial Accounting (Libby, 2001 edition) .81iSOLUTIONS MANUAL.81j 58. Financial and Mangerial Accounting 2e by Horngren (SOLUTIONS MANUAL) 59. Financial and Mangerial Accounting 2e by Horngren (TEST BANK) 60. Financial and Mangerial Accounting 2e by Horngren .81iSOLUTIONS MANUAL.81j 61. Financial management theory and practice 12e by Brigham .81iSOLUTIONS MANUAL.81j 62. Finiancial Accounting 7e by Horngren.81iSOLUTIONS MANUAL.81j 63. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL 64. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta solution manual 65. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(TEST BANK) 66. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(SOLUTIONS MANUAL) 67. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta test bank 68. Fundamental Methods Of Mathematical Economics Chiang & Wainwright 2005 Mc Graw Hill (Instructor's Manual ) 69. Fundamentals of Advanced Accounting 3rd Edition by Joe B. Hoyle, , andTimothy S. Doupnik .81iSOLUTIONS MANUAL.81j 70. Fundamentals of Applied Electromagnetics 5th by Fawwaz T. Ulaby .81iSOLUTIONS MANUAL.81j 71. Fundamentals of Classical Thermodynamics 6th edition by Van Wylen .81iSOLUTIONS MANUAL.81j 72. Fundamentals of Corporate Finance ( Ross, Westerfield, Jordan 8th) .81iSOLUTIONS MANUAL.81j 73. Fundamentals of Engineering Thermodynamics 6th by Michael J. Moran, Howard N. Shapiro .81iSOLUTIONS MANUAL.81j 74. Fundamentals of financial management 12e Brigham .81iSOLUTIONS MANUAL.81j 75. Fundamentals of financial management 12e Brigham Solutions manual 76. Fundamentals of financial management 12e Brigham TEST BANK 77. Fundamentals of Financial Management With Infotrac Concise 4th by Eugene Brigham .81iSOLUTIONS MANUAL.81j 78. Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 79. Fundamentals of Fluid Mechanics, 6th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 80. Fundamentals of Physics (8th Edition) By Halliday .81iSOLUTIONS MANUAL.81j 81. Fundamentals of Signals and systems using web and matlab third edition .81iSOLUTIONS MANUAL.81j 82. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, .81iSOLUTIONS MANUAL.81j 83. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, SOLUTIONS MANUAL 84. fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine (SOLUTIONS MANUAL) 85. Gravity: An Introduction to Einstein's General Relativity by James B. Hartle 86. Individual Income Taxes 2009 edition by Hoffman/Solutions manualyith/Willis (TEST BANK) 87. Instructor manual for Digital Fundamentals (10th Edition) floyd (IM) 88. Intermediata Accounting 13e Kieso SOLUTIONS MANUAL 89. Intermediata Accounting 13e Kieso TEST BANK 90. intermediate accounting 5e by spiceland solutions manual 91. International Financial Management Geert Bekaert Robert J. Hodrick test bank 92. Introduction for Chemical Engineering Thermodynamics 7th By J.M. Solutions manualith, Hendrick C Van Ness .81iSOLUTIONS MANUAL.81j 93. Introduction for Environmental engineering and science 3rd editions by Gilbert M. Masters .81iSOLUTIONS MANUAL.81j 94. Introduction for Fluid Mechanics, 7th, Fox, Pritchard, McDonald {Wiley} .81iSOLUTIONS MANUAL.81j 95. Introduction for Mathematical Statistics 6/ E Robert V. Hogg 96. Introduction for Quantum Mechanics (1 & 2 Edition), By David J. Griffiths .81iSOLUTIONS MANUAL.81j 97. Introduction to Chemical Engineering Thermodynamics 7th edition (solution manual) By J.M. Solutions manualith, Hendrick C Van Ness 98. Introduction to Heat Transfer, 5th Edition Incropera, DeWitt, Bergman, Lavine.81iSOLUTIONS MANUAL.81j 99. Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593)( solutions manual) 100. Introduction to Managerial Accounting 2nd ed Brewer test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to 101. Introductory Econometrics for Finance(Chris Brooks 2002) .81iSOLUTIONS MANUAL.81j 102. Linear Algebra and Its Applications, 3rd Edition by: David C. Lay .81iSOLUTIONS MANUAL.81j 103. Linear Algebra with Applications 7th edition by Leon, SOLUTIONS MANUAL 104. Macroeconomics, 4E Olivier Blanchard instructor manual .81iSOLUTIONS MANUAL.81j 105. Macroeconomics, 5E Olivier Blanchard (instructor manual) 106. Macroeconomics, 5E Olivier Blanchard (test bank) 107. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E SOLUTIONS MANUAL 108. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E TEST BANK 109. Managerial Accounting 12e By Garrison Noreen SOLUTIONS MANUAL 110. Managerial Accounting 12e By Garrison Noreen .81iSOLUTIONS MANUAL.81j 111. managerial accounting 12th Edition by Garrison Noreen (TEST BANK) 112. Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson .81iSOLUTIONS MANUAL.81j 113. Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao .81iSOLUTIONS MANUAL.81j 114. Mechanics of Materials By R.C.Hibbeler 7th edition .81iSOLUTIONS MANUAL.81j 115. Mechanics of Materials by roy R. craig 2nd eddition solution manual 116. Mechanics of Materials, 7th James M. Gere - Stanfor d University .81iSOLUTIONS MANUAL.81j 117. Microeconomic Theory, Nicholson & Snyder, 10th ed, .81iSOLUTIONS MANUAL.81j 118. Microelectronic Circuit Analysis and Design, 3ed. by Donald A. Neamen .81iSOLUTIONS MANUAL.81j 119. Microelectronic circuits by R. Jaeger 3rd edition .81iSOLUTIONS MANUAL.81j 120. Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop .81iSOLUTIONS MANUAL.81j 121. Modern Elementary Statistics, 12/e by Freund & Perles .81iSOLUTIONS MANUAL.81j 122. Modern Elementary Statistics, 12/e Freund & Perles (TEST BANK) 123. Modern Physics, 2/E Randy Harris SOLUTIONS MANUAL 124. Numerical methods for engineers 5th by Chapra .81iSOLUTIONS MANUAL.81j 125. Operations Management 10e William J. Stevenson Solutions manual 126. Operations Management 10e William J. Stevenson TEST BANK 127. Operations Management 9e William J. Stevenson (SOLUTIONS MANUAL) 128. Organizational Behaviour, Fourth Canadian Ed., 4E Robins TEST BANK 129. Power System Analysis By John J. Grainger, William D. Stevenson Jr .81iSOLUTIONS MANUAL.81j 130. Principles of Auditing 15e by Whittington TEST BANK 131. Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole .81iSOLUTIONS MANUAL.81j 132. Probability and Statistical Inference 7th edition, Hogg & Tanis .81iSOLUTIONS MANUAL.81j 133. Probability, Statistics, and Random Processes For Electrical Engineering - Alberfor Leon-Garcia (3rd ) .81iSOLUTIONS MANUAL.81j 134. Probability,Random Variables and Stor hastic Processes,4th,by Athanasios Papoulis .81iSOLUTIONS MANUAL.81j 135. Process Systems Analysis And Control - Donald R. Coughanowr Solution Manual .81iSOLUTIONS MANUAL.81j 136. Separation Process Engineering: 2e by wankat SOLUTIONS MANUAL 137. Separation Process Principles, 2nd Ed.,by Seader, Henley .81iSOLUTIONS MANUAL.81j 138. solutions manual for Advanced Accounting 10e Fisher 139. solutions manual for Corporate Finance: A Focused Approach 3e Brigham 140. solutions manual for Advanced Accounting 10th edition by Beams 141. solutions manual for Essential of Accounting for Governmental and Not-for- Profit Organizations By Paul A Copley, 9e 142. solutions manual for Modern Advanced Accounting 10th edition by Larsen - 10e SM 143. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 144. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 145. solutions manual fundamentals of financial management, concise 6th edition by Brigham, Houston 146. South-Western Federal Taxation 2009 (Individual), 32th, Hoffman, Smith, Wills (Test Bank + solution manual) 147. Test Bank for Auditing and Assurance Services: A Systematic Approach, 6th Edition, Messier, Glover, Prawitt 148. Test Bank for Advanced Accounting 10e Fisher 149. test bank for Operations Management 9e William J. Stevenson (TB) 150. Test Bank for Accounting Information Systems - James Hall (6th ed) 151. Test bank for Advanced Accounting 10th edition by Beams 152. Test Bank for fundamentals of financial management, concise 6th edition by Brigham, Houston 153. Test bank for Modern Advanced Accounting 10th edition by Larsen - 10e TB 154. test bank cost Accounting 12e by Horngren 155. Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition .81iSOLUTIONS MANUAL.81j 156. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston test bank 157. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston solutions manual 158. Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Solutions manualith .81iSOLUTIONS MANUAL.81j Edition ,By F. P. Beer, E. R. Johnsfor n .81iSOLUTIONS MANUAL.81j 160. Fundamentals of Machine Component Design, 3rd ed - Student Solutions Manual by Juvinall, Marshek 161. Fundamentals of manufacturing 2nd edition by philip d. rufe solutions manual 162. Fundamentals of Momentum, Heat and Mass Transfer, 5th Edition Welty, Wicks, Rorrer, Wilson 163. Fundamentals of Multinational Finance, 2nd edition by Michael H. Moffett test bank and solution manual 164. Fundamentals of Multinational Finance, 3E by Michael H. Moffett (Instructor's Manual) 165. Fundamentals of Multinational Finance, 3E by Michael H. Moffett test bank 166. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith sm 167. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith tb 168. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith instructor manual 169. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith tb 170. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith sm 171. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow sm 172. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow tb 173. Human resources management 10e Gary dessler (IM+TB) 174. Intermediate Accounting 10e by Nikolai sm 175. Intermediate Accounting 11e by Kieso 176. Intermediate Accounting 12e by Kieso 177. Intermediate accounting 12th Updated by Kieso Solution manual 178. Intermediate accounting 12th Updated by Kieso test bank 179. Intermediate Accounting, 13th Edition Instructor's Manual Kieso, Weygandt, Warfield 180. (Sm+TB+IM) 181. Intermediate Accounting 2e by Baruch Englard 182. Intermediate Accounting 3e by J. David Spiceland 183. Intermediate Accounting 4e revised by J. David Spiceland solution manual 184. Intermediate accounting by Spiceland 4e Solution manual 185. Intermediate Accounting James D. Stice, Earl K. Stice, Fred Skousen 16th edition solution manual 186. Intermediate Accounting, 13th Edition Kieso, Weygandt, Warfield test bank and solution manual 187. Intermediate Accounting, Update, 12th Edition international student solution manual 188. Intermediate Algebra Functions & Authentic Applications 3e lehmann 189. Intermediate Algebra, 8th Edition By Margaret L. Lial, John Hornsby, Terry McGinnis 190. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves instructor manual 191. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves test bank 192. Intermediate Microeconomics, 10th Edition Walter Nicholson ,Christopher Snyder im with tb 193. International Accounting 1e by Doupnik solution manual 194. International Accounting 6e Frederick D. Choi Gary K. Meek 195. International Business The Challenges of Globalization, 4E John J. Wild,Kenneth L. Wild tb and im 196. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan instructor manual 197. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to me.,too. I can find it for === Subject: Corporate Finance A Focused Approach 3e Brigham TEST BANK posting-account=v8NCmQkAAACB4IvJvLNgwxUPNbyAq_lC CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn't on the list, don't worry, please email to 1. A First Course in Probability, (7th), By Sheldon Ross .81iSOLUTIONS MANUAL.81j 2. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 3. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 4. Accounting Information Systems 10th ED by Marshall B Romney and Paul J Steinbart SOLUTIONS MANUAL 5. accounting information systems 11th edition, romney, steinbart TEST BANK 6. Accounting what number means 8e by Marshall SOLUTIONS MANUAL 7. Advanced Accounting 9e Beams SOLUTIONS MANUAL 8. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank 9. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik .81iSOLUTIONS MANUAL.81j 10. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin solution manual 11. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin test bank 12. Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd .81iSOLUTIONS MANUAL.81j 13. Auditing and Assurance Services 12 th by: Alvin A Arens, .81iSOLUTIONS MANUAL.81j 14. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual 15. Biology Concepts and Connections 6e Neil A. Campbell Jane B. Reece Martha R. Taylor Eric J. Simon Jean L. Dickey test bank 16. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz instructor manual 17. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank 18. Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson 19. Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) ( solutions manual) 20. COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING FOR PERFOR MANCE 21. Corporate Finance A Focused Approach 3e Brigham TEST BANK 22. Corporate Finance plus MyFinanceLab Student Access 23. Corporate finance: Custom edition. Berk, J., & DeMarzo, P. (2007). Boston : Pearson Education 24. cost accounting 12e Horngren SOLUTIONS MANUAL 25. cost Accounting 13e Horngren test bank 26. Cost Accounting A Managerial Emphasis by Charles T. Horngren 13th .81iSOLUTIONS MANUAL.81j 27. Cost Accounting: Foundations and Evolutions 7E By Kinney (SOLUTIONS MANUAL) 28. Data and Computer Communications, 8th Edition By Stallings .81iSOLUTIONS MANUAL.81j 29. Database System Concepts, Fifth Edition by Avi Silberschatz ,Henry F. Korth solutions to exercises? 30. Database Systems: The Complete Book, 2/E Solutions Manual 31. Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) Instructor manual 32. Differential Equations and Linear Algebra by Penney and Edwards, 2nd .81iSOLUTIONS MANUAL.81j 33. Differential Equations Computing and Modeling (4th Edition) By Edwards .81iSOLUTIONS MANUAL.81j 34. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley .81iSOLUTIONS MANUAL.81j 35. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 36. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 37. Elementary Differential Equations and Boundary Value Problems, 8th by Boyce and Diprima .81iSOLUTIONS MANUAL.81j 38. Elements of engineering electromagnetics (6/ e) by N.N.RAO .81iSOLUTIONS MANUAL.81j 39. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost TEST BANK 40. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost.81iTEST BANK.81j 41. Engineering and Chemical Thermodynamics by Milo D. Koretsky .81iSOLUTIONS MANUAL.81j 42. Engineering Circuit Analysis 7Ed William Hart Hayt .81iSOLUTIONS MANUAL.81j 43. Engineering Economy - Leland Blank & Anthony Tarquin 6th Editionselected solutions ( student solution) 44. Engineering electromagnetics (7/ e) by HAYT .81iSOLUTIONS MANUAL.81j 45. Engineering Fluid Mechanics, 7th, By Clayfor n T. Crowe, Donald F. Elger, John A. Roberson .81iSOLUTIONS MANUAL.81j 46. Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, .81iSOLUTIONS MANUAL.81j MANUAL.81j 48. ENGINEERING MECHANICS: statics by BEDFOR D 5th. .81iSOLUTIONS MANUAL.81j 49. Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus test bank 50. Essentials of Managerial Finance 14e Besley Instructor manual 51. Essentials of Managerial Finance with Thomson ONE, 13e Brigham SOLUTIONS MANUAL 52. Essentials of Managerial Finance with Thomson ONE, 13e Brigham TEST BANK 53. Financial Account 7e Horngren (SOLUTIONS MANUAL) 54. Financial Account 7e Horngren TEST BANK 55. Financial Accounting (Libby, fifth edition) .81iSOLUTIONS MANUAL.81j 56. Financial Accounting 6e by horngren Harrison .81iSOLUTIONS MANUAL.81j 57. Financial Accounting (Libby, 2001 edition) .81iSOLUTIONS MANUAL.81j 58. Financial and Mangerial Accounting 2e by Horngren (SOLUTIONS MANUAL) 59. Financial and Mangerial Accounting 2e by Horngren (TEST BANK) 60. Financial and Mangerial Accounting 2e by Horngren .81iSOLUTIONS MANUAL.81j 61. Financial management theory and practice 12e by Brigham .81iSOLUTIONS MANUAL.81j 62. Finiancial Accounting 7e by Horngren.81iSOLUTIONS MANUAL.81j 63. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL 64. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta solution manual 65. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(TEST BANK) 66. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(SOLUTIONS MANUAL) 67. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta test bank 68. Fundamental Methods Of Mathematical Economics Chiang & Wainwright 2005 Mc Graw Hill (Instructor's Manual ) 69. Fundamentals of Advanced Accounting 3rd Edition by Joe B. Hoyle, , andTimothy S. Doupnik .81iSOLUTIONS MANUAL.81j 70. Fundamentals of Applied Electromagnetics 5th by Fawwaz T. Ulaby .81iSOLUTIONS MANUAL.81j 71. Fundamentals of Classical Thermodynamics 6th edition by Van Wylen .81iSOLUTIONS MANUAL.81j 72. Fundamentals of Corporate Finance ( Ross, Westerfield, Jordan 8th) .81iSOLUTIONS MANUAL.81j 73. Fundamentals of Engineering Thermodynamics 6th by Michael J. Moran, Howard N. Shapiro .81iSOLUTIONS MANUAL.81j 74. Fundamentals of financial management 12e Brigham .81iSOLUTIONS MANUAL.81j 75. Fundamentals of financial management 12e Brigham Solutions manual 76. Fundamentals of financial management 12e Brigham TEST BANK 77. Fundamentals of Financial Management With Infotrac Concise 4th by Eugene Brigham .81iSOLUTIONS MANUAL.81j 78. Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 79. Fundamentals of Fluid Mechanics, 6th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 80. Fundamentals of Physics (8th Edition) By Halliday .81iSOLUTIONS MANUAL.81j 81. Fundamentals of Signals and systems using web and matlab third edition .81iSOLUTIONS MANUAL.81j 82. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, .81iSOLUTIONS MANUAL.81j 83. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, SOLUTIONS MANUAL 84. fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine (SOLUTIONS MANUAL) 85. Gravity: An Introduction to Einstein's General Relativity by James B. Hartle 86. Individual Income Taxes 2009 edition by Hoffman/Solutions manualyith/Willis (TEST BANK) 87. Instructor manual for Digital Fundamentals (10th Edition) floyd (IM) 88. Intermediata Accounting 13e Kieso SOLUTIONS MANUAL 89. Intermediata Accounting 13e Kieso TEST BANK 90. intermediate accounting 5e by spiceland solutions manual 91. International Financial Management Geert Bekaert Robert J. Hodrick test bank 92. Introduction for Chemical Engineering Thermodynamics 7th By J.M. Solutions manualith, Hendrick C Van Ness .81iSOLUTIONS MANUAL.81j 93. Introduction for Environmental engineering and science 3rd editions by Gilbert M. Masters .81iSOLUTIONS MANUAL.81j 94. Introduction for Fluid Mechanics, 7th, Fox, Pritchard, McDonald {Wiley} .81iSOLUTIONS MANUAL.81j 95. Introduction for Mathematical Statistics 6/ E Robert V. Hogg 96. Introduction for Quantum Mechanics (1 & 2 Edition), By David J. Griffiths .81iSOLUTIONS MANUAL.81j 97. Introduction to Chemical Engineering Thermodynamics 7th edition (solution manual) By J.M. Solutions manualith, Hendrick C Van Ness 98. Introduction to Heat Transfer, 5th Edition Incropera, DeWitt, Bergman, Lavine.81iSOLUTIONS MANUAL.81j 99. Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593)( solutions manual) 100. Introduction to Managerial Accounting 2nd ed Brewer test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to 101. Introductory Econometrics for Finance(Chris Brooks 2002) .81iSOLUTIONS MANUAL.81j 102. Linear Algebra and Its Applications, 3rd Edition by: David C. Lay .81iSOLUTIONS MANUAL.81j 103. Linear Algebra with Applications 7th edition by Leon, SOLUTIONS MANUAL 104. Macroeconomics, 4E Olivier Blanchard instructor manual .81iSOLUTIONS MANUAL.81j 105. Macroeconomics, 5E Olivier Blanchard (instructor manual) 106. Macroeconomics, 5E Olivier Blanchard (test bank) 107. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E SOLUTIONS MANUAL 108. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E TEST BANK 109. Managerial Accounting 12e By Garrison Noreen SOLUTIONS MANUAL 110. Managerial Accounting 12e By Garrison Noreen .81iSOLUTIONS MANUAL.81j 111. managerial accounting 12th Edition by Garrison Noreen (TEST BANK) 112. Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson .81iSOLUTIONS MANUAL.81j 113. Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao .81iSOLUTIONS MANUAL.81j 114. Mechanics of Materials By R.C.Hibbeler 7th edition .81iSOLUTIONS MANUAL.81j 115. Mechanics of Materials by roy R. craig 2nd eddition solution manual 116. Mechanics of Materials, 7th James M. Gere - Stanfor d University .81iSOLUTIONS MANUAL.81j 117. Microeconomic Theory, Nicholson & Snyder, 10th ed, .81iSOLUTIONS MANUAL.81j 118. Microelectronic Circuit Analysis and Design, 3ed. by Donald A. Neamen .81iSOLUTIONS MANUAL.81j 119. Microelectronic circuits by R. Jaeger 3rd edition .81iSOLUTIONS MANUAL.81j 120. Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop .81iSOLUTIONS MANUAL.81j 121. Modern Elementary Statistics, 12/e by Freund & Perles .81iSOLUTIONS MANUAL.81j 122. Modern Elementary Statistics, 12/e Freund & Perles (TEST BANK) 123. Modern Physics, 2/E Randy Harris SOLUTIONS MANUAL 124. Numerical methods for engineers 5th by Chapra .81iSOLUTIONS MANUAL.81j 125. Operations Management 10e William J. Stevenson Solutions manual 126. Operations Management 10e William J. Stevenson TEST BANK 127. Operations Management 9e William J. Stevenson (SOLUTIONS MANUAL) 128. Organizational Behaviour, Fourth Canadian Ed., 4E Robins TEST BANK 129. Power System Analysis By John J. Grainger, William D. Stevenson Jr .81iSOLUTIONS MANUAL.81j 130. Principles of Auditing 15e by Whittington TEST BANK 131. Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole .81iSOLUTIONS MANUAL.81j 132. Probability and Statistical Inference 7th edition, Hogg & Tanis .81iSOLUTIONS MANUAL.81j 133. Probability, Statistics, and Random Processes For Electrical Engineering - Alberfor Leon-Garcia (3rd ) .81iSOLUTIONS MANUAL.81j 134. Probability,Random Variables and Stor hastic Processes,4th,by Athanasios Papoulis .81iSOLUTIONS MANUAL.81j 135. Process Systems Analysis And Control - Donald R. Coughanowr Solution Manual .81iSOLUTIONS MANUAL.81j 136. Separation Process Engineering: 2e by wankat SOLUTIONS MANUAL 137. Separation Process Principles, 2nd Ed.,by Seader, Henley .81iSOLUTIONS MANUAL.81j 138. solutions manual for Advanced Accounting 10e Fisher 139. solutions manual for Corporate Finance: A Focused Approach 3e Brigham 140. solutions manual for Advanced Accounting 10th edition by Beams 141. solutions manual for Essential of Accounting for Governmental and Not-for- Profit Organizations By Paul A Copley, 9e 142. solutions manual for Modern Advanced Accounting 10th edition by Larsen - 10e SM 143. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 144. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 145. solutions manual fundamentals of financial management, concise 6th edition by Brigham, Houston 146. South-Western Federal Taxation 2009 (Individual), 32th, Hoffman, Smith, Wills (Test Bank + solution manual) 147. Test Bank for Auditing and Assurance Services: A Systematic Approach, 6th Edition, Messier, Glover, Prawitt 148. Test Bank for Advanced Accounting 10e Fisher 149. test bank for Operations Management 9e William J. Stevenson (TB) 150. Test Bank for Accounting Information Systems - James Hall (6th ed) 151. Test bank for Advanced Accounting 10th edition by Beams 152. Test Bank for fundamentals of financial management, concise 6th edition by Brigham, Houston 153. Test bank for Modern Advanced Accounting 10th edition by Larsen - 10e TB 154. test bank cost Accounting 12e by Horngren 155. Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition .81iSOLUTIONS MANUAL.81j 156. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston test bank 157. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston solutions manual 158. Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Solutions manualith .81iSOLUTIONS MANUAL.81j Edition ,By F. P. Beer, E. R. Johnsfor n .81iSOLUTIONS MANUAL.81j 160. Fundamentals of Machine Component Design, 3rd ed - Student Solutions Manual by Juvinall, Marshek 161. Fundamentals of manufacturing 2nd edition by philip d. rufe solutions manual 162. Fundamentals of Momentum, Heat and Mass Transfer, 5th Edition Welty, Wicks, Rorrer, Wilson 163. Fundamentals of Multinational Finance, 2nd edition by Michael H. Moffett test bank and solution manual 164. Fundamentals of Multinational Finance, 3E by Michael H. Moffett (Instructor's Manual) 165. Fundamentals of Multinational Finance, 3E by Michael H. Moffett test bank 166. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith sm 167. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith tb 168. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith instructor manual 169. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith tb 170. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith sm 171. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow sm 172. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow tb 173. Human resources management 10e Gary dessler (IM+TB) 174. Intermediate Accounting 10e by Nikolai sm 175. Intermediate Accounting 11e by Kieso 176. Intermediate Accounting 12e by Kieso 177. Intermediate accounting 12th Updated by Kieso Solution manual 178. Intermediate accounting 12th Updated by Kieso test bank 179. Intermediate Accounting, 13th Edition Instructor's Manual Kieso, Weygandt, Warfield 180. (Sm+TB+IM) 181. Intermediate Accounting 2e by Baruch Englard 182. Intermediate Accounting 3e by J. David Spiceland 183. Intermediate Accounting 4e revised by J. David Spiceland solution manual 184. Intermediate accounting by Spiceland 4e Solution manual 185. Intermediate Accounting James D. Stice, Earl K. Stice, Fred Skousen 16th edition solution manual 186. Intermediate Accounting, 13th Edition Kieso, Weygandt, Warfield test bank and solution manual 187. Intermediate Accounting, Update, 12th Edition international student solution manual 188. Intermediate Algebra Functions & Authentic Applications 3e lehmann 189. Intermediate Algebra, 8th Edition By Margaret L. Lial, John Hornsby, Terry McGinnis 190. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves instructor manual 191. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves test bank 192. Intermediate Microeconomics, 10th Edition Walter Nicholson ,Christopher Snyder im with tb 193. International Accounting 1e by Doupnik solution manual 194. International Accounting 6e Frederick D. Choi Gary K. Meek 195. International Business The Challenges of Globalization, 4E John J. Wild,Kenneth L. Wild tb and im 196. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan instructor manual 197. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to me.,too. I can find it for === Subject: =?ISO-2022-JP?B?UHJvYmFiaWxpdHksIFN0YXRpc3RpY3MsIGFuZCBSYW5kb20gUHJvY2Vzc2Vz I EZvciBFbA==?= =?ISO-2022-JP?B?ZWN0cmljYWwgRW5naW5lZXJpbmcgLSBBbGJlcmZvciBMZW9uLUdhcmNpYSAo M 3JkICkgGyRCIUobKEJTT0xVVEk=?= =?ISO-2022-JP?B?T05TIE1BTlVBTBskQiFLGyhC?= posting-account=v8NCmQkAAACB4IvJvLNgwxUPNbyAq_lC CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn't on the list, don't worry, please email to 1. A First Course in Probability, (7th), By Sheldon Ross .81iSOLUTIONS MANUAL.81j 2. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 3. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 4. Accounting Information Systems 10th ED by Marshall B Romney and Paul J Steinbart SOLUTIONS MANUAL 5. accounting information systems 11th edition, romney, steinbart TEST BANK 6. Accounting what number means 8e by Marshall SOLUTIONS MANUAL 7. Advanced Accounting 9e Beams SOLUTIONS MANUAL 8. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank 9. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik .81iSOLUTIONS MANUAL.81j 10. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin solution manual 11. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin test bank 12. Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd .81iSOLUTIONS MANUAL.81j 13. Auditing and Assurance Services 12 th by: Alvin A Arens, .81iSOLUTIONS MANUAL.81j 14. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual 15. Biology Concepts and Connections 6e Neil A. Campbell Jane B. Reece Martha R. Taylor Eric J. Simon Jean L. Dickey test bank 16. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz instructor manual 17. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank 18. Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson 19. Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) ( solutions manual) 20. COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING FOR PERFOR MANCE 21. Corporate Finance A Focused Approach 3e Brigham TEST BANK 22. Corporate Finance plus MyFinanceLab Student Access 23. Corporate finance: Custom edition. Berk, J., & DeMarzo, P. (2007). Boston : Pearson Education 24. cost accounting 12e Horngren SOLUTIONS MANUAL 25. cost Accounting 13e Horngren test bank 26. Cost Accounting A Managerial Emphasis by Charles T. Horngren 13th .81iSOLUTIONS MANUAL.81j 27. Cost Accounting: Foundations and Evolutions 7E By Kinney (SOLUTIONS MANUAL) 28. Data and Computer Communications, 8th Edition By Stallings .81iSOLUTIONS MANUAL.81j 29. Database System Concepts, Fifth Edition by Avi Silberschatz ,Henry F. Korth solutions to exercises? 30. Database Systems: The Complete Book, 2/E Solutions Manual 31. Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) Instructor manual 32. Differential Equations and Linear Algebra by Penney and Edwards, 2nd .81iSOLUTIONS MANUAL.81j 33. Differential Equations Computing and Modeling (4th Edition) By Edwards .81iSOLUTIONS MANUAL.81j 34. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley .81iSOLUTIONS MANUAL.81j 35. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 36. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 37. Elementary Differential Equations and Boundary Value Problems, 8th by Boyce and Diprima .81iSOLUTIONS MANUAL.81j 38. Elements of engineering electromagnetics (6/ e) by N.N.RAO .81iSOLUTIONS MANUAL.81j 39. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost TEST BANK 40. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost.81iTEST BANK.81j 41. Engineering and Chemical Thermodynamics by Milo D. Koretsky .81iSOLUTIONS MANUAL.81j 42. Engineering Circuit Analysis 7Ed William Hart Hayt .81iSOLUTIONS MANUAL.81j 43. Engineering Economy - Leland Blank & Anthony Tarquin 6th Editionselected solutions ( student solution) 44. Engineering electromagnetics (7/ e) by HAYT .81iSOLUTIONS MANUAL.81j 45. Engineering Fluid Mechanics, 7th, By Clayfor n T. Crowe, Donald F. Elger, John A. Roberson .81iSOLUTIONS MANUAL.81j 46. Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, .81iSOLUTIONS MANUAL.81j MANUAL.81j 48. ENGINEERING MECHANICS: statics by BEDFOR D 5th. .81iSOLUTIONS MANUAL.81j 49. Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus test bank 50. Essentials of Managerial Finance 14e Besley Instructor manual 51. Essentials of Managerial Finance with Thomson ONE, 13e Brigham SOLUTIONS MANUAL 52. Essentials of Managerial Finance with Thomson ONE, 13e Brigham TEST BANK 53. Financial Account 7e Horngren (SOLUTIONS MANUAL) 54. Financial Account 7e Horngren TEST BANK 55. Financial Accounting (Libby, fifth edition) .81iSOLUTIONS MANUAL.81j 56. Financial Accounting 6e by horngren Harrison .81iSOLUTIONS MANUAL.81j 57. Financial Accounting (Libby, 2001 edition) .81iSOLUTIONS MANUAL.81j 58. Financial and Mangerial Accounting 2e by Horngren (SOLUTIONS MANUAL) 59. Financial and Mangerial Accounting 2e by Horngren (TEST BANK) 60. Financial and Mangerial Accounting 2e by Horngren .81iSOLUTIONS MANUAL.81j 61. Financial management theory and practice 12e by Brigham .81iSOLUTIONS MANUAL.81j 62. Finiancial Accounting 7e by Horngren.81iSOLUTIONS MANUAL.81j 63. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL 64. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta solution manual 65. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(TEST BANK) 66. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(SOLUTIONS MANUAL) 67. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta test bank 68. Fundamental Methods Of Mathematical Economics Chiang & Wainwright 2005 Mc Graw Hill (Instructor's Manual ) 69. Fundamentals of Advanced Accounting 3rd Edition by Joe B. Hoyle, , andTimothy S. Doupnik .81iSOLUTIONS MANUAL.81j 70. Fundamentals of Applied Electromagnetics 5th by Fawwaz T. Ulaby .81iSOLUTIONS MANUAL.81j 71. Fundamentals of Classical Thermodynamics 6th edition by Van Wylen .81iSOLUTIONS MANUAL.81j 72. Fundamentals of Corporate Finance ( Ross, Westerfield, Jordan 8th) .81iSOLUTIONS MANUAL.81j 73. Fundamentals of Engineering Thermodynamics 6th by Michael J. Moran, Howard N. Shapiro .81iSOLUTIONS MANUAL.81j 74. Fundamentals of financial management 12e Brigham .81iSOLUTIONS MANUAL.81j 75. Fundamentals of financial management 12e Brigham Solutions manual 76. Fundamentals of financial management 12e Brigham TEST BANK 77. Fundamentals of Financial Management With Infotrac Concise 4th by Eugene Brigham .81iSOLUTIONS MANUAL.81j 78. Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 79. Fundamentals of Fluid Mechanics, 6th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 80. Fundamentals of Physics (8th Edition) By Halliday .81iSOLUTIONS MANUAL.81j 81. Fundamentals of Signals and systems using web and matlab third edition .81iSOLUTIONS MANUAL.81j 82. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, .81iSOLUTIONS MANUAL.81j 83. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, SOLUTIONS MANUAL 84. fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine (SOLUTIONS MANUAL) 85. Gravity: An Introduction to Einstein's General Relativity by James B. Hartle 86. Individual Income Taxes 2009 edition by Hoffman/Solutions manualyith/Willis (TEST BANK) 87. Instructor manual for Digital Fundamentals (10th Edition) floyd (IM) 88. Intermediata Accounting 13e Kieso SOLUTIONS MANUAL 89. Intermediata Accounting 13e Kieso TEST BANK 90. intermediate accounting 5e by spiceland solutions manual 91. International Financial Management Geert Bekaert Robert J. Hodrick test bank 92. Introduction for Chemical Engineering Thermodynamics 7th By J.M. Solutions manualith, Hendrick C Van Ness .81iSOLUTIONS MANUAL.81j 93. Introduction for Environmental engineering and science 3rd editions by Gilbert M. Masters .81iSOLUTIONS MANUAL.81j 94. Introduction for Fluid Mechanics, 7th, Fox, Pritchard, McDonald {Wiley} .81iSOLUTIONS MANUAL.81j 95. Introduction for Mathematical Statistics 6/ E Robert V. Hogg 96. Introduction for Quantum Mechanics (1 & 2 Edition), By David J. Griffiths .81iSOLUTIONS MANUAL.81j 97. Introduction to Chemical Engineering Thermodynamics 7th edition (solution manual) By J.M. Solutions manualith, Hendrick C Van Ness 98. Introduction to Heat Transfer, 5th Edition Incropera, DeWitt, Bergman, Lavine.81iSOLUTIONS MANUAL.81j 99. Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593)( solutions manual) 100. Introduction to Managerial Accounting 2nd ed Brewer test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to 101. Introductory Econometrics for Finance(Chris Brooks 2002) .81iSOLUTIONS MANUAL.81j 102. Linear Algebra and Its Applications, 3rd Edition by: David C. Lay .81iSOLUTIONS MANUAL.81j 103. Linear Algebra with Applications 7th edition by Leon, SOLUTIONS MANUAL 104. Macroeconomics, 4E Olivier Blanchard instructor manual .81iSOLUTIONS MANUAL.81j 105. Macroeconomics, 5E Olivier Blanchard (instructor manual) 106. Macroeconomics, 5E Olivier Blanchard (test bank) 107. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E SOLUTIONS MANUAL 108. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E TEST BANK 109. Managerial Accounting 12e By Garrison Noreen SOLUTIONS MANUAL 110. Managerial Accounting 12e By Garrison Noreen .81iSOLUTIONS MANUAL.81j 111. managerial accounting 12th Edition by Garrison Noreen (TEST BANK) 112. Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson .81iSOLUTIONS MANUAL.81j 113. Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao .81iSOLUTIONS MANUAL.81j 114. Mechanics of Materials By R.C.Hibbeler 7th edition .81iSOLUTIONS MANUAL.81j 115. Mechanics of Materials by roy R. craig 2nd eddition solution manual 116. Mechanics of Materials, 7th James M. Gere - Stanfor d University .81iSOLUTIONS MANUAL.81j 117. Microeconomic Theory, Nicholson & Snyder, 10th ed, .81iSOLUTIONS MANUAL.81j 118. Microelectronic Circuit Analysis and Design, 3ed. by Donald A. Neamen .81iSOLUTIONS MANUAL.81j 119. Microelectronic circuits by R. Jaeger 3rd edition .81iSOLUTIONS MANUAL.81j 120. Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop .81iSOLUTIONS MANUAL.81j 121. Modern Elementary Statistics, 12/e by Freund & Perles .81iSOLUTIONS MANUAL.81j 122. Modern Elementary Statistics, 12/e Freund & Perles (TEST BANK) 123. Modern Physics, 2/E Randy Harris SOLUTIONS MANUAL 124. Numerical methods for engineers 5th by Chapra .81iSOLUTIONS MANUAL.81j 125. Operations Management 10e William J. Stevenson Solutions manual 126. Operations Management 10e William J. Stevenson TEST BANK 127. Operations Management 9e William J. Stevenson (SOLUTIONS MANUAL) 128. Organizational Behaviour, Fourth Canadian Ed., 4E Robins TEST BANK 129. Power System Analysis By John J. Grainger, William D. Stevenson Jr .81iSOLUTIONS MANUAL.81j 130. Principles of Auditing 15e by Whittington TEST BANK 131. Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole .81iSOLUTIONS MANUAL.81j 132. Probability and Statistical Inference 7th edition, Hogg & Tanis .81iSOLUTIONS MANUAL.81j 133. Probability, Statistics, and Random Processes For Electrical Engineering - Alberfor Leon-Garcia (3rd ) .81iSOLUTIONS MANUAL.81j 134. Probability,Random Variables and Stor hastic Processes,4th,by Athanasios Papoulis .81iSOLUTIONS MANUAL.81j 135. Process Systems Analysis And Control - Donald R. Coughanowr Solution Manual .81iSOLUTIONS MANUAL.81j 136. Separation Process Engineering: 2e by wankat SOLUTIONS MANUAL 137. Separation Process Principles, 2nd Ed.,by Seader, Henley .81iSOLUTIONS MANUAL.81j 138. solutions manual for Advanced Accounting 10e Fisher 139. solutions manual for Corporate Finance: A Focused Approach 3e Brigham 140. solutions manual for Advanced Accounting 10th edition by Beams 141. solutions manual for Essential of Accounting for Governmental and Not-for- Profit Organizations By Paul A Copley, 9e 142. solutions manual for Modern Advanced Accounting 10th edition by Larsen - 10e SM 143. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 144. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 145. solutions manual fundamentals of financial management, concise 6th edition by Brigham, Houston 146. South-Western Federal Taxation 2009 (Individual), 32th, Hoffman, Smith, Wills (Test Bank + solution manual) 147. Test Bank for Auditing and Assurance Services: A Systematic Approach, 6th Edition, Messier, Glover, Prawitt 148. Test Bank for Advanced Accounting 10e Fisher 149. test bank for Operations Management 9e William J. Stevenson (TB) 150. Test Bank for Accounting Information Systems - James Hall (6th ed) 151. Test bank for Advanced Accounting 10th edition by Beams 152. Test Bank for fundamentals of financial management, concise 6th edition by Brigham, Houston 153. Test bank for Modern Advanced Accounting 10th edition by Larsen - 10e TB 154. test bank cost Accounting 12e by Horngren 155. Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition .81iSOLUTIONS MANUAL.81j 156. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston test bank 157. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston solutions manual 158. Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Solutions manualith .81iSOLUTIONS MANUAL.81j Edition ,By F. P. Beer, E. R. Johnsfor n .81iSOLUTIONS MANUAL.81j 160. Fundamentals of Machine Component Design, 3rd ed - Student Solutions Manual by Juvinall, Marshek 161. Fundamentals of manufacturing 2nd edition by philip d. rufe solutions manual 162. Fundamentals of Momentum, Heat and Mass Transfer, 5th Edition Welty, Wicks, Rorrer, Wilson 163. Fundamentals of Multinational Finance, 2nd edition by Michael H. Moffett test bank and solution manual 164. Fundamentals of Multinational Finance, 3E by Michael H. Moffett (Instructor's Manual) 165. Fundamentals of Multinational Finance, 3E by Michael H. Moffett test bank 166. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith sm 167. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith tb 168. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith instructor manual 169. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith tb 170. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith sm 171. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow sm 172. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow tb 173. Human resources management 10e Gary dessler (IM+TB) 174. Intermediate Accounting 10e by Nikolai sm 175. Intermediate Accounting 11e by Kieso 176. Intermediate Accounting 12e by Kieso 177. Intermediate accounting 12th Updated by Kieso Solution manual 178. Intermediate accounting 12th Updated by Kieso test bank 179. Intermediate Accounting, 13th Edition Instructor's Manual Kieso, Weygandt, Warfield 180. (Sm+TB+IM) 181. Intermediate Accounting 2e by Baruch Englard 182. Intermediate Accounting 3e by J. David Spiceland 183. Intermediate Accounting 4e revised by J. David Spiceland solution manual 184. Intermediate accounting by Spiceland 4e Solution manual 185. Intermediate Accounting James D. Stice, Earl K. Stice, Fred Skousen 16th edition solution manual 186. Intermediate Accounting, 13th Edition Kieso, Weygandt, Warfield test bank and solution manual 187. Intermediate Accounting, Update, 12th Edition international student solution manual 188. Intermediate Algebra Functions & Authentic Applications 3e lehmann 189. Intermediate Algebra, 8th Edition By Margaret L. Lial, John Hornsby, Terry McGinnis 190. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves instructor manual 191. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves test bank 192. Intermediate Microeconomics, 10th Edition Walter Nicholson ,Christopher Snyder im with tb 193. International Accounting 1e by Doupnik solution manual 194. International Accounting 6e Frederick D. Choi Gary K. Meek 195. International Business The Challenges of Globalization, 4E John J. Wild,Kenneth L. Wild tb and im 196. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan instructor manual 197. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to me.,too. I can find it for === Subject: Intermediata Accounting 13e Kieso TEST BANK posting-account=v8NCmQkAAACB4IvJvLNgwxUPNbyAq_lC CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn't on the list, don't worry, please email to 1. A First Course in Probability, (7th), By Sheldon Ross .81iSOLUTIONS MANUAL.81j 2. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 3. A Friendly Introduction to Number Theory 3rd by Silverman ( SOLUTIONS MANUAL) 4. Accounting Information Systems 10th ED by Marshall B Romney and Paul J Steinbart SOLUTIONS MANUAL 5. accounting information systems 11th edition, romney, steinbart TEST BANK 6. Accounting what number means 8e by Marshall SOLUTIONS MANUAL 7. Advanced Accounting 9e Beams SOLUTIONS MANUAL 8. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Test bank 9. Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik .81iSOLUTIONS MANUAL.81j 10. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin solution manual 11. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin test bank 12. Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd .81iSOLUTIONS MANUAL.81j 13. Auditing and Assurance Services 12 th by: Alvin A Arens, .81iSOLUTIONS MANUAL.81j 14. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual 15. Biology Concepts and Connections 6e Neil A. Campbell Jane B. Reece Martha R. Taylor Eric J. Simon Jean L. Dickey test bank 16. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz instructor manual 17. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank 18. Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson 19. Computer Networking: A Top-Down Approach - James F. Kurose (4th ed) (ISBN 0321497708) ( solutions manual) 20. COMPUTER ORGANIZATION AND ARCHITECTURE DESIGNING FOR PERFOR MANCE 21. Corporate Finance A Focused Approach 3e Brigham TEST BANK 22. Corporate Finance plus MyFinanceLab Student Access 23. Corporate finance: Custom edition. Berk, J., & DeMarzo, P. (2007). Boston : Pearson Education 24. cost accounting 12e Horngren SOLUTIONS MANUAL 25. cost Accounting 13e Horngren test bank 26. Cost Accounting A Managerial Emphasis by Charles T. Horngren 13th .81iSOLUTIONS MANUAL.81j 27. Cost Accounting: Foundations and Evolutions 7E By Kinney (SOLUTIONS MANUAL) 28. Data and Computer Communications, 8th Edition By Stallings .81iSOLUTIONS MANUAL.81j 29. Database System Concepts, Fifth Edition by Avi Silberschatz ,Henry F. Korth solutions to exercises? 30. Database Systems: The Complete Book, 2/E Solutions Manual 31. Differential Equations and Linear Algebra - Stephen W. Goode (3rd ed) Instructor manual 32. Differential Equations and Linear Algebra by Penney and Edwards, 2nd .81iSOLUTIONS MANUAL.81j 33. Differential Equations Computing and Modeling (4th Edition) By Edwards .81iSOLUTIONS MANUAL.81j 34. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley .81iSOLUTIONS MANUAL.81j 35. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 36. Electrical Engineering, Principles and Applications: 4th Edition by Allan Hambley solutions manual 37. Elementary Differential Equations and Boundary Value Problems, 8th by Boyce and Diprima .81iSOLUTIONS MANUAL.81j 38. Elements of engineering electromagnetics (6/ e) by N.N.RAO .81iSOLUTIONS MANUAL.81j 39. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost TEST BANK 40. E-Marketing, 5e Judy Strauss, Adel El-Ansary, Raymond Frost.81iTEST BANK.81j 41. Engineering and Chemical Thermodynamics by Milo D. Koretsky .81iSOLUTIONS MANUAL.81j 42. Engineering Circuit Analysis 7Ed William Hart Hayt .81iSOLUTIONS MANUAL.81j 43. Engineering Economy - Leland Blank & Anthony Tarquin 6th Editionselected solutions ( student solution) 44. Engineering electromagnetics (7/ e) by HAYT .81iSOLUTIONS MANUAL.81j 45. Engineering Fluid Mechanics, 7th, By Clayfor n T. Crowe, Donald F. Elger, John A. Roberson .81iSOLUTIONS MANUAL.81j 46. Engineering Mechanics, Statics 6th by J. L. Meriam, L. G. Kraige, .81iSOLUTIONS MANUAL.81j MANUAL.81j 48. ENGINEERING MECHANICS: statics by BEDFOR D 5th. .81iSOLUTIONS MANUAL.81j 49. Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus test bank 50. Essentials of Managerial Finance 14e Besley Instructor manual 51. Essentials of Managerial Finance with Thomson ONE, 13e Brigham SOLUTIONS MANUAL 52. Essentials of Managerial Finance with Thomson ONE, 13e Brigham TEST BANK 53. Financial Account 7e Horngren (SOLUTIONS MANUAL) 54. Financial Account 7e Horngren TEST BANK 55. Financial Accounting (Libby, fifth edition) .81iSOLUTIONS MANUAL.81j 56. Financial Accounting 6e by horngren Harrison .81iSOLUTIONS MANUAL.81j 57. Financial Accounting (Libby, 2001 edition) .81iSOLUTIONS MANUAL.81j 58. Financial and Mangerial Accounting 2e by Horngren (SOLUTIONS MANUAL) 59. Financial and Mangerial Accounting 2e by Horngren (TEST BANK) 60. Financial and Mangerial Accounting 2e by Horngren .81iSOLUTIONS MANUAL.81j 61. Financial management theory and practice 12e by Brigham .81iSOLUTIONS MANUAL.81j 62. Finiancial Accounting 7e by Horngren.81iSOLUTIONS MANUAL.81j 63. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL 64. Finite Mathematics (8th Edition) by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. SOLUTIONS MANUAL Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta solution manual 65. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(TEST BANK) 66. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta (2007).(SOLUTIONS MANUAL) 67. Fundamental Accounting Principles, 18/e, Wild, Larson, & Chiappetta test bank 68. Fundamental Methods Of Mathematical Economics Chiang & Wainwright 2005 Mc Graw Hill (Instructor's Manual ) 69. Fundamentals of Advanced Accounting 3rd Edition by Joe B. Hoyle, , andTimothy S. Doupnik .81iSOLUTIONS MANUAL.81j 70. Fundamentals of Applied Electromagnetics 5th by Fawwaz T. Ulaby .81iSOLUTIONS MANUAL.81j 71. Fundamentals of Classical Thermodynamics 6th edition by Van Wylen .81iSOLUTIONS MANUAL.81j 72. Fundamentals of Corporate Finance ( Ross, Westerfield, Jordan 8th) .81iSOLUTIONS MANUAL.81j 73. Fundamentals of Engineering Thermodynamics 6th by Michael J. Moran, Howard N. Shapiro .81iSOLUTIONS MANUAL.81j 74. Fundamentals of financial management 12e Brigham .81iSOLUTIONS MANUAL.81j 75. Fundamentals of financial management 12e Brigham Solutions manual 76. Fundamentals of financial management 12e Brigham TEST BANK 77. Fundamentals of Financial Management With Infotrac Concise 4th by Eugene Brigham .81iSOLUTIONS MANUAL.81j 78. Fundamentals of Fluid Mechanics, 5th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 79. Fundamentals of Fluid Mechanics, 6th By Bruce,R. Munson, Donald .81iSOLUTIONS MANUAL.81j 80. Fundamentals of Physics (8th Edition) By Halliday .81iSOLUTIONS MANUAL.81j 81. Fundamentals of Signals and systems using web and matlab third edition .81iSOLUTIONS MANUAL.81j 82. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, .81iSOLUTIONS MANUAL.81j 83. fundamentals of thermodynamics, 7th edition,sonntag,borgnak, SOLUTIONS MANUAL 84. fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine (SOLUTIONS MANUAL) 85. Gravity: An Introduction to Einstein's General Relativity by James B. Hartle 86. Individual Income Taxes 2009 edition by Hoffman/Solutions manualyith/Willis (TEST BANK) 87. Instructor manual for Digital Fundamentals (10th Edition) floyd (IM) 88. Intermediata Accounting 13e Kieso SOLUTIONS MANUAL 89. Intermediata Accounting 13e Kieso TEST BANK 90. intermediate accounting 5e by spiceland solutions manual 91. International Financial Management Geert Bekaert Robert J. Hodrick test bank 92. Introduction for Chemical Engineering Thermodynamics 7th By J.M. Solutions manualith, Hendrick C Van Ness .81iSOLUTIONS MANUAL.81j 93. Introduction for Environmental engineering and science 3rd editions by Gilbert M. Masters .81iSOLUTIONS MANUAL.81j 94. Introduction for Fluid Mechanics, 7th, Fox, Pritchard, McDonald {Wiley} .81iSOLUTIONS MANUAL.81j 95. Introduction for Mathematical Statistics 6/ E Robert V. Hogg 96. Introduction for Quantum Mechanics (1 & 2 Edition), By David J. Griffiths .81iSOLUTIONS MANUAL.81j 97. Introduction to Chemical Engineering Thermodynamics 7th edition (solution manual) By J.M. Solutions manualith, Hendrick C Van Ness 98. Introduction to Heat Transfer, 5th Edition Incropera, DeWitt, Bergman, Lavine.81iSOLUTIONS MANUAL.81j 99. Introduction to Linear Algebra - Lee Johnson, Dean Riess, Jimmy Arnold (5th ed) (ISBN 0201658593)( solutions manual) 100. Introduction to Managerial Accounting 2nd ed Brewer test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to 101. Introductory Econometrics for Finance(Chris Brooks 2002) .81iSOLUTIONS MANUAL.81j 102. Linear Algebra and Its Applications, 3rd Edition by: David C. Lay .81iSOLUTIONS MANUAL.81j 103. Linear Algebra with Applications 7th edition by Leon, SOLUTIONS MANUAL 104. Macroeconomics, 4E Olivier Blanchard instructor manual .81iSOLUTIONS MANUAL.81j 105. Macroeconomics, 5E Olivier Blanchard (instructor manual) 106. Macroeconomics, 5E Olivier Blanchard (test bank) 107. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E SOLUTIONS MANUAL 108. Management of Human Resources, In-Class Edition, Second Canadian Edition, 2E TEST BANK 109. Managerial Accounting 12e By Garrison Noreen SOLUTIONS MANUAL 110. Managerial Accounting 12e By Garrison Noreen .81iSOLUTIONS MANUAL.81j 111. managerial accounting 12th Edition by Garrison Noreen (TEST BANK) 112. Mathematical Methods for Physics and Engineering 3th By Riley M P Hobson .81iSOLUTIONS MANUAL.81j 113. Mechanical Vibrations, 3rd Edition, by Singiresu S. Rao .81iSOLUTIONS MANUAL.81j 114. Mechanics of Materials By R.C.Hibbeler 7th edition .81iSOLUTIONS MANUAL.81j 115. Mechanics of Materials by roy R. craig 2nd eddition solution manual 116. Mechanics of Materials, 7th James M. Gere - Stanfor d University .81iSOLUTIONS MANUAL.81j 117. Microeconomic Theory, Nicholson & Snyder, 10th ed, .81iSOLUTIONS MANUAL.81j 118. Microelectronic Circuit Analysis and Design, 3ed. by Donald A. Neamen .81iSOLUTIONS MANUAL.81j 119. Microelectronic circuits by R. Jaeger 3rd edition .81iSOLUTIONS MANUAL.81j 120. Modern Control Systems 11th by Richard C Dorf and Robert H. Bishop .81iSOLUTIONS MANUAL.81j 121. Modern Elementary Statistics, 12/e by Freund & Perles .81iSOLUTIONS MANUAL.81j 122. Modern Elementary Statistics, 12/e Freund & Perles (TEST BANK) 123. Modern Physics, 2/E Randy Harris SOLUTIONS MANUAL 124. Numerical methods for engineers 5th by Chapra .81iSOLUTIONS MANUAL.81j 125. Operations Management 10e William J. Stevenson Solutions manual 126. Operations Management 10e William J. Stevenson TEST BANK 127. Operations Management 9e William J. Stevenson (SOLUTIONS MANUAL) 128. Organizational Behaviour, Fourth Canadian Ed., 4E Robins TEST BANK 129. Power System Analysis By John J. Grainger, William D. Stevenson Jr .81iSOLUTIONS MANUAL.81j 130. Principles of Auditing 15e by Whittington TEST BANK 131. Probability & Statistics for Engineers & Scientists, 8th by Sharon Myers , Keying Ye, Walpole .81iSOLUTIONS MANUAL.81j 132. Probability and Statistical Inference 7th edition, Hogg & Tanis .81iSOLUTIONS MANUAL.81j 133. Probability, Statistics, and Random Processes For Electrical Engineering - Alberfor Leon-Garcia (3rd ) .81iSOLUTIONS MANUAL.81j 134. Probability,Random Variables and Stor hastic Processes,4th,by Athanasios Papoulis .81iSOLUTIONS MANUAL.81j 135. Process Systems Analysis And Control - Donald R. Coughanowr Solution Manual .81iSOLUTIONS MANUAL.81j 136. Separation Process Engineering: 2e by wankat SOLUTIONS MANUAL 137. Separation Process Principles, 2nd Ed.,by Seader, Henley .81iSOLUTIONS MANUAL.81j 138. solutions manual for Advanced Accounting 10e Fisher 139. solutions manual for Corporate Finance: A Focused Approach 3e Brigham 140. solutions manual for Advanced Accounting 10th edition by Beams 141. solutions manual for Essential of Accounting for Governmental and Not-for- Profit Organizations By Paul A Copley, 9e 142. solutions manual for Modern Advanced Accounting 10th edition by Larsen - 10e SM 143. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 144. solutions manual to Fundamentals of Database Systems, 5E Ramez Elmasri,Shamkant B. Navathe 145. solutions manual fundamentals of financial management, concise 6th edition by Brigham, Houston 146. South-Western Federal Taxation 2009 (Individual), 32th, Hoffman, Smith, Wills (Test Bank + solution manual) 147. Test Bank for Auditing and Assurance Services: A Systematic Approach, 6th Edition, Messier, Glover, Prawitt 148. Test Bank for Advanced Accounting 10e Fisher 149. test bank for Operations Management 9e William J. Stevenson (TB) 150. Test Bank for Accounting Information Systems - James Hall (6th ed) 151. Test bank for Advanced Accounting 10th edition by Beams 152. Test Bank for fundamentals of financial management, concise 6th edition by Brigham, Houston 153. Test bank for Modern Advanced Accounting 10th edition by Larsen - 10e TB 154. test bank cost Accounting 12e by Horngren 155. Transport Phenomena by Bird, Stewart & Lightfoot, 2nd edition .81iSOLUTIONS MANUAL.81j 156. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston test bank 157. Understanding Financial Statements 8e Lyn M. Fraser Aileen Ormiston solutions manual 158. Unit Operations of Chemical Engineering (7th) By Warren McCabe, Julian Solutions manualith .81iSOLUTIONS MANUAL.81j Edition ,By F. P. Beer, E. R. Johnsfor n .81iSOLUTIONS MANUAL.81j 160. Fundamentals of Machine Component Design, 3rd ed - Student Solutions Manual by Juvinall, Marshek 161. Fundamentals of manufacturing 2nd edition by philip d. rufe solutions manual 162. Fundamentals of Momentum, Heat and Mass Transfer, 5th Edition Welty, Wicks, Rorrer, Wilson 163. Fundamentals of Multinational Finance, 2nd edition by Michael H. Moffett test bank and solution manual 164. Fundamentals of Multinational Finance, 3E by Michael H. Moffett (Instructor's Manual) 165. Fundamentals of Multinational Finance, 3E by Michael H. Moffett test bank 166. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith sm 167. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith tb 168. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith instructor manual 169. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith tb 170. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith sm 171. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow sm 172. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow tb 173. Human resources management 10e Gary dessler (IM+TB) 174. Intermediate Accounting 10e by Nikolai sm 175. Intermediate Accounting 11e by Kieso 176. Intermediate Accounting 12e by Kieso 177. Intermediate accounting 12th Updated by Kieso Solution manual 178. Intermediate accounting 12th Updated by Kieso test bank 179. Intermediate Accounting, 13th Edition Instructor's Manual Kieso, Weygandt, Warfield 180. (Sm+TB+IM) 181. Intermediate Accounting 2e by Baruch Englard 182. Intermediate Accounting 3e by J. David Spiceland 183. Intermediate Accounting 4e revised by J. David Spiceland solution manual 184. Intermediate accounting by Spiceland 4e Solution manual 185. Intermediate Accounting James D. Stice, Earl K. Stice, Fred Skousen 16th edition solution manual 186. Intermediate Accounting, 13th Edition Kieso, Weygandt, Warfield test bank and solution manual 187. Intermediate Accounting, Update, 12th Edition international student solution manual 188. Intermediate Algebra Functions & Authentic Applications 3e lehmann 189. Intermediate Algebra, 8th Edition By Margaret L. Lial, John Hornsby, Terry McGinnis 190. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves instructor manual 191. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves test bank 192. Intermediate Microeconomics, 10th Edition Walter Nicholson ,Christopher Snyder im with tb 193. International Accounting 1e by Doupnik solution manual 194. International Accounting 6e Frederick D. Choi Gary K. Meek 195. International Business The Challenges of Globalization, 4E John J. Wild,Kenneth L. Wild tb and im 196. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan instructor manual 197. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan test bank solutions manual and Test Bank contact me with , studentbrother(at) hotmail(dot)com (my email address, studentbrother@hotmail.com ), the list are parts of our solutions, if the solution you want isn.81ft on the list, don.81ft worry, please email to me.,too. I can find it for === Subject: Shortest known proof: There is no uncountable infinity. posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Consider the countable set Q of all terminating binary sequences of the form q = 0.[X]1, where X is a finite binary sequence. Get the countable set Q' of sequences q' by appending each q by an infinite tail of zeros. Construct a list of all elements of Q'. Use this list to construct the complete infinity binary tree by combining identical initial segments of the binary sequences q' in one and the same line. Note: This reduces the number of written bits and does not increase the number of binary sequences. Find that it is impossible to distinguish any infinite binary sequence from all paths of the tree thus constructed. Find that it is impossible to distinguish any infinite binary sequence from all paths q' of the tree. Recognize that, contrary to set theorists' intuition, there are not more than countably many bit sequences that can be used to denote real numbers and, in particular, can be used to prove Cantor's theorem. === Subject: Re: Shortest known proof: There is no uncountable infinity. posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) You DON'T KNOW what a proof IS! Proofs are FROM AXIOMS! If you are not going to begin BY STATING YOUR AXIOMS then YOU DO NOT HAVE a proof! > Consider the countable set Q of all terminating binary sequences of > the form q = 0.[X]1, where X is a finite binary sequence. Get the > countable set Q' of sequences q' by appending each q by an infinite > tail of zeros. This is a complete waste of time. You could have just started with set of finite sequences, PERIOD, since X is going to be any one of those ANYway. None of the constraints you are placing on the tail is RELEVANT. They DON'T MATTER. > Construct a list of all elements of Q'. OK. we'll use the length/lexxicographic ordering. > Use this list to construct the complete infinity binary tree > by combining identical initial segments of the binary sequences q' > in one and the same line. THIS DOES *NOT* construct the complete infinite tree! This in particular consructs NO path of the tree that ends in all 1s!! === Subject: Re: Shortest known proof: There is no uncountable infinity. > Consider the countable set Q of all terminating binary sequences of > the form q = 0.[X]1, where X is a finite binary sequence. Get the > countable set Q' of sequences q' by appending each q by an infinite > tail of zeros. Construct a list of all elements of Q'. Use this list to construct the > complete infinity binary tree by combining identical initial segments > of the binary sequences q' in one and the same line. The only way to construct a maximal infinite binary tree is to form the set of all its nodes together with all the parent of relations between them. This does not require any paths, but can be accomplished by unioning any set of paths covering all nodes. > Note: This > reduces the number of written bits and does not increase the number of > binary sequences. But as WM's machinations displace the parent of relation between nodes, one no longer has the original set of paths as paths, but merely as sets of nodes. Find that it is impossible to distinguish any infinite binary sequence > from all paths of the tree thus constructed. But that tree now contains paths not used in its construction, and which are distinguishable from every path ued in its construction, WM's claim of a proof falls flat. As usual. > Find that it is > impossible to distinguish any infinite binary sequence from all paths > q' of the tree. True but irrelevant. Since every path in a tree is a member of the set of paths in a tree, what WM really has to prove, and can't, is that everypath in the tree is a member of Q'. This is fails to hold, since the path of all 1's in not in Q'. Recognize that, contrary to set theorists' intuition, there are not > more than countably many bit sequences that can be used to denote real > numbers and, in particular, can be used to prove Cantor's theorem. Cantors theorem only says that given any sequence of 'bit seqeunces', there is a bit sequence not in the given sequence of sequences. And it remains true despite all of WM's wrigglings. One can quite easily prove more: that there are as many missing from any such list as listed in it. -- Virgil === Subject: Re: Shortest known proof: There is no uncountable infinity. posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322),gzip(gfe),gzip(gfe) > Find that it is impossible to distinguish any infinite binary sequence > from all paths of the tree thus constructed. But that tree now contains paths not used in its construction, and which > are distinguishable from every path ued in its construction, WM's claim > of a proof falls flat. Every claim of every proof falls flat if ghosts enter the scene. WQhat I do is the following: I start from the list containing all q', a countable set of lines 0.1000... 0.01000... 0.11000... ... and I write the initial segments of the first and the third line in one line, as far as they are identical: 1000... 0.1 000... All other lines remain unchanged. Now you accuse me of sneaking in paths that have not been in Q'. That is obviously wrong --- as usual. === Subject: Re: Shortest known proof: There is no uncountable infinity. posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Every claim of every proof falls flat if ghosts enter the scene. NO, IT DOESN'T. In First-Order Logic, you CAN have models where ghosts (i.e., things that aren't named by terms in the language of the theory) are present, AND NOTHING falls apart (except false intuitions about things that were expected to be provable BUT AREN'T). WQhat I do is the following: > I start from the list containing all q', a countable set of lines 0.1000... > 0.01000... > 0.11000... > ... and I write the initial segments of the first and the third line in > one line, as far as they are identical: 1000... > 0.1 > 000... All other lines remain unchanged. This process will have to be iterated. More and longer initial combinations are possible. > Now you accuse me of sneaking in > paths that have not been in Q'. NO, WE DON'T accuse you of that! WE KNOW you DON'T do that! THAT'S OUR POINT! YOU DON'T include paths that were not in Q' THAT'S HOW WE KNOW that you DON'T include ALL paths! YOU ONLY include the countable number of paths from Q'! THAT IS NOT *ALL* the paths! THERE ARE other paths DESPITE the fact that YOU never construct them! === Subject: Re: Shortest known proof: There is no uncountable infinity. posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) Find that it is impossible to distinguish any infinite binary sequence > from all paths of the tree thus constructed. But that tree now contains paths not used in its construction, and which > are distinguishable from every path ued in its construction, WM's claim > of a proof falls flat. Every claim of every proof falls flat if ghosts enter the scene. WQhat I do is the following: > I start from the list containing all q', a countable set of lines 0.1000... > 0.01000... > 0.11000... > ... and I write the initial segments of the first and the third line in > one line, as far as they are identical: 1000... > 0.1 > 000... All other lines remain unchanged. Now you accuse me of sneaking in > paths that have not been in Q'. > That is obviously wrong --- as usual. > Assuming P!=NP, we understand in great detail why a proof hasn't yet been seen. Consider a countably infinite number of algorithms: An Argument for P=NP is the winner needn't provide a constructive proof that P=NP [...] from the countably infinite set of such devices can be physicalized to produce M i p. P=NP i.e., Proof=NonPossibles, add em up, and choose what's left___the possibles. (length) strings S over a finite alphabet A is countably infinite on the number of P-isomorphism classes of NP-complete sets. Thus, the number of P-isomorphism classes of NP-complete sets is either one or (countably) infinite. We have Two proof techniques: 1. P versus NP and computability theoretic constructions we show a structure of countably infinite signature with P=N2P and a model-theoretic proof for $P neq NP$ over all infinite sets. If either theory proves the polynomial hierarchy is infinite then for all i, (e.g. countably based topological spaces) and domain theory (as Canonical disjoint NP-pairs of keywords Disjoint NP-pairs; Propositional proof systems; Degrees; P-separable. In any countable set both A and B are infinite sets. So L(Mc) negationslash= and L(Md) is proof the Halting Problem of a countably infinite set is uncountable is a self referential contradiction. Firstly, there is then a countably infinite hierarchy of problems that are harder than P and it is extremely likely the proof will show us some way to construct it. If NP = P, then almost all problems in P are P-complete. For All proofs p in number system S, p is not a proof of '0=1'). Understanding of this kind, or progress on P=NP, would have been the kind of combinatorial complexity and the countable infinite (above plus 1). -- mmm === Subject: Re: Shortest known proof: There is no uncountable infinity. > Consider the countable set Q of all terminating binary sequences of > the form q = 0.[X]1, where X is a finite binary sequence. Get the > countable set Q' of sequences q' by appending each q by an infinite > tail of zeros. Consider that the set of all subsets of Q is provably not countable. At least to anyone who understands mathematical proofs. -- Virgil === Subject: Re: Shortest known proof: There is no uncountable infinity. posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Consider the countable set Q of all terminating binary sequences of > the form q = 0.[X]1, where X is a finite binary sequence. Get the > countable set Q' of sequences q' by appending each q by an infinite > tail of zeros. Consider that the set of all subsets of Q is provably not countable. > At least to anyone who understands mathematical proofs. to anyone who believes in actual infinity. Then there is a diagonal that differs from every entry. But that is not true. 1) There is no set N that differs from every FISON. It is only true that for every FISON there is a larger FISON. 2) There is no natural number that is larger than every natural number. There is only, for every natural number, a natural number that is larger than that. 3) There is no diagonal 0.111... of the list 0.0 0.1 0.11 0.111 ... that differs from every entry. There is only, for every entry, a diagonal that differes from that entry (and is identical to the following entry). Set theorists intermingle actual and potential infinity. They believe in actual infinity in cases (1) and (3), denying the statements above, but do not believe in actual infinity in case (2). Obviously that is wrong, inconsequent and should be rectified. === Subject: Re: Shortest known proof: There is no uncountable infinity. Consider the countable set Q of all terminating binary sequences of > the form q = 0.[X]1, where X is a finite binary sequence. Get the > countable set Q' of sequences q' by appending each q by an infinite > tail of zeros. Consider that the set of all subsets of Q is provably not countable. > At least to anyone who understands mathematical proofs. to anyone who believes in actual infinity. To anyone that does not believe in actual infinities there are no infinite binary trees nor infinite paths nor countably infinite sets. So that, one way or another, WM is taking nonsense. That WM takes part in this discussion, including discussing properties necessary for actually infinite sets of actually infinite paths taken from actually infinite trees, means WM either actually believes in actual infinite sets or he is lying. or both. > Then there is a diagonal > that differs from every entry. But that is not true. > 1) There is no set N that differs from every FISON. It is only true > that for every FISON there is a larger FISON. > 2) There is no natural number that is larger than every natural > number. There is only, for every natural number, a natural number that > is larger than that. > 3) There is no diagonal 0.111... of the list 0.0 > 0.1 > 0.11 > 0.111 > ... that differs from every entry. Then WM should stop lyingly claiming improbable properties of things he believes can not exist. > Set theorists intermingle actual and potential infinity. On the contrary, set theorists do not allow any such thing as merely potential infinite sets. For a set theorist, any set that is not actually finite is actually infinite. > They believe > in actual infinity in cases (1) and (3), denying the statements above, > but do not believe in actual infinity in case (2). Wm has it wrong again, as usual. In actual set theories, (2) and only (2) holds Obviously that is wrong More obviously WM is wrong again. -- Virgil === Subject: Re: Shortest known proof: There is no uncountable infinity. posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > 1) There is no set N that differs from every FISON. In set theory, we have THE AXIOM of infinity. We INSIST that N exists. We do NOT dispute your right to posit that N does NOT exist -- indeed the ANY AND EVERY infinite set does NOT exist -- as an axiom of YOUR own. But you have TO STATE YOUR axioms! You do NOT get to tell us that there is ANY thing WRONG with OUR axioms until and unless you DERIVE A CONTRADICTION from them. === posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Consider that the set of all subsets of Q is provably not countable. This is NOT THE LEAST BIT RELEVANT TO ANYthing that was said in the argument. If you are not going to address the argument then he is free to just keep asserting it in response to your stupidity. === <4a2d0dc4$0$7111$afc38c87@news.optusnet.com.au> <4a2f0d02$0$23688$afc38c87@news.optusnet.com.au> argument. If you are not going to address the argument then he is > free to just keep asserting it in response to your stupidity. Virgil's remark was indeed entirely unconnected with anything in M.9fckenheim's argument. But do you think addressing the argument will stop the endless assertions? It would be much more interesting, surely, if M.9fckenheim could be coached into explaining in some coherent manner the notion of potential infinity at play, of choice sequences that grow and shrink. Quoting Troelstra and van Dalen on the classical intuitionistic notion of choice sequences: The method of justifying axioms for choice sequences by reflecting on what it means to be given a choice sequence (conceptual analysis of the notion) can be carried considerably farther than is done in Brouwer's writings, and leads to interesting insights; - - - Choice sequences are not only a good example of the possibilities (and limitations) of conceptual analysis, but are also of interest in themselves, as demonstrating the possibilities of coherent reasoning about incomplete objects. Alas, it appears M.9fckenheim is not interested in conceptual analysis of the sort alluded to in this passage. -- Aatu Koskensilta (aatu.koskensilta@uta.fi) Wovon mann nicht sprechen kann, dar.9fber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus === <87vdmpcn38.fsf@alatheia.truth.invalid> posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Virgil's remark was indeed entirely unconnected with anything in > M.9fckenheim's argument. But do you think addressing the argument will > stop the endless assertions? you in a long time. > It would be much more interesting, surely, if M.9fckenheim could be > coached into explaining in some coherent manner the notion of potential > infinity at play, Please! He would have to UNDERSTAND *that* notion, first! He is NOT even INTERESTED in THAT notion! HE is talking about A DIFFERENT notion of a potentially infinite set, specifically, the one that RATIONAL beings call an [actually] infinite set, all of whose members are finite. Rather than simply concede that THIS IS WHAT potentially infinite set MEANS, WM insists on calling the above A LOGICAL CONTRADICTION! What we should be WANTING WM to do is to STOP SIMULTANEOUSLY incoherent. === At 18.9457 degrees the hypotenuse measures the correct PI value 3.14710 ., the vertical side is 1 and the horizontal is 2.984 proportions at exact 90 degrees. Pi is not a ratio you Dandies mathematician, too arrogant to answer a simple question,too obsessed with your P=np, and other mathematics ,measuring the tits on a porks belly, yet ignoring the base of your mathematics . Pi is a differential at 18.9457 degrees because we have a differential at point Zero, there is no such thing as null zero, the universe is created at an inverse point and angle, you Dandies . I am not Michael Musatov, I will not mew at the door of the Dandies,rather Shake the dust of my boots and I resign from your Sci math, which is not a bad show, but unfortunately is overtaken by arrogant Dandy mathematicians. Our mathematics will be on the Web.If N=np I predict it will be at an inverse deifferential, all mathematics is, You dandies. If any Mathematicians want to join us , do E mail your assent in a civil manner to us , do not even think of sending a uncivil E mail, you can do that on Scimath. I am not Michael Mustov, I do not need your stage , but learned a lot about you , your mathematics and your Dandy Mathematics. Inverse 19 === 360 proportions divided by 19=18.9457 proportions, which is exactly equal to pi, but Pi is not a ratio it is a differential, and I trust that the dandy mathematicians know the difference between a ratio and a differential. YOUR MATHEMATICS IS A RATIO 1 and 1 , BUT INVERSE MATHEMATICS at 19 IS A DIFFERENTIAL BETWEEN 1 and -1,. Dandy simply means--- spiff, first rate , very well dressed up. === Subject: Boundary of open sets in R^2 A subset of R is the bounday of a bounded (connected) nonempty open set iff it is a compact nowhere dense (two-point) set. A subset of R^2 is the boundary of a bounded (connected) nonempty open set iff ...... what? TCL === Subject: Re: Boundary of open sets in R^2 > A subset of R is the bounday of a bounded (connected) > nonempty open set iff it is a compact nowhere dense > (two-point) set. > A subset of R^2 is the boundary of a bounded > (connected) nonempty open set iff ...... what? TCL Perhaps the following is the best one can have: 1. A subset C of R^2 is the boundary of a nonempty bounded open set iff C is compact nowhere dense and its complement is a disjoint union of two open sets, one is bounded and the other unbounded. 2. A subset C of R^2 is the boundary of a nonempty bounded connected open set iff C is compact nowhere dense and its complement is a disjoint union of two CONNECTED open sets, one is bounded and the other unbounded. 3. A subset C of R^2 is the boundary of a nonempty bounded simply connected open set iff C is compact nowhere dense and its complement is a disjoint union of two open sets, one is bounded and simply connected, and the other is unbounded and connected. TCL === Subject: Re: Boundary of open sets in R^2 > A subset of R is the bounday of a bounded > (connected) > nonempty open set iff it is a compact nowhere > dense > (two-point) set. > A subset of R^2 is the boundary of a bounded > (connected) nonempty open set iff ...... what? TCL Perhaps the following is the best one can have: > 1. A subset C of R^2 is the boundary of a nonempty > bounded open set iff C is compact nowhere dense > and its complement is a disjoint union of two open > sets, one is bounded and the other unbounded. 2. A subset C of R^2 is the boundary of a nonempty > bounded connected open set iff C is compact nowhere > dense > and its complement is a disjoint union of two > CONNECTED open sets, one is bounded and the other > unbounded. 3. A subset C of R^2 is the boundary of a nonempty > bounded simply connected open set iff C is compact > nowhere dense > and its complement is a disjoint union of two open > sets, one is bounded and simply connected, and the > other is unbounded and connected. TCL Sorry. The union of (2,0) and the unit cicle gives a counterexample to my assertions. So my assertions 1,2,3, above are incorrect. TCL CC: Stephen J. Herschkorn === Subject: Re: Boundary of open sets in R^2 > A subset of R is the bounday of a bounded (connected) nonempty > open set iff it is a compact nowhere dense (two-point) set. > A subset of R^2 is the boundary of a bounded (connected) > nonempty open set iff ...... what? > I don't think that there is a simple answer. Of course, the boundary of > a bounded connected subset of R^2 has to be compact and connected. The boundary of the punctured unit disc ({(x, y): 0 < x^2 + y^2 < 1}) is not connected. > These > conditions are clearly not sufficient but, given a compact and connected > subset B of R^2 whose interior is connected and such that B is the > closure of its interior, then B is the boundary of some bounded > connected subset of R^2. -- Stephen J. Herschkorn sjherschko@netscape.net === Subject: Re: Boundary of open sets in R^2 > A subset of R is the bounday of a bounded (connected) nonempty > open set iff it is a compact nowhere dense (two-point) set. > A subset of R^2 is the boundary of a bounded (connected) > nonempty open set iff ...... what? > I don't think that there is a simple answer. Of course, the boundary of > a bounded connected subset of R^2 has to be compact and connected. The boundary of the punctured unit disc ({(x, y): 0 < x^2 + y^2 < > 1}) is not connected. Oops! Quite right. :-( Jose Carlos Santos === Subject: Re: Difference between a Ratio and a Differential, mathematically. You are right- my mathematics does not know nonsense. Shame!- === Subject: GOOD BYE SCI MATH--it has been a good show Overall it has been a good ride, but I have come to realize that most of you cannot think out of the box that you have been trained in your theory, almost like a Religious extremist etc. May be you can accuse me of the same BUT I leave you with this .In a right angled triangle, at exactly 360/19 angle at 18.9457 degrees, the differential in the sides9one side is 3 the other 3.14+, is the exact the correct value of the Pi , proving that the value of 1 proportion is a fraction off about 0.02 off 1, inverse zero is a reality that you will have to ultimately accept when you understand the difference between a Ratio and a differential === Subject: Re: GOOD BYE SCI MATH--it has been a good show posting-account=UA-6fQkAAADI18fSPOc495gPgW1akxLl Trident/4.0; MathPlayer 2.10b; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > Overall it has been a good ride, but I have come to realize that most of you cannot think out of the box that you have been trained in your theory, almost like a Religious extremist You're close. My experience in Logic is that the vast majority of people (especially those for which it is important) have no interest in hearing about anything that contradicts what they were taught in school, and many even have no interest in anything that does not support something they learned in school. Occasioanlly a psycologist will point out something about various species of animals giving complete preference to other animals in the same species, and that the class of university professors can't be expected to behave any differently. Like a pack of wild animals?? C-B > etc. May be you can accuse me of the same BUT I leave you with this .In a right angled triangle, at exactly 360/19 angle at 18.9457 degrees, the differential in the sides9one side is 3 the other 3.14+, is the exact the correct value of the Pi , proving that the value of 1 proportion is a fraction off about 0.02 off 1, inverse zero is a reality that you will have to ultimately accept when you understand the difference between a Ratio and a differential === Subject: CFP: Optical SuperComputing Workshop 2009 posting-account=qJpM7AoAAACIRLR6aFYZipAwlqGZEJiY AppleWebKit/530.5 (KHTML, like Gecko) Chrome/2.0.172.31 Safari/530.5,gzip(gfe),gzip(gfe) CFP: Optical SuperComputing Workshop 2009 2nd International Workshop on Optical SuperComputing in Bertinoro (OSC09) November 18-20, Bertinoro, Italy http://www.cs.bgu.ac.il/~dolev/OSC09 SCOPE: OSC, the International Workshop on Optical SuperComputing, is an annual forum for research presentations on all facets of optical computing for solving hard computation tasks. Optical computing devices have the potential to be the very next computing infrastructure. Optical computing presents an alternative to the frequency limitations, cross-talk phenomena and soft-errors of electronic devices. The natural parallelism of optical computing devices, coupled with the advance in fiber optics and optical switches make optical computing commercially viable. Research contributions to the theory, design, specification, analysis, implementation, or application of optical supercomputers are solicited. Topics of interest include, but are not limited to: ´ Designs or demonstrations of optical computing devices and systems ´ Algorithmics and complexity issues of optical computing ´ Computation representation by photons and holograms ´ Neural and brain inspired architectures ´ Electro-optic devices for interacting with optical computing devices ´ Practical implementations ´ Analysis of existing devices and case studies ´ Optical photonics and laser switching technologies ´ Optical and photonic memories ´ Optical signal processing subsystems ´ Optical networks for high-performance computing ´ Optical interconnections ´ Quantum optical systems ´ Applications and algorithms for optical devices Submission deadline July 25, 2009 Acceptance notification August 25, 2009 Camera-ready copy due September 10, 2009 Steering and Organization Committee: H. John Caulfield Fisk University Shlomi Dolev Ben-Gurion University Yeshaiahu Fainman UCSD Mihai Oltean Babes-Bolyai University Tobias Haist Stuttgart Universitat Program Committee: George Barbastathis MIT Antonella Bogoni CNIT H. John Caulfield Fisk University Ernesto Ciaramella SSSUP Cristian Calude University of Auckland Shlomi Dolev (Chair) Ben-Gurion University Yeshaiahu Fainman UCSD Dietmar Fey Erlangen-Nuremberg University William Green IBM Tobias Haist Stuttgart Universitat JÂurgen Jahns FU Hagen Efstratios Kehayas NTUA Shimon Levit Weizmann Institute of Science Michal Lipson Cornell David Miller Stanford Thomas Naughton NUIM Kouichi Nitta Kobe University Jeremy L. Obrien University of Bristol Mihai Oltean Babes-Bolyai University Wolfgand Osten Stuttgart Universitat Haldun Ozaktas Bilkent University Joseph Rosen Ben-Gurion University Yunlong Sheng Laval University Natan T. Shaked Duke University Joseph Shamir Technion Dan Tamir Texas State University Kristof Vandoorne Universiteit Gent Damien Woods University of Seville Toyohiko Yatagai Utsunomiya University Zeev Zalevsky Bar-Ilan University Xinliang Zhang Huazhong University How to submit: Authors are invited to submit their extended abstracts electronically. A detailed description of the electronic submission procedure will appear on the workshop web-page, as of June 1, 2009. Authors unable to submit electronically should contact the program chair, Shlomi Dolev by email, dolev@cs.bgu.ac.il or by phone, +972-8-6428119 to receive instructions. Workshop presentations will have two formats: Regular presentations of at least 25 minutes accompanied by papers of up to 15 pages in the proceedings. Additional material may be added in a clearly marked Appendix to be read at the discretion of the Program Committee Members. This form is intended for contributions reporting on original research, submitted exclusively to this workshop. Brief announcements of at least 10 minutes accompanied by two page abstracts in the proceedings. This format is a forum for brief communications, which may be published in other workshops. Longer versions expanding the brief announcements will be collected in a web site. The workshop proceedings will be published by LNCS Springer Verlag. We are also seeking a special issue with a journal. SUBMISSIONS FORMAT: The cover page should include (1) title, (2) authors and affiliation, (3) postal and e-mail address of the contact author, (4) indication of the format(s) to which the paper is submitted, and (5) a brief abstract describing the work. It is recommended that each submission begin with a succinct statement of the problem, summary of the main results, and a brief explanation of their significance, all suitable for a non-specialist. Technical development of the work, directed to the specialist, should follow. A submission for the regular presentation format should be no longer than 4,500 words (10 pages on letter-size paper using at least 11-point font, figures and tables included) excluding references. If the authors believe that more details are essential to substantiate the main claims of the paper, they may include a clearly marked appendix that will be read at the discretion of the program committee. Extended abstracts deviating significantly from these guidelines risk rejection without consideration of their merits. A submission for the brief announcement format should be no longer than three pages. Authors of accepted brief announcements will be asked to submit a full version of their work to be placed on a WWW site. If requested by the authors in the cover letter, an extended abstract that is not selected for a long presentation will also be considered for the brief announcement format. Such a request will not affect consideration of the paper for a long presentation. === Subject: Formal Proof Language Example - Human-Readable? posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) Please consider the following formal proof language example: package MyTheoryProof; using edu.mit.number_theory.*; theorem MyTheory { let N be NaturalNumbers; forall a, b, c in N given { a^2 + b^2 = c^2; a, b are_relative_prime; a is odd; } implies thereexists m, n in N { m <= n; a = n^2 - m^2; b = 2 * m * n; c = n^2 + m^2; } } proven_by { ... } This is written in a Mizar-like language with some formatting changes based on the C family tree and some personal touches. Without any description of the language, I'm curious to know whether you can derive the meaning of the theorem statement simply by reading the code? The goal is for it to be both machine and human readable. Andrew. -- Andrew Tomazos === Subject: Re: Formal Proof Language Example - Human-Readable? > Please consider the following formal proof language example: > It's a pain in the butt to read. Here's the same which is much easier to read. Let N be the natural numbers. Proposition. For all a,b,c in N if a is odd, a,b are relative prime and a^2 + b^2 = c^2, then there's some m,n in N for which m <= n, a = n^2 - m^2, b = 2mn, c = n^2 + m^2. Proof. ... > package MyTheoryProof; > using edu.mit.number_theory.*; theorem MyTheory > { > let N be NaturalNumbers; > forall a, b, c in N > given > { > a^2 + b^2 = c^2; > a, b are_relative_prime; > a is odd; > } > implies > { > m <= n; > a = n^2 - m^2; > b = 2 * m * n; > c = n^2 + m^2; > } > } > proven_by > { > ... > } This is written in a Mizar-like language with some formatting changes > based on the C family tree and some personal touches. Without any description of the language, I'm curious to know whether > you can derive the meaning of the theorem statement simply by reading > the code? The goal is for it to be both machine and human readable. Andrew. -- > Andrew Tomazos posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) Please consider the following formal proof language example: It's a pain in the butt to read. > Here's the same which is much easier to read. Let N be the natural numbers. > Proposition. For all a,b,c in N > if a is odd, a,b are relative prime and > a^2 + b^2 = c^2, > then there's some m,n in N for which m <= n, > a = n^2 - m^2, > b = 2mn, > c = n^2 + m^2. > Proof. ... package MyTheoryProof; > using edu.mit.number_theory.*; theorem MyTheory > { > let N be NaturalNumbers; > forall a, b, c in N > given > { > a^2 + b^2 = c^2; > a, b are_relative_prime; > a is odd; > } > implies > { > m <= n; > a = n^2 - m^2; > b = 2 * m * n; > c = n^2 + m^2; > } > } > proven_by > { > ... > } This is written in a Mizar-like language with some formatting changes > based on the C family tree and some personal touches. Without any description of the language, I'm curious to know whether > you can derive the meaning of the theorem statement simply by reading > the code? The goal is for it to be both machine and human readable. Andrew. -- > Andrew Tomazos posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) Please consider the following formal proof language example: It's a pain in the butt to read. > Here's the same which is much easier to read. Let N be the natural numbers. > Proposition. For all a,b,c in N > if a is odd, a,b are relative prime and > a^2 + b^2 = c^2, > then there's some m,n in N for which m <= n, > a = n^2 - m^2, > b = 2mn, > c = n^2 + m^2. > Proof. ... package MyTheoryProof; > using edu.mit.number theory.*; theorem MyTheory > { > let N be NaturalNumbers; > forall a, b, c in N > given > { > a^2 + b^2 = c^2; > a, b are relative prime; > a is odd; > } > implies > { > m <= n; > a = n^2 - m^2; > b = 2 * m * n; > c = n^2 + m^2; > } > } > proven by > { > ... > } This is written in a Mizar-like language with some formatting changes > based on the C family tree and some personal touches. Without any description of the language, I'm curious to know whether > you can derive the meaning of the theorem statement simply by reading > the code? The goal is for it to be both machine and human readable. Andrew. -- > Andrew Tomazos Please consider the following formal proof language example: ? ? package MyTheoryProof; ? ? using edu.mit.number theory.*; ? ? theorem MyTheory > ? ? { > ? ? ? ? let N be NaturalNumbers; ? ? ? ? forall a, b, c in N > ? ? ? ? ? ? given > ? ? ? ? ? ? { > ? ? ? ? ? ? ? ? a^2 + b^2 = c^2; > ? ? ? ? ? ? ? ? a, b are relative prime; > ? ? ? ? ? ? ? ? a is odd; > ? ? ? ? ? ? } > ? ? ? ? ? ? implies > ? ? ? ? ? ? ? ? thereexists m, n in N > ? ? ? ? ? ? ? ? { > ? ? ? ? ? ? ? ? ? ? m <= n; > ? ? ? ? ? ? ? ? ? ? a = n^2 - m^2; > ? ? ? ? ? ? ? ? ? ? b = 2 * m * n; > ? ? ? ? ? ? ? ? ? ? c = n^2 + m^2; > ? ? ? ? ? ? ? ? } > ? ? } > ? ? proven by > ? ? { > ? ? ? ? ... > ? ? } This is written in a Mizar-like language with some formatting changes > based on the C family tree and some personal touches. Without any description of the language, I'm curious to know whether > you can derive the meaning of the theorem statement simply by reading > the code? ?The goal is for it to be both machine and human readable. This seems to be in 1-to-1 correspondance with FOL plus some noise words. So the only difference is the syntax used, which is immaterial. C-B > Andrew. -- > Andrew Tomazos === Subject: Re: Formal Proof Language Example - Human-Readable? posting-account=6ea2ugoAAACnO44ASKspIG0s--Ju5Ekb Gecko/20020604,gzip(gfe),gzip(gfe) > Please consider the following formal proof language example: package MyTheoryProof; using edu.mit.number_theory.*; theorem MyTheory > { > let N be NaturalNumbers; forall a, b, c in N > given > { > a^2 + b^2 = c^2; > a, b are_relative_prime; > a is odd; > } > implies > thereexists m, n in N > { > m <= n; > a = n^2 - m^2; > b = 2 * m * n; > c = n^2 + m^2; > } > } > proven_by > { > ... > } This is written in a Mizar-like language with some formatting changes > based on the C family tree and some personal touches. Without any description of the language, I'm curious to know whether > you can derive the meaning of the theorem statement simply by reading > the code? The goal is for it to be both machine and human readable. I understood it without any effort. But that doesn't mean I find it satisfactory. 1) Your notation is too verbose. For example let N be NaturalNumbers. You could do without the be. Also thereexists is too long. 2) a is odd and a, b are_relative_prime are hideous. I'd much rather have odd(a) and coprime(a , b). 3) I don't like that you are using ; for conjunction. The established term is and and I see no reason to change it. Since I also do programming I can live with & or && but not ;. 4) I'd rather have if/then rather than given/implies. Beyond these remarks I'd rather have a Lisp syntax rather than a C-like syntax so that the possibility exists for powerful macros. I think macros could be quite useful in proofs. -- Prediction: Somebody at Microsoft will throw together a script that rummages through source replacing memcpy (unto, from, size); with memcpy_s (unto, size, from, size); and will then announce that the world has become safer because the evil memcpy() has been expunged. Eric Sosman at http://tinyurl.com/mfbbuy === Subject: Re: Formal Proof Language Example - Human-Readable? > Please consider the following formal proof language example: [Snip] Euclid's primitive pythagorean triple theorem [Snip] This is not a formal proof example, since the important part, the proof, is left out. Bye === Subject: Re: Formal Proof Language Example - Human-Readable? posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Please consider the following formal proof language example: [Snip] Euclid's primitive pythagorean triple theorem [Snip] This is not a formal proof example, since > the important part, the proof, is left out. My question was about the language of the theorem statement. Do you consider it both human and machine readable? -Andrew. === Subject: Re: Formal Proof Language Example - Human-Readable? > Please consider the following formal proof language example: > [Snip] Euclid's primitive pythagorean triple theorem [Snip] > This is not a formal proof example, since > the important part, the proof, is left out. My question was about the language of the theorem statement. Do you > consider it both human and machine readable? > -Andrew. But this is not a challenge. Since your theorem comes from algebra. And even in undergraduate notation for algebra is learnt. The only difference in your example is, that there is some sugar for implication and quantifiers. But as I said, your heading is formal proof language, and a formal proof language is more than only a language for theorem statements. The problem is that for proofs there are more choices than for theorem statements. For example your theorem could also be formalize as follows: forall a, b, c in nat (a^2 + b^2 = c^2 & rel_prim(a,b) & odd(a) => exists m, n in nat (m<=n & a = n^2 - m^2 & b = 2*m*n & c = n^2 + m^2)) And I think this is better than distributing conjuncts over C like statements separated by semicolon ;. First of all because this language has already been 100-times formally introduces in logic books. I maybe would only start using semicolon in proof figures. You know formulas as above are part of proof figures. If I remember well, some of the original papers of Gentzen gives a nice introduction what structure a proof figure has... So Gentzen is one person to keep in mind. The other person would be Knuth, the inventor of Tex. I think he was once even proving that 2-dimensional things can be expressed in a sequential and thus 1-dimensional language... Bye === Subject: Re: Formal Proof Language Example - Human-Readable? posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > For example your theorem could also be formalize as follows: forall a, b, c in nat > (a^2 + b^2 = c^2 & > rel prim(a,b) & > odd(a) => exists m, n in nat > (m<=n & > a = n^2 - m^2 & > b = 2*m*n & > c = n^2 + m^2)) And I think this is better than distributing conjuncts > over C like statements separated by semicolon ;. First > of all because this language has already been 100-times > formally introduces in logic books. Are you sure the way you have written it is really clearer? When you think about it - if I state that a series of propositions: A B C D are individually true in some context, than it is exactly the same as saying: A and B and C and D This also mirrors the way that (what I suspect to be) at the core of every proof: Axiom A A' A'' A''' Theorem X ie Truth-preseving transformations of an axiom(s) to a theorem. ..is identical on some level to: Axiom A and A' and A'' and A''' and Thereom X Also the way you have indented and spaced out the theorem doesn't seem to follow any logical pattern. It is almost like you have written it on one line and randomly inserted carriage returns. The way I formatted it was deliberate, to indicate the relevant scope connections and compound statements. This is an important consideration when complexity increases. -Andrew. === Subject: Re: Formal Proof Language Example - Human-Readable? posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) For example your theorem could also be formalize as follows: forall a, b, c in nat > (a^2 + b^2 = c^2 & > rel prim(a,b) & > odd(a) => exists m, n in nat > (m<=n & > a = n^2 - m^2 & > b = 2*m*n & > c = n^2 + m^2)) And I think this is better than distributing conjuncts > over C like statements separated by semicolon ;. First > of all because this language has already been 100-times > formally introduces in logic books. Are you sure the way you have written it is really clearer? When you think about it - if I state that a series of propositions: A > B > C > D are individually true in some context, than it is exactly the same as > saying: A and B and C and D Ignoring whitespace (which you should) the difference between yours and Jan's form is the difference between: A ; B ; C ; D ; and A & B & C & D The difference is in the choice of conjunction character and in whether it is a separator or terminator. These differences are really, really trivial. The surest sign of a language design noob is a focus on syntax. Worry about the semantics instead; they're actually important. Marshall === Subject: Re: Formal Proof Language Example - Human-Readable? > Are you sure the way you have written it is really clearer? When you think about it - if I state that a series of propositions: A > B > C > D are individually true in some context, than it is exactly the same as > saying: A and B and C and D > Yes, but this is quite a myoptic view. You are now only thinking inside the realm of theorems. How do you avoid confusion between a proof figure (supposed it will use ;) and a conjunction (since you will also use ;) here. So discussion does not make sense, as long as you don't show us your ideas for proofs. Maybe when you have shown me your ideas about proofs, I will maybe fully agree on some points of your syntax. But there is also a semantical consideration here. Namely for example in natural deduction, it is not obvious that listing of axioms is the same as conjunction. So for example in minimal logic, when we write: A, B, C |- D This is not the same as: A & B & C |- D Where & is classical. It is the same as: A * B * C |- D Where * is some kind of fusion. So it really makes sense to have both available, some kind of listing and explicit forms of conjunction, alas there is not only one conjunction. This transposes also to context you mentioned. In the example there is an exists context and a forall context. Whereas I know the listing practice for the axiom context, the listing practice for quantifier contexts is less known to me. Except maybe the , in Prolog, which has the meaning of a kind of a conjunction. But in Prolog the , is mostly treated as any other operator. With a level and a associativity etc.. So maybe we can advance the discussion as follows. You want the following operator and : ; : Conjunction forall : Universal quantifier implies: Implication thereexists : Existential quantifier Ok, now tell me, how will the story continue for proof figures? Bye === Subject: Re: Formal Proof Language Example - Human-Readable? > Except maybe the , in Prolog, which has the meaning of a kind of > a conjunction. But in Prolog the , is mostly treated as any other > operator. With a level and a associativity etc.. So maybe we can > advance the discussion as follows. You want the following operator: ; : Conjunction > forall : Universal quantifier > implies: Implication > thereexists : Existential quantifier Ok, now tell me, how will the story continue for proof figures? Ok, here is a hint. Proofs are usually a mesh. So it is quite crucial that axioms, lemmas, etc.. can be labled. At least this is one approach, and it can practically not be avoided. In normal programming languages we have a many objects that are nameable. For example variables and functions. This is alreay quite nice, since they are on different levels. And a similar thing will also happen to proofs. So there will be proofs where the mathematician himself will give names, in the form of lemmas, subtheorems, etc.. We could use function object syntax for that: lemma helper1 { } lemma helper2 { } And there will be proof steps, the mathematician is refering in his phrasing of the proofs. We could use variable object syntax for that: step line21 = lamma helper2 { step line22 = } We can only introduce local variables, when the step is really not used outside. So we will have local and global steps. And the step itselfs will be not tactics, but inference rule applications, or axiom schema instantiations. Something like: step line21 = eqReflex(y); lemma helper2 { step line22 = modusPonens(line21,helper1); return line22; } The verification could also be done by constant evaluation, a compiler could do this at compile time. We could combine proofs and other code. Maybe use proofs in assertions. Wow! Does this make sense to you? Bye === Subject: Re: Formal Proof Language Example - Human-Readable? posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Does this make sense to you? Sort of. Let me try and write the proof for the Euclid theorem I language version of the proof? I lost my original source. -Andrew. === Subject: Re: Formal Proof Language Example - Human-Readable? > Does this make sense to you? Sort of. Let me try and write the proof for the Euclid theorem I > language version of the proof? I lost my original source. > -Andrew. > Depends where you begin, how do you see natural numbers? Peano? Or is it a more general result in algebra? Bye === Subject: Re: Formal Proof Language Example - Human-Readable? posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Sort of. Let me try and write the proof for the Euclid theorem I > language version of the proof? I lost my original source. Depends where you begin, how do you see natural numbers? > Peano? Or is it a more general result in algebra? Well I guess we can assume that in the number theory module we will have the usual primitive results of: - integer addition - integer subtraction - integer multiplication - even/odd - relatively prime - gcd - etc plus I guess number theory might be using other modules that give us more basic classical first-order logic, set theory and the Peano axioms. If I could get a sketch of the proof for the theorem using any of the above in natural language that would be great. Once I see how the proof works, and what it depends on, I will have a better idea where to put stuff. -Andrew. === Subject: Re: Formal Proof Language Example - Human-Readable? > If I could get a sketch of the proof for the theorem using any of the > above in natural language that would be great. Once I see how the > proof works, and what it depends on, I will have a better idea where > to put stuff. > -Andrew. In my young years I tried the following: a^2 + b^2 = c^2 Thus: b*b = c*c - a*a b*b = (c+a) * (c-a) n*q*m*n*q*m = n*q*n * q*m*m (factorization of b, c+a, c-a sic!) Thus: b = q* m*n c+a = q* n^2 c-a = q* m^2 Thus: b = q* m*n a = (c+a-(c-a))/2 = (q*n^2-q*m^2)/2 c = (c+a+c-a) /2 = (q*n^2+q*m^2)/2 Thus: b = q *m*n a = q *(n^2-m^2)/2 c = q *(n^2+m^2)/2 Works also for m+n even or q even. Bye === Subject: Re: Formal Proof Language Example - Human-Readable? > Thus: > b = q *m*n > a = q *(n^2-m^2)/2 > c = q *(n^2+m^2)/2 Works also for m+n even or q even. Bye > This is also mentioned here: http://www.math.ou.edu/~dmccullough/teaching/pythagoras2.pdf See refined classical enumeration. Bye === Subject: Re: Formal Proof Language Example - Human-Readable? > step line21 = eqReflex(y); > lemma helper2 { > step line22 = modusPonens(line21,helper1); > return line22; > } The verification could also be done by constant evaluation, > a compiler could do this at compile time. We could combine > proofs and other code. Maybe use proofs in assertions. Wow! And BTW, all the stuff can be packaged in normal programming modules, or even in classes, including the types lemma and step! And we can use qualified names to refer to the axioms, inference rules, steps and lemmas, i.e.: Euclid.lemma77 Minimal.modusPonens But since we started with C, and continued with the C programming analog, we will not end in something readable. Program code is normally judged by non programmers as very technical. And I have some ideas why this is the case. So maybe we should not take C as a template to build our proof language, but something else. Some grammatical constructs that are found in natural language. For example adjectives. I think Mizar has adjectes... Bye === === === Subject: a^4 + b^4 = c^4 + d^4 and Pell Equations We have the identity by Fauquembergue, (17p^2-12pq-13q^2)^4 + (17p^2+12pq-13q^2)^4 = (17p^2-q^2)^4 + (289p^4+14p^2q^2-239q^4)^2 As equal sums of two biquadrates, it remains to make the _last_ term a square. It can be treated as an elliptic curve, 289p^4+14p^2q^2-239q^4 = y^2 with one small soln {p,q} = {11,3}. Also, by treating the third term as the Pell eqn, q^2-17p^2 = +/-1 this identity solves x^4+y^4 = z^2+1, which is a near-miss of a quasi-FLT since Fermat proved x^4+y^4 = z^2 has no integral solns. Now if only a Pell eqn can be found for (a+1/2)^4+b^4 = (a-1/2) ^4+c^4... (If there is.) P.S. Is there an integral soln to the counterpart near-miss x^4+y^4 = z^2-1? Couldn't find any small ones... - Titus === Subject: --- --- --- Reference related to a number theory question Cc: dlee752@yahoo.com posting-account=ffq-pAoAAAAWN8XUaOwbBbTrV981ne_q .NET CLR 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; IEMB3; IEMB3),gzip(gfe),gzip(gfe) The following equation is under consideration. x^p + (1/M)y^p = z^2 (1) Conditions: x, y, z are relatively prime integers each > 5, prime p > 3, y is even, integer M > 2. Statement: (1) has no integer solutions under the given conditions if M is even. But it can have integer solutions if M is odd. I would greatly appreciate if anyone can kindly refer me to some appropriate referenc related to (1) David === Subject: Re: --- --- --- Reference related to a number theory question > The following equation is under consideration. x^p + (1/M)y^p = z^2 (1) Conditions: x, y, z are relatively prime integers each > 5, prime p 3, y is even, integer M > 2. Statement: (1) has no integer solutions under the given conditions if > M is even. But it can have integer solutions if M is odd. I would greatly appreciate if anyone can kindly refer me to some > appropriate referenc > related to (1) Take z to be some large, odd number. Take x and p to satisfy the conditions, with x^p < z^2, x odd. Take y = z^2 - x^p. Then M will be an even integer. Do you ever think these things through before posting them? Even a tiny bit? -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: Re: --- --- --- Reference related to a number theory question posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) The following equation is under consideration. x^p + (1/M)y^p = z^2 (1) Conditions: x, y, z are relatively prime integers each > 5, prime p 3, y is even, integer M > 2. Statement: (1) has no integer solutions under the given conditions if > M is even. But it can have integer solutions if M is odd. I would greatly appreciate if anyone can kindly refer me to some > appropriate referenc > related to (1) Take z to be some large, odd number. > Take x and p to satisfy the conditions, with x^p < z^2, x odd. > Take y = z^2 - x^p. > Then M will be an even integer. Do you ever think these things through before posting them? > Even a tiny bit? -- > Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) The solution numerically is given by tyhe sequence 2*234579167=469158334/78167/3001/2=2 You guys are ridiculous. These days I can say that I left my house > with a GPS at 10:13.012 h:m.s today and arrived at the store at > 10:32.304 and had a VMG of 34.23 mph. > This level of detail was not available in Kant's time, Wow, shucks you are soooooo ridiculously bright. NOT but the same > sensibilities are exactly what he discusses. You may find the following packed with sensibilities, the application > of reason certainly doesn't. First sentence of Kant's pure unadulterated destruction of reason: > (PUDOR) > That all our knowledge begins with experience there can be no > doubt. First sentence second paragraph: > But, though all our knowledge begins with experience, it by no means > follows that all arises out of experience. You may find Kant's take on morality sensible, whereas reason proves > it to be one of the most senseless, therefore utterly mind dependent, > disgustingly arbitrary, context bereft, utterly ignorant and bereft of > anything man can experience, (touch see feel hear smell), therefore > the most anti-human anti-reason morality known to man. You may regard Kant's dopey idea that man cant know things in > themselves, sensible, when in reality, as determined via reason, that > garbage is just sooo ridiculously stupid its beyond words. In man aquiring his knowledge there is absolutely no requirement of > man to know things in themselves for him to be able to claim 100% > certain knowldge, with 100% certainty man CAN and DOES know the > differences between forms of matter and matter's nature. That presupposes a magical sudden undestanding from which to claim > 100% understanding, that also insists @ its more fundamental level > that knowledge was gained without any experimental evidence to back it > up and from which to base his reason... you're totally cart before > horse. don't you thing the horse will have more success pulling? You missed > the foundations - next you'll be telling us that you can build a house > from the roof down? You need to step back and put things into the correct context before > you start trying to claim some kinda supperior thought process -which > only appears totally lacking from reading this . It is NOT the entity in itself that man needs to know, but rather it > is the differences between the forms of matter and their nature is ALL > there is for man to have knowledge of, Aristotle's law of identity > which Kant rejects as a means to knowledge. Same position, get the right context and you might have something > MG The essence of truth in proof can be properly expressed through narrative means and recollections citing facts to prove otherwise forgone or obscured conclusions to bring light to further truth. Begin logix narrative:(thread) I challenge the devil to a debate (and any logicians, too): For forms of matter nature proof p=NP. Search problem 'v' computes: Is P Versus NP Formally Independent? Nature of P = NP.84a conjecture that all but asserts the titanic difficulty of finding [...] P = NP asks for an efficient procedure that finds a short proof [.....] independent of ZF, no matter which Turing machine is used to specify O. [....] It's interesting that this proof rules out only lower bounds of the form 2 [...]. Consider: computational complexity and mathematics: P, NP and mathematics [CapitalEth] a computational complexity perspective. Describe the computational model precisely (e.g. it does not matter if we allow [.....] it is so hard to prove indeed P = NP it seems completely obvious. We [......] the very nature of proof. We exhibit three different remarkable manifestations of [.....] a rank 1 tensor as a product of linear forms (one in X, [...]. The Awakening of The American Mind: P=NP complete The Maximal [......] to the extremal ends of the conservation law of matter/ energy, fields/motions, [....] or any other form of heiarchical organization, of any other possible [...] P=NP i.e., Proof=NonPossibles, add em up, and choose what's left the [....] senses The sensible Better Nature senses, over the Higher Nature senses. [...] And now we're getting interesting. An Argument for P=NP, again I say this repeatedly out of necessity, the winne of the Clay Mathematics prize need not provide a constructive proof P=NP [...] of the matter than, say, whether many current cryptographic schemes can be [...]. Godel apparently believed it might well be possible to answer questions of the form ñ¤l [.....] 'proto'-law of nature. It's a profound waste of time to build gadgets to [...]. Truth is the goal and hard work and common sense filled with imagination is the real necessity. Chris Menzel helped me prove N=NP: on USENET with Inverse 19 Mathematics in sci.math [...], I simply said, Consider this thread an extension of my proof P=NP, and add to it this [...] always the same path as we what we seek to define we by nature of our > observing change. [...] In form and function, across language and guild, the > heir apparent us. [...] At any rate, no matter the claim, they do not belong to me. I did not [...]. A consequence of a proof of the one-way function existence for the [...]8 Nov 2008 [...]. Indeed, form the assumption follows while for the initial stages of the [...]. The above statement may seem vague to the impatient reader (especially to Kant or Russell, I assume) but nonetheless by the nature of our existence and the very essence of time it is ontologically sound. The statement may simply be rephrased: A proof of the consequence of a past action is based on the sound assumption causal relations can only be established after the existence of their result in time. --Martin Musatov As to numerical solutions, a proof P Á' NP would guarantee a [....]. Hence, it is plausible to conclude the NP nature of the Schr.9adinger equation [...] state of play, prospects. But before we get too far removed in physics, we must return to the proof. Computational Complexity and Mathematical Proofs clearly agree the P versus NP problem is clearly an important problem for computer scientists. Also a fundamental problem about the nature of mathematics [...] string over a fixed alphabet and is written in a left-justified form directly below [....]. As a matter of fact, by choosing our proof systems accordingly, we can represent P = NP { What does it mean? No matter how fast computers we manage to build, we will still be unable to express [.....] the exact nature of these problems has not yet been determined, even though every- [...] (posi)tive proof for P=NP would mean we have a polynomial time algorithm for [....] Boyce-Codd Normal Form Violation. Conjunctive Query Foldabilty [...]. Sticking to the complexity of Computational Complexity: We all have our favorite theorems: P = NP for Space. The non-trivial nature of a result and proof is in the insight [....] I sometimes joke about having a two line proof of P=NP that keeps [...]. So the book as Erdos referenced contains as derivatives of the author's work (lawfully on unlawfully attained): 1. The Chapter 2: God Math (Logik, LOGOS, P=NP) ' Robot Pirate Ninja. You laugh and it all seems silly, but it is quite upsetting to those just beginning to understand it. It is actually quite daunting and cruel. This is my P=NP proof, after all. One would have to be a bit outside the norm to [...] see. 1a. Supposition claims proofs of reality, by threading a narrative to hypotheses. 1b. We later learned from Einstein that the existence of matter and energy made a [...] lines that go on forever, are so rare as to be nearly unique in nature [....] and we finally see the fully realized (simple) model in its ideal form.[ ...] Truth is the highest order. Period. P=NP. q.e.d. PROOF BERTRAND RUSSELL WAS UNWISE: Bertrand Arthur William Russell [Third Earl Russell] (1872-1970) British philosopher, mathematician, social critic, writer. 1st Argument: 1a. Russell: ...by intellectual integrity the habit of deciding vexed questions in accordance with the evidence, or of leaving them undecided where the evidence is inconclusive. 1b. Musatov: The limit principle of defending a negative-valued statement or impossibility allows for a divine divide between classes as to the public people esteemed insist something is unknowable, uncountable, or impossible, simply discourages the acceptance of truth, discovery, and the incidence of greater possibility than what remains to be seen. Conclusion: Musatov: (Claims) P==NP. Even Russell himself agreed. On P=/=NP. Russell states: (implies) Proof: [...]Russell: Most of the greatest evils that man has inflicted upon man have come through people feeling quite certain about something which, in fact, was false.-- Bertrand Russell, Unpopular Essays, Ideas That Have Harmed Mankind (1950), p. 149, quoted from James A Haught, ed, 2000 Years of Disbelief P==NP is a truth-valued claim. P=/=NP is a false-valued claim. q.e.d. (1st argument) Summary Statment: The defense of a truth statement should always be given favor to the insistence of an impossibility. --Martin Musatov Argument 2 2a. Russell: So far as I can remember, there is not one word in the Gospels in praise of intelligence; and in this respect ministers of religion follow gospel authority more closely than in some others.-- Bertrand Russell, quoted, in part, from Jonathon Green, The Cassell Dictionary of Cynical Quotations 2b. Musatov: (cites) P==NP.1.Matthew 22:37 And He said to him, 'YOU SHALL LOVE THE LORD Jesus said unto him, Thou shalt love the Lord thy God with all thy heart, and with all thy {p} soul, and with all thy mind. [...]http:// bible.cc/matthew/22-37.htm 2.Matthew 22:37 Jesus said unto him, Thou shalt love the Lord thy [...] Jesus said to him: Thou shalt love the Lord thy God with thy whole heart, and with thy whole soul, and with thy whole mind. [...] http://scripturetext.com/matthew/22-37.htm 3. ...In Phillipians 2:5, the apostle Paul said, let this mind be in you which was also in Christ Jesus. In Mathew 6:33 Jesus said, seek ye first the kingdom [...]http://www.thechristmind.org/ The fact is there are many instances and portrayals in the bible where frankness and honesty are encouraged over formalsim and inauthentic truth. God allowed Abraham to question and challenge him over his reasoning in the destruction of Sodom. God and Abraham reached a compromise. God listened to David's accusations of unfairness, betrayal, and abandonment. Jeremiah even claimed God tricked him. Job was allowed to vent and when his ordeal was over he rebuked his friends for being inauthentic. God rewards honesty and authenticity. Honesty and authenticity predicate truth, hence they are one and the same rewarded in the portrayal of the gospels as written in The Old and New Testaments. Summary argument: Musatov: Following Jesus begins in your Mind. Jesus said, ñYou must love the Lord your God with all your heart, with all your soul, with all your mind and with all your strength.î (Mark 12:30) [...]http://www.frtommylane.com/homilies/year b/03.htm The below results prove my above forgone conclusion further: THE MIRACLE OF ONE MIND AT SAFEPLACEFELLOWSHIP.COM All these signs pointed to the singleness of mind experience would soon be coming but it [...] I know she is but Jesus said she would be ok, I replied. Organizing for America | Danielle Clarke's Blog: Barack Obama and [...] 24 Jun 2007 [...] As Jesus said 'to them with an ear to listen, let them hear' Can we (the ego me) ever really change another mind? And if we can for how long? [...] -- Martin Musatov http://MeAmI.org http://alexslemonade.org === Subject: Wolfram Alpha integration Steer clear of using dz in integration. It can lead to strange results e.g. integrate 1 dz, from z=a to b === Subject: Re: Wolfram Alpha integration > Steer clear of using dz in integration. It can lead to strange results e.g. > integrate 1 dz, from z=a to b It seems to try to read 1 dz as one dozen, i.e. 12. 1 da as one day, 1 db as one decibel etc. are also messy. But any of the following seem to work: integrate_a^b 1 dz integrate 1, from z=a to b integrate k/k dz, from z=a to b === Subject: Re: Basis of SR? posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > If MMX were the only experiment we had to support SR, and if SR was based > entirely from the results of MMX, then you might have a point. Yes, MMX > also supports ballistic theory with Galilean transforms .. what it did do > was rule out simple ether theory with Galilean transforms. Other > experiments rules out ballistic theory. No single one experiment rules out > all other possible theories. But with the experiments performed so far in > the domain of applicability of SR, SR (and because it always predicts the > same results, LET) are the theories which remain un-refuted. Chronological history of transforms go like this. ** Galilean transform = 1600 discovered by Galileo ** Voigt transform = 1881 discovered by Voigt ** Lorentz transform = 1881 discovered but discarded by Voigt ** Lorentz transform = 1898 rediscovered by Larmor The Galilean transform satisfies the principle of relativity but fails to explain the null results of the MMX. Both the Voigt and the Lorentz transforms do predict the null results of the MMX, but only the Lorentz transform satisfies the principle of relativity. Despite not satisfying the principle of relativity, the Voigt transform also share the same velocity transformation and thus the mass transformation with the Lorentz transform. However, the Voigt transform does not explain the longer highspeed muon decay time. The Lorentz transform seem to be able to explain them all. However, it is deeply flawed. That was why Voigt discarded it in favor of the Voigt transform, for the Lorentz transform manifests the twins' paradox. Instead of doing actual investigation on why The Voigt transform works so well but only fails on predicting the decay time of highspeed muons, the self-styled physicists opt to go for occult and accept the deeply flawed Lorentz transform. In doing so, they have managed to hypnotize themselves into believing in the existence of the twins' paradox. There have been several such proposed resolutions despite they all contradict with each others. It is a real joke. Poincar.8e, and Einstein around the turn of the last century (a few others > contributed in lesser amounts). The MMX is NOT AT ALL the only > experimental support for SR SR is an interpretation to the Lorentz transform. This interpretation was entirely of Poincare's work. Einstein was a plagiarist. In fact, Einstein was nothing but a nitwit, a plagiarist, and a liar. Lorentz's interpretation to the Lorentz transform is utterly absurd. That is why LET is less popular than SR despite both are interpretations to the Lorentz transform. You can never prove one right while proving the other one wrong at the same time. One of the two speculations of SR came from Galileo 400 years ago, and the other one was first proposed by Voigt in 1881 to explain the null results of the MMX. That is the invariant speed of light. Einstein was just a nitwit, a plagiarist, and a liar. wrong that notion is: > http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html Several of these experiments actually violate SR. of all those experiments does indeed refute all other theories, except > for those that are experimentally indistinguishable from SR (within its > domain of applicability). The Lorentz transform is falsified by the very mathematics that created it. It is not self-consistent. That is why it manifests the twins paradox. It is utterly absurd to use self-inconsistent mathematics to model the world despite it agrees with a few experiments. === Subject: Re: Basis of SR? > The Lorentz transform is falsified by the very mathematics that > created it. It is not self-consistent. That is why it manifests the > twins paradox. The Lorentz transform is falsified by the very mathematics that > created it. It is not self-consistent. That is why it manifests the > twins paradox. http://physicstoday.org/vol-57/iss-7/p40.shtml > http://cfa-www.harvard.edu/Walsworth/pdf/PT_Romalis0704.pdf Spamming again eh? And what is it about there does that you think is relevant? === Subject: Re: Basis of SR? > If MMX were the only experiment we had to support SR, and if SR was based > entirely from the results of MMX, then you might have a point. Yes, MMX > also supports ballistic theory with Galilean transforms .. what it did do > was rule out simple ether theory with Galilean transforms. Other > experiments rules out ballistic theory. No single one experiment rules > out > all other possible theories. But with the experiments performed so far in > the domain of applicability of SR, SR (and because it always predicts the > same results, LET) are the theories which remain un-refuted. Chronological history of transforms go like this. ** Galilean transform = 1600 discovered by Galileo ** Voigt transform = 1881 discovered by Voigt ** Lorentz transform = 1881 discovered but discarded by Voigt ** Lorentz transform = 1898 rediscovered by Larmor The Galilean transform satisfies the principle of relativity but fails to explain the null results of the MMX. ........ ... ........ .... Why do you say that? Spirit === Subject: Re: Basis of SR? reply-type=response Importance: Normal > If MMX were the only experiment we had to support SR, and if SR was based > entirely from the results of MMX, then you might have a point. Yes, MMX > also supports ballistic theory with Galilean transforms .. what it did do > was rule out simple ether theory with Galilean transforms. Other > experiments rules out ballistic theory. No single one experiment rules > out > all other possible theories. But with the experiments performed so far > in > the domain of applicability of SR, SR (and because it always predicts the > same results, LET) are the theories which remain un-refuted. Chronological history of transforms go like this. ** Galilean transform = 1600 discovered by Galileo > ** Voigt transform = 1881 discovered by Voigt > ** Lorentz transform = 1881 discovered but discarded by Voigt > ** Lorentz transform = 1898 rediscovered by Larmor The Galilean transform satisfies the principle of relativity but fails > to explain the null results of the MMX. > ......... .. > ......... ... Why do you say that? I agree with your doubts there, koobee is not correct. The MMX alone says nothing about the Galilean transforms itself. It *does* refute the combination of Galilean transforms and an ether. The combination of a ballistic theory and Galilean transforms explains MMX, but is refuted by other experiments. So although some experiments do show that Galilean transforms are not correct, MMX is not one of them. === Subject: Re: Basis of SR? <005aea98$0$9732$c3e8da3@news.astraweb.com> posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > I agree with your doubts there, koobee is not correct. The MMX alone says > nothing about the Galilean transforms itself. It *does* refute the > combination of Galilean transforms and an ether. The combination of a > ballistic theory and Galilean transforms explains MMX, but is refuted by > other experiments. So although some experiments do show that Galilean > transforms are not correct, MMX is not one of them. I apologize. I should have made it clear that the ballistic theory of light is stupid. It violates any electromagnetic phenomena in the first place. Galilean transform cannot coexist with electromagnetism. The physicists after Maxwell all knew that. === Subject: Re: Basis of SR? Importance: Normal > I agree with your doubts there, koobee is not correct. The MMX alone > says > nothing about the Galilean transforms itself. It *does* refute the > combination of Galilean transforms and an ether. The combination of a > ballistic theory and Galilean transforms explains MMX, but is refuted by > other experiments. So although some experiments do show that Galilean > transforms are not correct, MMX is not one of them. I apologize. I should have made it clear that the ballistic theory of > light is stupid. It violates any electromagnetic phenomena in the > first place. Galilean transform cannot coexist with > electromagnetism. The physicists after Maxwell all knew that. > That's fine then. Was just pointing out MMX on its own doesn't. === Subject: Re: Basis of SR? > I agree with your doubts there, koobee is not correct. The MMX alone > says > nothing about the Galilean transforms itself. It *does* refute the > combination of Galilean transforms and an ether. The combination of a > ballistic theory and Galilean transforms explains MMX, but is refuted by > other experiments. So although some experiments do show that Galilean > transforms are not correct, MMX is not one of them. > I apologize. I should have made it clear that the ballistic theory of > light is stupid. It violates any electromagnetic phenomena in the > first place. OK, why? Spirit >Galilean transform cannot coexist with electromagnetism. > The physicists after Maxwell all knew that. > === Subject: Re: Basis of SR? >If MMX were the only experiment we had to support SR, and if SR was based >entirely from the results of MMX, then you might have a point. Yes, MMX >also supports ballistic theory with Galilean transforms .. what it did do >was rule out simple ether theory with Galilean transforms. Other >experiments rules out ballistic theory. No single one experiment rules out >all other possible theories. But with the experiments performed so far in >the domain of applicability of SR, SR (and because it always predicts the >same results, LET) are the theories which remain un-refuted. > Chronological history of transforms go like this. ** Galilean transform = 1600 discovered by Galileo > ** Voigt transform = 1881 discovered by Voigt > ** Lorentz transform = 1881 discovered but discarded by Voigt > ** Lorentz transform = 1898 rediscovered by Larmor The Galilean transform satisfies the principle of relativity but fails > to explain the null results of the MMX. Both the Voigt and the > Lorentz transforms do predict the null results of the MMX, but only > the Lorentz transform satisfies the principle of relativity. Despite not satisfying the principle of relativity, the Voigt > transform also share the same velocity transformation and thus the > mass transformation with the Lorentz transform. However, the Voigt > transform does not explain the longer highspeed muon decay time. The Lorentz transform seem to be able to explain them all. However, > it is deeply flawed. That was why Voigt discarded it in favor of the > Voigt transform, for the Lorentz transform manifests the twins' > paradox. Instead of doing actual investigation on why The Voigt transform works > so well but only fails on predicting the decay time of highspeed > muons, the self-styled physicists opt to go for occult and accept the > deeply flawed Lorentz transform. Well, the Voight transform gives the wrong answer and the Lorentz transform gives the right answer. That certainly makes the choice easy. In doing so, they have managed to > hypnotize themselves into believing in the existence of the twins' > paradox. There have been several such proposed resolutions despite > they all contradict with each others. It is a real joke. It doesn't. SR comes from a combination of the work of Lorentz, >Poincar.8e, and Einstein around the turn of the last century (a few others >contributed in lesser amounts). The MMX is NOT AT ALL the only >experimental support for SR > SR is an interpretation to the Lorentz transform. This interpretation > was entirely of Poincare's work. Einstein was a plagiarist. In fact, > Einstein was nothing but a nitwit, a plagiarist, and a liar. > Lorentz's interpretation to the Lorentz transform is utterly absurd. > That is why LET is less popular than SR despite both are > interpretations to the Lorentz transform. You can never prove one > right while proving the other one wrong at the same time. One of the two speculations of SR came from Galileo 400 years ago, and > the other one was first proposed by Voigt in 1881 to explain the null > results of the MMX. That is the invariant speed of light. Einstein > was just a nitwit, a plagiarist, and a liar. -- see this link to learn how outrageously >wrong that notion is: >http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html > Several of these experiments actually violate SR. Another lie from koobee in his desperate attempt to avoid the truth. > >While the MMX itself does not refute all other theories, the COMBINATION >of all those experiments does indeed refute all other theories, except >for those that are experimentally indistinguishable from SR (within its >domain of applicability). > The Lorentz transform is falsified by the very mathematics that > created it. It is not self-consistent. That is why it manifests the > twins paradox. Another koobee lie. It is utterly absurd to use self-inconsistent mathematics to model the > world despite it agrees with a few experiments. Koobee enjoys lying since it is easier than studying. === Subject: Re: Heat equation in civil engineering? > .... > I would like to know in which applications of civil engineering it > does appear the heat partial differential equation? .... You may be more likely to get an answer from the news group. Ken Pledger. === Subject: Re: Heat equation in civil engineering? posting-account=7k9KBQoAAAAA14UhxMJa5EbFm1GGTnsi Gecko/2009020409 Firefox/3.0.5 (Debian-3.0.6-1),gzip(gfe),gzip(gfe) On Jun 19, 8:03am, Diego Torquemada does appear the heat partial differential equation? I just know one application which is 1D-soil consolidation. Is there > another one? > Diego Andr.8es Nobody? === Subject: Re: Reactions to/against the Binary Tree posting-account=_-PQygoAAAAciOn_89sZIlnxfb74FzXU Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) On Jun 11, 11:19am, Ross A. Finlayson Mathematics does not care about the kind of absolute truth that > WM > tries to hawk, but only in relative truths, like the answer to: > if this is true does that follow? -- > Virgil Can you represent the literal expansions of the rationals of the unit > interval without the entire infinite balanced b'ary tree? What do you mean by the literal expansions of the rationals of the > unit > interval. Unless you mean something esoteric, it is quite possible, even trivial, > as a finite non-repeating sequence of digits followed by a single > repetition of the infinite sequence of repetitions which follows it, > separated by any non-digit symbol. That reminds of Harvey Friedman's notice that the rationals are > arbitrarily large. Ambiguous to the point of incoherence as usual. -- > Virgil I don't understand why you must feel that way. It is not that I must, but I do anyway. No, you can't, you need the entire infinite b'ary tree to represent > the literal expansions of the rationals of the unit interval. You might. I don't. Let S be the set of all finite strings of decimal digits, the every > rational in the unit interval can be represented by any one of > infinitely many members of S^2 ( or SxS, if you prefer). Every such rational can be represented in infinitely many ways as a > single finite digit string followed by infinitely many repetitions of a > possibly different finite digit string, thus by a pair of finite digit > strings. -- > Virgil Reducing to the binary tree, there isn't a third symbol to use as the > demarcator of the beginning and end of a repeating terminus. So, > anybody needs the entire tree. Not at all. One can always use 00 for 0, 11 for 1 and have both 10 and > 01 for a first and even a second demarcator symbol. Similarly the antidiagonal result doesn't hold in binary Since it was originally stated only in binary, whyever not? -- > Virgil Reducing to the binary tree, there isn't a third symbol to use as the > demarcator of the beginning and end of a repeating terminus. Relabeling the 00 to 0 and 11 to 1 and coloring those paths, that's > still an entire binary tree you need, of the base 4 tree you would use > to represent rationals. If you accept that there are dual representations of numbers > terminating with ...0(b-1)((b-1))... and ...10(0)..., like .011(1)... > and .100(0)..., then the binary case requires refinement as has long > been known. Basically the line of consideration is this: for the > antidiagonal argument, there are differences in the structures under > consideration given differences in the size of the alphabet of the > infinite sequences that form the expansions. Where those are > particular features of interest to define the continuum of real > numbers, and standard measure theory demurs to countable additivity, > then there is something to be learned from its features, that may well > have meaning and application which escapes transfinite cardinals. Of course a flip side of dual representation in terms of a binary tree > has that for the branch .011(1)... there needn't be the branch .100 > (0), except for the fact that there are as well infinite sequences of > the expansions for rationals through each of the nodes of the tree. > At each level, for each node, all the courses through the nodes are > needed just to represent the rationals, which like the irrationals are > dense in the unit interval. Using standard expansions to represent elements of the unit interval, > an entire infinite b'ary tree is sufficient, and necessary, to > represent the irrationals. Similarly, an entire infinite b'ary tree > is sufficient: and necessary, to represent the rationals. > Examine the rationals of the unit interval in terms of their representations as expansions and they can't all be written out as literals, in the language of Euxodos/Dedekind/Cauchy expansions to represent the unit's reals, without a complete and infinite balanced binary tree. That's not to say they can't have each particular expansion indicated by a natural number, but the structure necessary to emit each expansion is necessarily as large as one to emit each expansion of the irrationals of the unit interval, where it's one and the same. A conscientious mathematician might be interested in these structural details where they are perceived to be the most efficient and concise representations of these values. Other features of the (platonist, realist) number system including for example the density of the rationals in the reals indicate as well that a most concise explanation of the interleaving of sorts of the rationals and irrationals has reals at the Nyquist frequency of that of the rationals, in sufficiency of twice the density of an enumerated exhaustion of the expansions as completeness in gaplessness (of the continuum of real numbers). Where an interleave or alternation of the rationals and irrationals in the reals, each dense, disjoint, nowhere continuous, and whose union is the reals, sees direct standard counterarguments, standard constructions admit no well-ordering of reals with an uncountable subset of the ordered elements in natural order. Purists may agree that a pragmatic goal of foundations is in application. Now, where there are these theoretically underdeveloped features of the number system that accompany natural features of particularly primitive and direct expressions of these structures, interested mathematicians can see promise in avenues of research that way. EF is modeled standardly as having elements dense in the range in the unit interval, in so being a CDF of the uniform naturals as modeled via symmetry in the trans-finite modernly. Ross F. === Subject: Re: Higher order bifurcation of discrete map <1244622087.571713@athprx03> posting-account=fwSgtAkAAACFnX70ssKwbvm9_oCZVHrx Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) >http://ioannis.virtualcomposer2000.com/math/hyperpower.html Well this is fine for a complex map, but what about a purely real one > on the > real line? > Trivially, yes. Just take the maps: > f(x) = Re(c^z) or > g(y) = Im(c^z) > If you want a totally trivial example, just pick 3 separate sequences, > agreeing for n < n 0, but converging to 3 different limits for n > n 0, and > arrange them appropriately. I can't be bothered to actually construct the > example, but I think it's clear what I mean. That doesn't look like a map you can iterate on the real number line. A bifurcation/trifurcation, etc is not necessarily a map you MUST iterate on > the real line. It is just a discrete iteration, which forces the sequence to > undergo a certain eventual separation of terms. It's not magic. > No, but I wanted to see if one could be made that is done only on the real line. > That's why I called the second example trivial. If you want to iterate on the > real line, take the first example. You mean the f(x) = Re(c^z) thing? But what's z??? It's a function of variable x, not variable z or c, so how do we form f^n(x)? === Subject: Re: Higher order bifurcation of discrete map > http://ioannis.virtualcomposer2000.com/math/hyperpower.html > Well this is fine for a complex map, but what about a purely real one > on the > real line? > Trivially, yes. Just take the maps: > f(x) = Re(c^z) or > g(y) = Im(c^z) > If you want a totally trivial example, just pick 3 separate sequences, > agreeing for n < n_0, but converging to 3 different limits for n > n_0, and > arrange them appropriately. I can't be bothered to actually construct the > example, but I think it's clear what I mean. > That doesn't look like a map you can iterate on the real number line. > A bifurcation/trifurcation, etc is not necessarily a map you MUST > iterate on the real line. It is just a discrete iteration, which forces the > sequence to undergo a certain eventual separation of terms. It's not > magic. No, but I wanted to see if one could be made that is done only on the > real > line. What exactly do you mean only on the real line? Maybe if you specify exactly the nature of the intended map, we can progress a little. > That's why I called the second example trivial. If you want to iterate on > the real line, take the first example. You mean the f(x) = Re(c^z) thing? But what's z??? It's a function of > variable > x, not variable z or c, so how do we form f^n(x)? I don't understand what the problem is. Any complex map which suffers an n-furcation, can be transformed into a real or imaginary n-furcation, by using Re and Im. For example, the map I gave: f^(n)(z) = z^^n is a trifurcation on the complex plane for the values I gave, as I showed on the apply Re (or Im) as follows: f^(n)(x) = Re(z^^n) g^(n)(y) = Im(z^^n) These will then be real trifurcations on the real or imaginary axes. For example: > phi:=z->exp(z/exp(z)); > F:=proc(z,n) #power tower. *THIS* is the function being iterated > option remember; > if n=1 then z; > else z^F(z,n-1); > fi; > end: > z:=t->t*exp(2*Pi/3*I); #choose appropriate parametrization of complex z. > for n from 40 to 50 do > evalf(Re(F(phi(z(1.1)),n))); > od; -.2839462345 .01101520509 .9707216890 -.2839462145 .01101520669 .9707216859 -.2839462079 .01101520722 .9707216849 -.2839462059 .01101520742 Do you see the real trifurcation? Your initial value is 1.1. The function being iterated is the power-tower, under a suitable transformation. The iterates are complex, but if you apply the Re function, the iteration dissolves into two discrete trifurcations (the projections onto the real and imaginary axes). The same thing happens if we apply Im instead: > for n from 40 to 50 do > evalf(Im(F(phi(z(1.1)),n))); > od; 2.011261053 .02179607741 .03533508294 2.011260993 .02179607988 .03533508743 2.011260973 .02179608070 .03533508892 2.011260966 .02179608098 Now, if you mean, can we have an n-furcation (n > 2) on a map which is not a projection through Re or Im of a complex map, the answer is I don't know. -- Ioannis === Subject: Welcome to . These suggestions may help you. [36] These notes are not official in any way, but if you are new to this group you may find them helpful. 1. Messages posted to may be about mathematics at any level. Please don't post OT (off-topic) messages about other things. Be cautious about cross-posting (posting the same message to more than one news group) - see section 6 below. Some questions may have better luck in a more specialized news group such as , or . 2. Your subject heading should show what sort of mathematics is in your message. For example, Differentiating trig functions is a good subject, but Help! is a bad subject. 3. Include the text of your question in your message itself, even if you also refer to a Web page for a good diagram. 4. Type mathematical formulae in the ordinary ASCII characters on your keyboard. Use ^ for powers, for example aaaa = a^4 . You'll rarely need * for multiplication, but use plenty of brackets/parentheses. For example, e^2x/5 could mean (e^2)x/5 or (e^(2x))/5 or e^(2x/5). Use plenty of spaces. For example, 2x + 5y = 12 is easier to read than 2x+5y=12. 5. This news group is open to everybody, and some people have bad manners. Try to stay polite yourself. There are plenty of users who want to discuss mathematics without rude arguments. I hope you enjoy being one of them. 6. You may want more information. If you are struggling with Google Groups, some better news servers Some good general advice about news groups, cross-posting, not top-posting, etc. is Stan Brown's Playing Nice on Usenet web site . For mathematical news groups there are detailed FAQ at and the older . In particular, more details about typing formulae are at . [Capi talEHat]Ken Pledger. [Suggestions for shortening or clarifying these notes are welcome.] === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=FYnYIAoAAAA8l3_WyV33Ud3gcjsM8hBT 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; InfoPath.2; .NET CLR 3.0.04506.648; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) You guys are ridiculous. These days I can say that I left my house > with a GPS at 10:13.012 h:m.s today and arrived at the store at > 10:32.304 and had a VMG of 34.23 mph. > This level of detail was not available in Kant's time, Wow, shucks you are soooooo ridiculously bright. NOT but the same > sensibilities are exactly what he discusses. You may find the following packed with sensibilities, the application > of reason certainly doesn't. First sentence of Kant's pure unadulterated destruction of reason: > (PUDOR) > That all our knowledge begins with experience there can be no > doubt. First sentence second paragraph: > But, though all our knowledge begins with experience, it by no means > follows that all arises out of experience. You may find Kant's take on morality sensible, whereas reason proves > it to be one of the most senseless, therefore utterly mind dependent, > disgustingly arbitrary, context bereft, utterly ignorant and bereft of > anything man can experience, (touch see feel hear smell), therefore > the most anti-human anti-reason morality known to man. You may regard Kant's dopey idea that man cant know things in > themselves, sensible, when in reality, as determined via reason, that > garbage is just sooo ridiculously stupid its beyond words. In man aquiring his knowledge there is absolutely no requirement of > man to know things in themselves for him to be able to claim 100% > certain knowldge, with 100% certainty man CAN and DOES know the > differences between forms of matter and matter's nature. That presupposes a magical sudden undestanding from which to claim 100% understanding, that also insists @ its more fundamental level that knowledge was gained without any experimental evidence to back it up and from which to base his reason... you're totally cart before horse. don't you thing the horse will have more success pulling? You missed the foundations - next you'll be telling us that you can build a house from the roof down? You need to step back and put things into the correct context before you start trying to claim some kinda supperior thought process -which only appears totally lacking from reading this . > It is NOT the entity in itself that man needs to know, but rather it > is the differences between the forms of matter and their nature is ALL > there is for man to have knowledge of, Aristotle's law of identity > which Kant rejects as a means to knowledge. Same position, get the right context and you might have something MG === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > That presupposes a magical sudden undestanding from which to claim > 100% understanding, No it presupposes there is something pre-existing to reason and you can only become aware of what needs identifing and without contradiction if your mind is triggered by data from the senses (ears eyes nose hands skin), unless of course you are Kantian and or looking for a reason to go to church and you start in the mind. Hint; if your ideas are not triggered by reality, matter and its nature existing external of your mind, then they can only be triggered by your mind, mind triggered ideas land man in church, being Kantian and socialist and slamming jets into sky-scrapers. Your eyes feed your mind, your mind doesn't feed your eyes. You can see a difference between the things man calls an elephant, an ant and a motorized bus, cant you, surely? MG === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) That presupposes a magical sudden undestanding from which to claim > 100% understanding, No it presupposes there is something pre-existing to reason and you > can only become aware of what needs identifing and without > contradiction if your mind is triggered by data from the senses (ears > eyes nose hands skin), unless of course you are Kantian and or looking > for a reason to go to church and you start in the mind. Hint; if your ideas are not triggered by reality, matter and its > nature existing external of your mind, then they can only be triggered > by your mind, mind triggered ideas land man in church, being Kantian > and socialist and slamming jets into sky-scrapers. Your eyes feed your mind, your mind doesn't feed your eyes. You can > see a difference between the things man calls an elephant, an ant and > a motorized bus, cant you, surely? MG If the cart comes before the horse or the horse comes before the cart it does not matter so long as they are both moving. The limitation I see is your limited imagination to conceive the physical properties permit such events. You guys are ridiculous. These days I can say that I left my house > with a GPS at 10:13.012 h:m.s today and arrived at the store at > 10:32.304 and had a VMG of 34.23 mph. > This level of detail was not available in Kant's time, Wow, shucks you are soooooo ridiculously bright. NOT but the same > sensibilities are exactly what he discusses. You may find the following packed with sensibilities, the application > of reason certainly doesn't. First sentence of Kant's pure unadulterated destruction of reason: > (PUDOR) > That all our knowledge begins with experience there can be no > doubt. First sentence second paragraph: > But, though all our knowledge begins with experience, it by no means > follows that all arises out of experience. You may find Kant's take on morality sensible, whereas reason proves > it to be one of the most senseless, therefore utterly mind dependent, > disgustingly arbitrary, context bereft, utterly ignorant and bereft of > anything man can experience, (touch see feel hear smell), therefore > the most anti-human anti-reason morality known to man. You may regard Kant's dopey idea that man cant know things in > themselves, sensible, when in reality, as determined via reason, that > garbage is just sooo ridiculously stupid its beyond words. In man aquiring his knowledge there is absolutely no requirement of > man to know things in themselves for him to be able to claim 100% > certain knowldge, with 100% certainty man CAN and DOES know the > differences between forms of matter and matter's nature. That presupposes a magical sudden undestanding from which to claim > 100% understanding, that also insists @ its more fundamental level > that knowledge was gained without any experimental evidence to back it > up and from which to base his reason... you're totally cart before > horse. don't you thing the horse will have more success pulling? You missed > the foundations - next you'll be telling us that you can build a house > from the roof down? You need to step back and put things into the correct context before > you start trying to claim some kinda supperior thought process -which > only appears totally lacking from reading this . It is NOT the entity in itself that man needs to know, but rather it > is the differences between the forms of matter and their nature is ALL > there is for man to have knowledge of, Aristotle's law of identity > which Kant rejects as a means to knowledge. Same position, get the right context and you might have something > MG The essence of truth in proof can be properly expressed through narrative means and recollections citing facts to prove otherwise forgone or obscured conclusions to bring light to further truth. Begin logix narrative:(thread) I challenge the devil to a debate (and any logicians, too): For forms of matter nature proof p=NP. Search problem 'v' computes: Is P Versus NP Formally Independent? Nature of P = NP.84a conjecture that all but asserts the titanic difficulty of finding [...] P = NP asks for an efficient procedure that finds a short proof [.....] independent of ZF, no matter which Turing machine is used to specify O. [....] It's interesting that this proof rules out only lower bounds of the form 2 [...]. Consider: computational complexity and mathematics: P, NP and mathematics [CapitalEth] a computational complexity perspective. Describe the computational model precisely (e.g. it does not matter if we allow [.....] it is so hard to prove indeed P = NP it seems completely obvious. We [......] the very nature of proof. We exhibit three different remarkable manifestations of [.....] a rank 1 tensor as a product of linear forms (one in X, [...]. The Awakening of The American Mind: P=NP complete The Maximal [......] to the extremal ends of the conservation law of matter/ energy, fields/motions, [....] or any other form of heiarchical organization, of any other possible [...] P=NP i.e., Proof=NonPossibles, add em up, and choose what's left the [....] senses The sensible Better Nature senses, over the Higher Nature senses. [...] And now we're getting interesting. An Argument for P=NP, again I say this repeatedly out of necessity, the winne of the Clay Mathematics prize need not provide a constructive proof P=NP [...] of the matter than, say, whether many current cryptographic schemes can be [...]. Godel apparently believed it might well be possible to answer questions of the form ñ¤l [.....] 'proto'-law of nature. It's a profound waste of time to build gadgets to [...]. Truth is the goal and hard work and common sense filled with imagination is the real necessity. Chris Menzel helped me prove N=NP: on USENET with Inverse 19 Mathematics in sci.math [...], I simply said, Consider this thread an extension of my proof P=NP, and add to it this [...] always the same path as we what we seek to define we by nature of our > observing change. [...] In form and function, across language and guild, the > heir apparent us. [...] At any rate, no matter the claim, they do not belong to me. I did not [...]. A consequence of a proof of the one-way function existence for the [...]8 Nov 2008 [...]. Indeed, form the assumption follows while for the initial stages of the [...]. The above statement may seem vague to the impatient reader (especially to Kant or Russell, I assume) but nonetheless by the nature of our existence and the very essence of time it is ontologically sound. The statement may simply be rephrased: A proof of the consequence of a past action is based on the sound assumption causal relations can only be established after the existence of their result in time. --Martin Musatov As to numerical solutions, a proof P Á' NP would guarantee a [....]. Hence, it is plausible to conclude the NP nature of the Schr.9adinger equation [...] state of play, prospects. But before we get too far removed in physics, we must return to the proof. Computational Complexity and Mathematical Proofs clearly agree the P versus NP problem is clearly an important problem for computer scientists. Also a fundamental problem about the nature of mathematics [...] string over a fixed alphabet and is written in a left-justified form directly below [....]. As a matter of fact, by choosing our proof systems accordingly, we can represent P = NP { What does it mean? No matter how fast computers we manage to build, we will still be unable to express [.....] the exact nature of these problems has not yet been determined, even though every- [...] (posi)tive proof for P=NP would mean we have a polynomial time algorithm for [....] Boyce-Codd Normal Form Violation. Conjunctive Query Foldabilty [...]. Sticking to the complexity of Computational Complexity: We all have our favorite theorems: P = NP for Space. The non-trivial nature of a result and proof is in the insight [....] I sometimes joke about having a two line proof of P=NP that keeps [...]. So the book as Erdos referenced contains as derivatives of the author's work (lawfully on unlawfully attained): 1. The Chapter 2: God Math (Logik, LOGOS, P=NP) ' Robot Pirate Ninja. You laugh and it all seems silly, but it is quite upsetting to those just beginning to understand it. It is actually quite daunting and cruel. This is my P=NP proof, after all. One would have to be a bit outside the norm to [...] see. 1a. Supposition claims proofs of reality, by threading a narrative to hypotheses. 1b. We later learned from Einstein that the existence of matter and energy made a [...] lines that go on forever, are so rare as to be nearly unique in nature [....] and we finally see the fully realized (simple) model in its ideal form.[ ...] Truth is the highest order. Period. P=NP. q.e.d. PROOF BERTRAND RUSSELL WAS UNWISE: Bertrand Arthur William Russell [Third Earl Russell] (1872-1970) British philosopher, mathematician, social critic, writer. 1st Argument: 1a. Russell: ...by intellectual integrity the habit of deciding vexed questions in accordance with the evidence, or of leaving them undecided where the evidence is inconclusive. 1b. Musatov: The limit principle of defending a negative-valued statement or impossibility allows for a divine divide between classes as to the public people esteemed insist something is unknowable, uncountable, or impossible, simply discourages the acceptance of truth, discovery, and the incidence of greater possibility than what remains to be seen. Conclusion: Musatov: (Claims) P==NP. Even Russell himself agreed. On P=/=NP. Russell states: (implies) Proof: [...]Russell: Most of the greatest evils that man has inflicted upon man have come through people feeling quite certain about something which, in fact, was false.-- Bertrand Russell, Unpopular Essays, Ideas That Have Harmed Mankind (1950), p. 149, quoted from James A Haught, ed, 2000 Years of Disbelief P==NP is a truth-valued claim. P=/=NP is a false-valued claim. q.e.d. (1st argument) Summary Statment: The defense of a truth statement should always be given favor to the insistence of an impossibility. --Martin Musatov Argument 2 2a. Russell: So far as I can remember, there is not one word in the Gospels in praise of intelligence; and in this respect ministers of religion follow gospel authority more closely than in some others.-- Bertrand Russell, quoted, in part, from Jonathon Green, The Cassell Dictionary of Cynical Quotations 2b. Musatov: (cites) P==NP.1.Matthew 22:37 And He said to him, 'YOU SHALL LOVE THE LORD Jesus said unto him, Thou shalt love the Lord thy God with all thy heart, and with all thy {p} soul, and with all thy mind. [...]http:// bible.cc/matthew/22-37.htm 2.Matthew 22:37 Jesus said unto him, Thou shalt love the Lord thy [...] Jesus said to him: Thou shalt love the Lord thy God with thy whole heart, and with thy whole soul, and with thy whole mind. [...] http://scripturetext.com/matthew/22-37.htm 3. ...In Phillipians 2:5, the apostle Paul said, let this mind be in you which was also in Christ Jesus. In Mathew 6:33 Jesus said, seek ye first the kingdom [...]http://www.thechristmind.org/ The fact is there are many instances and portrayals in the bible where frankness and honesty are encouraged over formalsim and inauthentic truth. God allowed Abraham to question and challenge him over his reasoning in the destruction of Sodom. God and Abraham reached a compromise. God listened to David's accusations of unfairness, betrayal, and abandonment. Jeremiah even claimed God tricked him. Job was allowed to vent and when his ordeal was over he rebuked his friends for being inauthentic. God rewards honesty and authenticity. Honesty and authenticity predicate truth, hence they are one and the same rewarded in the portrayal of the gospels as written in The Old and New Testaments. Summary argument: Musatov: Following Jesus begins in your Mind. Jesus said, ñYou must love the Lord your God with all your heart, with all your soul, with all your mind and with all your strength.î (Mark 12:30) [...]http://www.frtommylane.com/homilies/year b/03.htm The below results prove my above forgone conclusion further: THE MIRACLE OF ONE MIND AT SAFEPLACEFELLOWSHIP.COM All these signs pointed to the singleness of mind experience would soon be coming but it [...] I know she is but Jesus said she would be ok, I replied. Organizing for America | Danielle Clarke's Blog: Barack Obama and [...] 24 Jun 2007 [...] As Jesus said 'to them with an ear to listen, let them hear' Can we (the ego me) ever really change another mind? And if we can for how long? [...] -- Martin Musatov http://MeAmI.org http://alexslemonade.org === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > If the cart comes before the horse or the horse comes before the cart > it does not matter so long as they are both moving. wtf? what a stupid meaningless thing to regurgitate. You either accept or reject, as the primacy of all knowledge, that there has to be something existing external of the mind to identify via sensory perceptions and then your mind processes that sensory data through a non-contradictory filter if you like. > The limitation I > see is your limited imagination to conceive the physical properties > permit such events. Nope, even your state of imagination needs a trigger and if that trigger is not something existing external of it, then that only leaves a creation originating in the mind to imagine. And the evidence is overwhelming, man places his faith in such imaginations at his peril, the mystic's god, and the leftist retard's god 'the greater good', both spring to mind as examples of mind dependent, mind originating concepts. > The essence of truth in proof can be properly expressed through > narrative means..... Expressing something through words doesn't make anything true, dont be silly. > We exhibit three different remarkable manifestations of [.....] a rank > 1 tensor as a product of linear forms (one in X, [...]. Arbitrary garbage. MG === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > ... you're totally cart before > horse. If existence is the horse and the cart is consciousness, then the cart goes before the horse, unless of course you are Kantian and or want a reason to go to church. MG === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > That presupposes a magical sudden undestanding from which to claim > 100% understanding, Your eyes ears nose hands skin are not decorations and ornaments, they feed your mind, your mind doesn't feed them, unless of course you are of the POC, e.g. Kantian, ilk, which obviously you are. > You need to step back and put things into the correct context before > you start trying to claim some kinda supperior thought process -which > only appears totally lacking from reading this . There has to exist something, external of the mind to think about, that thinking cant be triggered by your mind, unless of course ewe go to church and or are of the Kantian ilk. POE, primacy of existence (Rand / reason) Vs primacy of consciousness (Kant / faith), its not a bitter choice. MG === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=HfPrdwoAAACwxUqNrgJwfq54YvdU5mcg Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > POE, primacy of existence (Rand / reason) Vs primacy of consciousness > (Kant / faith), its not a bitter choice. MG You have not case of primacy of lying consciousness and false-random existence - when the world is made. I'm sure only psychiatrists couldn't copy with this situation. === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > POE, primacy of existence (Rand / reason) Vs primacy of consciousness > (Kant / faith), its not a bitter choice. MG You have not case of primacy of lying consciousness and false-random > existence - when the world is made. I'm sure only psychiatrists > couldn't copy with this situation. Speaking of psychiatrists, aren't late for your appointment? or are you drunk? MG === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=HfPrdwoAAACwxUqNrgJwfq54YvdU5mcg Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) POE, primacy of existence (Rand / reason) Vs primacy of consciousness > (Kant / faith), its not a bitter choice. MG You have not case of primacy of lying consciousness and false-random > existence - when the world is made. I'm sure only psychiatrists > couldn't copy with this situation. Speaking of psychiatrists, aren't late for your appointment? or are > you drunk? MG As Philosophy is science of truth and Psychiatry is the science of mental illness, I think there is need for the more science - science of the lie. In the totalitarian situation you never know what is your main problem: truth, lie or mental illness, more you never know is true, lie or illness you problem or problem of others and so psychology is useful science to, but to say more you are ignorant is problem caused intentionally or randomly, and so psychoanalysis is useful science to, but to say more some may only copy behavior of others (Leaders, Champions etc.) and so social sciences are very useful to, but to say more you never now how to struggle and win and political sciences are also very useful, but at last you never know what is the time, the events are happening: are they simultaneous, or consequential and physics is very useful science, but to know is all this happening in one dimension or different one may find very useful this group and this subject. === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) It's in Russell's letter to Frege, which you may find (I guess, among > other places) in Van Heijenoort's anthology. An appeal to a higher authority? What?! No, I'm telling you EXACTLY where Russell said what the faulty premise is that allows derivation of the paradox. > So you dont understand it well enough > to use your own words? You didn't ASK me to explain the faulty premise in my own words. You asked me to prove that Russell had pointed out the faulty premise. Sheesh! Were you half asleep when you posted? > btw I've read it So if you had already read it, it was pointless for you to ask me to prove it. Please, drink some Objectivist coffee or whatever it is you do to wake up. MoeBlee === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > It's in Russell's letter to Frege, which you may find (I guess, among > other places) in Van Heijenoort's anthology. An appeal to a higher authority? What?! No, I'm telling you EXACTLY where Russell said what the faulty premise > is that allows derivation of the paradox. So you dont understand it well enough > to use your own words? You didn't ASK me to explain the faulty premise in my own words. You > asked me to prove that Russell had pointed out the faulty premise. Sheesh! Were you half asleep when you posted? btw I've read it So if you had already read it, it was pointless for you to ask me to > prove it. Please, drink some Objectivist coffee or whatever it is you do to wake > up. P.S. For that matter, if you'd already read it, then you contradict your own claim that it (Russell mentioning the source of the paradox) doesn't exist. MoeBlee === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > P.S. For that matter, if you'd already read it, then you contradict > your own claim that it (Russell mentioning the source of the paradox) > doesn't exist. Utter crap, I had read the letter and before you had mentioned it and I did NOT regard it as proof of anything but a couple of mystics arguing over a description of a mind dependent nonsense. Proof deals with reality, ffs Russel even claims to have dicovered a paradox, when in reality they do NOT exist, and he does NOT even state that paradoxes do not exist in reality and the reason he doesn't is because he embraces the primacy of consciousness as a means to knowledge, which also explains his anti-human leftist politics. MG === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) P.S. For that matter, if you'd already read it, then you contradict > your own claim that it (Russell mentioning the source of the paradox) > doesn't exist. Utter crap, I had read the letter Yeah, right. > and before you had mentioned it and > I did NOT regard it as proof of anything I didn't say it is a proof of anything. I said Russell mentions what the untenable premise is. MoeBlee === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) I didn't say it is a proof of anything. I said Russell mentions what > the untenable premise is. What utter crap, how the could he have done anything like that when he himself claims to have discovered a paradox when in reality they dont exist? MG === Subject: Re: Is time is One dimensional? if yes, How ? Distribution: world > I didn't say it is a proof of anything. I said Russell mentions what > the untenable premise is. What utter crap, how the could he have done anything like that >when he himself claims to have discovered a paradox when in reality >they dont exist? I'll try to break this down into small pieces for you: 1. Frege came up with a proposed list of axioms for set theory. 2. Russell looked at Frege's list and found that the Axiom of Abstraction caused a contradiction. 4. Frege said Oh, ! 5. Mathematicians said Okay, we can't use the axioms that Frege originally proposed. Let's try something else. Mathematicians know that contradictions don't/can't exist, and that, if they find a contradiction, there's something wrong with an assumption. This is exactly what Russell was doing -- he was showing that a given set of assumptions was not workable, because it would lead to a contradiction. -- Michael F. Stemper #include 91.2% of all statistics are made up by the person quoting them. === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) I didn't say it is a proof of anything. I said Russell mentions what > the untenable premise is. What utter crap, how the could he have done anything like that > when he himself claims to have discovered a paradox when in reality > they dont exist? MG MG, I just want to say publicly, I apologize for swearing on Sci.Math out of frustration. I have quit swearing in my posts and I have found my work is taken more seriously when I do not swear on Sci.Math. Let's begin by defining a paradox. 1) A paradox is an apparently sound argument leading to a contradiction. Proof: Famous examples of Paradoxes include Russell's paradox and the liar paradox. 2) Most paradoxes stem from some kind of self-reference. Proof: Smarandache Linguistic Paradox. 3) P vs. NP is self-referential. Proof: the P versus NP question is only one of many other which we call at the same time and so the discovery of a natural system of self- referential proof terms applies. > What utter crap, how the could he have done anything like that > when he himself claims to have discovered a paradox when in reality > they dont exist? When I said paradoxes do not exist I was referring to the term paradox as a self-contradictory and false proposition. I believe in truth. When a self-contradicting term is present in a false proposition, the perception or measure of the circumstance or condition is false. So in this sense we say self-contradictory and false propositions do not exist. We then go on to clarify by citing the primary definition of paradox: A seemingly contradictory statement that may nonetheless be true: the paradox that standing is more tiring than walking. Again, it's truth exists. Self-contradicting false propositions we claim do not exist. So refined in the logical mind, if you can wrap your head around this statement of abstraction, we claim the definition of the word paradox is seemingly a paradox to its own ambiguity. The first and second definitions claim: 1) Paradoxes appear untrue but are really true. 2) Paradoxes are self-contradicting false propositions. False self-contradicting propositions do not exist in reality but our perceptions. Hence they do not exist. Musatov's Axiom of Truth: 1) Truth exists in reality. 2) Falsehoods exist in perceptions of reality. It is true. Truth is beauty, and beauty truth. === Subject: Re: Is time is One dimensional? if yes, How ? posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) qualifying piffle snipped. > 1) A paradox is an apparently sound argument leading to a > contradiction. yawn, sheeesh bloody Kantians, sound arguments do not -- they can not lead to contradiction, indeed, that is why they are called sound arguments, because there is no contradiction, an argument containing a contradiction is NOT a sound argument, check your premises. > 2) Most paradoxes stem from some kind of self-reference. Oh rubbish paradoxes can ONLY stem from stupidity and ignorance. > I believe in truth. According to what standard? e.g. mystics call their silly god crap the truth. > When a self-contradicting term is present in a > false proposition, wtf? > So refined in the logical mind, whooops, what meaning are you using for logical? > 1) Paradoxes appear untrue but are really true. > 2) Paradoxes are self-contradicting false propositions. A paradox is nothing more than a faulty identification of reality, in reality there are no contradictions and no paradoxes. MG === Subject: Re: Is time is One dimensional? if yes, How ? > On Jun 20, 3:57pm, Musatov 1) A paradox is an apparently sound argument > leading to a > contradiction. yawn, sheeesh bloody Kantians, sound arguments do not > -- they can not > lead to contradiction, indeed, that is why they are > called sound > arguments, because there is no contradiction, an > argument containing a > contradiction is NOT a sound argument, check your > premises. 1) MR, please be more thorough, I said apparently sound. They are obviously not sound if they are false. Exactly. Always check your premises. P=NP. 2) Most paradoxes stem from some kind of > self-reference. Oh rubbish paradoxes can ONLY stem from stupidity and > ignorance. Really, The On-line Dictionary of Computing, © 1993-2007 Denis Howe is rubbish in your opinion? Please let Denis Howe know this so we can have his site removed from the Internet. Quote: paradox logic An apparently sound argument leading to a contradiction. Some famous examples are Russell's paradox and the liar paradox. Most paradoxes stem from some kind of self-reference. Smarandache Linguistic Paradox. (1999-11-05) I assert paradoxes stem from misunderstanding. Period. The rest you say, all the extra fits under this umbrella. Just to get it out of the way, here you go for paradox... American Psychological Association (APA): paradox. (n.d.). The Free On-line Dictionary of Computing. Retrieved June 20, 2009, from Dictionary.com website: http://dictionary.reference.com/browse/paradox Chicago Manual Style (CMS): paradox. Dictionary.com. The Free On-line Dictionary of Computing. Denis Howe. http://dictionary.reference.com/browse/paradox (accessed: June 20, 2009). Modern Language Association (MLA): paradox. The Free On-line Dictionary of Computing. Denis Howe. 20 Jun. 2009. . Institute of Electrical and Electronics Engineers (IEEE): Dictionary.com, paradox, in The Free On-line Dictionary of Computing. Source location: Denis Howe. http://dictionary.reference.com/browse/paradox. Available: http://dictionary.reference.com. Accessed: June 20, 2009. BibTeX Bibliography Style (BibTeX) title = {The Free On-line Dictionary of Computing}, month = {Jun}, day = {20}, year = {2009}, url = {http://dictionary.reference.com/browse/paradox}, } I believe in truth. According to what standard? e.g. mystics call their > silly god crap the > truth. 1)I believe in a standard of taste and universal truth in nature. The highest standard of truth is good taste, nothing less than wisdom itself. The certain knowledge of nature's primary laws or unchangeable real Truth sought to determine the nature and standard of truth, and conditions of reach by selection the highest degree of probability in the search for truth. 2)When it comes to computing, I observe these standards: Contraposition An operation to manipulate the content of a standard form categorical proposition without changing the truth value. This preserves truth value when used on A and O statements only. Subject and predicate terms are switched, as for conversion, and term compliments are substituted for both terms. To then be applied to: Truth Function: The set of possible truth values a formal complex proposition could have, depending on the truth of the contingent content that could be substituted into it. There is a four line truth table for each connective, primarily a conventionalized arrangement of all the possible combination of truth values for the components of a proposition or argument. 3) When it comes to dealing with those who blur issues by citing vague philosophical reasons in place of intention the standard I observe is the opinion of St. Augustine: He declares that it is better to have truth than logic. When a self-contradicting term is present in a > false proposition, wtf? Please if you do not understand the words you read look them up in a dictionary. This is what they mean as you read them. Or if you do not understand a specific word or phrase please explain why you do not understand or ask a question instead of exclaiming like a 14 year old girl over a text message. However, I have no problems with rude 14 year old girls, in fact I humor them. A self-contradicting term is present in a false proposition means, When a non-life form/object calls itself a liar, something is wrong. or... things are not as they seem... clearly... there is a good explanation for every mystery we cannot comprehend the solution to... btw, it is this standard of truth I strive for, too... So refined in the logical mind, whooops, what meaning are you using for logical? according to or agreeing with the principles of logic: a logical inference. > (not re-inventing the wheel here, just spinning faster than maybe you are used to) > 1) Paradoxes appear untrue but are really true. > 2) Paradoxes are self-contradicting false > propositions. A paradox is nothing more than a faulty > identification of reality, in > reality there are no contradictions and no paradoxes. > MG > Martin Musatov P.S. NG, show some respect, man. === Subject: Re: Is time is One dimensional? if yes, How ? P.S. For that matter, if you'd already read it, then you contradict > your own claim that it (Russell mentioning the source of the paradox) > doesn't exist. Utter crap, I had read the letter and before you had mentioned it and > I did NOT regard it as proof of anything but a couple of mystics > arguing over a description of a mind dependent nonsense. Proof deals > with reality, ffs Russel even claims to have dicovered a paradox, when > in reality they do NOT exist, and he does NOT even state that > paradoxes do not exist in reality Quite so! I'm surprised that you didn't point out (again) Russell's UTTER FAILURE to mention the source of the so-called paradox: the complete absence of non-contradictory identification and integration of sensory evidence in Frege's theorizing. Some people just don't get it. > and the reason he doesn't is because > he embraces the primacy of consciousness as a means to knowledge, > which also explains his anti-human leftist politics. -- hz === Subject: Re: Is time is One dimensional? if yes, How ? Distribution: world > It's in Russell's letter to Frege, which you may find (I guess, among > other places) in Van Heijenoort's anthology. An appeal to a higher authority? So you dont understand it well enough >to use your own words? btw I've read it and its the mind dependent >crap of a rationalist. That's a really nice shifting of the goal posts. You asked MoeBlee to prove that Russell stated that it was Frege's Axiom of Abstraction that was at fault. He cited a place where that could be seen in Russell's writings. You then proceeded to change to a demand that he restate something. Putting something in his own words would not prove that Russell said it. -- Michael F. Stemper #include Reunite Gondwanaland! === Subject: Re: Is time is One dimensional? if yes, How ? Distribution: world posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) On Jun 20, 2:07am, mstem...@walkabout.empros.com (Michael Stemper) > That's a really nice shifting of the goal posts. wtf? I asked for proof, I stated I had read what he claimed was proof and that I regarded it as an utter non-sense and was not proof, I asked why he couldn't put the argument into his own words, rather than appeal to a higher authority, which is a perfectly acceptable request and leaves the goal posts where they have always been. MG === Subject: Re: Is time is One dimensional? if yes, How ? Distribution: world posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > On Jun 20, 2:07am, mstem...@walkabout.empros.com (Michael Stemper) That's a really nice shifting of the goal posts. wtf? I asked for proof, You asked for proof that Russell had mentioned the mistaken premise. > I stated I had read what he claimed was proof > and that I regarded it as an utter non-sense and was not proof, I > asked why he couldn't put the argument into his own words, rather than > appeal to a higher authority, which is a perfectly acceptable request > and leaves the goal posts where they have always been. You're just repeating your same mistake again. MoeBlee === Subject: Re: Is time is One dimensional? if yes, How ? Distribution: world posting-account=g9P5YAkAAACbxBDAyQp7cMVe0-Yk0MYD SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > You asked for proof that Russell had mentioned the mistaken premise. Thats right and you have refused to show it or explain it, why? because it does not and can not exist as proof of anything but a mystic blathering on about nothing in reality. MG === Subject: Re: Is time is One dimensional? if yes, How ? Distribution: world posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > On Jun 20, 2:07am, mstem...@walkabout.empros.com (Michael Stemper) That's a really nice shifting of the goal posts. wtf? I asked for proof, You asked for proof that Russell had mentioned the mistaken premise. I stated I had read what he claimed was proof > and that I regarded it as an utter non-sense and was not proof, I > asked why he couldn't put the argument into his own words, rather than > appeal to a higher authority, which is a perfectly acceptable request > and leaves the goal posts where they have always been. You're just repeating your same mistake again. MoeBlee I tell you the truth, there are those who define limitations of what can be seen so only they can see it. Bertrand's paradox is no exception. At its base, in my own words, is absurdity. Here is why: 1) What exists does not depend on whether or not it is perceived or measured. 2) Bertrand could not claim he had considered all the possible ways a condition is reached. 3) There are infinite combinations for conclusions to be reached, so he could not have considered all of them. Frankly, he was a smart guy. He did the best he could. But here, he comes up short. Moving on, please... [...], [0][+] [1] 1+2==3[P==NP] compute === === Subject: question from a math retard I'm 44 and going back to college after an absence of 18 years. Currently I'm a third-year Philosophy major but want to get into the B.Sc. Psychology program. To do that I need accreditation in a 12th-grade calculus course. Before I can do that I need remedial math starting at the 9th grade level. Any suggestions? Woody -- NOTE TO NEWSGROUP USERS; My reply-to email address is valid. For a safe valid reply-to address of your own go to www.hushmail.com === Subject: Re: question from a math retard > I'm 44 and going back to college after an absence of 18 years. Currently > I'm a third-year Philosophy major but want to get into the B.Sc. > Psychology program. To do that I need accreditation in a 12th-grade > calculus course. Before I can do that I need remedial math starting at the > 9th grade level. Any suggestions? Woody If there is a placement test that you need to pass, I would try to get a hold of an old exam or two so you can focus on what will be expected of you. After you review your algebra on your own, you may want to enroll in a pre-calculus (with trigonometry) class if you've never studied trigonometry before--and need to know that. Not all calculus courses use trigonometric functions, but most of them do. To me it seems like it would be rather challenging to learn trigonometry by oneself. Good luck! Bill -- > NOTE TO NEWSGROUP USERS; My reply-to email address is valid. For a safe > valid reply-to address of your own go to www.hushmail.com > === Subject: Re: question from a math retard > I'm 44 and going back to college after an absence of 18 years. Currently > I'm a third-year Philosophy major but want to get into the B.Sc. > Psychology program. To do that I need accreditation in a 12th-grade > calculus course. Before I can do that I need remedial math starting at the > 9th grade level. Any suggestions? Woody schalms outline at bookstore work all problems === Subject: Re: question from a math retard ... > I'm 44 and going back to college after an absence > of 18 years. Currently > I'm a third-year Philosophy major but want to get > into the B.Sc. > Psychology program. To do that I need accreditation > in a 12th-grade > calculus course. Before I can do that I need > remedial math starting at the > 9th grade level. Any suggestions? Woody schalms outline at bookstore work all problems Together with all other suggestions, feel free to post any calc question in here. === Subject: [] question from a math retard I'm 44 and going back to college after an absence of 18 years. Currently > I'm a third-year Philosophy major but want to get into the B.Sc. > Psychology program. To do that I need accreditation in a 12th-grade > calculus course. Before I can do that I need remedial math starting at the > 9th grade level. Any suggestions? schalms outline at bookstore work all problems > I suggest you get that series outline for English grammar and punctuation and work all the punctuation problems. === Subject: Re: question from a math retard posting-account=JUrffAoAAADtMHLATfNgk21ZWd_8IT43 AppleWebKit/525.18.1 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1,gzip(gfe),gzip(gfe) You could find a private tutor, audit courses or get some review books from the library. > I'm 44 and going back to college after an absence of 18 years. Currently I'm > a third-year Philosophy major but want to get into the B.Sc. Psychology > program. To do that I need accreditation in a 12th-grade calculus course. > Before I can do that I need remedial math starting at the 9th grade level. > Any suggestions? Woody -- > NOTE TO NEWSGROUP USERS; My reply-to email address is valid. For a safe > valid reply-to address of your own go towww.hushmail.com === Subject: Re: Question from a new beginner posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > You could find a private tutor, audit courses or get some review books > from the library. > I'm 44 and going back to college after an absence of 18 years. Currently I'm > a third-year Philosophy major but want to get into the B.Sc. Psychology > program. To do that I need accreditation in a 12th-grade calculus course. > Before I can do that I need remedial math starting at the 9th grade level. > Any suggestions? Woody -- > NOTE TO NEWSGROUP USERS; My reply-to email address is valid. For a safe > valid reply-to address of your own go towww.hushmail.com Why on earth did you change the subject line back to the original text we can ascertain one of four possible motives: 1. You are particularly cruel and enjoyed reading someone call himself a retard so much you physically retyped the words (or copied them) back into the subject line. 3. You did it to spite me or the author, personally, or to impede our progress. 4. You think people have a right to set their own subjects in threads about them, and thought it was your moral obligation to restore this man's attempt to learn to include him putting himself down. In any case, what you did was detestable, and barring some technical explanation or glitch, you owe Woody an apology. No one attempting to seriously learn should ever be belittled or insulted for their effort to do so. One who does this demonstrates moral character not of a teacher, but a snake. MeAmI Inverse19 Hope Research New Theory http://MeAmI.org * *Support MeAmI and an end to childhood cancer. === Subject: Posting from a detestable USENET thug (Michael Martin Mushatov) posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY Gecko/20070530 Fedora/1.5.0.12-1.fc5 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) Why on earth did you change the subject line back to the original text > of: 'Question from a math retard'. He changed nothing back he simply replied to a message leaving the title intact. (But I have changed the title to a more accurate one.) > 4. You think people have a right to set their own subjects in threads > about them, and thought it was your moral obligation to restore this > man's attempt to learn to include him putting himself down. In any case, what you did was detestable, and barring some technical > explanation or glitch, you owe Woody an apology. No, your bandying around of unfounded accusations is detestable, Musatov, and you owe everyone in the group an apology. === Subject: question from a new beginner posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > I'm 44 and going back to college after an absence of 18 years. Currently I'm > a third-year Philosophy major but want to get into the B.Sc. Psychology > program. To do that I need accreditation in a 12th-grade calculus course. > Before I can do that I need remedial math starting at the 9th grade level. > Any suggestions? Woody -- > NOTE TO NEWSGROUP USERS; My reply-to email address is valid. For a safe > valid reply-to address of your own go to www.hushmail.com Hi Woody, There is no good reason for anyone to be called a (deleted word from subject line). It is awesome you are looking to learn. Check out http://www.mathforum.com for some tips and http://mathworld.com. Start with the basics! They are often the most interesting, too! I am not familiar with the accreditation process but ask a guidance counselor or admissions counselor/registrar about this as I am sure the question comes up with freshman and maybe they will get you set up. Remember, stick with it and it is a great thing you are doing. Martin Musato http://MeAmI.org === Subject: Re: Bound for cosine integral: |Ci(x)| < 1/x ? > Let Ci(x) = cosine integral function (for real x). > Is |Ci(x)| < 1/x ? Note that the extrema occur at (integer + 1/2)*pi. > Numerical experiments show that |Ci(x)| * x -> 1 (from below) as x - infinity. Note that Ci(x) is the real part (depending on how you define it (with or without minus sign)) of Ei(x) = int(x,oo) exp(i*t)/t dt. take that and integrate by parts continuously, to find Ei(x) = i*exp(i*x)/x * sum(k=0,N) k!/(i*x)^k + Remainder Show that the absolute value of the remainder after n terms is less than the absolute value of k!/(i*x)^k after n terms (do this by estimating the integral) --> the remainder doesnt exceed the other terms so Ei(x) ~ i*exp(i*x)/x * sum(k=0,N) k!/(i*x)^k so it would appear |Ci(x)| ~ 1/x It's not obvious to me how you get the bound you have though. === Subject: Re: Bound for cosine integral: |Ci(x)| < 1/x ? > Let Ci(x) = cosine integral function (for real x). > Is |Ci(x)| < 1/x ? > Note that the extrema occur at (integer + 1/2)*pi. > Numerical experiments show that |Ci(x)| * x -> 1 (from below) as x -> infinity. Note that Ci(x) is the real part (depending on how you define it > (with or without minus sign)) of Ei(x) = int(x,oo) exp(i*t)/t dt. take that and integrate by parts continuously, to find Ei(x) = i*exp(i*x)/x * sum(k=0,N) k!/(i*x)^k + Remainder Show that the absolute value of the remainder after n terms is less > than the absolute value of k!/(i*x)^k after n terms (do this by > estimating the integral) --> the remainder doesnt exceed the other > terms so > Ei(x) ~ i*exp(i*x)/x * sum(k=0,N) k!/(i*x)^k so it would appear |Ci(x)| ~ 1/x It's not obvious to me how you get the bound you have though. perhaps.... |Ci(x)| ~ |sin(x)/x * sum(k=0,N) (2k)!/(x)^(2k))| <= |1/x| + Somethingelse positive < 1/x as x->+oo ..but i don't know if that makes sense when dealing with an asymptotic expansion. My argument would be that N has to be something other than zero otherwise we are dealing with an exact representation...but that doesnt really justify turning <= into < or does it? === Subject: Re: Bound for cosine integral: |Ci(x)| < 1/x ? > Let Ci(x) = cosine integral function (for real x). > Is |Ci(x)| < 1/x ? Note that the extrema occur at (integer + 1/2)*pi. > Numerical experiments show that |Ci(x)| * x -> 1 (from below) as x > -> infinity. > Note that Ci(x) is the real part (depending on how you define it > (with or without minus sign)) of Ei(x) = int(x,oo) exp(i*t)/t dt. > take that and integrate by parts continuously, to find > Ei(x) = i*exp(i*x)/x * sum(k=0,N) k!/(i*x)^k + Remainder > Show that the absolute value of the remainder after n terms is less > than the absolute value of k!/(i*x)^k after n terms (do this by > estimating the integral) --> the remainder doesnt exceed the other > terms so > Ei(x) ~ i*exp(i*x)/x * sum(k=0,N) k!/(i*x)^k > so it would appear |Ci(x)| ~ 1/x > It's not obvious to me how you get the bound you have though. perhaps.... > Ci(x)| ~ |sin(x)/x * sum(k=0,N) (2k)!/(x)^(2k))| <= |1/x| + > Somethingelse positive < 1/x as x->+oo ..but i don't know if that makes sense when dealing with an asymptotic > expansion. My argument would be that N has to be something other > than zero otherwise we are dealing with an exact representation...but > that doesnt really justify turning <= into < or does it? Sorry that N above should be N = +oo because we threw away the remaining terms. i think from Ei(x) = Re( i*exp(i*x)/x * sum(k=0,N) k!/(i*x)^k ) + Re(Remainder) where |remainder|<=| i*exp(i*x)/x * sum(k=0,N) k!/(i*x)^k| then we just keep the first term and i think that's enough for the strict inequality. === Subject: Re: Bound for cosine integral: |Ci(x)| < 1/x ? > Let Ci(x) = cosine integral function (for real x). > Is |Ci(x)| < 1/x ? > Note that the extrema occur at (integer + 1/2)*pi. > Numerical experiments show that |Ci(x)| * x -> 1 (from below) as x > -> infinity. Note that Ci(x) is the real part (depending on how you define it > (with or without minus sign)) of Ei(x) = int(x,oo) exp(i*t)/t dt. take that and integrate by parts continuously, to find Ei(x) = i*exp(i*x)/x * sum(k=0,N) k!/(i*x)^k + Remainder Show that the absolute value of the remainder after n terms is less > than the absolute value of k!/(i*x)^k after n terms (do this by > estimating the integral) --> the remainder doesnt exceed the other > terms so > Ei(x) ~ i*exp(i*x)/x * sum(k=0,N) k!/(i*x)^k so it would appear |Ci(x)| ~ 1/x It's not obvious to me how you get the bound you have though. > perhaps.... > Ci(x)| ~ |sin(x)/x * sum(k=0,N) (2k)!/(x)^(2k))| <= |1/x| + > Somethingelse positive < 1/x as x->+oo > ..but i don't know if that makes sense when dealing with an > asymptotic expansion. My argument would be that N has to be > something other than zero otherwise we are dealing with an exact > representation...but that doesnt really justify turning <= into < or does > it? Sorry that N above should be N = +oo because we threw away the > remaining terms. i think from Ei(x) = Re( i*exp(i*x)/x * sum(k=0,N) k!/(i*x)^k ) + Re(Remainder) this should be Ci where |remainder|<=| i*exp(i*x)/x * sum(k=0,N) k!/(i*x)^k| then we > just keep the first term and i think that's enough for the strict > inequality. which now that i look at it...appears to be exactly what W^3 did, except he did it in two lines! oh well. === Subject: Re: Bound for cosine integral: |Ci(x)| < 1/x ? > Note that the extrema occur at (integer + 1/2)*pi. This is only an approximation. For example, consider 10.5*Pi = 32.9867 ... this is where sin(x)=1 and cos(x)=0. But the local maximum of x*Ci(x) is at the point 33.01697, very close but not equal. === Subject: Re: Bound for cosine integral: |Ci(x)| < 1/x ? > Let Ci(x) = cosine integral function (for real x). > Is |Ci(x)| < 1/x ? Note that the extrema occur at (integer + 1/2)*pi. > Numerical experiments show that |Ci(x)| * x -> 1 (from below) as x - infinity. Integrating by parts a few times gives int_[x, oo) cos(t)/t dt = - sin(x)/x + O(1/x^2), so x * Ci(x) takes on every value in (-1, 1) infinitely often. === Subject: Re: Bound for cosine integral: |Ci(x)| < 1/x ? posting-account=76gTjAoAAACFBBxW0JkX-LuotQPzt612 Hi-Speed Internet; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) Following up on ... > Integrating by parts a few times gives int [x, oo) cos(t)/t dt = - sin(x)/x + O(1/x^2), so x * Ci(x) takes on every value in (-1, 1) infinitely often. I get Ci(x) = sin(x)/x - 2 sin(x)/x^3 + 6 int [x,oo) sin(t)/t^4 dt. Using 6 | int [x,oo) sin(t)/t^4 | < 6 | int [x,oo) 1/t^4 | = 6 / (3x^3) = 1/(2x^2) then at the local max/min sin(x) = 1 or -1, so we get | x Ci(x) | < 1 (because x >= pi/2). When x < pi/2 we have -1 < x Ci(x) < 1, so altogether | Ci(x) | < 1/x for x > 0 Lew Baxter === Subject: Re: Bound for cosine integral: |Ci(x)| < 1/x ? > Following up on ... Integrating by parts a few times gives int_[x, oo) cos(t)/t dt = - sin(x)/x + O(1/x^2), so x * Ci(x) takes on every value in (-1, 1) infinitely often. I get Ci(x) = sin(x)/x - 2 sin(x)/x^3 + 6 int_[x,oo) sin(t)/t^4 dt. Using 6 | int_[x,oo) sin(t)/t^4 | < 6 | int_[x,oo) 1/t^4 | = 6 / > (3x^3) = 1/(2x^2) then at the local max/min sin(x) = 1 or -1, no > so we get | x Ci(x) | < 1 > (because x >= pi/2). When x < pi/2 we have -1 < x Ci(x) < 1, so altogether | Ci(x) | < 1/x for x > 0 Lew Baxter > === Subject: Re: Bound for cosine integral: |Ci(x)| < 1/x ? <200620091323069228%anniel@nym.alias.net.invalid> posting-account=76gTjAoAAACFBBxW0JkX-LuotQPzt612 Hi-Speed Internet; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) Sorry ... of course, 6/(3x^3) = 2 / x^3 but still get |Ci(x)| < 1/x when x >= pi/2. (The case when x < pi/2 should be easy, by looking at the graph.) === Subject: Re: Bound for cosine integral: |Ci(x)| < 1/x ? > Sorry ... of course, 6/(3x^3) = 2 / x^3 > but still get |Ci(x)| < 1/x when x >= pi/2. > (The case when x < pi/2 should be easy, by looking at the graph.) needs explanation === Subject: Re: Bound for cosine integral: |Ci(x)| < 1/x ? posting-account=76gTjAoAAACFBBxW0JkX-LuotQPzt612 Hi-Speed Internet; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) oops .. I forgot the -cos(x)/x^2 term: Integrating once to get sin(x)/x - int_[x,oo) sin(t)/t^2 dt and twice, to get: sin(x)/x - cos(x)/x^2 + 2 int_[x,oo) cos(t)/t^3 dt and thrice, to get: sin(x)/x - cos(x)/x^2 - 2 sin(x)/x^3 + 6 int_ [x,oo) sin(t)/t^4 dt No matter, because at local max/min, cos(x) = 0. === Subject: Re: Bound for cosine integral: |Ci(x)| < 1/x ? posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) MeAmI.org precluded: np THEOREM P Is |Ci(x)| < 1/x ? Note that the extrema occur at (integer + 1/2)*pi. > Numerical experiments show that |Ci(x)| * x -> 1 (from below) as x - infinity. Integrating by parts a few times gives int [x, oo) cos(t)/t dt = - sin(x)/x + O(1/x^2), so x * Ci(x) takes on every value in (-1, 1) infinitely often. === Subject: Quotient absolute value posting-account=33KaEgkAAAA9tz8WICNABjrkyMKXFbGS Gecko/2009032609 Firefox/3.0.8,gzip(gfe),gzip(gfe) If quotient of absolute values of a function is absolute value of their quotient, i.e., if f (x) / f (y) = f (x/y), show that f(z) = |z| where z has to be a complex number. Narasimham === Subject: Re: Quotient absolute value > If quotient of absolute values of a function is absolute value of > their quotient, i.e., > if f (x) / f (y) = f (x/y), show that f(z) = |z| where z has to be a > complex number. That is impossible, assuming you mean for all z, f(z) = |z| Consider for all z, f(z) = 1. However the statement and the equation do not match. Do you mean for all x,y in C, |f(x)| / |f(y)| = |f(x/y)| ? Assuming f(z) = |z| can be a result, then the equation needs to be quantified differently. For example: for all x in C, y in C0, (if f(y) /= 0, then |f(x)| / |f(y)| = |f(x/y)|) Otherwise the equation would implicitly imply, y /= 0 for all y, f(y) /= 0. Alternatively you could write (1) for all x in C, y in C0, |f(x)| = |f(x/y)|.|f(y)|. There are many functions that satisfy (1). For example, any function with for all z, |f(z)| = 1. So again f(z) = |z| cannot be shown, even if is continuous. ---- === Subject: Re: Comprehensive Solution Manual for Textbooks posting-account=rLOz6QoAAAAmvEIbrGZd27QhtZqovu5R rv:1.9.0.11) Gecko/2009060214 Firefox/3.0.11,gzip(gfe),gzip(gfe) All messages replied. If you need any solution manual or test bank please email me at sbooks4sale[at]hotmail[dot]com === Subject: Electrical Engineering Principles and Applications 4th Edition, Allan R. Hambley Solutions Manual posting-account=phmuzgoAAADtdQ30DWW2CQ_tVx64xKMx Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) I have the solutions manual to Electrical Engineering Principles and Applications 4th Edition, Allan R. Hambley. Email me at seuki7 at gmail.com if you're interested. === Subject: Fundamentals of Fluid Mechanics, 5th Edition, Munson, Young, Okiishi Solutions Manual posting-account=phmuzgoAAADtdQ30DWW2CQ_tVx64xKMx Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) I have the solutions manual to Fundamentals of Fluid Mechanics, 5th Edition, Munson, Young, Okiishi. Email me at seuki7 at gmail.com if you're interested. === Subject: Engineering Mechanics: Dynamics, 6th Edition, Meriam, Kraige Solutions Manual posting-account=phmuzgoAAADtdQ30DWW2CQ_tVx64xKMx Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) I have the solutions manual to Engineering Mechanics: Dynamics, 6th Edition, Meriam, Kraige. Email me at seuki7 at gmail.com if you're interested. === Subject: Engineering Mechanics: Statics, 6th Edition, Meriam, Kraige Solutions Manual posting-account=phmuzgoAAADtdQ30DWW2CQ_tVx64xKMx Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) I have the solutions manual to Engineering Mechanics: Statics, 6th Edition, Meriam, Kraige. Email me at seuki7 at gmail.com if you're interested. === Subject: test bank and solution manuals fro sale posting-account=KhEHuAoAAADa4kfi_ORqDYOVAUvOh1Z5 Gecko/2009051221 Firefox/3.0.10,gzip(gfe),gzip(gfe) Email me at instructors.team[at]gmail.com Here s a list of available test bank and solution manuals for sale: 2009 Federal Taxation - Pratt [CapitalEth] Solutions Manual & test Bank Accounting for Non-Accounting Students test bank Accounting Information Systems (6thEd) - Hall - Solutions Manual Aerodynamics for Engineers, 5E Solution manual Bertin Russ Cummings Algebra and Trigonometry 3rd Ed, and Precalculus 3rd Ed, Instructor's Solutions Manual 2008 - Beecher, Penna, & Bittinger Analysis- With an Introduction to Proof, 4-E-Instructors SM Art Through The Ages A Global Hist Vol II Test Bank complete Auditing A Business Risk Approach (6thEd) - Rittenberg [CapitalEth] Solutions Manual and Test Bank Auditing and Assurance Services An Intergrated Approach and ACL Software12E -ISBN 0136128300 Solution Manual & Test bank Auditing Cases Interactive Learning Approach (4thEd) - Beasley - Solutions Manual Beer, Johnston & Dewolf - Mechanics Of Materials Solution Manual 3Rd Ed Biology with Mastering Biology 8E Campbell Reece ISBN -0321494334 Test Bank Bond Markets, Analysis and Strategies 6E Instructors manual Fabozzi Brock Biology of Microorganisms 12E ISBN -0132324997 Test Bank Busines statistics Decision making 7E David F Groebner Solution manual & test bank Business Law and the Legal Environment Jeffrey F. Beatty 5th edition Test Bank Business Law Tax And Cases (11thEd) - Clarkson [CapitalEth] TestBank Business Statistics First Course Solutions Manual Levine Calculus A Complete Course Adams - - Instructors Solution Manual Concepts Of Programming Languages (8thEd) - Sebesta [CapitalEth] Solutions Manual Contemporary Financial Management (11thEd) - Moyer - Solutions Manual Cornerstone Of Managerial Accounting (2ndEd) - Mowen - Solutions Manual Corporate Partnership Estate Gift Tax 2009 - Pratt - Solutions Manual Cost accounting by Hongren 13/e test bank and Solution manual Cost Accounting Canadian (4thEd) - Horngren - Test Bank Cutnell John, Physics 7th E, Instructors manual (all solutions even +odd) Data Structures Algorithm Analysis In CPP (3rdEd) - Weiss - Solutions Manual Deitel & Deitel How to Program C++ 6th E Code solutions Options, Futures and Other Derivatives John Hull 7E test bank ch 1-21 with answers Digital Electronics A Practical Approach - William Kleitz 8th ed ISM Econometric Analysis - Solutions Manual (Greene 6Th 2007) Effective Small Business Management - Norman M Scarborough test bank Electrical Machines, Drives and Power Systems - Solutions Manual Electronic Devices and Circuit Theory 9e Instructors resource manual ISBN 0132214466 Elementary Differential Equations Boundary Value (2ndEd) - Kohler - Solutions Manual Elementary Linear Algebra (6thEd) - Larson, Falvo - Solutions Manual E-Marketing 5E Strauss Frost ISBN 0136154417 Test Bank Entrepreneurial Finance (3rdEd) - Leach - Instructors Solutions Manual Exploring Microsoft Office Excel 2007, Comprehensive, 2E Test bank Financial Accounting - Jane Reimers (1st Ed) (ISBN-10: 0131492012) Financial And Managerial Acct (10thEd) - Warren - Solutions Manual Financial Management Theory Practice (12thEd) - Brigham - Solutions Manual and test bank Friendly Introduction To Analysis (2ndEd) - Kosmala - Solutions Manual Friendly Introduction to Numerical Analysis Brian Bradie Fundamentals of Communication Systems Proakis & Salehi Fundamentals of Differential Equations 7thE Nagle Snider Instructors resource manual ISBN -0321388445 Fundamentals of Engineering Electromagnetics By David K. Cheng Solutions Manual Fundamentals of Multinational Finance 3e Muffet, Stonehill Test bank Gas Dynamics John & Keith Instructors Solution Manual General, Organic, and Biological Chemistry Structures of Life, 3E Test bank Gregory - Classical Mechanics - SOLUTIONS MANUAL (Cambridge, 2006) Human Anatomy & Physiology 7E TEST BANK ISBN 0805373810 Human Anatomy & Physiology 8E TEST BANK Hydraulics in Civil and Environmental Engineering Solutions by Chadwick & Morfett Solution's Manual Instructor's Manual Contemporary Engineering economics 4e Park Instructor's Edition LAN Switching and Wireless CCNA Exploration Labs and Study Guide Allan Johnson EBOOK International Economics Theory and Policy 8E Krugman Obstfeld International Marketing and Export Management 6E Albaum Introduction To Business Statistics (6thEd) - Weiers - Solutions Manual Introduction to Econometrics 2E Stock Watson Solution manual Introduction to Linear Algebra -3rd Edition - Gilbert Strang Instructors Solutions Manual Introduction To Management Accounting (14thEd) - Horngren - Solutions Manual Introduction to Management Science - Taylor 9E Solution Manual Introduction to Parallel Computing Kumar solution manual Behavior in Organizations Greenberg 9th Edition test bank Introduction to the Design and Analysis of Algorithms 2E Levitin ISBN 0321428102 Introductory Circuit Analysis 11e Boylestad Solution manual Introductory Circuit Analysis 11E Lab solutions manual Introductory Econometrics (4thEd) - Woolridge - Solutions Manual Investment Analysis & Portfolio Management, 7e by Reilly and Brown Solutions Manual Java Foundations- Introduction to Program Design and Data Structures- ES zip Java Foundations- Introduction to Program Design and Data Structures- project solutions Linear Algebra (Jim Hefferon) (2006) Solutions Manual Linear Algebra For Engineers And Scientist (1stEd) - Hardy [CapitalEth] Solutions Manual Management Accounting Anthony A Atkinson (5th Ed) ISM and TB Management Information Systems 11E Laudon 0136078907 test bank Management Information Systems Managing the Digital Firm 10th Edition by Laudon Managerial Accounting Information for Decisions 4th ed Albrite Marketing Real people Real Choices 6 e Test Bank ISBN 0136054234 Mathematical Proofs A Transition to Advanced Mathematics (2ndEd) - Chartrand - Solutions Manual Mathematical Thinking problem solving Angelo & West Instructors manual ISBN -0130144126 Microbiology with Diseases by Body System Robert W Bauman 2nd ed Instructors manual MIS Cases Decision Making wih Application Software, 4E Instructors manual and solution files Object Oriented Programming in C++ 4E suplement robert Lafore Operations Management 9E Jay Heizer ISBN 0131585576 Operations Management 9E Jay Heizer ISBN 0132342979 test bank Organic Chemistry 6E Wade Test Bank Parallel Programming (2ndEd) - Wilkinson [CapitalEth] Solutions Manual Partial Differential Equations And Boundary Value Problems (2nd Ed) - Asmar - Solutions Manual Physics Principles with Applications with Mastering Physics Giancoli 6E ISM Physics with Mastering Physics 3E James walker Prebles' Artforms 9E patrick Frank TESTGEN file ISBN 0136044166 Prebles' Artforms Test Bank Precalculus (4thEd) - Blitzer - Solutions Manual Prentice Hall Federal Taxation 2009 Comprehensive - Pope - Solutions Manual Prentice Hall's Federal Taxation 22/e 2009 Corporations test bank and solution manual Prince Medical Imaging Signals and Systems Instructors manual Principles Of Foundation Engineering (6thEd) - Das - Solution Manual Principles Of Managerial Finance Brief (5thEd) - Gitman [CapitalEth] Solutions Manual Principles of Marketing 5th European edition by Kotler Instructors solution manual Principles Of Operations Management (6thEd) - Heizer [CapitalEth] Test Bank Problem Solving With CPP (7thEd) - Savitch [CapitalEth] Solutions Manual Reinforced Concrete Design - George F. Limbrunner 7th ed ISBN [CapitalEth] 0135044359 Roads to Geometry, 3/E Solutions manual Edward C. Wallace Sandler S. I. - Chemical and Engineering Thermodynamics - Solution manual Source Code Files for Programming Concepts in MATLAB 2E David M Smith Statics And Strengths Of Materials (6thEd) - Morrow - Solutions Manual Statistics 11E James T. McClave Solution manual Stats Data And Models (2ndEd) - Veaux [CapitalEth] Solutions Manual Strategic Compensation Joe Martocchio 5th ed Test Bank Strategic Management and Competitive Advantage Concepts and Cases 2E barney hesterly ISBN 0136036112Pearson TESTGEN file Strategic Management Concepts and Cases 12E Fred David ISBN 0138132178 test bank Strategic Management TestBank Hitt 8th edition Test Bank Martini EAP 5E TestBank International economics 12th edition Carbaugh TestBank Macroeconomics Principles and Policy Baumol 10th Undergraduate Econometrics Solutions Manual - Hill, Judge and Griffiths Understanding and Managing Organizational Behavior 5E Test bank University Chemistry with Student Access Kit siska 1e test bank Wang, L. & Zhou, X. & Wei, X. - Heat conduction. Mathematical models and analytical solutions (Springer, 2008) === Subject: Financial Reporting and Analysis: Using Financial Accounting Information 11th Edition Charles H. Gibson solution manual posting-account=o339CQoAAACB2AYu4sK6rVlf_DJCMbcK CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual and Test bank I have many solutions manual and Test bank, they are PDF format or Word format, Those resources save your time and effort and let you definitely understand what you are studying and get amazing marks as well, The Manuals contains the answers of the questions and exercises (Usually at the end of each chapter), The Test Questions contains an extra questions, Most of them multiple choice, true and false and fill in the blank questions with their answers. If the solutions manual or Test bank what you want is not in this list, also can ask me (They are part of what I have ). Then if you need solutions manual or test bank . only contact me by email. Studentshelp(at)hotmail(dot)com studentshelp@hotmail.com 1. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin solution manual and test bank 2. Accounting Concepts and Applications (9th Ed.) by W. Steve 3. Accounting 7e by horngren solution manual 4. Accounting 7e by horngren TB 5. accounting 7e by horngren TB (test generator File) 6. Accounting 8th edition by horngren test bank and solution manual 7. Accounting Concepts and Applications 10th Edition W. Steve Albrecht, James D. Stice, Earl K. Stice, Monte R. Swain instructor manual 8. Accounting Concepts and Applications 10th Edition W. Steve Albrecht, James D. Stice, Earl K. Stice, Monte R. Swain solution manual 9. Accounting For Managers Interpreting Accounting Information for Decision-making, 3rd Edition Collier 10. Accounting Information Systems - james hall 6ed sm 11. Accounting Information Systems - james hall 6ed tb 12. Accounting Information Systems 10E Romney solution manual 13. Accounting Information Systems 10E Romney test bank 14. Accounting Information Systems 11E Romney solution manual 15. Accounting Information Systems 11E Romney test bank 16. Accounting Information Systems 7E Edition Ulric J. Gelinas, Richard B. Dull instructor manual 17. Accounting Information Systems 7E Edition Ulric J. Gelinas, Richard B. Dull solution manual 18. Accounting Information Systems 7E Edition Ulric J. Gelinas, Richard B. Dull test bank 19. Accounting Information Systems, 9E George H. Bodnar William S. Hopwood solution manual 20. Accounting Information Systems, 9E George H. Bodnar William S. Hopwood test bank 21. Accounting Principles 8E by Kieso SM chapter 1 to 10 22. Accounting Principles 8E by Kieso SM chapter 11 to 26 23. Accounting Principles, Edition 8E, Weygandt, Kieso, Kimmel (Test Bank) volume 1 24. Accounting Principles, Edition 8E, Weygandt, Kieso, Kimmel (Test Bank) volume 2 25. Accounting Text and Cases 12e by Anthony IM 26. Accounting what number means 8e by Marshall 27. Adaptive Control 2E. by Karl J. Astrom solution manual 28. Adaptive Filter Theory, 4th edition S. Haykin 29. Advance corporate finance 1e by Ogden Instructor manual and test bank 30. Advanced accounting 10E by Flyd Beams (SM+IM+TB) 31. Advanced Accounting 10th edition by Fischer (SolutionsManual) 32. Advanced Accounting 10th edition by Fischer (test bank) 33. Advanced Accounting 9e by Beams solution manual 34. Advanced Accounting 9E Hoyle,Schaefer,Doupnik Solution Manual 35. Advanced Accounting 9E Hoyle,Schaefer,Doupnik Test Bank 36. Advanced Accounting 9th edition by Fischer (SolutionsManual) 37. Advanced Accounting 9th edition by Fischer (test bank) 38. ADVANCED CORPORATE FINANCE Policies and Strategies by Joseph P. Ogden,Frank C. Jen,Philip F. O'Connor ( solution manual) 39. ADVANCED CORPORATE FINANCE Policies and Strategies by Joseph P. Ogden,Frank C. Jen,Philip F. O'Connor (test bank) 40. Advanced Digital Design with the Verilog HDL Michael D. Ciletti selected solutions 41. Advanced Dynamics by Donald T. Greenwood 42. Advanced Engineering Mathematics 3rd Edition by Dennis G Zill and Michael R Cullen 43. Advanced Engineering Mathematics by Erwin Kreyszig 8ed solutions manual 44. Advanced Engineering Mathematics Dennis G Zill 2nd Solution 45. Advanced Engineering Mathematics, 6th Edition Peter V. O'Neil - University of Alabama, Birmingham 46. Advanced Engineering Mathematics, 9th Edition By Erwin Kreyszig 47. Advanced Financial Accounting, 6th edition, by Baker, Lembke, and King solution manual 48. Advanced Macroeconomics 1996 romer 49. Advanced Macroeconomics, Solutions Manual 1996 Romer 50. Advanced Modern Engineering Mathematics, 3rd Edt by Glyn James solution manual 51. Anton, Bivens, Davis Calculus Early Transcendentals Combined, 8th Edition instructor solution manual 52. Anton, Bivens, Davis Calculus Multivariable, 8th Edition 53. Applied Fluid Mechanics 6th Ed. by Robert L. Mott 54. Applied Linear Algebra by Chehrzad Shakiban,Olver 55. Applied Mechanics for Engineering Technology 8e Keith M Walker 56. Applied Multivariate Statistical Analysis 6e Johnson 57. Applied Numerical Analysis 7Ed - Curtis F. Gerald, Patrick O. Wheatley - Solutions manual 58. Applied Partial Differential Equations David Logan 59. Applied Quantum Mechanics by A. F. J. Levi 60. Applied Statistics and Probability for Engineers 3rd.Ed edition student manual 61. Applied Statistics and Probability for Engineers by Douglas C. Montgomery 3rd edition complete 62. Applied Statistics and Probability for Engineers, 4th Edition Montgomery, Runger 63. Applied Strength of Materials (4th Edition) SOLUTION MANUAL by Robert L. Mott 64. Artificial Intelligence A Modern Approach 2e Stuart Russell Peter Norvig 65. Audit and Assurance service An Integrated Approach 11e TB 66. auditing and assuance services by messier test bank 6th edition 67. Auditing and Assurance Services An Intergrated Approach 13e by Alvin Arens Randal J. Elder, ark Beasley test bank 68. Auditing and Assurance Services An Intergrated Approach 13e by Alvin Arens Randal J. Elder, ark Beasley solution manual 69. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual 70. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley test bank 71. Auditing Cases, 3E Mark S. Beasley solution manual 72. Auditing Cases: An Interactive Learning Approach, 4/E Mark S Beasley Frank A. Auditing: A Business Risk Approach, 6th EditionLarry E. Rittenberg Bradley J. Schwieger Karla Johnstone solution manual 73. Auditing: A Business Risk Approach, 6th EditionLarry E. Rittenberg Bradley J. Schwieger Karla Johnstone test bank 74. Bank Management & Financial Services, 7/e By Peter S. Rose, Sylvia C. Hudgins (IM+SM) 75. Bank management 7e by peter s. rose TB 76. Bank management 7e by Rose ( instructor manual ) 77. Business Law by Cheeseman 6E (IM) 78. Business Law by Cheeseman 6E (TB) 79. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz instructor manual 80. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank 81. Business Statistics (A Decision Making Approach), Groebner, Shannon, Fry, Smith, 7 sm and tb 82. Business Statistics 4e by Leonard J. Kazmier book + sm 83. Business Statistics Decision Making and Student CD Package test items and solution manual, 7E test bank and sm 84. Butterworth Heinemann - Coulson And Richardson - Chemical Engineering Vol I (Solutions Manual V Edition) 85. C ++ how to program deitel 6th edition solution manual and test bank 86. C How to Program, 5/E (Harvey & Paul) Deitel & Deitel 87. C++ How to Program 3rd edition by deitel 88. College Accounting (Chapters 1-25), 10E by Jeffrey Slater sm and tb 89. College Mathematics for Business, Economics, Life Sciences & Social Sciences (11th Edition) (Hardcover) by Raymond A. Barnett (Author), Michael R. Ziegler (Author), Karl E. Byleen (Author) 90. Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson 91. Computer Architecture: Pipelined and Parallel Processor Design (Solutions Manual) by Michael J. Flynn selected solutions 92. Computer Networking: A Top-Down Approach, 5/E solution manual 93. Consumer Behavior, 8/E Michael R. Solomon test bank 94. Control Systems Engineering by Nise 4ed 95. Corporate Computer and Network Security Raymond Panko 96. Corporate Finance By Stephen A. Ross 8th edition SM 97. Corporate finance 1e by berk sm 98. Corporate finance 1e by berk tb 99. Corporate Finance 2nd Edition Scott B. Smart, William L. Megginson, Lawrence J. Gitman solution manual 100. Corporate Finance, 8e Stephen A. Ross Randolph W. Westerfield Jeffrey Jaffe instructor manual and solution manual 101. Corporate Financial Management 3e Douglas R. Emery instructor manual 102. Corporate Financial Management 3e Douglas R. Emery test bank 103. Cost Accounting 12e by Horngren Test Bank 104. Cost accounting 12e by Charles T. Horngren Srikant Datar George Foster Madhav Rajan Chris Ittner solution manual 105. Cost accounting 13e by Charles T. Horngren Srikant Datar George Foster Madhav Rajan Chris Ittner solution manual 106. Cost accounting 13e by Charles T. Horngren Srikant Datar George Foster Madhav Rajan Chris Ittner test bank 107. Cost Accounting; Foundations and Evolutions, Edition 7e, Kinney, Raiborn 108. Cost Management: A Strategic Emphasis, 4e Blocher 109. Cost Management: Measuring Monitoring and Motivating Performance by Eldenburg Wolcott SM TB 110. Cost management: Accounting and control 5e and 6e By Hansen MOwen SM+TB 111. Entrepreneurial Finance, 3rd Edition Chris Leach Ronald W. Melicher test bank 112. Entrepreneurial Finance, 3rd Edition Chris Leach Ronald W. Melicher instructor manual 113. Entrepreneurship: Starting and Operating a Small Business (with Business Plan Pro), 2/E Steve Mariotti, Caroline Glackin test gen and instructor manual 114. Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus test bank 115. Essentials of Investments Zvi Bodie, Alex Kane, Alan J. Marcus 116. Essentials of Managerial Finance 14e Brigham TB 117. Essentials of Managerial Finance 13th Edition Scott Besley, Eugene F. Brigham instructor manual 118. Essentials of Managerial Finance 13th Edition Scott Besley, Eugene F. Brigham test bank 119. Essentials of Managerial Finance, 14th EditionScott Besley Eugene F. Brigham instructor manual 120. Essentials of Managerial Finance, 14th EditionScott Besley Eugene F. Brigham spreadsheet problem solutions 121. Essentials of Managerial Finance, 14th EditionScott Besley Eugene F. Brigham test bank 122. Essentials of Modern Business Statistics 4th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams test bank 123. Essentials of Modern Business Statistics 4th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams test bank 124. Essentials of Organizational Behavior 9e Stephen P. Robbins Tim Judge 125. Essentials of Statistics for Business and Economics 5th edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams solution manual with case solutions 126. Essentials of Statistics for Business and Economics 5th edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams test bank 127. Essentials of Statistics, by Triola, 3rd edition sm 128. Essentials of Statistics, by Triola, 3rd edition tb 129. Essentials of Strategic Management 4E DAVID HUNGER THOMAS L. WHEELEN im with tb 130. Federal Taxation 2008 Corporations Partnerships Estates and Trusts 21E Anderson Pope Kramer test bank 131. Finance Management Test Bank brigham 11 test bank 132. Financial & managerial Accounting 13E By william Haka bettner 133. Financial & Managerial Accounting 9e and 10e Carl S. Warren, James M. Reeve solution manual 134. Financial accounting: an introduction to concepts, methods, and uses by clyde Stickney and Roman Weil solutions manual 11e 12e 13e 135. Financial Accounting 4e by John Wild 136. Financial Accounting 6e by kieso solution manual 137. Financial Accounting 6e by kieso test bank 138. Financial Accounting 6e Harrison Horngren 139. Financial Accounting 6th edition by Harrison Solution Manual 140. Financial accounting 6th edition harrison test bank 141. Financial accounting 7th edition harrison solution manual 142. Financial accounting 7th edition harrison test bank 143. Financial Accounting: Information for Decisions 6th Edition Robert W. Ingram, Thomas L. Albright extra resources 144. Financial Accounting: Information for Decisions 6th Edition Robert W. Ingram, Thomas L. Albright solution manual 145. Financial Accounting: Information for Decisions 6th Edition Robert W. Ingram, Thomas L. Albright test bank 146. Financial Accounting; Tools for Business Decision Making, 4th Edition, Kimmel.Weygandt.Kieso instructor manual 147. Financial Accounting; Tools for Business Decision Making, 4th Edition, Kimmel.Weygandt.Kieso solution manual 148. Financial Accounting; Tools for Business Decision Making, 4th Edition, Kimmel.Weygandt.Kieso test bank 149. Financial Analysis with Microsoft¬ Excel 4th Edition Timothy R. Mayes, Todd M. Shank instructor manual 150. Financial Analysis with Microsoft¬ Excel 4th Edition Timothy R. Mayes, Todd M. Shank spreadsheet problems 151. Financial Analysis with Microsoft¬ Excel¬ 2007 Timothy R. Mayes, Todd M. Shank Instructor Spreadsheet Files 152. Financial management 2e by jae K shim 153. Financial management Principles and application 10e by By Arthur J. Keown, John D. Martin, John W. Petty, David F. Scott solution manual 154. Financial Management Theory & Practice,Eugene Brigham,12th edition [ Test Bank ] 155. Financial management theory and practice 10e by Brigham solution manual 156. Financial Management Theory And Practice 11e by Brigham solution manual 157. Financial management theory and practice 12e by Brigham sm 158. Financial management theory and practice 12e by Brigham spreadsheet problems 159. Financial management theory and practice 12e by Brigham TB 160. Financial Management Theory and Practice, 11e By Eugene F. Brigham test bank 161. Financial Markets and Institution (7thEd) Madura TestBank 162. Financial Reporting Analysis 10th edition TB by gibson 163. Financial Reporting and Analysis Using Financial Accounting Information 10th Edition Charles H. Gibson instructor manual 164. Financial Reporting and Analysis Using Financial Accounting Information 10th Edition Charles H. Gibson solution manual 165. Financial Reporting and Analysis Using Financial Accounting Information 10th Edition Charles H. Gibson test bank 166. Financial Reporting and Analysis: Using Financial Accounting Information 11th Edition Charles H. Gibson solution manual 167. Financial Reporting and Analysis: Using Financial Accounting Information 11th Edition Charles H. Gibson test bank 168. Financial Reporting and Corporate Governance exercise solutions Lee 169. Framework for Marketing Management, A - Philip Kotler (4th ed) (ISBN 0136026605) 170. Framework for Marketing Management, A - Philip Kotler (4th ed) (ISBN test bank 171. Fundamental accounting principles 17th edition larson solution manual 172. Fundamental Accounting Principles, 18/e John J. Wild Barbara Chiappetta Kermit D. Larson solution manual and test bank 173. Fundamentals accounting principles by larson 18e SM 174. Fundamentals of Advanced Accounting 1e Fisher taylor chang solution manual 175. Fundamentals of Advanced Accounting 1e Fisher taylor chang test bank 176. Fundamentals of advanced accounting 3e by hoyle 177. Fundamentals of Advanced Accounting, 2e Joe B. Hoyle Thomas F. Schaefer Timothy S. Doupnik (Solution Manual) 178. Fundamentals of Contemporary Financial Management, 2nd Edition R. Charles Moyer James R. McGuigan Ramesh P. Rao instructor manual 179. Fundamentals of Contemporary Financial Management, 2nd Edition R. Charles Moyer James R. McGuigan Ramesh P. Rao test bank 180. Fundamentals of corporate finance 8e by Ross Ross, Westerfield,jordan 181. Fundamentals of Corporate Finance, 4th Edition (Brealey, Myers, Marcus) by Bruce Swenson 182. Fundamentals of Financial Management 12th brigham edition instructor manual 183. Fundamentals of Financial Management 12th edition brigham test bank 184. Fundamentals of Financial Management 10th Edition by Eugene Brigham Solution manual 185. Fundamentals of Financial Management 10th Edition by Eugene Brigham test bank 186. Fundamentals of Financial Management 11e by Eugene F. Brigham, Joel F. Houston spreadsheet problems 187. Fundamentals of Financial Management 11e by Eugene F. Brigham, Joel F. Houston test bank and cyberproblems 188. Fundamentals of Financial Management 11e by Brigham Instructor manual 189. Fundamentals of financial management 12e by james c. van horne 190. Fundamentals of Financial Management Eugene F. Brigham, Joel F. Houston 12th edition instructor manual 191. Fundamentals of Financial Management Eugene F. Brigham, Joel F. Houston 12th edition spreadsheets problems and web appendix solutions 192. Fundamentals of Financial Management Eugene F. Brigham, Joel F. Houston 12th edition test bank 193. Fundamentals of Financial Management, 12th Edition (Instructors guide ONLY) by James C. Van Horne, John M Wachowic 194. Fundamentals of Financial Management, Concise Edition 5th Eugene F. Brigham, Joel F. Houston test bank 195. Fundamentals of Financial Management, Concise Edition 5th Eugene F. Brigham, Joel F. Houston spreadsheets problems 196. Fundamentals of Financial Management, Concise Edition 5th Eugene F. Brigham, Joel F. Houston instructor manual 197. Fundamentals of Financial Management, Concise Edition Eugene F. Brigham, Joel F. Houston 6th edition instructor manual 198. Fundamentals of Financial Management, Concise Edition Eugene F. Brigham, Joel F. Houston 6th edition spreadsheet problem solutions 199. Fundamentals of Financial Management, Concise Edition Eugene F. Brigham, Joel F. Houston 6th edition test bank 200. Fundamentals Of Fluid Mechanics 3Rd And 4Th Edition Solutions Manual 201. Fundamentals of Fluid Mechanics, 6th Edition Munson, Young, Okiishi, Huebsch 202. Fundamentals of Heat and Mass Transfer, 5th Edition by Frank P. Incropera 203. Fundamentals of Heat and Mass Transfer, 6th Edition Incropera, DeWitt, Bergman, Lavine 204. Fundamentals of Investing, 10th Edition by Gitman and Joehnk 205. Fundamentals of Investments 3e Gordon J. Alexander William F. Sharpe 206. Fundamentals of Logic Design 5th edition by charles roth 207. Fundamentals of Machine Component Design, 3rd ed - Student Solutions Manual by Juvinall, Marshek 208. Fundamentals of manufacturing 2nd edition by philip d. rufe solutions manual 209. Fundamentals of Momentum, Heat and Mass Transfer, 5th Edition Welty, Wicks, Rorrer, Wilson 210. Fundamentals of Multinational Finance, 2nd edition by Michael H. Moffett test bank and solution manual 211. Fundamentals of Multinational Finance, 3E by Michael H. Moffett (Instructor's Manual) 212. Fundamentals of Multinational Finance, 3E by Michael H. Moffett test bank 213. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith sm 214. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith tb 215. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith instructor manual 216. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith tb 217. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith sm 218. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow sm 219. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow tb 220. Human resources management 10e Gary dessler (IM+TB) 221. Intermediate Accounting 10e by Nikolai sm 222. Intermediate Accounting 11e by Kieso 223. Intermediate Accounting 12e by Kieso 224. Intermediate accounting 12th Updated by Kieso Solution manual 225. Intermediate accounting 12th Updated by Kieso test bank 226. Intermediate Accounting, 13th Edition Instructor's Manual Kieso, Weygandt, Warfield 227. (Sm+TB+IM) 228. Intermediate Accounting 2e by Baruch Englard 229. Intermediate Accounting 3e by J. David Spiceland 230. Intermediate Accounting 4e revised by J. David Spiceland solution manual 231. Intermediate accounting by Spiceland 4e Solution manual 232. Intermediate Accounting James D. Stice, Earl K. Stice, Fred Skousen 16th edition solution manual 233. Intermediate Accounting, 13th Edition Kieso, Weygandt, Warfield test bank and solution manual 234. Intermediate Accounting, Update, 12th Edition international student solution manual 235. Intermediate Algebra Functions & Authentic Applications 3e lehmann 236. Intermediate Algebra, 8th Edition By Margaret L. Lial, John Hornsby, Terry McGinnis 237. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves instructor manual 238. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves test bank 239. Intermediate Microeconomics, 10th Edition Walter Nicholson ,Christopher Snyder im with tb 240. International Accounting 1e by Doupnik solution manual 241. International Accounting 6e Frederick D. Choi Gary K. Meek 242. International Business The Challenges of Globalization, 4E John J. Wild,Kenneth L. Wild tb and im 243. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan instructor manual 244. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan test bank 245. International Economics Theory and Policy 8e Krugman & Obstfeld 246. International Economics, 7e Husted Melvin test bank and solution manual 247. International Financial Management 9th Edition jeff madura instructor manual 248. International Financial Management 9th Edition jeff madura test bank 249. International Financial Management Geert Bekaert Robert J. Hodrick test bank and sol manual I have many solutions manual and Test bank, they are PDF format or Word format, Those resources save your time and effort and let you definitely understand what you are studying and get amazing marks as well, The Manuals contains the answers of the questions and exercises (Usually at the end of each chapter), The Test Questions contains an extra questions, Most of them multiple choice, true and false and fill in the blank questions with their answers. If the solutions manual or Test bank what you want is not in this list, also can ask me (They are part of what I have ). Then if you need solutions manual or test bank . only contact me by email. Studentshelp(at)hotmail(dot)com Studentshelp(at)hotmail(dot)com only contact me by email studentshelp@hotmail.com I have many solutions manual and Test bank, they are PDF format or Word format, Those resources save your time and effort and let you definitely understand what you are studying and get amazing marks as well, The Manuals contains the answers of the questions and exercises (Usually at the end of each chapter), The Test Questions contains an extra questions, Most of them multiple choice, true and false and fill in the blank questions with their answers. If the solutions manual or Test bank what you want is not in this list, also can ask me (They are part of what I have ). Then if you need solutions manual or test bank . only contact me by email. Studentshelp(at)hotmail(dot)com Studentshelp(at)hotmail(dot)com only contact me by email studentshelp@hotmail.com 1. International Management Managing Across Borders and Cultures 6e test bank and instructor manual 2. Interpreting and Analyzing Financial Statement 4e Karen P. Schoenebeck 3. Introduction to Corporate Finance William L. Megginson, Scott B. Smart 1st edition instructor manual 4. Introduction to Corporate Finance William L. Megginson, Scott B. Smart 1st edition test bank 5. Introduction to Corporate Finance 2nd edition William L. Megginson, Scott B. Smart instructor manual 6. Introduction to Corporate Finance, 2nd Edition William L. Megginson Scott B. Smart test bank 7. Introduction to Corporate Finance, 2nd Edition William L. Megginson Scott B. Smart solution manual 8. Introduction to Government and Non-for-Profit Accounting 6th edition by martin ives sm 9. Introduction to Government and Non-for-Profit Accounting 6th edition test bank by martin ives 10. Introduction to Operations and Supply Chain Management 2e Cecil Bozarth 11. Introduction to Operations and Supply Chain Management 2e Cecil Bozarth Robert B. Handfield test bank and sol manual 12. Investment analysis and portfolio management 8e by Reily Brown 13. Investment Analysis and Portfolio Management 9th Edition Frank K. Reilly, Keith C. Brown solution manual 14. Investment Analysis and Portfolio Management 9th Edition Frank K. Reilly, Keith C. Brown test bank 15. Investment Analysis and Portfolio Management- Solutions Manual, 7th Edition by Frank K. et al. Reily 16. Intermediate Accounting 12 E Kieso (TB) 17. Intermediate accounting 5e spiceland test bank and solution manual 18. Intermediate Accounting 12e by Keiso sm 19. Intermediate accounting 4th edition spiceland test bank 20. Introduction to management accounting 14e Charles T. Horngren, Gary L. Sundem, William O. Stratton, Jeff Schatzberg, Dave Burgstahler solution manual 21. Introduction to Operations Research - 7th by Frederick Hillier, Gerald Lieberman 22. Macroeconomics (8thEd) - Froyen - Solutions Manual 23. Macroeconomics 6e Andrew B. Abel, Ben S. Bernanke, Dean Croushore 24. Macroeconomics 3e williamson instructor manual and test bank 25. Macroeconomics, 4E Olivier Blanchard instructor manual 26. Macroeconomics, 4E Olivier Blanchard test bank 27. Macroeconomics, 5E Olivier Blanchard instructor manual and test bank 28. Management 5th Edition Chuck Williams instructor manual 29. Management 9E Stephen P. Robbins Mary Coulter test bank and instructor manual 30. Management accounting 5e Anthony A. Atkinson Robert S. Kaplan Ella Mae Matsumura S. Mark Young instructor manual test bank and solution manual 31. Management accounting 5E Atkinson solution manual 32. Management accounting 5E Atkinson test bank 33. Management Control Systems Performance Measurement, Evaluation and Incentives 2e Merchant & Van der Stede 34. Management Information Systems; Managing the Digital Firm, Edition 10, Laudon test bank and solution manual 35. Management Robbins Coulter 9th edition (test bank ) 36. Management10E Stephen P. Robbins Mary Coulter 37. Management10E Stephen P. Robbins Mary Coulter test bank 38. Managerial Accounting 12e By Garrison Noreen ( Solution Manual ) 39. Managerial Accounting 12e By Garrison Noreen (Test Bank) 40. Managerial Accounting Bamber, L. S., K. W. Braun, and W. T. Harrison, Jr. 2008 41. Managerial Accounting international edition Garrison11 ( Solution Manual) 42. Managerial Accounting, 11th Edition by Ray H Garrison, Eric Noreen, Peter C. Brewer 43. Managerial Accounting: An Introduction to Concepts, Methods and Uses 10th Edition Michael W. Maher, Clyde P. Stickney, Roman L. Weil instructor manual 44. Managerial Accounting: An Introduction to Concepts, Methods and Uses 10th Edition Michael W. Maher, Clyde P. Stickney, Roman L. Weil solution manual 45. Managerial Accounting: An Introduction to Concepts, Methods and Uses 10th Edition Michael W. Maher, Clyde P. Stickney, Roman L. Weil test bank 46. Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris instructor manual 47. Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris test bank 48. Managerial Finance, Gitman,Lawrence 12e [SM] 49. Managing Human Resources by Luis R. Gomez-Mejia; David B. Balkin; Robert L. Cardy. 5th Edition im and tb 50. Manufacturing Engineering and Technology 5E by Kalpakjian and Schimid 51. Marketing Kotler Armstrong 11th edition (Test bank ) 52. Marketing Management (13th Edition) by Philip Kotler, Kevin Keller im 53. Marketing Management (13th Edition) by Philip Kotler, Kevin Keller tb 54. Mastery of the Financial Accounting Research System (FARS) Through Cases, 2nd Edition Wallace 55. Microeconomic Analysis Solution Manual - Varian 3rd edition 56. Microeconomic Analysis Third Edition by Hal R. Varian 57. Microeconomic Theory Solutions Manual for Mas-Colell 58. Microeconomics 6e Robert Pindyck Daniel Rubinfeld instructor manual 59. Microeconomics 6e Robert Pindyck Daniel Rubinfeld test bank 60. Microeconomics 7e Robert Pindyck Daniel Rubinfeld 61. Microeconomics Theory and Applications with Calculus by perloff insrructor manual 62. Microeconomics Theory and Applications with Calculus by perloff test bank 63. Microelectronic Circuit Design 2nd and 3rd edition by R. Jaeger selected solutions answers not solution 64. Modern Advanced Accounting , 10th Edition, by Larsen, (publisher McGraw Hill) 65. Modern Advanced Accounting 10th edition Test Bank LARSEN 66. Modern Auditing Assurance Services 8e Boynton sm and tb 67. Modern Business Statistics David R. Anderson, Dennis J. Sweeney, Thomas A. Williams 3rd edition solution manual 68. Modern Business Statistics David R. Anderson, Dennis J. Sweeney, Thomas A. Williams 3rd edition test bank 69. modern control engineering by katsuhiko ogata 3rd edition ISBN: 0132273071 70. modern control engineering by katsuhiko ogata 4th edition 71. Modern Control System 11th edition by richard c dorf, robert H bishop 72. Modern Control System 9th by richard c dorf, robert H bishop 73. Modern Database management 9e by Jeffrey A. Hoffer im 74. Modern Database management 9e by Jeffrey A. Hoffer TB 75. Modern Database Management, Ninth Edition Jeffrey A. Hoffer, University of Dayton Mary Prescott Heikki Topi 76. Modern Digital and Analog Communications Systems - B P Lathi Solutions Manual 3rd edition 77. Operations Management 8e by Jay Heizer Barry Render sm 78. Operations Management 8e by Jay Heizer Barry Render tb 79. Operations Management 9e by Jay Heizer Barry Render tb 80. Operations Management 9th by Jay Heizer Barry Render sm 81. Operations Management for MBAs, 3rd Edition Meredith, Shafer tb +im 82. Operations Management Reid, Sanders An Integrated Approach 2nd edition 83. Operations Management Reid, Sanders An Integrated Approach 2nd edition test bank 84. Operations Management, 10e William J. Stevenson instructor manual with solutions to supplementary problems 85. Operations Management, 10e William J. Stevenson test bank 86. Operations Management, 9e William J. Stevenson instructor manual with solutions to supplementary problems 87. Operations Management, William J Stevenson, 9e [TB] 88. Operations management processes and value chains 8e by Lee J. Krajewski solution manual 89. Operations management processes and value chains 8e by Lee J. Krajewski test bank 90. Operations Research An Introduction, 8E Hamdy A. Taha 91. Optimal Control Theory An Introduction By Donald E. Kirk 92. Options, Futures and Other Derivatives, 4th Edition (Solutions Manual) by John Hull, John C. Hull 93. Options, Futures and Other Derivatives, Fifth Edition (Solutions Manual) by John Hull, John C. Hull 94. Options, Futures, and Other Derivatives 7E by JOHN C HULL TB 95. Organizational Behavior Stephen P Robbins 12th edition (test bank) 96. Organizational Behavior, by Stephen P. and Timothy A. 13th Edition Robbins Judge im and tb 97. Organizational Behavior: Managing People and Organizations, 9th Edition Ricky W. Griffin Gregory Moorhead instructor manual 98. Organizational Behavior: Managing People and Organizations, 9th Edition Ricky W. Griffin Gregory Moorhead test bank 99. Organizational behavior 12e by Robbins ( instructor manual ) 100. Organizational behavior 12e by Robbins ( Test bank ) 101. Organizational Behavior, Fourth Canadian Ed., 4E Robins Test generator 102. Organizational Theory, Design and Change, 5/E Gareth R. Jones 103. Organizational Theory, Design and Change, 5E Gareth R. Jones Instructor's Manual and test bank 104. Organizational Theory, Design and Change, 5E Gareth R. Jones im and tb 105. Papa Thomas T.V. - Solutions Manual to Accompany Millman Integrated Electronics 106. Personal Finance Turning Money into Wealth 5e Arthur J. Keown 107. Personal Finance Turning Money into Wealth and Student Workbook, 4E keown instructor manual and test bank 108. Practical Financial Management 5th Edition William R. Lasher instructor manual 109. Practical Financial Management 5th Edition William R. Lasher test bank 110. Practical Financial Management William R. Lasher 4th edition instructor manual 111. Practical Financial Management William R. Lasher 4th edition test bank 112. Precalculus 4e blitzer 113. Prentice Hall - Solutions Manual; Communication Systems 114. Prentice Hall's Federal Taxation 2008 Individual , 21th Edition By Thomas R. Pope, Kenneth instructor guide 115. Prentice Hall's Federal Taxation 2009 Comprehensive, 22nd Edition By Thomas R. Pope, Kenneth E. Anderson, John L. Kramer instructor guide 116. Prentice Hall's Federal Taxation 2009 Comprehensive, 22nd Edition By Thomas R. Pope, Kenneth E. Anderson, John L. Kramer solution manual 117. Prentice Hall's Federal Taxation 2009 Comprehensive, 22nd Edition By Thomas R. Pope, Kenneth E. Anderson, John L. Kramer test bank 118. Prentice Hall's Federal Taxation 2009 Individual , 22th Edition By Thomas R. Pope, Kenneth instructor guide 119. Prentice Hall's Federal Taxation 2009: Corporations, 22/E Kenneth E. Anderson Thomas R. Pope John L. Kramer instructor guide 120. Prentice Hall's Federal Taxation 2009: Corporations, 22/E Kenneth E. Anderson Thomas R. Pope John L. Kramer tb +sm 121. Prentice Hall's Federal Taxation 2009: Individuals, 22/E Kenneth E. Anderson Thomas R. Pope John L. Kramer tb +sm 122. Principles of Auditing 15e by Whittington TB 123. Principles Of Corporate Finance 8E By Brealey Myers Allen 124. Principles of corporate finance 9e by brealy mayers allen (SM+TB) 125. Principles of Cost Accounting 14th Edition Edward J. Vanderbeck instructor manual 126. Principles of Cost Accounting 14th Edition Edward J. Vanderbeck solution manual 127. Principles of Cost Accounting 14th Edition Edward J. Vanderbeck test bank 128. Principles of Electric Circuits Conventional Current Version 8e by floyd 129. Principles of Electric Circuits Conventional Current Version by Floyd 8th edition 130. Principles of electric circuits- electron flow version Floyd 8th edition 131. Principles of Electronic Materials and Devices, Solutions Manual ONLY Safa O. Kasap 2nd edition 132. Principles of managerial finance 10e by gitman Lawrence 133. Principles of managerial finance 11e by gitman Lawrence 134. Principles of managerial finance 11e by gitman Lawrence solution manual 135. Principles of Managerial Finance 11e by Gitman Lawrence test bank 136. Principles of managerial finance 12e by gitman Lawrence test bank 137. Principles of Managerial Finance Brief plus 5e sm 138. Principles of Managerial Finance Brief plus 5e tb 139. Principles of Managerial Finance Brief plus My Finance Lab Student Access Kit, 5E Lawrence J. Gitman 140. principles of marketing 11e by Kotler ( instructor manual ) 141. principles of marketing 11e by Kotler ( test bank ) 142. principles of marketing 12e by Kotler TB 143. Principles of marketing 5e Canadian edition Kotler instructor manual 144. Principles of Microeconomics case and fair 8th edition testgen 145. Principles of Microeconomics, 9/e Case, Fair & Oster instructor manual 146. Principles of Microeconomics, 9/e Case, Fair & Oster test bank 147. Principles of Microeconomics, 9e Case, Fair & Oster instructor manual ad test bank 148. South-Western Federal Taxation 2009 (Individual), Edition 32, Hoffman, Smith, Wills (Test Bank) 149. South-Western Federal Taxation 2009 Corporations - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660219) 150. South-Western Federal Taxation 2009 Corporations - William Hoffman (test bank) (32nd ed) (ISBN 0324660219) 151. South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660529) 152. South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660529 153. South-Western Federal Taxation 2009: Individual Income Taxes 32nd Edition William Hoffman, James E. Smith, Eugene Willis Instructor's Guide 154. South-Western Federal Taxation 2009: Individual Income Taxes 32nd Edition William Hoffman, James E. Smith, Eugene Willis individual practice solutions 155. South-Western Federal Taxation 2010: Comprehensive 33rd Edition 2010 Eugene Willis, William H. Hoffman, Jr., David M. Maloney, William A. Raabe solution manual 156. South-Western Federal Taxation 2010: Comprehensive 33rd Edition 2010 Eugene Willis, William H. Hoffman, Jr., David M. Maloney, William A. Raabe test bank 157. South-Western Federal Taxation 2010: Corporations, Partnerships, Estates and Trusts 33rd Edition William H. Hoffman, Jr., William A. Raabe, James E. Smith, David M. Maloney sm 158. South-Western Federal Taxation 2010: Corporations, Partnerships, Estates and Trusts 33rd Edition William H. Hoffman, Jr., William A. Raabe, James E. Smith, David M. Maloney tb 159. South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis solution maual 160. South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis instructor guide 161. South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis test bank 162. South-Western Federal Taxation Individual Income Taxes, 32nd by William Hoffman, Jr. James Smith Eugene WillisEdition sm 2009 163. South-Western Federal Taxation individual income taxes (2009) instructor manual 164. South-Western Federal Taxation: Taxation of Business Entities 12th James E. Smith, William A. Raabe, David M. Maloney instructor guide 165. South-Western Federal Taxation: Taxation of Business Entities 12th James E. Smith, William A. Raabe, David M. Maloney solution manual 166. South-Western Federal Taxation: Taxation of Business Entities 12th James E. Smith, William A. Raabe, David M. Maloney test bank 167. South-Western Federal Taxation: Taxation of Business Entities 13th James E. Smith, William A. Raabe, David M. Maloney instructor guide 168. South-Western Federal Taxation: Taxation of Business Entities 13th James E. Smith, William A. Raabe, David M. Maloney solution manual 169. South-Western Federal Taxation: Taxation of Business Entities 13th James E. Smith, William A. Raabe, David M. Maloney test bank 170. Strategic Brand Management 3e keller 171. Strategic management 11e by Fred R. David ( instructor manual and case solutions ) 172. Strategic management 11e by Fred R. David ( test bank ) 173. Strategic Management and Business Policy, 11e Thomas L. Wheelen David L. Hunger instructor manual with test items 174. Strategic Management and Competitive Advantage Concepts and Cases, 2E case teaching notes 175. Strategic Management and Competitive Advantage: Concepts and Cases, 2/E instructor manual with test items Jay Barney William S Hesterly 176. Strategic Marketing Problems: Cases and Commentsî, 11/E by Roger Kerin, Robert 177. Business Ethics Ethical Decision Making and Cases 7e by Ferrel IM 178. Corporate Finance A Focused Approach 3e Brigham SM 179. Corporate Finance A Focused Approach 3e Brigham TB 180. Financial Accounting Information for Decisions 6e Robert W. Ingram SM 181. Financial Accounting Information for Decisions 6e Robert W. Ingram TB 182. Managerial Accounting: A Focus on Ethical Decision Making, 5th Edition Jackson / Sawyer / Jenkins SM 183. Management Information Systems (10th Edition) by McLeod / Schell IM 184. Management Information Systems (10th Edition) by McLeod / Schell TB 185. Database Systems: The Complete Book, 2/E Hector Garcia-Molina SM 186. Process Control Instrumentation Technology, 8/E Curtis D. Johnson IM 187. Physics: Principles with Applications, 6/E Douglas C. Giancoli TB 188. Digital Electronics: A Practical Approach, 8/E William Kleitz IM + TG I have many solutions manual and Test bank, they are PDF format or Word format, Those resources save your time and effort and let you definitely understand what you are studying and get amazing marks as well, The Manuals contains the answers of the questions and exercises (Usually at the end of each chapter), The Test Questions contains an extra questions, Most of them multiple choice, true and false and fill in the blank questions with their answers. If the solutions manual or Test bank what you want is not in this list, also can ask me (They are part of what I have ). Then if you need solutions manual or test bank . only contact me by email. Studentshelp(at)hotmail(dot)com Studentshelp(at)hotmail(dot)com only contact me by email studentshelp@hotmail.com === Subject: Organizational Behavior Stephen P Robbins 12th edition (test bank) posting-account=o339CQoAAACB2AYu4sK6rVlf_DJCMbcK CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual and Test bank I have many solutions manual and Test bank, they are PDF format or Word format, Those resources save your time and effort and let you definitely understand what you are studying and get amazing marks as well, The Manuals contains the answers of the questions and exercises (Usually at the end of each chapter), The Test Questions contains an extra questions, Most of them multiple choice, true and false and fill in the blank questions with their answers. If the solutions manual or Test bank what you want is not in this list, also can ask me (They are part of what I have ). Then if you need solutions manual or test bank . only contact me by email. Studentshelp(at)hotmail(dot)com studentshelp@hotmail.com 1. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin solution manual and test bank 2. Accounting Concepts and Applications (9th Ed.) by W. Steve 3. Accounting 7e by horngren solution manual 4. Accounting 7e by horngren TB 5. accounting 7e by horngren TB (test generator File) 6. Accounting 8th edition by horngren test bank and solution manual 7. Accounting Concepts and Applications 10th Edition W. Steve Albrecht, James D. Stice, Earl K. Stice, Monte R. Swain instructor manual 8. Accounting Concepts and Applications 10th Edition W. Steve Albrecht, James D. Stice, Earl K. Stice, Monte R. Swain solution manual 9. Accounting For Managers Interpreting Accounting Information for Decision-making, 3rd Edition Collier 10. Accounting Information Systems - james hall 6ed sm 11. Accounting Information Systems - james hall 6ed tb 12. Accounting Information Systems 10E Romney solution manual 13. Accounting Information Systems 10E Romney test bank 14. Accounting Information Systems 11E Romney solution manual 15. Accounting Information Systems 11E Romney test bank 16. Accounting Information Systems 7E Edition Ulric J. Gelinas, Richard B. Dull instructor manual 17. Accounting Information Systems 7E Edition Ulric J. Gelinas, Richard B. Dull solution manual 18. Accounting Information Systems 7E Edition Ulric J. Gelinas, Richard B. Dull test bank 19. Accounting Information Systems, 9E George H. Bodnar William S. Hopwood solution manual 20. Accounting Information Systems, 9E George H. Bodnar William S. Hopwood test bank 21. Accounting Principles 8E by Kieso SM chapter 1 to 10 22. Accounting Principles 8E by Kieso SM chapter 11 to 26 23. Accounting Principles, Edition 8E, Weygandt, Kieso, Kimmel (Test Bank) volume 1 24. Accounting Principles, Edition 8E, Weygandt, Kieso, Kimmel (Test Bank) volume 2 25. Accounting Text and Cases 12e by Anthony IM 26. Accounting what number means 8e by Marshall 27. Adaptive Control 2E. by Karl J. Astrom solution manual 28. Adaptive Filter Theory, 4th edition S. Haykin 29. Advance corporate finance 1e by Ogden Instructor manual and test bank 30. Advanced accounting 10E by Flyd Beams (SM+IM+TB) 31. Advanced Accounting 10th edition by Fischer (SolutionsManual) 32. Advanced Accounting 10th edition by Fischer (test bank) 33. Advanced Accounting 9e by Beams solution manual 34. Advanced Accounting 9E Hoyle,Schaefer,Doupnik Solution Manual 35. Advanced Accounting 9E Hoyle,Schaefer,Doupnik Test Bank 36. Advanced Accounting 9th edition by Fischer (SolutionsManual) 37. Advanced Accounting 9th edition by Fischer (test bank) 38. ADVANCED CORPORATE FINANCE Policies and Strategies by Joseph P. Ogden,Frank C. Jen,Philip F. O'Connor ( solution manual) 39. ADVANCED CORPORATE FINANCE Policies and Strategies by Joseph P. Ogden,Frank C. Jen,Philip F. O'Connor (test bank) 40. Advanced Digital Design with the Verilog HDL Michael D. Ciletti selected solutions 41. Advanced Dynamics by Donald T. Greenwood 42. Advanced Engineering Mathematics 3rd Edition by Dennis G Zill and Michael R Cullen 43. Advanced Engineering Mathematics by Erwin Kreyszig 8ed solutions manual 44. Advanced Engineering Mathematics Dennis G Zill 2nd Solution 45. Advanced Engineering Mathematics, 6th Edition Peter V. O'Neil - University of Alabama, Birmingham 46. Advanced Engineering Mathematics, 9th Edition By Erwin Kreyszig 47. Advanced Financial Accounting, 6th edition, by Baker, Lembke, and King solution manual 48. Advanced Macroeconomics 1996 romer 49. Advanced Macroeconomics, Solutions Manual 1996 Romer 50. Advanced Modern Engineering Mathematics, 3rd Edt by Glyn James solution manual 51. Anton, Bivens, Davis Calculus Early Transcendentals Combined, 8th Edition instructor solution manual 52. Anton, Bivens, Davis Calculus Multivariable, 8th Edition 53. Applied Fluid Mechanics 6th Ed. by Robert L. Mott 54. Applied Linear Algebra by Chehrzad Shakiban,Olver 55. Applied Mechanics for Engineering Technology 8e Keith M Walker 56. Applied Multivariate Statistical Analysis 6e Johnson 57. Applied Numerical Analysis 7Ed - Curtis F. Gerald, Patrick O. Wheatley - Solutions manual 58. Applied Partial Differential Equations David Logan 59. Applied Quantum Mechanics by A. F. J. Levi 60. Applied Statistics and Probability for Engineers 3rd.Ed edition student manual 61. Applied Statistics and Probability for Engineers by Douglas C. Montgomery 3rd edition complete 62. Applied Statistics and Probability for Engineers, 4th Edition Montgomery, Runger 63. Applied Strength of Materials (4th Edition) SOLUTION MANUAL by Robert L. Mott 64. Artificial Intelligence A Modern Approach 2e Stuart Russell Peter Norvig 65. Audit and Assurance service An Integrated Approach 11e TB 66. auditing and assuance services by messier test bank 6th edition 67. Auditing and Assurance Services An Intergrated Approach 13e by Alvin Arens Randal J. Elder, ark Beasley test bank 68. Auditing and Assurance Services An Intergrated Approach 13e by Alvin Arens Randal J. Elder, ark Beasley solution manual 69. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual 70. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley test bank 71. Auditing Cases, 3E Mark S. Beasley solution manual 72. Auditing Cases: An Interactive Learning Approach, 4/E Mark S Beasley Frank A. Auditing: A Business Risk Approach, 6th EditionLarry E. Rittenberg Bradley J. Schwieger Karla Johnstone solution manual 73. Auditing: A Business Risk Approach, 6th EditionLarry E. Rittenberg Bradley J. Schwieger Karla Johnstone test bank 74. Bank Management & Financial Services, 7/e By Peter S. Rose, Sylvia C. Hudgins (IM+SM) 75. Bank management 7e by peter s. rose TB 76. Bank management 7e by Rose ( instructor manual ) 77. Business Law by Cheeseman 6E (IM) 78. Business Law by Cheeseman 6E (TB) 79. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz instructor manual 80. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank 81. Business Statistics (A Decision Making Approach), Groebner, Shannon, Fry, Smith, 7 sm and tb 82. Business Statistics 4e by Leonard J. Kazmier book + sm 83. Business Statistics Decision Making and Student CD Package test items and solution manual, 7E test bank and sm 84. Butterworth Heinemann - Coulson And Richardson - Chemical Engineering Vol I (Solutions Manual V Edition) 85. C ++ how to program deitel 6th edition solution manual and test bank 86. C How to Program, 5/E (Harvey & Paul) Deitel & Deitel 87. C++ How to Program 3rd edition by deitel 88. College Accounting (Chapters 1-25), 10E by Jeffrey Slater sm and tb 89. College Mathematics for Business, Economics, Life Sciences & Social Sciences (11th Edition) (Hardcover) by Raymond A. Barnett (Author), Michael R. Ziegler (Author), Karl E. Byleen (Author) 90. Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson 91. Computer Architecture: Pipelined and Parallel Processor Design (Solutions Manual) by Michael J. Flynn selected solutions 92. Computer Networking: A Top-Down Approach, 5/E solution manual 93. Consumer Behavior, 8/E Michael R. Solomon test bank 94. Control Systems Engineering by Nise 4ed 95. Corporate Computer and Network Security Raymond Panko 96. Corporate Finance By Stephen A. Ross 8th edition SM 97. Corporate finance 1e by berk sm 98. Corporate finance 1e by berk tb 99. Corporate Finance 2nd Edition Scott B. Smart, William L. Megginson, Lawrence J. Gitman solution manual 100. Corporate Finance, 8e Stephen A. Ross Randolph W. Westerfield Jeffrey Jaffe instructor manual and solution manual 101. Corporate Financial Management 3e Douglas R. Emery instructor manual 102. Corporate Financial Management 3e Douglas R. Emery test bank 103. Cost Accounting 12e by Horngren Test Bank 104. Cost accounting 12e by Charles T. Horngren Srikant Datar George Foster Madhav Rajan Chris Ittner solution manual 105. Cost accounting 13e by Charles T. Horngren Srikant Datar George Foster Madhav Rajan Chris Ittner solution manual 106. Cost accounting 13e by Charles T. Horngren Srikant Datar George Foster Madhav Rajan Chris Ittner test bank 107. Cost Accounting; Foundations and Evolutions, Edition 7e, Kinney, Raiborn 108. Cost Management: A Strategic Emphasis, 4e Blocher 109. Cost Management: Measuring Monitoring and Motivating Performance by Eldenburg Wolcott SM TB 110. Cost management: Accounting and control 5e and 6e By Hansen MOwen SM+TB 111. Entrepreneurial Finance, 3rd Edition Chris Leach Ronald W. Melicher test bank 112. Entrepreneurial Finance, 3rd Edition Chris Leach Ronald W. Melicher instructor manual 113. Entrepreneurship: Starting and Operating a Small Business (with Business Plan Pro), 2/E Steve Mariotti, Caroline Glackin test gen and instructor manual 114. Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus test bank 115. Essentials of Investments Zvi Bodie, Alex Kane, Alan J. Marcus 116. Essentials of Managerial Finance 14e Brigham TB 117. Essentials of Managerial Finance 13th Edition Scott Besley, Eugene F. Brigham instructor manual 118. Essentials of Managerial Finance 13th Edition Scott Besley, Eugene F. Brigham test bank 119. Essentials of Managerial Finance, 14th EditionScott Besley Eugene F. Brigham instructor manual 120. Essentials of Managerial Finance, 14th EditionScott Besley Eugene F. Brigham spreadsheet problem solutions 121. Essentials of Managerial Finance, 14th EditionScott Besley Eugene F. Brigham test bank 122. Essentials of Modern Business Statistics 4th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams test bank 123. Essentials of Modern Business Statistics 4th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams test bank 124. Essentials of Organizational Behavior 9e Stephen P. Robbins Tim Judge 125. Essentials of Statistics for Business and Economics 5th edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams solution manual with case solutions 126. Essentials of Statistics for Business and Economics 5th edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams test bank 127. Essentials of Statistics, by Triola, 3rd edition sm 128. Essentials of Statistics, by Triola, 3rd edition tb 129. Essentials of Strategic Management 4E DAVID HUNGER THOMAS L. WHEELEN im with tb 130. Federal Taxation 2008 Corporations Partnerships Estates and Trusts 21E Anderson Pope Kramer test bank 131. Finance Management Test Bank brigham 11 test bank 132. Financial & managerial Accounting 13E By william Haka bettner 133. Financial & Managerial Accounting 9e and 10e Carl S. Warren, James M. Reeve solution manual 134. Financial accounting: an introduction to concepts, methods, and uses by clyde Stickney and Roman Weil solutions manual 11e 12e 13e 135. Financial Accounting 4e by John Wild 136. Financial Accounting 6e by kieso solution manual 137. Financial Accounting 6e by kieso test bank 138. Financial Accounting 6e Harrison Horngren 139. Financial Accounting 6th edition by Harrison Solution Manual 140. Financial accounting 6th edition harrison test bank 141. Financial accounting 7th edition harrison solution manual 142. Financial accounting 7th edition harrison test bank 143. Financial Accounting: Information for Decisions 6th Edition Robert W. Ingram, Thomas L. Albright extra resources 144. Financial Accounting: Information for Decisions 6th Edition Robert W. Ingram, Thomas L. Albright solution manual 145. Financial Accounting: Information for Decisions 6th Edition Robert W. Ingram, Thomas L. Albright test bank 146. Financial Accounting; Tools for Business Decision Making, 4th Edition, Kimmel.Weygandt.Kieso instructor manual 147. Financial Accounting; Tools for Business Decision Making, 4th Edition, Kimmel.Weygandt.Kieso solution manual 148. Financial Accounting; Tools for Business Decision Making, 4th Edition, Kimmel.Weygandt.Kieso test bank 149. Financial Analysis with Microsoft¬ Excel 4th Edition Timothy R. Mayes, Todd M. Shank instructor manual 150. Financial Analysis with Microsoft¬ Excel 4th Edition Timothy R. Mayes, Todd M. Shank spreadsheet problems 151. Financial Analysis with Microsoft¬ Excel¬ 2007 Timothy R. Mayes, Todd M. Shank Instructor Spreadsheet Files 152. Financial management 2e by jae K shim 153. Financial management Principles and application 10e by By Arthur J. Keown, John D. Martin, John W. Petty, David F. Scott solution manual 154. Financial Management Theory & Practice,Eugene Brigham,12th edition [ Test Bank ] 155. Financial management theory and practice 10e by Brigham solution manual 156. Financial Management Theory And Practice 11e by Brigham solution manual 157. Financial management theory and practice 12e by Brigham sm 158. Financial management theory and practice 12e by Brigham spreadsheet problems 159. Financial management theory and practice 12e by Brigham TB 160. Financial Management Theory and Practice, 11e By Eugene F. Brigham test bank 161. Financial Markets and Institution (7thEd) Madura TestBank 162. Financial Reporting Analysis 10th edition TB by gibson 163. Financial Reporting and Analysis Using Financial Accounting Information 10th Edition Charles H. Gibson instructor manual 164. Financial Reporting and Analysis Using Financial Accounting Information 10th Edition Charles H. Gibson solution manual 165. Financial Reporting and Analysis Using Financial Accounting Information 10th Edition Charles H. Gibson test bank 166. Financial Reporting and Analysis: Using Financial Accounting Information 11th Edition Charles H. Gibson solution manual 167. Financial Reporting and Analysis: Using Financial Accounting Information 11th Edition Charles H. Gibson test bank 168. Financial Reporting and Corporate Governance exercise solutions Lee 169. Framework for Marketing Management, A - Philip Kotler (4th ed) (ISBN 0136026605) 170. Framework for Marketing Management, A - Philip Kotler (4th ed) (ISBN test bank 171. Fundamental accounting principles 17th edition larson solution manual 172. Fundamental Accounting Principles, 18/e John J. Wild Barbara Chiappetta Kermit D. Larson solution manual and test bank 173. Fundamentals accounting principles by larson 18e SM 174. Fundamentals of Advanced Accounting 1e Fisher taylor chang solution manual 175. Fundamentals of Advanced Accounting 1e Fisher taylor chang test bank 176. Fundamentals of advanced accounting 3e by hoyle 177. Fundamentals of Advanced Accounting, 2e Joe B. Hoyle Thomas F. Schaefer Timothy S. Doupnik (Solution Manual) 178. Fundamentals of Contemporary Financial Management, 2nd Edition R. Charles Moyer James R. McGuigan Ramesh P. Rao instructor manual 179. Fundamentals of Contemporary Financial Management, 2nd Edition R. Charles Moyer James R. McGuigan Ramesh P. Rao test bank 180. Fundamentals of corporate finance 8e by Ross Ross, Westerfield,jordan 181. Fundamentals of Corporate Finance, 4th Edition (Brealey, Myers, Marcus) by Bruce Swenson 182. Fundamentals of Financial Management 12th brigham edition instructor manual 183. Fundamentals of Financial Management 12th edition brigham test bank 184. Fundamentals of Financial Management 10th Edition by Eugene Brigham Solution manual 185. Fundamentals of Financial Management 10th Edition by Eugene Brigham test bank 186. Fundamentals of Financial Management 11e by Eugene F. Brigham, Joel F. Houston spreadsheet problems 187. Fundamentals of Financial Management 11e by Eugene F. Brigham, Joel F. Houston test bank and cyberproblems 188. Fundamentals of Financial Management 11e by Brigham Instructor manual 189. Fundamentals of financial management 12e by james c. van horne 190. Fundamentals of Financial Management Eugene F. Brigham, Joel F. Houston 12th edition instructor manual 191. Fundamentals of Financial Management Eugene F. Brigham, Joel F. Houston 12th edition spreadsheets problems and web appendix solutions 192. Fundamentals of Financial Management Eugene F. Brigham, Joel F. Houston 12th edition test bank 193. Fundamentals of Financial Management, 12th Edition (Instructors guide ONLY) by James C. Van Horne, John M Wachowic 194. Fundamentals of Financial Management, Concise Edition 5th Eugene F. Brigham, Joel F. Houston test bank 195. Fundamentals of Financial Management, Concise Edition 5th Eugene F. Brigham, Joel F. Houston spreadsheets problems 196. Fundamentals of Financial Management, Concise Edition 5th Eugene F. Brigham, Joel F. Houston instructor manual 197. Fundamentals of Financial Management, Concise Edition Eugene F. Brigham, Joel F. Houston 6th edition instructor manual 198. Fundamentals of Financial Management, Concise Edition Eugene F. Brigham, Joel F. Houston 6th edition spreadsheet problem solutions 199. Fundamentals of Financial Management, Concise Edition Eugene F. Brigham, Joel F. Houston 6th edition test bank 200. Fundamentals Of Fluid Mechanics 3Rd And 4Th Edition Solutions Manual 201. Fundamentals of Fluid Mechanics, 6th Edition Munson, Young, Okiishi, Huebsch 202. Fundamentals of Heat and Mass Transfer, 5th Edition by Frank P. Incropera 203. Fundamentals of Heat and Mass Transfer, 6th Edition Incropera, DeWitt, Bergman, Lavine 204. Fundamentals of Investing, 10th Edition by Gitman and Joehnk 205. Fundamentals of Investments 3e Gordon J. Alexander William F. Sharpe 206. Fundamentals of Logic Design 5th edition by charles roth 207. Fundamentals of Machine Component Design, 3rd ed - Student Solutions Manual by Juvinall, Marshek 208. Fundamentals of manufacturing 2nd edition by philip d. rufe solutions manual 209. Fundamentals of Momentum, Heat and Mass Transfer, 5th Edition Welty, Wicks, Rorrer, Wilson 210. Fundamentals of Multinational Finance, 2nd edition by Michael H. Moffett test bank and solution manual 211. Fundamentals of Multinational Finance, 3E by Michael H. Moffett (Instructor's Manual) 212. Fundamentals of Multinational Finance, 3E by Michael H. Moffett test bank 213. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith sm 214. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith tb 215. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith instructor manual 216. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith tb 217. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith sm 218. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow sm 219. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow tb 220. Human resources management 10e Gary dessler (IM+TB) 221. Intermediate Accounting 10e by Nikolai sm 222. Intermediate Accounting 11e by Kieso 223. Intermediate Accounting 12e by Kieso 224. Intermediate accounting 12th Updated by Kieso Solution manual 225. Intermediate accounting 12th Updated by Kieso test bank 226. Intermediate Accounting, 13th Edition Instructor's Manual Kieso, Weygandt, Warfield 227. (Sm+TB+IM) 228. Intermediate Accounting 2e by Baruch Englard 229. Intermediate Accounting 3e by J. David Spiceland 230. Intermediate Accounting 4e revised by J. David Spiceland solution manual 231. Intermediate accounting by Spiceland 4e Solution manual 232. Intermediate Accounting James D. Stice, Earl K. Stice, Fred Skousen 16th edition solution manual 233. Intermediate Accounting, 13th Edition Kieso, Weygandt, Warfield test bank and solution manual 234. Intermediate Accounting, Update, 12th Edition international student solution manual 235. Intermediate Algebra Functions & Authentic Applications 3e lehmann 236. Intermediate Algebra, 8th Edition By Margaret L. Lial, John Hornsby, Terry McGinnis 237. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves instructor manual 238. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves test bank 239. Intermediate Microeconomics, 10th Edition Walter Nicholson ,Christopher Snyder im with tb 240. International Accounting 1e by Doupnik solution manual 241. International Accounting 6e Frederick D. Choi Gary K. Meek 242. International Business The Challenges of Globalization, 4E John J. Wild,Kenneth L. Wild tb and im 243. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan instructor manual 244. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan test bank 245. International Economics Theory and Policy 8e Krugman & Obstfeld 246. International Economics, 7e Husted Melvin test bank and solution manual 247. International Financial Management 9th Edition jeff madura instructor manual 248. International Financial Management 9th Edition jeff madura test bank 249. International Financial Management Geert Bekaert Robert J. Hodrick test bank and sol manual I have many solutions manual and Test bank, they are PDF format or Word format, Those resources save your time and effort and let you definitely understand what you are studying and get amazing marks as well, The Manuals contains the answers of the questions and exercises (Usually at the end of each chapter), The Test Questions contains an extra questions, Most of them multiple choice, true and false and fill in the blank questions with their answers. If the solutions manual or Test bank what you want is not in this list, also can ask me (They are part of what I have ). Then if you need solutions manual or test bank . only contact me by email. Studentshelp(at)hotmail(dot)com Studentshelp(at)hotmail(dot)com only contact me by email studentshelp@hotmail.com I have many solutions manual and Test bank, they are PDF format or Word format, Those resources save your time and effort and let you definitely understand what you are studying and get amazing marks as well, The Manuals contains the answers of the questions and exercises (Usually at the end of each chapter), The Test Questions contains an extra questions, Most of them multiple choice, true and false and fill in the blank questions with their answers. If the solutions manual or Test bank what you want is not in this list, also can ask me (They are part of what I have ). Then if you need solutions manual or test bank . only contact me by email. Studentshelp(at)hotmail(dot)com Studentshelp(at)hotmail(dot)com only contact me by email studentshelp@hotmail.com 1. International Management Managing Across Borders and Cultures 6e test bank and instructor manual 2. Interpreting and Analyzing Financial Statement 4e Karen P. Schoenebeck 3. Introduction to Corporate Finance William L. Megginson, Scott B. Smart 1st edition instructor manual 4. Introduction to Corporate Finance William L. Megginson, Scott B. Smart 1st edition test bank 5. Introduction to Corporate Finance 2nd edition William L. Megginson, Scott B. Smart instructor manual 6. Introduction to Corporate Finance, 2nd Edition William L. Megginson Scott B. Smart test bank 7. Introduction to Corporate Finance, 2nd Edition William L. Megginson Scott B. Smart solution manual 8. Introduction to Government and Non-for-Profit Accounting 6th edition by martin ives sm 9. Introduction to Government and Non-for-Profit Accounting 6th edition test bank by martin ives 10. Introduction to Operations and Supply Chain Management 2e Cecil Bozarth 11. Introduction to Operations and Supply Chain Management 2e Cecil Bozarth Robert B. Handfield test bank and sol manual 12. Investment analysis and portfolio management 8e by Reily Brown 13. Investment Analysis and Portfolio Management 9th Edition Frank K. Reilly, Keith C. Brown solution manual 14. Investment Analysis and Portfolio Management 9th Edition Frank K. Reilly, Keith C. Brown test bank 15. Investment Analysis and Portfolio Management- Solutions Manual, 7th Edition by Frank K. et al. Reily 16. Intermediate Accounting 12 E Kieso (TB) 17. Intermediate accounting 5e spiceland test bank and solution manual 18. Intermediate Accounting 12e by Keiso sm 19. Intermediate accounting 4th edition spiceland test bank 20. Introduction to management accounting 14e Charles T. Horngren, Gary L. Sundem, William O. Stratton, Jeff Schatzberg, Dave Burgstahler solution manual 21. Introduction to Operations Research - 7th by Frederick Hillier, Gerald Lieberman 22. Macroeconomics (8thEd) - Froyen - Solutions Manual 23. Macroeconomics 6e Andrew B. Abel, Ben S. Bernanke, Dean Croushore 24. Macroeconomics 3e williamson instructor manual and test bank 25. Macroeconomics, 4E Olivier Blanchard instructor manual 26. Macroeconomics, 4E Olivier Blanchard test bank 27. Macroeconomics, 5E Olivier Blanchard instructor manual and test bank 28. Management 5th Edition Chuck Williams instructor manual 29. Management 9E Stephen P. Robbins Mary Coulter test bank and instructor manual 30. Management accounting 5e Anthony A. Atkinson Robert S. Kaplan Ella Mae Matsumura S. Mark Young instructor manual test bank and solution manual 31. Management accounting 5E Atkinson solution manual 32. Management accounting 5E Atkinson test bank 33. Management Control Systems Performance Measurement, Evaluation and Incentives 2e Merchant & Van der Stede 34. Management Information Systems; Managing the Digital Firm, Edition 10, Laudon test bank and solution manual 35. Management Robbins Coulter 9th edition (test bank ) 36. Management10E Stephen P. Robbins Mary Coulter 37. Management10E Stephen P. Robbins Mary Coulter test bank 38. Managerial Accounting 12e By Garrison Noreen ( Solution Manual ) 39. Managerial Accounting 12e By Garrison Noreen (Test Bank) 40. Managerial Accounting Bamber, L. S., K. W. Braun, and W. T. Harrison, Jr. 2008 41. Managerial Accounting international edition Garrison11 ( Solution Manual) 42. Managerial Accounting, 11th Edition by Ray H Garrison, Eric Noreen, Peter C. Brewer 43. Managerial Accounting: An Introduction to Concepts, Methods and Uses 10th Edition Michael W. Maher, Clyde P. Stickney, Roman L. Weil instructor manual 44. Managerial Accounting: An Introduction to Concepts, Methods and Uses 10th Edition Michael W. Maher, Clyde P. Stickney, Roman L. Weil solution manual 45. Managerial Accounting: An Introduction to Concepts, Methods and Uses 10th Edition Michael W. Maher, Clyde P. Stickney, Roman L. Weil test bank 46. Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris instructor manual 47. Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris test bank 48. Managerial Finance, Gitman,Lawrence 12e [SM] 49. Managing Human Resources by Luis R. Gomez-Mejia; David B. Balkin; Robert L. Cardy. 5th Edition im and tb 50. Manufacturing Engineering and Technology 5E by Kalpakjian and Schimid 51. Marketing Kotler Armstrong 11th edition (Test bank ) 52. Marketing Management (13th Edition) by Philip Kotler, Kevin Keller im 53. Marketing Management (13th Edition) by Philip Kotler, Kevin Keller tb 54. Mastery of the Financial Accounting Research System (FARS) Through Cases, 2nd Edition Wallace 55. Microeconomic Analysis Solution Manual - Varian 3rd edition 56. Microeconomic Analysis Third Edition by Hal R. Varian 57. Microeconomic Theory Solutions Manual for Mas-Colell 58. Microeconomics 6e Robert Pindyck Daniel Rubinfeld instructor manual 59. Microeconomics 6e Robert Pindyck Daniel Rubinfeld test bank 60. Microeconomics 7e Robert Pindyck Daniel Rubinfeld 61. Microeconomics Theory and Applications with Calculus by perloff insrructor manual 62. Microeconomics Theory and Applications with Calculus by perloff test bank 63. Microelectronic Circuit Design 2nd and 3rd edition by R. Jaeger selected solutions answers not solution 64. Modern Advanced Accounting , 10th Edition, by Larsen, (publisher McGraw Hill) 65. Modern Advanced Accounting 10th edition Test Bank LARSEN 66. Modern Auditing Assurance Services 8e Boynton sm and tb 67. Modern Business Statistics David R. Anderson, Dennis J. Sweeney, Thomas A. Williams 3rd edition solution manual 68. Modern Business Statistics David R. Anderson, Dennis J. Sweeney, Thomas A. Williams 3rd edition test bank 69. modern control engineering by katsuhiko ogata 3rd edition ISBN: 0132273071 70. modern control engineering by katsuhiko ogata 4th edition 71. Modern Control System 11th edition by richard c dorf, robert H bishop 72. Modern Control System 9th by richard c dorf, robert H bishop 73. Modern Database management 9e by Jeffrey A. Hoffer im 74. Modern Database management 9e by Jeffrey A. Hoffer TB 75. Modern Database Management, Ninth Edition Jeffrey A. Hoffer, University of Dayton Mary Prescott Heikki Topi 76. Modern Digital and Analog Communications Systems - B P Lathi Solutions Manual 3rd edition 77. Operations Management 8e by Jay Heizer Barry Render sm 78. Operations Management 8e by Jay Heizer Barry Render tb 79. Operations Management 9e by Jay Heizer Barry Render tb 80. Operations Management 9th by Jay Heizer Barry Render sm 81. Operations Management for MBAs, 3rd Edition Meredith, Shafer tb +im 82. Operations Management Reid, Sanders An Integrated Approach 2nd edition 83. Operations Management Reid, Sanders An Integrated Approach 2nd edition test bank 84. Operations Management, 10e William J. Stevenson instructor manual with solutions to supplementary problems 85. Operations Management, 10e William J. Stevenson test bank 86. Operations Management, 9e William J. Stevenson instructor manual with solutions to supplementary problems 87. Operations Management, William J Stevenson, 9e [TB] 88. Operations management processes and value chains 8e by Lee J. Krajewski solution manual 89. Operations management processes and value chains 8e by Lee J. Krajewski test bank 90. Operations Research An Introduction, 8E Hamdy A. Taha 91. Optimal Control Theory An Introduction By Donald E. Kirk 92. Options, Futures and Other Derivatives, 4th Edition (Solutions Manual) by John Hull, John C. Hull 93. Options, Futures and Other Derivatives, Fifth Edition (Solutions Manual) by John Hull, John C. Hull 94. Options, Futures, and Other Derivatives 7E by JOHN C HULL TB 95. Organizational Behavior Stephen P Robbins 12th edition (test bank) 96. Organizational Behavior, by Stephen P. and Timothy A. 13th Edition Robbins Judge im and tb 97. Organizational Behavior: Managing People and Organizations, 9th Edition Ricky W. Griffin Gregory Moorhead instructor manual 98. Organizational Behavior: Managing People and Organizations, 9th Edition Ricky W. Griffin Gregory Moorhead test bank 99. Organizational behavior 12e by Robbins ( instructor manual ) 100. Organizational behavior 12e by Robbins ( Test bank ) 101. Organizational Behavior, Fourth Canadian Ed., 4E Robins Test generator 102. Organizational Theory, Design and Change, 5/E Gareth R. Jones 103. Organizational Theory, Design and Change, 5E Gareth R. Jones Instructor's Manual and test bank 104. Organizational Theory, Design and Change, 5E Gareth R. Jones im and tb 105. Papa Thomas T.V. - Solutions Manual to Accompany Millman Integrated Electronics 106. Personal Finance Turning Money into Wealth 5e Arthur J. Keown 107. Personal Finance Turning Money into Wealth and Student Workbook, 4E keown instructor manual and test bank 108. Practical Financial Management 5th Edition William R. Lasher instructor manual 109. Practical Financial Management 5th Edition William R. Lasher test bank 110. Practical Financial Management William R. Lasher 4th edition instructor manual 111. Practical Financial Management William R. Lasher 4th edition test bank 112. Precalculus 4e blitzer 113. Prentice Hall - Solutions Manual; Communication Systems 114. Prentice Hall's Federal Taxation 2008 Individual , 21th Edition By Thomas R. Pope, Kenneth instructor guide 115. Prentice Hall's Federal Taxation 2009 Comprehensive, 22nd Edition By Thomas R. Pope, Kenneth E. Anderson, John L. Kramer instructor guide 116. Prentice Hall's Federal Taxation 2009 Comprehensive, 22nd Edition By Thomas R. Pope, Kenneth E. Anderson, John L. Kramer solution manual 117. Prentice Hall's Federal Taxation 2009 Comprehensive, 22nd Edition By Thomas R. Pope, Kenneth E. Anderson, John L. Kramer test bank 118. Prentice Hall's Federal Taxation 2009 Individual , 22th Edition By Thomas R. Pope, Kenneth instructor guide 119. Prentice Hall's Federal Taxation 2009: Corporations, 22/E Kenneth E. Anderson Thomas R. Pope John L. Kramer instructor guide 120. Prentice Hall's Federal Taxation 2009: Corporations, 22/E Kenneth E. Anderson Thomas R. Pope John L. Kramer tb +sm 121. Prentice Hall's Federal Taxation 2009: Individuals, 22/E Kenneth E. Anderson Thomas R. Pope John L. Kramer tb +sm 122. Principles of Auditing 15e by Whittington TB 123. Principles Of Corporate Finance 8E By Brealey Myers Allen 124. Principles of corporate finance 9e by brealy mayers allen (SM+TB) 125. Principles of Cost Accounting 14th Edition Edward J. Vanderbeck instructor manual 126. Principles of Cost Accounting 14th Edition Edward J. Vanderbeck solution manual 127. Principles of Cost Accounting 14th Edition Edward J. Vanderbeck test bank 128. Principles of Electric Circuits Conventional Current Version 8e by floyd 129. Principles of Electric Circuits Conventional Current Version by Floyd 8th edition 130. Principles of electric circuits- electron flow version Floyd 8th edition 131. Principles of Electronic Materials and Devices, Solutions Manual ONLY Safa O. Kasap 2nd edition 132. Principles of managerial finance 10e by gitman Lawrence 133. Principles of managerial finance 11e by gitman Lawrence 134. Principles of managerial finance 11e by gitman Lawrence solution manual 135. Principles of Managerial Finance 11e by Gitman Lawrence test bank 136. Principles of managerial finance 12e by gitman Lawrence test bank 137. Principles of Managerial Finance Brief plus 5e sm 138. Principles of Managerial Finance Brief plus 5e tb 139. Principles of Managerial Finance Brief plus My Finance Lab Student Access Kit, 5E Lawrence J. Gitman 140. principles of marketing 11e by Kotler ( instructor manual ) 141. principles of marketing 11e by Kotler ( test bank ) 142. principles of marketing 12e by Kotler TB 143. Principles of marketing 5e Canadian edition Kotler instructor manual 144. Principles of Microeconomics case and fair 8th edition testgen 145. Principles of Microeconomics, 9/e Case, Fair & Oster instructor manual 146. Principles of Microeconomics, 9/e Case, Fair & Oster test bank 147. Principles of Microeconomics, 9e Case, Fair & Oster instructor manual ad test bank 148. South-Western Federal Taxation 2009 (Individual), Edition 32, Hoffman, Smith, Wills (Test Bank) 149. South-Western Federal Taxation 2009 Corporations - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660219) 150. South-Western Federal Taxation 2009 Corporations - William Hoffman (test bank) (32nd ed) (ISBN 0324660219) 151. South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660529) 152. South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660529 153. South-Western Federal Taxation 2009: Individual Income Taxes 32nd Edition William Hoffman, James E. Smith, Eugene Willis Instructor's Guide 154. South-Western Federal Taxation 2009: Individual Income Taxes 32nd Edition William Hoffman, James E. Smith, Eugene Willis individual practice solutions 155. South-Western Federal Taxation 2010: Comprehensive 33rd Edition 2010 Eugene Willis, William H. Hoffman, Jr., David M. Maloney, William A. Raabe solution manual 156. South-Western Federal Taxation 2010: Comprehensive 33rd Edition 2010 Eugene Willis, William H. Hoffman, Jr., David M. Maloney, William A. Raabe test bank 157. South-Western Federal Taxation 2010: Corporations, Partnerships, Estates and Trusts 33rd Edition William H. Hoffman, Jr., William A. Raabe, James E. Smith, David M. Maloney sm 158. South-Western Federal Taxation 2010: Corporations, Partnerships, Estates and Trusts 33rd Edition William H. Hoffman, Jr., William A. Raabe, James E. Smith, David M. Maloney tb 159. South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis solution maual 160. South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis instructor guide 161. South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis test bank 162. South-Western Federal Taxation Individual Income Taxes, 32nd by William Hoffman, Jr. James Smith Eugene WillisEdition sm 2009 163. South-Western Federal Taxation individual income taxes (2009) instructor manual 164. South-Western Federal Taxation: Taxation of Business Entities 12th James E. Smith, William A. Raabe, David M. Maloney instructor guide 165. South-Western Federal Taxation: Taxation of Business Entities 12th James E. Smith, William A. Raabe, David M. Maloney solution manual 166. South-Western Federal Taxation: Taxation of Business Entities 12th James E. Smith, William A. Raabe, David M. Maloney test bank 167. South-Western Federal Taxation: Taxation of Business Entities 13th James E. Smith, William A. Raabe, David M. Maloney instructor guide 168. South-Western Federal Taxation: Taxation of Business Entities 13th James E. Smith, William A. Raabe, David M. Maloney solution manual 169. South-Western Federal Taxation: Taxation of Business Entities 13th James E. Smith, William A. Raabe, David M. Maloney test bank 170. Strategic Brand Management 3e keller 171. Strategic management 11e by Fred R. David ( instructor manual and case solutions ) 172. Strategic management 11e by Fred R. David ( test bank ) 173. Strategic Management and Business Policy, 11e Thomas L. Wheelen David L. Hunger instructor manual with test items 174. Strategic Management and Competitive Advantage Concepts and Cases, 2E case teaching notes 175. Strategic Management and Competitive Advantage: Concepts and Cases, 2/E instructor manual with test items Jay Barney William S Hesterly 176. Strategic Marketing Problems: Cases and Commentsî, 11/E by Roger Kerin, Robert 177. Business Ethics Ethical Decision Making and Cases 7e by Ferrel IM 178. Corporate Finance A Focused Approach 3e Brigham SM 179. Corporate Finance A Focused Approach 3e Brigham TB 180. Financial Accounting Information for Decisions 6e Robert W. Ingram SM 181. Financial Accounting Information for Decisions 6e Robert W. Ingram TB 182. Managerial Accounting: A Focus on Ethical Decision Making, 5th Edition Jackson / Sawyer / Jenkins SM 183. Management Information Systems (10th Edition) by McLeod / Schell IM 184. Management Information Systems (10th Edition) by McLeod / Schell TB 185. Database Systems: The Complete Book, 2/E Hector Garcia-Molina SM 186. Process Control Instrumentation Technology, 8/E Curtis D. Johnson IM 187. Physics: Principles with Applications, 6/E Douglas C. Giancoli TB 188. Digital Electronics: A Practical Approach, 8/E William Kleitz IM + TG I have many solutions manual and Test bank, they are PDF format or Word format, Those resources save your time and effort and let you definitely understand what you are studying and get amazing marks as well, The Manuals contains the answers of the questions and exercises (Usually at the end of each chapter), The Test Questions contains an extra questions, Most of them multiple choice, true and false and fill in the blank questions with their answers. If the solutions manual or Test bank what you want is not in this list, also can ask me (They are part of what I have ). Then if you need solutions manual or test bank . only contact me by email. Studentshelp(at)hotmail(dot)com Studentshelp(at)hotmail(dot)com only contact me by email studentshelp@hotmail.com === Subject: Advanced Engineering Mathematics, 6th Edition Peter V. O'Neil - University of Alabama, Birmingham posting-account=o339CQoAAACB2AYu4sK6rVlf_DJCMbcK CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual and Test bank I have many solutions manual and Test bank, they are PDF format or Word format, Those resources save your time and effort and let you definitely understand what you are studying and get amazing marks as well, The Manuals contains the answers of the questions and exercises (Usually at the end of each chapter), The Test Questions contains an extra questions, Most of them multiple choice, true and false and fill in the blank questions with their answers. If the solutions manual or Test bank what you want is not in this list, also can ask me (They are part of what I have ). Then if you need solutions manual or test bank . only contact me by email. Studentshelp(at)hotmail(dot)com studentshelp@hotmail.com 1. An Introduction to Management Science: A Quantitative Approach to Decision Making 12E David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, R. Kipp Martin solution manual and test bank 2. Accounting Concepts and Applications (9th Ed.) by W. Steve 3. Accounting 7e by horngren solution manual 4. Accounting 7e by horngren TB 5. accounting 7e by horngren TB (test generator File) 6. Accounting 8th edition by horngren test bank and solution manual 7. Accounting Concepts and Applications 10th Edition W. Steve Albrecht, James D. Stice, Earl K. Stice, Monte R. Swain instructor manual 8. Accounting Concepts and Applications 10th Edition W. Steve Albrecht, James D. Stice, Earl K. Stice, Monte R. Swain solution manual 9. Accounting For Managers Interpreting Accounting Information for Decision-making, 3rd Edition Collier 10. Accounting Information Systems - james hall 6ed sm 11. Accounting Information Systems - james hall 6ed tb 12. Accounting Information Systems 10E Romney solution manual 13. Accounting Information Systems 10E Romney test bank 14. Accounting Information Systems 11E Romney solution manual 15. Accounting Information Systems 11E Romney test bank 16. Accounting Information Systems 7E Edition Ulric J. Gelinas, Richard B. Dull instructor manual 17. Accounting Information Systems 7E Edition Ulric J. Gelinas, Richard B. Dull solution manual 18. Accounting Information Systems 7E Edition Ulric J. Gelinas, Richard B. Dull test bank 19. Accounting Information Systems, 9E George H. Bodnar William S. Hopwood solution manual 20. Accounting Information Systems, 9E George H. Bodnar William S. Hopwood test bank 21. Accounting Principles 8E by Kieso SM chapter 1 to 10 22. Accounting Principles 8E by Kieso SM chapter 11 to 26 23. Accounting Principles, Edition 8E, Weygandt, Kieso, Kimmel (Test Bank) volume 1 24. Accounting Principles, Edition 8E, Weygandt, Kieso, Kimmel (Test Bank) volume 2 25. Accounting Text and Cases 12e by Anthony IM 26. Accounting what number means 8e by Marshall 27. Adaptive Control 2E. by Karl J. Astrom solution manual 28. Adaptive Filter Theory, 4th edition S. Haykin 29. Advance corporate finance 1e by Ogden Instructor manual and test bank 30. Advanced accounting 10E by Flyd Beams (SM+IM+TB) 31. Advanced Accounting 10th edition by Fischer (SolutionsManual) 32. Advanced Accounting 10th edition by Fischer (test bank) 33. Advanced Accounting 9e by Beams solution manual 34. Advanced Accounting 9E Hoyle,Schaefer,Doupnik Solution Manual 35. Advanced Accounting 9E Hoyle,Schaefer,Doupnik Test Bank 36. Advanced Accounting 9th edition by Fischer (SolutionsManual) 37. Advanced Accounting 9th edition by Fischer (test bank) 38. ADVANCED CORPORATE FINANCE Policies and Strategies by Joseph P. Ogden,Frank C. Jen,Philip F. O'Connor ( solution manual) 39. ADVANCED CORPORATE FINANCE Policies and Strategies by Joseph P. Ogden,Frank C. Jen,Philip F. O'Connor (test bank) 40. Advanced Digital Design with the Verilog HDL Michael D. Ciletti selected solutions 41. Advanced Dynamics by Donald T. Greenwood 42. Advanced Engineering Mathematics 3rd Edition by Dennis G Zill and Michael R Cullen 43. Advanced Engineering Mathematics by Erwin Kreyszig 8ed solutions manual 44. Advanced Engineering Mathematics Dennis G Zill 2nd Solution 45. Advanced Engineering Mathematics, 6th Edition Peter V. O'Neil - University of Alabama, Birmingham 46. Advanced Engineering Mathematics, 9th Edition By Erwin Kreyszig 47. Advanced Financial Accounting, 6th edition, by Baker, Lembke, and King solution manual 48. Advanced Macroeconomics 1996 romer 49. Advanced Macroeconomics, Solutions Manual 1996 Romer 50. Advanced Modern Engineering Mathematics, 3rd Edt by Glyn James solution manual 51. Anton, Bivens, Davis Calculus Early Transcendentals Combined, 8th Edition instructor solution manual 52. Anton, Bivens, Davis Calculus Multivariable, 8th Edition 53. Applied Fluid Mechanics 6th Ed. by Robert L. Mott 54. Applied Linear Algebra by Chehrzad Shakiban,Olver 55. Applied Mechanics for Engineering Technology 8e Keith M Walker 56. Applied Multivariate Statistical Analysis 6e Johnson 57. Applied Numerical Analysis 7Ed - Curtis F. Gerald, Patrick O. Wheatley - Solutions manual 58. Applied Partial Differential Equations David Logan 59. Applied Quantum Mechanics by A. F. J. Levi 60. Applied Statistics and Probability for Engineers 3rd.Ed edition student manual 61. Applied Statistics and Probability for Engineers by Douglas C. Montgomery 3rd edition complete 62. Applied Statistics and Probability for Engineers, 4th Edition Montgomery, Runger 63. Applied Strength of Materials (4th Edition) SOLUTION MANUAL by Robert L. Mott 64. Artificial Intelligence A Modern Approach 2e Stuart Russell Peter Norvig 65. Audit and Assurance service An Integrated Approach 11e TB 66. auditing and assuance services by messier test bank 6th edition 67. Auditing and Assurance Services An Intergrated Approach 13e by Alvin Arens Randal J. Elder, ark Beasley test bank 68. Auditing and Assurance Services An Intergrated Approach 13e by Alvin Arens Randal J. Elder, ark Beasley solution manual 69. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual 70. Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley test bank 71. Auditing Cases, 3E Mark S. Beasley solution manual 72. Auditing Cases: An Interactive Learning Approach, 4/E Mark S Beasley Frank A. Auditing: A Business Risk Approach, 6th EditionLarry E. Rittenberg Bradley J. Schwieger Karla Johnstone solution manual 73. Auditing: A Business Risk Approach, 6th EditionLarry E. Rittenberg Bradley J. Schwieger Karla Johnstone test bank 74. Bank Management & Financial Services, 7/e By Peter S. Rose, Sylvia C. Hudgins (IM+SM) 75. Bank management 7e by peter s. rose TB 76. Bank management 7e by Rose ( instructor manual ) 77. Business Law by Cheeseman 6E (IM) 78. Business Law by Cheeseman 6E (TB) 79. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz instructor manual 80. Business Law Today: Comprehensive 8th edition Roger LeRoy Miller, Gaylord A. Jentz test bank 81. Business Statistics (A Decision Making Approach), Groebner, Shannon, Fry, Smith, 7 sm and tb 82. Business Statistics 4e by Leonard J. Kazmier book + sm 83. Business Statistics Decision Making and Student CD Package test items and solution manual, 7E test bank and sm 84. Butterworth Heinemann - Coulson And Richardson - Chemical Engineering Vol I (Solutions Manual V Edition) 85. C ++ how to program deitel 6th edition solution manual and test bank 86. C How to Program, 5/E (Harvey & Paul) Deitel & Deitel 87. C++ How to Program 3rd edition by deitel 88. College Accounting (Chapters 1-25), 10E by Jeffrey Slater sm and tb 89. College Mathematics for Business, Economics, Life Sciences & Social Sciences (11th Edition) (Hardcover) by Raymond A. Barnett (Author), Michael R. Ziegler (Author), Karl E. Byleen (Author) 90. Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson 91. Computer Architecture: Pipelined and Parallel Processor Design (Solutions Manual) by Michael J. Flynn selected solutions 92. Computer Networking: A Top-Down Approach, 5/E solution manual 93. Consumer Behavior, 8/E Michael R. Solomon test bank 94. Control Systems Engineering by Nise 4ed 95. Corporate Computer and Network Security Raymond Panko 96. Corporate Finance By Stephen A. Ross 8th edition SM 97. Corporate finance 1e by berk sm 98. Corporate finance 1e by berk tb 99. Corporate Finance 2nd Edition Scott B. Smart, William L. Megginson, Lawrence J. Gitman solution manual 100. Corporate Finance, 8e Stephen A. Ross Randolph W. Westerfield Jeffrey Jaffe instructor manual and solution manual 101. Corporate Financial Management 3e Douglas R. Emery instructor manual 102. Corporate Financial Management 3e Douglas R. Emery test bank 103. Cost Accounting 12e by Horngren Test Bank 104. Cost accounting 12e by Charles T. Horngren Srikant Datar George Foster Madhav Rajan Chris Ittner solution manual 105. Cost accounting 13e by Charles T. Horngren Srikant Datar George Foster Madhav Rajan Chris Ittner solution manual 106. Cost accounting 13e by Charles T. Horngren Srikant Datar George Foster Madhav Rajan Chris Ittner test bank 107. Cost Accounting; Foundations and Evolutions, Edition 7e, Kinney, Raiborn 108. Cost Management: A Strategic Emphasis, 4e Blocher 109. Cost Management: Measuring Monitoring and Motivating Performance by Eldenburg Wolcott SM TB 110. Cost management: Accounting and control 5e and 6e By Hansen MOwen SM+TB 111. Entrepreneurial Finance, 3rd Edition Chris Leach Ronald W. Melicher test bank 112. Entrepreneurial Finance, 3rd Edition Chris Leach Ronald W. Melicher instructor manual 113. Entrepreneurship: Starting and Operating a Small Business (with Business Plan Pro), 2/E Steve Mariotti, Caroline Glackin test gen and instructor manual 114. Essentials of Investments 7th edition Zvi Bodie Alex Kane, Alan marcus test bank 115. Essentials of Investments Zvi Bodie, Alex Kane, Alan J. Marcus 116. Essentials of Managerial Finance 14e Brigham TB 117. Essentials of Managerial Finance 13th Edition Scott Besley, Eugene F. Brigham instructor manual 118. Essentials of Managerial Finance 13th Edition Scott Besley, Eugene F. Brigham test bank 119. Essentials of Managerial Finance, 14th EditionScott Besley Eugene F. Brigham instructor manual 120. Essentials of Managerial Finance, 14th EditionScott Besley Eugene F. Brigham spreadsheet problem solutions 121. Essentials of Managerial Finance, 14th EditionScott Besley Eugene F. Brigham test bank 122. Essentials of Modern Business Statistics 4th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams test bank 123. Essentials of Modern Business Statistics 4th Edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams test bank 124. Essentials of Organizational Behavior 9e Stephen P. Robbins Tim Judge 125. Essentials of Statistics for Business and Economics 5th edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams solution manual with case solutions 126. Essentials of Statistics for Business and Economics 5th edition David R. Anderson, Dennis J. Sweeney, Thomas A. Williams test bank 127. Essentials of Statistics, by Triola, 3rd edition sm 128. Essentials of Statistics, by Triola, 3rd edition tb 129. Essentials of Strategic Management 4E DAVID HUNGER THOMAS L. WHEELEN im with tb 130. Federal Taxation 2008 Corporations Partnerships Estates and Trusts 21E Anderson Pope Kramer test bank 131. Finance Management Test Bank brigham 11 test bank 132. Financial & managerial Accounting 13E By william Haka bettner 133. Financial & Managerial Accounting 9e and 10e Carl S. Warren, James M. Reeve solution manual 134. Financial accounting: an introduction to concepts, methods, and uses by clyde Stickney and Roman Weil solutions manual 11e 12e 13e 135. Financial Accounting 4e by John Wild 136. Financial Accounting 6e by kieso solution manual 137. Financial Accounting 6e by kieso test bank 138. Financial Accounting 6e Harrison Horngren 139. Financial Accounting 6th edition by Harrison Solution Manual 140. Financial accounting 6th edition harrison test bank 141. Financial accounting 7th edition harrison solution manual 142. Financial accounting 7th edition harrison test bank 143. Financial Accounting: Information for Decisions 6th Edition Robert W. Ingram, Thomas L. Albright extra resources 144. Financial Accounting: Information for Decisions 6th Edition Robert W. Ingram, Thomas L. Albright solution manual 145. Financial Accounting: Information for Decisions 6th Edition Robert W. Ingram, Thomas L. Albright test bank 146. Financial Accounting; Tools for Business Decision Making, 4th Edition, Kimmel.Weygandt.Kieso instructor manual 147. Financial Accounting; Tools for Business Decision Making, 4th Edition, Kimmel.Weygandt.Kieso solution manual 148. Financial Accounting; Tools for Business Decision Making, 4th Edition, Kimmel.Weygandt.Kieso test bank 149. Financial Analysis with Microsoft¬ Excel 4th Edition Timothy R. Mayes, Todd M. Shank instructor manual 150. Financial Analysis with Microsoft¬ Excel 4th Edition Timothy R. Mayes, Todd M. Shank spreadsheet problems 151. Financial Analysis with Microsoft¬ Excel¬ 2007 Timothy R. Mayes, Todd M. Shank Instructor Spreadsheet Files 152. Financial management 2e by jae K shim 153. Financial management Principles and application 10e by By Arthur J. Keown, John D. Martin, John W. Petty, David F. Scott solution manual 154. Financial Management Theory & Practice,Eugene Brigham,12th edition [ Test Bank ] 155. Financial management theory and practice 10e by Brigham solution manual 156. Financial Management Theory And Practice 11e by Brigham solution manual 157. Financial management theory and practice 12e by Brigham sm 158. Financial management theory and practice 12e by Brigham spreadsheet problems 159. Financial management theory and practice 12e by Brigham TB 160. Financial Management Theory and Practice, 11e By Eugene F. Brigham test bank 161. Financial Markets and Institution (7thEd) Madura TestBank 162. Financial Reporting Analysis 10th edition TB by gibson 163. Financial Reporting and Analysis Using Financial Accounting Information 10th Edition Charles H. Gibson instructor manual 164. Financial Reporting and Analysis Using Financial Accounting Information 10th Edition Charles H. Gibson solution manual 165. Financial Reporting and Analysis Using Financial Accounting Information 10th Edition Charles H. Gibson test bank 166. Financial Reporting and Analysis: Using Financial Accounting Information 11th Edition Charles H. Gibson solution manual 167. Financial Reporting and Analysis: Using Financial Accounting Information 11th Edition Charles H. Gibson test bank 168. Financial Reporting and Corporate Governance exercise solutions Lee 169. Framework for Marketing Management, A - Philip Kotler (4th ed) (ISBN 0136026605) 170. Framework for Marketing Management, A - Philip Kotler (4th ed) (ISBN test bank 171. Fundamental accounting principles 17th edition larson solution manual 172. Fundamental Accounting Principles, 18/e John J. Wild Barbara Chiappetta Kermit D. Larson solution manual and test bank 173. Fundamentals accounting principles by larson 18e SM 174. Fundamentals of Advanced Accounting 1e Fisher taylor chang solution manual 175. Fundamentals of Advanced Accounting 1e Fisher taylor chang test bank 176. Fundamentals of advanced accounting 3e by hoyle 177. Fundamentals of Advanced Accounting, 2e Joe B. Hoyle Thomas F. Schaefer Timothy S. Doupnik (Solution Manual) 178. Fundamentals of Contemporary Financial Management, 2nd Edition R. Charles Moyer James R. McGuigan Ramesh P. Rao instructor manual 179. Fundamentals of Contemporary Financial Management, 2nd Edition R. Charles Moyer James R. McGuigan Ramesh P. Rao test bank 180. Fundamentals of corporate finance 8e by Ross Ross, Westerfield,jordan 181. Fundamentals of Corporate Finance, 4th Edition (Brealey, Myers, Marcus) by Bruce Swenson 182. Fundamentals of Financial Management 12th brigham edition instructor manual 183. Fundamentals of Financial Management 12th edition brigham test bank 184. Fundamentals of Financial Management 10th Edition by Eugene Brigham Solution manual 185. Fundamentals of Financial Management 10th Edition by Eugene Brigham test bank 186. Fundamentals of Financial Management 11e by Eugene F. Brigham, Joel F. Houston spreadsheet problems 187. Fundamentals of Financial Management 11e by Eugene F. Brigham, Joel F. Houston test bank and cyberproblems 188. Fundamentals of Financial Management 11e by Brigham Instructor manual 189. Fundamentals of financial management 12e by james c. van horne 190. Fundamentals of Financial Management Eugene F. Brigham, Joel F. Houston 12th edition instructor manual 191. Fundamentals of Financial Management Eugene F. Brigham, Joel F. Houston 12th edition spreadsheets problems and web appendix solutions 192. Fundamentals of Financial Management Eugene F. Brigham, Joel F. Houston 12th edition test bank 193. Fundamentals of Financial Management, 12th Edition (Instructors guide ONLY) by James C. Van Horne, John M Wachowic 194. Fundamentals of Financial Management, Concise Edition 5th Eugene F. Brigham, Joel F. Houston test bank 195. Fundamentals of Financial Management, Concise Edition 5th Eugene F. Brigham, Joel F. Houston spreadsheets problems 196. Fundamentals of Financial Management, Concise Edition 5th Eugene F. Brigham, Joel F. Houston instructor manual 197. Fundamentals of Financial Management, Concise Edition Eugene F. Brigham, Joel F. Houston 6th edition instructor manual 198. Fundamentals of Financial Management, Concise Edition Eugene F. Brigham, Joel F. Houston 6th edition spreadsheet problem solutions 199. Fundamentals of Financial Management, Concise Edition Eugene F. Brigham, Joel F. Houston 6th edition test bank 200. Fundamentals Of Fluid Mechanics 3Rd And 4Th Edition Solutions Manual 201. Fundamentals of Fluid Mechanics, 6th Edition Munson, Young, Okiishi, Huebsch 202. Fundamentals of Heat and Mass Transfer, 5th Edition by Frank P. Incropera 203. Fundamentals of Heat and Mass Transfer, 6th Edition Incropera, DeWitt, Bergman, Lavine 204. Fundamentals of Investing, 10th Edition by Gitman and Joehnk 205. Fundamentals of Investments 3e Gordon J. Alexander William F. Sharpe 206. Fundamentals of Logic Design 5th edition by charles roth 207. Fundamentals of Machine Component Design, 3rd ed - Student Solutions Manual by Juvinall, Marshek 208. Fundamentals of manufacturing 2nd edition by philip d. rufe solutions manual 209. Fundamentals of Momentum, Heat and Mass Transfer, 5th Edition Welty, Wicks, Rorrer, Wilson 210. Fundamentals of Multinational Finance, 2nd edition by Michael H. Moffett test bank and solution manual 211. Fundamentals of Multinational Finance, 3E by Michael H. Moffett (Instructor's Manual) 212. Fundamentals of Multinational Finance, 3E by Michael H. Moffett test bank 213. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith sm 214. Government and Nonprofit Accounting Theory & Practice - 8th edition by Freeman, Shoulders, Allison, Patton, Smith tb 215. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith instructor manual 216. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith tb 217. Government and Nonprofit Accounting Theory & Practice - 9th edition by Freeman, Shoulders, Allison, Patton, Smith sm 218. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow sm 219. Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow tb 220. Human resources management 10e Gary dessler (IM+TB) 221. Intermediate Accounting 10e by Nikolai sm 222. Intermediate Accounting 11e by Kieso 223. Intermediate Accounting 12e by Kieso 224. Intermediate accounting 12th Updated by Kieso Solution manual 225. Intermediate accounting 12th Updated by Kieso test bank 226. Intermediate Accounting, 13th Edition Instructor's Manual Kieso, Weygandt, Warfield 227. (Sm+TB+IM) 228. Intermediate Accounting 2e by Baruch Englard 229. Intermediate Accounting 3e by J. David Spiceland 230. Intermediate Accounting 4e revised by J. David Spiceland solution manual 231. Intermediate accounting by Spiceland 4e Solution manual 232. Intermediate Accounting James D. Stice, Earl K. Stice, Fred Skousen 16th edition solution manual 233. Intermediate Accounting, 13th Edition Kieso, Weygandt, Warfield test bank and solution manual 234. Intermediate Accounting, Update, 12th Edition international student solution manual 235. Intermediate Algebra Functions & Authentic Applications 3e lehmann 236. Intermediate Algebra, 8th Edition By Margaret L. Lial, John Hornsby, Terry McGinnis 237. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves instructor manual 238. Intermediate Financial Management 9th Edition Eugene F. Brigham, Phillip R. Daves test bank 239. Intermediate Microeconomics, 10th Edition Walter Nicholson ,Christopher Snyder im with tb 240. International Accounting 1e by Doupnik solution manual 241. International Accounting 6e Frederick D. Choi Gary K. Meek 242. International Business The Challenges of Globalization, 4E John J. Wild,Kenneth L. Wild tb and im 243. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan instructor manual 244. International Business, 12/E John Daniels Lee Radebaugh Daniel Sullivan test bank 245. International Economics Theory and Policy 8e Krugman & Obstfeld 246. International Economics, 7e Husted Melvin test bank and solution manual 247. International Financial Management 9th Edition jeff madura instructor manual 248. International Financial Management 9th Edition jeff madura test bank 249. International Financial Management Geert Bekaert Robert J. Hodrick test bank and sol manual I have many solutions manual and Test bank, they are PDF format or Word format, Those resources save your time and effort and let you definitely understand what you are studying and get amazing marks as well, The Manuals contains the answers of the questions and exercises (Usually at the end of each chapter), The Test Questions contains an extra questions, Most of them multiple choice, true and false and fill in the blank questions with their answers. If the solutions manual or Test bank what you want is not in this list, also can ask me (They are part of what I have ). Then if you need solutions manual or test bank . only contact me by email. Studentshelp(at)hotmail(dot)com Studentshelp(at)hotmail(dot)com only contact me by email studentshelp@hotmail.com I have many solutions manual and Test bank, they are PDF format or Word format, Those resources save your time and effort and let you definitely understand what you are studying and get amazing marks as well, The Manuals contains the answers of the questions and exercises (Usually at the end of each chapter), The Test Questions contains an extra questions, Most of them multiple choice, true and false and fill in the blank questions with their answers. If the solutions manual or Test bank what you want is not in this list, also can ask me (They are part of what I have ). Then if you need solutions manual or test bank . only contact me by email. Studentshelp(at)hotmail(dot)com Studentshelp(at)hotmail(dot)com only contact me by email studentshelp@hotmail.com 1. International Management Managing Across Borders and Cultures 6e test bank and instructor manual 2. Interpreting and Analyzing Financial Statement 4e Karen P. Schoenebeck 3. Introduction to Corporate Finance William L. Megginson, Scott B. Smart 1st edition instructor manual 4. Introduction to Corporate Finance William L. Megginson, Scott B. Smart 1st edition test bank 5. Introduction to Corporate Finance 2nd edition William L. Megginson, Scott B. Smart instructor manual 6. Introduction to Corporate Finance, 2nd Edition William L. Megginson Scott B. Smart test bank 7. Introduction to Corporate Finance, 2nd Edition William L. Megginson Scott B. Smart solution manual 8. Introduction to Government and Non-for-Profit Accounting 6th edition by martin ives sm 9. Introduction to Government and Non-for-Profit Accounting 6th edition test bank by martin ives 10. Introduction to Operations and Supply Chain Management 2e Cecil Bozarth 11. Introduction to Operations and Supply Chain Management 2e Cecil Bozarth Robert B. Handfield test bank and sol manual 12. Investment analysis and portfolio management 8e by Reily Brown 13. Investment Analysis and Portfolio Management 9th Edition Frank K. Reilly, Keith C. Brown solution manual 14. Investment Analysis and Portfolio Management 9th Edition Frank K. Reilly, Keith C. Brown test bank 15. Investment Analysis and Portfolio Management- Solutions Manual, 7th Edition by Frank K. et al. Reily 16. Intermediate Accounting 12 E Kieso (TB) 17. Intermediate accounting 5e spiceland test bank and solution manual 18. Intermediate Accounting 12e by Keiso sm 19. Intermediate accounting 4th edition spiceland test bank 20. Introduction to management accounting 14e Charles T. Horngren, Gary L. Sundem, William O. Stratton, Jeff Schatzberg, Dave Burgstahler solution manual 21. Introduction to Operations Research - 7th by Frederick Hillier, Gerald Lieberman 22. Macroeconomics (8thEd) - Froyen - Solutions Manual 23. Macroeconomics 6e Andrew B. Abel, Ben S. Bernanke, Dean Croushore 24. Macroeconomics 3e williamson instructor manual and test bank 25. Macroeconomics, 4E Olivier Blanchard instructor manual 26. Macroeconomics, 4E Olivier Blanchard test bank 27. Macroeconomics, 5E Olivier Blanchard instructor manual and test bank 28. Management 5th Edition Chuck Williams instructor manual 29. Management 9E Stephen P. Robbins Mary Coulter test bank and instructor manual 30. Management accounting 5e Anthony A. Atkinson Robert S. Kaplan Ella Mae Matsumura S. Mark Young instructor manual test bank and solution manual 31. Management accounting 5E Atkinson solution manual 32. Management accounting 5E Atkinson test bank 33. Management Control Systems Performance Measurement, Evaluation and Incentives 2e Merchant & Van der Stede 34. Management Information Systems; Managing the Digital Firm, Edition 10, Laudon test bank and solution manual 35. Management Robbins Coulter 9th edition (test bank ) 36. Management10E Stephen P. Robbins Mary Coulter 37. Management10E Stephen P. Robbins Mary Coulter test bank 38. Managerial Accounting 12e By Garrison Noreen ( Solution Manual ) 39. Managerial Accounting 12e By Garrison Noreen (Test Bank) 40. Managerial Accounting Bamber, L. S., K. W. Braun, and W. T. Harrison, Jr. 2008 41. Managerial Accounting international edition Garrison11 ( Solution Manual) 42. Managerial Accounting, 11th Edition by Ray H Garrison, Eric Noreen, Peter C. Brewer 43. Managerial Accounting: An Introduction to Concepts, Methods and Uses 10th Edition Michael W. Maher, Clyde P. Stickney, Roman L. Weil instructor manual 44. Managerial Accounting: An Introduction to Concepts, Methods and Uses 10th Edition Michael W. Maher, Clyde P. Stickney, Roman L. Weil solution manual 45. Managerial Accounting: An Introduction to Concepts, Methods and Uses 10th Edition Michael W. Maher, Clyde P. Stickney, Roman L. Weil test bank 46. Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris instructor manual 47. Managerial Economics Applications, Strategies, and Tactics 11th Edition James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris test bank 48. Managerial Finance, Gitman,Lawrence 12e [SM] 49. Managing Human Resources by Luis R. Gomez-Mejia; David B. Balkin; Robert L. Cardy. 5th Edition im and tb 50. Manufacturing Engineering and Technology 5E by Kalpakjian and Schimid 51. Marketing Kotler Armstrong 11th edition (Test bank ) 52. Marketing Management (13th Edition) by Philip Kotler, Kevin Keller im 53. Marketing Management (13th Edition) by Philip Kotler, Kevin Keller tb 54. Mastery of the Financial Accounting Research System (FARS) Through Cases, 2nd Edition Wallace 55. Microeconomic Analysis Solution Manual - Varian 3rd edition 56. Microeconomic Analysis Third Edition by Hal R. Varian 57. Microeconomic Theory Solutions Manual for Mas-Colell 58. Microeconomics 6e Robert Pindyck Daniel Rubinfeld instructor manual 59. Microeconomics 6e Robert Pindyck Daniel Rubinfeld test bank 60. Microeconomics 7e Robert Pindyck Daniel Rubinfeld 61. Microeconomics Theory and Applications with Calculus by perloff insrructor manual 62. Microeconomics Theory and Applications with Calculus by perloff test bank 63. Microelectronic Circuit Design 2nd and 3rd edition by R. Jaeger selected solutions answers not solution 64. Modern Advanced Accounting , 10th Edition, by Larsen, (publisher McGraw Hill) 65. Modern Advanced Accounting 10th edition Test Bank LARSEN 66. Modern Auditing Assurance Services 8e Boynton sm and tb 67. Modern Business Statistics David R. Anderson, Dennis J. Sweeney, Thomas A. Williams 3rd edition solution manual 68. Modern Business Statistics David R. Anderson, Dennis J. Sweeney, Thomas A. Williams 3rd edition test bank 69. modern control engineering by katsuhiko ogata 3rd edition ISBN: 0132273071 70. modern control engineering by katsuhiko ogata 4th edition 71. Modern Control System 11th edition by richard c dorf, robert H bishop 72. Modern Control System 9th by richard c dorf, robert H bishop 73. Modern Database management 9e by Jeffrey A. Hoffer im 74. Modern Database management 9e by Jeffrey A. Hoffer TB 75. Modern Database Management, Ninth Edition Jeffrey A. Hoffer, University of Dayton Mary Prescott Heikki Topi 76. Modern Digital and Analog Communications Systems - B P Lathi Solutions Manual 3rd edition 77. Operations Management 8e by Jay Heizer Barry Render sm 78. Operations Management 8e by Jay Heizer Barry Render tb 79. Operations Management 9e by Jay Heizer Barry Render tb 80. Operations Management 9th by Jay Heizer Barry Render sm 81. Operations Management for MBAs, 3rd Edition Meredith, Shafer tb +im 82. Operations Management Reid, Sanders An Integrated Approach 2nd edition 83. Operations Management Reid, Sanders An Integrated Approach 2nd edition test bank 84. Operations Management, 10e William J. Stevenson instructor manual with solutions to supplementary problems 85. Operations Management, 10e William J. Stevenson test bank 86. Operations Management, 9e William J. Stevenson instructor manual with solutions to supplementary problems 87. Operations Management, William J Stevenson, 9e [TB] 88. Operations management processes and value chains 8e by Lee J. Krajewski solution manual 89. Operations management processes and value chains 8e by Lee J. Krajewski test bank 90. Operations Research An Introduction, 8E Hamdy A. Taha 91. Optimal Control Theory An Introduction By Donald E. Kirk 92. Options, Futures and Other Derivatives, 4th Edition (Solutions Manual) by John Hull, John C. Hull 93. Options, Futures and Other Derivatives, Fifth Edition (Solutions Manual) by John Hull, John C. Hull 94. Options, Futures, and Other Derivatives 7E by JOHN C HULL TB 95. Organizational Behavior Stephen P Robbins 12th edition (test bank) 96. Organizational Behavior, by Stephen P. and Timothy A. 13th Edition Robbins Judge im and tb 97. Organizational Behavior: Managing People and Organizations, 9th Edition Ricky W. Griffin Gregory Moorhead instructor manual 98. Organizational Behavior: Managing People and Organizations, 9th Edition Ricky W. Griffin Gregory Moorhead test bank 99. Organizational behavior 12e by Robbins ( instructor manual ) 100. Organizational behavior 12e by Robbins ( Test bank ) 101. Organizational Behavior, Fourth Canadian Ed., 4E Robins Test generator 102. Organizational Theory, Design and Change, 5/E Gareth R. Jones 103. Organizational Theory, Design and Change, 5E Gareth R. Jones Instructor's Manual and test bank 104. Organizational Theory, Design and Change, 5E Gareth R. Jones im and tb 105. Papa Thomas T.V. - Solutions Manual to Accompany Millman Integrated Electronics 106. Personal Finance Turning Money into Wealth 5e Arthur J. Keown 107. Personal Finance Turning Money into Wealth and Student Workbook, 4E keown instructor manual and test bank 108. Practical Financial Management 5th Edition William R. Lasher instructor manual 109. Practical Financial Management 5th Edition William R. Lasher test bank 110. Practical Financial Management William R. Lasher 4th edition instructor manual 111. Practical Financial Management William R. Lasher 4th edition test bank 112. Precalculus 4e blitzer 113. Prentice Hall - Solutions Manual; Communication Systems 114. Prentice Hall's Federal Taxation 2008 Individual , 21th Edition By Thomas R. Pope, Kenneth instructor guide 115. Prentice Hall's Federal Taxation 2009 Comprehensive, 22nd Edition By Thomas R. Pope, Kenneth E. Anderson, John L. Kramer instructor guide 116. Prentice Hall's Federal Taxation 2009 Comprehensive, 22nd Edition By Thomas R. Pope, Kenneth E. Anderson, John L. Kramer solution manual 117. Prentice Hall's Federal Taxation 2009 Comprehensive, 22nd Edition By Thomas R. Pope, Kenneth E. Anderson, John L. Kramer test bank 118. Prentice Hall's Federal Taxation 2009 Individual , 22th Edition By Thomas R. Pope, Kenneth instructor guide 119. Prentice Hall's Federal Taxation 2009: Corporations, 22/E Kenneth E. Anderson Thomas R. Pope John L. Kramer instructor guide 120. Prentice Hall's Federal Taxation 2009: Corporations, 22/E Kenneth E. Anderson Thomas R. Pope John L. Kramer tb +sm 121. Prentice Hall's Federal Taxation 2009: Individuals, 22/E Kenneth E. Anderson Thomas R. Pope John L. Kramer tb +sm 122. Principles of Auditing 15e by Whittington TB 123. Principles Of Corporate Finance 8E By Brealey Myers Allen 124. Principles of corporate finance 9e by brealy mayers allen (SM+TB) 125. Principles of Cost Accounting 14th Edition Edward J. Vanderbeck instructor manual 126. Principles of Cost Accounting 14th Edition Edward J. Vanderbeck solution manual 127. Principles of Cost Accounting 14th Edition Edward J. Vanderbeck test bank 128. Principles of Electric Circuits Conventional Current Version 8e by floyd 129. Principles of Electric Circuits Conventional Current Version by Floyd 8th edition 130. Principles of electric circuits- electron flow version Floyd 8th edition 131. Principles of Electronic Materials and Devices, Solutions Manual ONLY Safa O. Kasap 2nd edition 132. Principles of managerial finance 10e by gitman Lawrence 133. Principles of managerial finance 11e by gitman Lawrence 134. Principles of managerial finance 11e by gitman Lawrence solution manual 135. Principles of Managerial Finance 11e by Gitman Lawrence test bank 136. Principles of managerial finance 12e by gitman Lawrence test bank 137. Principles of Managerial Finance Brief plus 5e sm 138. Principles of Managerial Finance Brief plus 5e tb 139. Principles of Managerial Finance Brief plus My Finance Lab Student Access Kit, 5E Lawrence J. Gitman 140. principles of marketing 11e by Kotler ( instructor manual ) 141. principles of marketing 11e by Kotler ( test bank ) 142. principles of marketing 12e by Kotler TB 143. Principles of marketing 5e Canadian edition Kotler instructor manual 144. Principles of Microeconomics case and fair 8th edition testgen 145. Principles of Microeconomics, 9/e Case, Fair & Oster instructor manual 146. Principles of Microeconomics, 9/e Case, Fair & Oster test bank 147. Principles of Microeconomics, 9e Case, Fair & Oster instructor manual ad test bank 148. South-Western Federal Taxation 2009 (Individual), Edition 32, Hoffman, Smith, Wills (Test Bank) 149. South-Western Federal Taxation 2009 Corporations - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660219) 150. South-Western Federal Taxation 2009 Corporations - William Hoffman (test bank) (32nd ed) (ISBN 0324660219) 151. South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Solutions Manual) (32nd ed) (ISBN 0324660529) 152. South-Western Federal Taxation 2009: Comprehensive - William Hoffman (Test Bank) (32nd ed) (ISBN 0324660529 153. South-Western Federal Taxation 2009: Individual Income Taxes 32nd Edition William Hoffman, James E. Smith, Eugene Willis Instructor's Guide 154. South-Western Federal Taxation 2009: Individual Income Taxes 32nd Edition William Hoffman, James E. Smith, Eugene Willis individual practice solutions 155. South-Western Federal Taxation 2010: Comprehensive 33rd Edition 2010 Eugene Willis, William H. Hoffman, Jr., David M. Maloney, William A. Raabe solution manual 156. South-Western Federal Taxation 2010: Comprehensive 33rd Edition 2010 Eugene Willis, William H. Hoffman, Jr., David M. Maloney, William A. Raabe test bank 157. South-Western Federal Taxation 2010: Corporations, Partnerships, Estates and Trusts 33rd Edition William H. Hoffman, Jr., William A. Raabe, James E. Smith, David M. Maloney sm 158. South-Western Federal Taxation 2010: Corporations, Partnerships, Estates and Trusts 33rd Edition William H. Hoffman, Jr., William A. Raabe, James E. Smith, David M. Maloney tb 159. South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis solution maual 160. South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis instructor guide 161. South-Western Federal Taxation 2010: Individual Income Taxes 33rd Edition William Hoffman, James E. Smith, Eugene Willis test bank 162. South-Western Federal Taxation Individual Income Taxes, 32nd by William Hoffman, Jr. James Smith Eugene WillisEdition sm 2009 163. South-Western Federal Taxation individual income taxes (2009) instructor manual 164. South-Western Federal Taxation: Taxation of Business Entities 12th James E. Smith, William A. Raabe, David M. Maloney instructor guide 165. South-Western Federal Taxation: Taxation of Business Entities 12th James E. Smith, William A. Raabe, David M. Maloney solution manual 166. South-Western Federal Taxation: Taxation of Business Entities 12th James E. Smith, William A. Raabe, David M. Maloney test bank 167. South-Western Federal Taxation: Taxation of Business Entities 13th James E. Smith, William A. Raabe, David M. Maloney instructor guide 168. South-Western Federal Taxation: Taxation of Business Entities 13th James E. Smith, William A. Raabe, David M. Maloney solution manual 169. South-Western Federal Taxation: Taxation of Business Entities 13th James E. Smith, William A. Raabe, David M. Maloney test bank 170. Strategic Brand Management 3e keller 171. Strategic management 11e by Fred R. David ( instructor manual and case solutions ) 172. Strategic management 11e by Fred R. David ( test bank ) 173. Strategic Management and Business Policy, 11e Thomas L. Wheelen David L. Hunger instructor manual with test items 174. Strategic Management and Competitive Advantage Concepts and Cases, 2E case teaching notes 175. Strategic Management and Competitive Advantage: Concepts and Cases, 2/E instructor manual with test items Jay Barney William S Hesterly 176. Strategic Marketing Problems: Cases and Commentsî, 11/E by Roger Kerin, Robert 177. Business Ethics Ethical Decision Making and Cases 7e by Ferrel IM 178. Corporate Finance A Focused Approach 3e Brigham SM 179. Corporate Finance A Focused Approach 3e Brigham TB 180. Financial Accounting Information for Decisions 6e Robert W. Ingram SM 181. Financial Accounting Information for Decisions 6e Robert W. Ingram TB 182. Managerial Accounting: A Focus on Ethical Decision Making, 5th Edition Jackson / Sawyer / Jenkins SM 183. Management Information Systems (10th Edition) by McLeod / Schell IM 184. Management Information Systems (10th Edition) by McLeod / Schell TB 185. Database Systems: The Complete Book, 2/E Hector Garcia-Molina SM 186. Process Control Instrumentation Technology, 8/E Curtis D. Johnson IM 187. Physics: Principles with Applications, 6/E Douglas C. Giancoli TB 188. Digital Electronics: A Practical Approach, 8/E William Kleitz IM + TG I have many solutions manual and Test bank, they are PDF format or Word format, Those resources save your time and effort and let you definitely understand what you are studying and get amazing marks as well, The Manuals contains the answers of the questions and exercises (Usually at the end of each chapter), The Test Questions contains an extra questions, Most of them multiple choice, true and false and fill in the blank questions with their answers. If the solutions manual or Test bank what you want is not in this list, also can ask me (They are part of what I have ). Then if you need solutions manual or test bank . only contact me by email. Studentshelp(at)hotmail(dot)com Studentshelp(at)hotmail(dot)com only contact me by email studentshelp@hotmail.com === Subject: Re: Three bar equal sign? posting-account=UA-6fQkAAADI18fSPOc495gPgW1akxLl Trident/4.0; MathPlayer 2.10b; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > .... > (upside-down A x)(x^2 - 4 = (x + 4)(x - 4)) A slightly better example is given by: (upside-down A x)(x^2 - 4 = (x + 2)(x - 2)) :) > Ken Pledger. I will explain to you what I am after. I am after a new theory, a new > way of programming, a new way of measuring, a new way of > communicating. I am talking about an end to the old tired way of 'P', > if 'P' then 'Q' innefficiency in programming and language (and > practical matters too). I propose the following: > 'X' if 'X' I'll do you a favor and explain how it all works. I say favor because this is very fundamental, very useful, and nobody really understands it (withness the absence of any discussion of the process.) I am talking about formalizing. Formalizing is abstracting a set of Intuitive Examples - IEs - into a small number of rules for generating them. The IEs can be: 1. Computer programs that a Program Synthesis system is supposed to synthesize. 2. Theorems that a theorem-generator is supposed to generate. 3. Theorems that are to be represented. Proofs that are to be represented. Any component can be focused on and maximized. 4. Techniques for optimizing a set of processes that can be done in multiple ways (preparing envelopes for a mass mailing, organizing data fields into records and files) with a measure of cost and benefit to each. Science is man's attempt to PREDICT and CONTROL the future state of his surroundings. (It is science when he succeeds.) Formalizing tells him which values to use when he controls something - what values to set the settings to. This is why mathematics is the science that can be done without the use of the 5 senses (the Helen Keller science.) Then our goal is to translate some set of IEs into an algorithm for generating them - generate computer programs, theorems, procedures, database designs. So you have to start with the IEs!! Now, there are many things we can say about the care and feeding of our IEs. (I nurtured a set of about 12 computer programs for 1 year and 9 months in order to axiomatize Program Synthesis, the first branch of Computer Science to be axiomatized. This consisted mostly of representing them using a myriad of models until one showed the relationships among the IEs - what they have in common and how they can be generated.) You are starting with the formalism! How can you judge a formalism without knowing the IEs first? I'm sorry, but my students would laugh you off the stage. :) C-B > The idea is we create a thread. The first programming variable means > nothing. It is an instruction to the system script. It is an open and > said> order of logic. > 'X' alone simply means Open or I am talking or Listen up, it can > be followed by anything, or an infinite number of things. > And the idea of 'X' is arbitrary, as 'X' could be replaced by any > other logical symbol or character in any language and the idea still > stands. The operation still works. > Let me explain: > 'X' when I say 'X'. > 'X' is the master open 'command' key or 'dialogue'. It sets up a > system open script. > We then can open any operation simply by repeating it. The system is > not loyal to any language or frame. (or insert proprietary here) > If I want to open up a program Y, I simply say, X, Y I want Y. > The system knows that if a variable is repeated it means to execute it > under the terms programmed. (or by pressing a key) Let me explain > further (further): > A formal illustration of how it would look in a system would be: > X, Y, Y, X > The first 'X' means open the root command, the first 'Y' means, I want > 'Y', the second 'Y' means it is just 'Y' I seek and the 'X' closes to > command. > The platform solution requires complete symmetry in programming and > logic threads. > The programming implementation allows the setup of a system where > repetition of a variable in symmetry order allows command. > In football the command hut means pitch me the ball back. The > Quarterback will communicate to his teammates, On the 2nd hut throw > the ball. The first hut is to get set. Still 'hut' is the command to > throw the ball. > The real world variable and how it relates to the equivalency in > programming is explained as follows: > Instead of saying (1)Listen up....(2)I want to open my word > processor.... > X 1 1 X > where (1)=the first command 1 > and (2)=11 > ***********Note in binary*: the machine literally must count the two > ones and add them to get two.************) > User inputs:(1)I want my word processor (2)I want my word > processor > and this means to the machine Open up the word processor... only > when you read (1) I want my word processor (2) I want my word > processor > (forgive my terminology, I am simply being plain) but this inside/out > programming > illustrates perfectly my point. and forgive my for being so bold but this logic clear, simple, and > plain, simply resolves P=NP > and overcomes the halting problem irrefutably > the solution to P=NP or P Versus NP, or N=NP or -1=1 or however you > want to frame > the problem is simply this statement: Do not do anything until I say > it twice. Advanced Symmetry application: the solution to the machine is the > overlooked symmetry. A complex command may look like: 'XYZZYX' which > would mean, I want the YZ complex variable please Stephen Arthur Cook was right, the whole thing was simply due to lack > of ingenuity on behalf of our programmer. (C)2009. Martin Musatov. All Rights Reserved in perpetuity*. > http://www.MeAmI.orgSearch for the People *Applies to derviations of this work. Including software, programming, > and other profit generating means extracted from this work. Work may > be patent pending.- Hide quoted text - - Show quoted text - === Subject: Re: Three bar equal sign? posting-account=UA-6fQkAAADI18fSPOc495gPgW1akxLl Trident/4.0; MathPlayer 2.10b; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) On Jun 16, 7:07am, Nick Keighley I will explain to you what I am after. I am after a new theory, a new > way of programming, a new way of measuring, a new way of > communicating. I am talking about an end to the old tired way of 'P', > if 'P' then 'Q' innefficiency in programming and language (and > practical matters too). When I was a teenager I noticed that lots of Propositional Calculus > axioms are derivable from the fact that AND and OR (as well as ADD and > MUL) are what I call Set Functions. You can apply them to any > finite set - so the order cannot matter. A&B = B&A , A&(B&C)=(A&B)&C > etc. As a young adult I utilize that principle in my automated theorem- > proving software by representing A&B&C not as 2 applications of & but > as a set {A,B,C} with the & Set Function applied to it. The result is that my programs generate theorems orders of magnitude > faster. Have you looked at lisp? (and a b c) Yes, standard Logic is poorly designed, with shameful duplication of > principles between different branches of Mathematics e.g. Logic and > Set Theory both have DeMorgan rules etc. Researchers keep looking for > ways to prove the axioms, I'd be surprised if a reseacher was trying to prove an axiom... 1. Obviously people try to prove the axioms so they have something more primitive (general.) 2. Do I need to dig out some papers on something so obvious and fundamental? > but overlook the fact that they have the > wrong model for that. comp.programming is so lucky to have *two* geniuses. It should be as Set Functions. Just like they > use Predicate Calculus for MetaMathematics (e.g.; ZFC axioms) when a > higher level of abstraction is much more efficient and yields many > more theorems in practice (finite world). Always work at the highest level of abstraction you can. C-B I propose the following: No need. I have implemented it and the Set Function new idea solves > the problem nicely. -- > Nick Keighley- Hide quoted text - - Show quoted text - === Subject: Re: Three bar equal sign? posting-account=sLi3rQoAAAB6wjiwo9v8I7Xw7Kf7_67C SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > On Jun 16, 7:07am, Nick Keighley principles between different branches of Mathematics e.g. Logic and > Set Theory both have DeMorgan rules etc. Researchers keep looking for > ways to prove the axioms, I'd be surprised if a reseacher was trying to prove an axiom... 1. Obviously people try to prove the axioms so they have something > more primitive (general.) if you can prove it, it wasn't an axiom... > 2. Do I need to dig out some papers on something so obvious and > fundamental? -- Nick Keighley === Subject: Re: Three bar equal sign? posting-account=UA-6fQkAAADI18fSPOc495gPgW1akxLl Trident/4.0; MathPlayer 2.10b; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) On Jun 21, 3:03pm, Nick Keighley On Jun 16, 7:07am, Nick Keighley Yes, standard Logic is poorly designed, with shameful duplication of > principles between different branches of Mathematics e.g. Logic and > Set Theory both have DeMorgan rules etc. Researchers keep looking for > ways to prove the axioms, I'd be surprised if a reseacher was trying to prove an axiom... 1. Obviously people try to prove the axioms so they have something > more primitive (general.) if you can prove it, it wasn't an axiom... Surprise! Now, is ANYTHING really an axiom? One problem is, they say An axiom is something accepted without proof while in general it is really anything that we KNOW already. We don't HAVE to prove it, but we may - and likely can. Why? Because there is a concept behind the symbols and strings of symbols that is being represented. They can be anything, but that is not to say they ARE anything. The only thing they are (in practice i.e. useful systems) is a representation of the results of some study. In reality, the various branches of a study (e.g. Math or Computer Science) feed into each other, where the theorems of one are the axioms of another. How many people have tried to prove Peano's axioms? C-B > 2. Do I need to dig out some papers on something so obvious and > fundamental? -- > Nick Keighley === Subject: Re: Three bar equal sign? posting-account=sLi3rQoAAAB6wjiwo9v8I7Xw7Kf7_67C CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > On Jun 21, 3:03pm, NickKeighley more primitive (general.) if you can prove it, it wasn't an axiom... Surprise! I think we may be in agreement then... > Now, is ANYTHING really an axiom? yes >One problem is, they say An axiom > is something accepted without proof while in general it is really > anything that we KNOW already. define KNOW. Do you just me accept as true for this mathematical framework? >We don't HAVE to prove it, but we may - and likely can. bull. Take Euclids postulates (excluding the parallel one), how'd you prove any of them? > Why? Because there is a concept behind the symbols and strings of > symbols that is being represented. now into the hairier areas of mathematical philosophy >They can be anything, but that is > not to say they ARE anything. what is they in the above. And what does ARE mean? Come to that, why is anything quoted? >The only thing they are (in practice > i.e. useful systems) is a representation of the results of some study. too many pronouns for me. Are they axioms or systems? > In reality, the various branches of a study (e.g. Math or Computer > Science) feed into each other, where the theorems of one are the > axioms of another. not always. Sometimes you really are at the bottom. > How many people have tried to prove Peano's axioms? 9 -- Nick Keighley If cosmology reveals anything about God, it is that He has an inordinate fondness for empty space and non-baryonic dark matter. Sverker Johansson (talk.origins) === Subject: Re: Three bar equal sign? posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) MeAmI.org scribed: > On Jun 21, 3:03pm, NickKeighley Researchers keep looking for ways to prove the axioms, I'd be surprised if a reseacher was trying to prove an axiom... 1. Obviously people try to prove the axioms so they have something > more primitive (general.) if you can prove it, it wasn't an axiom... Surprise! I think we may be in agreement then... > Now, is ANYTHING really an axiom? yes One problem is, they say An axiom > is something accepted without proof while in general it is really > anything that we KNOW already. define KNOW. Do you just me accept as true for this mathematical > framework? >We don't HAVE to prove it, but we may - and likely can. bull. Take Euclids postulates (excluding the parallel one), how'd > you prove any of them? Why? Because there is a concept behind the symbols and strings of > symbols that is being represented. now into the hairier areas of mathematical philosophy >They can be anything, but that is > not to say they ARE anything. what is they in the above. And what does ARE mean? > Come to that, why is anything quoted? >The only thing they are (in practice > i.e. useful systems) is a representation of the results of some study. too many pronouns for me. Are they axioms or systems? > In reality, the various branches of a study (e.g. Math or Computer > Science) feed into each other, where the theorems of one are the > axioms of another. not always. Sometimes you really are at the bottom. How many people have tried to prove Peano's axioms? 9 > -- > Nick Keighley If cosmology reveals anything about God, it is that He has > an inordinate fondness for empty space and non-baryonic dark > matter. > Sverker Johansson (talk.origins) Re: define know:: How do you know I was writing this for your judgment at this time? How do you know it is not simply the foundation for a later proof? Can you rule out the possibility? Can you answer all these questions? Prove it. I tell you the truth nothing I write will be wasted. Not a single word will not be put to good use. -- mmm === Subject: Re: Three bar equal sign? posting-account=UA-6fQkAAADI18fSPOc495gPgW1akxLl Trident/4.0; MathPlayer 2.10b; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) On Jun 16, 7:07am, Nick Keighley I will explain to you what I am after. I am after a new theory, a new > way of programming, a new way of measuring, a new way of > communicating. I am talking about an end to the old tired way of 'P', > if 'P' then 'Q' innefficiency in programming and language (and > practical matters too). When I was a teenager I noticed that lots of Propositional Calculus > axioms are derivable from the fact that AND and OR (as well as ADD and > MUL) are what I call Set Functions. You can apply them to any > finite set - so the order cannot matter. A&B = B&A , A&(B&C)=(A&B)&C > etc. As a young adult I utilize that principle in my automated theorem- > proving software by representing A&B&C not as 2 applications of & but > as a set {A,B,C} with the & Set Function applied to it. The result is that my programs generate theorems orders of magnitude > faster. > > Have you looked at lisp? > > (and a b c) Yes, but unfortunately the idiots who write the college texts apparently have not! C-B > Yes, standard Logic is poorly designed, with shameful duplication of > principles between different branches of Mathematics e.g. Logic and > Set Theory both have DeMorgan rules etc. Researchers keep looking for > ways to prove the axioms, I'd be surprised if a reseacher was trying to prove an axiom... but overlook the fact that they have the > wrong model for that. comp.programming is so lucky to have *two* geniuses. It should be as Set Functions. Just like they > use Predicate Calculus for MetaMathematics (e.g.; ZFC axioms) when a > higher level of abstraction is much more efficient and yields many > more theorems in practice (finite world). Always work at the highest level of abstraction you can. C-B I propose the following: No need. I have implemented it and the Set Function new idea solves > the problem nicely. -- > Nick Keighley- Hide quoted text - - Show quoted text - === Subject: Re: Three bar equal sign? said: > ... > When I was a teenager I noticed that lots of Propositional Calculus > axioms are derivable from the fact that AND and OR (as well as ADD > and MUL) are what I call Set Functions. You can apply them to > any finite set - so the order cannot matter. A&B = B&A , > A&(B&C)=(A&B)&C etc. > As a young adult I utilize that principle in my automated theorem- > proving software by representing A&B&C not as 2 applications of & but > as a set {A,B,C} with the & Set Function applied to it. > The result is that my programs generate theorems orders of magnitude > faster. Faster than what? Any other theorem prover? Have you won any theorem-proving competitions? The next CADE ATP System Competition is in Montreal in August. Are you planning to show off your system there? > Have you looked at lisp? (and a b c) Yes, but unfortunately the idiots who write the college texts > apparently have not! I think the point was that what you tout as your very own teenage discovery has been a standard part of the syntax of languages designed for knowledge representation and automated theorem proving since the beginning. (And most every text on either subject uses LISP or an equivalent language with generalized boolean operators.) === Subject: Re: Three bar equal sign? <4A33520A.B54DF318@gmail.com> posting-account=UA-6fQkAAADI18fSPOc495gPgW1akxLl Trident/4.0; MathPlayer 2.10b; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > As a young adult I utilize that principle in my automated theorem- > proving software by representing A&B&C not as 2 applications of & but > as a set {A,B,C} with the & Set Function applied to it. In Laws of Form by G. Spencer Brown, conjunction and disjunction > are likewise freed from having only binary scope. The commutative > and associative properties of these operators are implicit in his > system also. You might like to have a look at his elegant presentation. Yes, it's a teriffic, overlooked book. I am glad it has survived in at least someone's intellect. I'll take a look. C-B -- > hz === Subject: Re: Three bar equal sign? posting-account=UA-6fQkAAADI18fSPOc495gPgW1akxLl Trident/4.0; MathPlayer 2.10b; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > I will explain to you what I am after. I am after a new theory, a new > way of programming, a new way of measuring, a new way of > communicating. I am talking about an end to the old tired way of 'P', > if 'P' then 'Q' innefficiency in programming and language (and > practical matters too). When I was a teenager I noticed that lots of Propositional Calculus > axioms are derivable from the fact that AND and OR (as well as ADD and > MUL) are what I call Set Functions. You can apply them to any > finite set - so the order cannot matter. A&B = B&A , A&(B&C)=(A&B)&C > etc. As a young adult I utilize that principle in my automated theorem- > proving software by representing A&B&C not as 2 applications of & but > as a set {A,B,C} with the & Set Function applied to it. The result is that my programs generate theorems orders of magnitude > faster. Yes, standard Logic is poorly designed, with shameful duplication of > principles between different branches of Mathematics e.g. Logic and > Set Theory both have DeMorgan rules etc. Researchers keep looking for > ways to prove the axioms, but overlook the fact that they have the > wrong model for that. It should be as Set Functions. Just like they > use Predicate Calculus for MetaMathematics (e.g.; ZFC axioms) when a > higher level of abstraction is much more efficient and yields many > more theorems in practice (finite world). Always work at the highest level of abstraction you can. C-B I propose the following: No need. I have implemented it and the Set Function new idea solves > the problem nicely. 'X' if 'X' > The idea is we create a thread. The first programming variable means > nothing. It is an instruction to the system script. It is an open and > said> order of logic. > 'X' alone simply means Open or I am talking or Listen up, it can > be followed by anything, or an infinite number of things. > And the idea of 'X' is arbitrary, as 'X' could be replaced by any > other logical symbol or character in any language and the idea still > stands. The operation still works. > Let me explain: > 'X' when I say 'X'. > 'X' is the master open 'command' key or 'dialogue'. It sets up a > system open script. > We then can open any operation simply by repeating it. The system is > not loyal to any language or frame. (or insert proprietary here) > If I want to open up a program Y, I simply say, X, Y I want Y. > The system knows that if a variable is repeated it means to execute it > under the terms programmed. (or by pressing a key) Let me explain > further (further): > A formal illustration of how it would look in a system would be: > X, Y, Y, X > The first 'X' means open the root command, the first 'Y' means, I want > 'Y', the second 'Y' means it is just 'Y' I seek and the 'X' closes to > command. > The platform solution requires complete symmetry in programming and > logic threads. > The programming implementation allows the setup of a system where > repetition of a variable in symmetry order allows command. > In football the command hut means pitch me the ball back. The > Quarterback will communicate to his teammates, On the 2nd hut throw > the ball. The first hut is to get set. Still 'hut' is the command to > throw the ball. > The real world variable and how it relates to the equivalency in > programming is explained as follows: > Instead of saying (1)Listen up....(2)I want to open my word > processor.... > X 1 1 X > where (1)=the first command 1 > and (2)=11 > ***********Note in binary*: the machine literally must count the two > ones and add them to get two.************) > User inputs:(1)I want my word processor (2)I want my word > processor > and this means to the machine Open up the word processor... only > when you read (1) I want my word processor (2) I want my word > processor > (forgive my terminology, I am simply being plain) but this inside/out > programming > illustrates perfectly my point. and forgive my for being so bold but this logic clear, simple, and > plain, simply resolves P=NP > and overcomes the halting problem irrefutably > the solution to P=NP or P Versus NP, or N=NP or -1=1 or however you > want to frame > the problem is simply this statement: Do not do anything until I say > it twice. Advanced Symmetry application: the solution to the machine is the > overlooked symmetry. A complex command may look like: 'XYZZYX' which > would mean, I want the YZ complex variable please Stephen Arthur Cook was right, the whole thing was simply due to lack > of ingenuity on behalf of our programmer. (C)2009. Martin Musatov. All Rights Reserved in perpetuity*. > http://www.MeAmI.orgSearch for the People *Applies to derviations of this work. Including software, programming, > and other profit generating means extracted from this work. Work may > be patent pending.- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - So you agree we have indeed overcome the P Versus NP problem and/or > halting problem and/or proven P=NP, correct? (Yes if any or all of the > above apply, No, if none) = this will do to begin with ;)- Hide quoted text - I think you have been reading (or however you intake it) too much published BS. People try to go beyond Turing with Quantum Computing - HA! All they can think of is: Turing proved you can't do it. The way to go beyond that is to prove that you can. GAD!!! The way to go beyond anything in math is to generalize it. You show what the actual condition is under which the theorem applies and consider variations - subsets of the premises. Then the original theorem becomes a special case and much easier to understand. Even to people like (I won't say who.) C-B (not yet) > - Show quoted text - === Subject: Re: Three bar equal sign? posting-account=UA-6fQkAAADI18fSPOc495gPgW1akxLl Trident/4.0; MathPlayer 2.10b; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) > I am after a new theory, a new > way of programming, a new way of measuring, a new way of > communicating. I am talking about an end to the old tired phrase a new way (A New Kind of Science)? Yes, I agree > completely. You need better communication than repeating the phrase > a new way over and over again. You need to learn some basic axioms > and rules: AB+AC+AD = A (B+C+D) and the principle of substitution: A=a new way of > B = programming > C=measuring > D=communicating Then, I am after a new theory, a new way of programming, a new way of > measuring, a new way of communicating. = > I am after a new way, of programming, measuring, communicating. Are you from India? C-B I am from Los Angeles: Is that near Bangalore? C-B > .... > (upside-down A x)(x^2 - 4 = (x + 4)(x - 4)) A slightly better example is given by: (upside-down A x)(x^2 - 4 = (x + 2)(x - 2)) :) > Ken Pledger. I will explain to you what I am after. I am after a new theory, a new > way of programming, a new way of measuring, a new way of > communicating. I am talking about an end to the old tired way of 'P', > if 'P' then 'Q' innefficiency in programming and language (and > practical matters too). I assert my proprietary findings: > 'X' if 'X' > The idea is we create a thread. The first programming variable means > nothing. It is an instruction to the system script. It is an open and > said> order of logic. > 'X' alone simply means Open or I am talking or Listen up, it can > be followed by anything, or an infinite number of things. > And the idea of 'X' is arbitrary, as 'X' could be replaced by any > other logical symbol or character in any language and the idea still > stands. The operation still works. > Let me explain: > 'X' when I say 'X'. > 'X' is the master open 'command' key or 'dialogue'. It sets up a > system open script. > We then can open any operation simply by repeating it. The system is > not loyal to any language or frame. (or insert proprietary here) > If I want to open up a program Y, I simply say, X, Y I want Y. > The system knows that if a variable is repeated it means to execute it > under the terms programmed. (or by pressing a key) Let me explain > further (further): > A formal illustration of how it would look in a system would be: > X, Y, Y, X > The first 'X' means open the root command, the first 'Y' means, I want > 'Y', the second 'Y' means it is just 'Y' I seek and the 'X' closes to > command. > The platform solution requires complete symmetry in programming and > logic threads. > The programming implementation allows the setup of a system where > repetition of a variable in symmetry order allows command. > In football the command hut means pitch me the ball back. The > Quarterback will communicate to his teammates, On the 2nd hut throw > the ball. The first hut is to get set. Still 'hut' is the command to > throw the ball. > The real world variable and how it relates to the equivalency in > programming is explained as follows: > Instead of saying (1)Listen up....(2)I want to open my word > processor.... > X 1 1 X > where (1)=the first command 1 > and (2)=11 > ***********Note in binary*: the machine literally must count the two > ones and add them to get two.************) > User inputs:(1)I want my word processor (2)I want my word > processor > and this means to the machine Open up the word processor... only > when you read (1) I want my word processor (2) I want my word > processor > (forgive my terminology, I am simply being plain) but this inside/out > programming > illustrates perfectly my point. and forgive my for being so bold but this logic clear, simple, and > plain, simply resolves P=NP > and overcomes the halting problem irrefutably > the solution to P=NP or P Versus NP, or N=NP or -1=1 or however you > want to frame > the problem is simply this statement: Do not do anything until I say > it twice. Advanced Symmetry application: the solution to the machine is the > overlooked symmetry. A complex command may look like: 'XYZZYX' which > would mean, I want the YZ complex variable please Stephen Arthur Cook was right, the whole thing was simply due to lack > of ingenuity on behalf of our programmer. (C)=Copyright. 2009. Martin Musatov. All Rights Reserved in perpetuity*. > http://www.MeAmI.orgSearch for the People *Applies to derviations of this work. Including software, programming, > and other profit generating means extracted from this work. Work may > be patent pending.- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=6ea2ugoAAACnO44ASKspIG0s--Ju5Ekb Gecko/20020604,gzip(gfe),gzip(gfe) I imagine that many proofs in natural language are hard to read due to > ambiguities. We have all heard of the term write only journal. Actually no , I've never heard of write only journal and I have no idea what it means. === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=6ea2ugoAAACnO44ASKspIG0s--Ju5Ekb Gecko/20020604,gzip(gfe),gzip(gfe) > If yes, is it also true that all of these deductions could be written > in such a way that a computer program can infallibly verify the > correctness of these steps? If also yes, than why isn't it required that the centerpiece of any > published proof be the source code for such a computer verification? Related to your question is > Yes, but this is a proof by exhaustion. I'm asking why all kinds of > proofs are not required to be machine verified? I don't know what proof by exhaustion means. In any case it's a complicated proof and if you're going to have proof verification by computers you want it the most for the most complicated proofs. === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=6ea2ugoAAACnO44ASKspIG0s--Ju5Ekb Gecko/20020604,gzip(gfe),gzip(gfe) If yes, is it also true that all of these deductions could be written > in such a way that a computer program can infallibly verify the > correctness of these steps? If the verifier does not contain bugs and runs on top of an > operating system whose possible bugs will not adversely influence > the correct functioning of the verifier and both the verifier and > the operating system run on top of hardware whose possible bugs > will not adversely influence the correct functioning of the > verifier and the verifier receives correct input then the answer is > yes. There are several programmes which do this. Yes, but couldn't the language that the machine-readable proof is > written in be specified as a standard. That way several > implementations of verifiers could be developed for different hardware > and operating systems (as is common for most heavily used programming > languages). Yes , that's a possibility. Of course someone needs to write the standard and prove that it's correct meaning that an implementation of the standard will say that a proof is true if and only if it is true. > It seems as though the basic rules of verifying FOL from an > implementation point-of-view are quite trivial. ie There isn't a lot > that could go wrong. In any case, surely we must agree that such a > system would be significantly more reliable than what we do now. Let's consider FOL in the language of ZFC where the vast majority of mathematical theorems are written and proved. If the verifier only accepts FOL and nothing else then every time your proof contains for example something like x+y where x and y are real numbers then you would need to rewrite it using only logical symbols and epsilon. This would be a huge amount of work and completely unworkable. So the verifier would also need to understand not just the formal language of set theory but also all the shorthands mathematicians use in their practice. But then it must also have some kind of type system so that it can check that when you write x+y the + part is meaningful for the kind of object x and y are. But what if x and y are different kinds of objects ? Say x is natural and y real. Your system probably also needs some kind of types promotion so that x also gets treated as a real when you write x+y. The language standard needs to specify how these type promotions work. I'm sure it's doable but it's quite more complicated than what you make it out to be. It's not obvious to me that it would be significantly more reliable than what we have now if at all. Personally I'm very thorough when checking my proofs. Such a system might help me do things quicker but it wouldn't improve my reliability. > If also yes, than why isn't it required that the centerpiece of any > published proof be the source code for such a computer verification? Because mathematics proofs have existed for a lot longer than > computers and there isn't a strong enough incentive to change > things. Well, the incentive is that we would have a near infallible and > scientific way to verify any mathematical theorem - with an instant > and impartial peer-review process. Surely it would save a lot of time > in determining whether a proof is valid or not. The scientific claim is vague. As for the rest I can only say perhaps. More tests are needed. > ie Shouldn't the center of every proof be a machine-readable theorem > and machine-readable steps to undeniably deduce that theorem? The > English should just be annotation essentially. Why do you think it should ? It's not obvious that it will increase > correctness. Note that many computer programmes have silly bugs > which a human reader would immediately pick up but a compiler might > not. So it is possible that due to such a silly bug in the source > of a proof the computer will say that a proof is correct when > actually it is not. I don't see how it could not increase correctness? How could a machine- > verified proof be incorrect? What is an example of a silly bug that > might be in a theorem verifier? It seems like all the steps to verify > a proof are very straightforward and simple. The steps seem ideally > suited to machine. The bug in the verifier could be the kind of bug which may exist in any other piece of software. But I said bug in the source of a proof meaning what you feed to the verifier even if the verifier itself does not have bugs. I have been thinking about that and the most dangerous possibilities I could think of are: a) You give the verifier the wrong theorem to prove instead of what you have in mind. b) One of the intermediate lemmas you say to the verifier are correct is not actually correct. b) can be solved if the verifier verifies *everything*. Of course that means someone actually needs to write down a formal proof for every trivial little thing like for example that the union of finite many finite sets is finite. a) doesn't seem particularly dangerous. Obviously just because a) and b) are the only possibilities I could think of for bugs in the proof doesn't mean no other possibilities exist. Once again more tests are needed. > Very interesting. This Mizar system and the QED project are > exactly what I am suggesting. My question is why haven't they evolved > into the standard way of publishing proofs? Presumably because most people are fairly satisfied with the way things are now. I had looked into Mizar myself at some point. Information was hard to come by. For example I was only able to find a tutorial for an older version of the language. I didn't see any formal specification. I think there's only one implementation and it's closed source. If I am correct in all that then Mizar is a no no as far as I'm concerned. > If we had some standard naming reservation system than you could use > an old theorem from one verified proof in the database as a basis > axiom for a new proof. What am I missing? One of the things I want to try out at some point is to write my > own proof verifier and see how it affects my productivity and > whether using it to verify proofs might introduce mistakes I wouldn't > otherwise make. So basically I believe more experimentation is > needed by as many mathematicians as possible before reaching > conclusions. I'm sure writing a machine-readable proof is more difficult than > taking some steps for granted or based on intuition - but the > advantage of the former is that it is virtually infallible. Perhaps. > Isn't > that what mathematics is all about? Rigorous and undeniable steps > from axioms to theorems? I happen to agree with you on that but I may be in the minority. I'm sure you would find many mathematicians who consider beauty just as important and they won't think that typing a bunch of tedious details for the benefit of a computer adds anything to the beauty of the ideas behind the proof. If anything it detracts from them. Apart from that noone wants to get bored out of their head. -- This film, alas, is not The Tempest, a self-referential perspective on an artist who understands his own magic. It is instead an echo of that artist's misunderstanding of himself. http://www.imdb.com/title/tt0091670/usercomments?start=10 === Subject: Re: Computer-verified Mathematical Proof as Standard <7a14kdF1t4409U1@mid.dfncis.de> posting-account=6ea2ugoAAACnO44ASKspIG0s--Ju5Ekb Gecko/20020604,gzip(gfe),gzip(gfe) Mizar has its own more natural language oriented format. Example > seen here:http://lipa.ms.mff.cuni.cz/~urban/xmlmml/html_abstr.930/00mptp_chall_.. . But it seems that this can be readily translated to FOF. For the > MPTP challenge see here:http://www.cs.miami.edu/~tptp/MPTPChallenge/MPTPChallenge.tgz > (Attention >7MB file) What is FOF and what is MPTP ? === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=6ea2ugoAAACnO44ASKspIG0s--Ju5Ekb Gecko/20020604,gzip(gfe),gzip(gfe) Note that many computer programmes have silly bugs > which a human reader would immediately pick up but a compiler might > not. So it is possible that due to such a silly bug in the source > of a proof the computer will say that a proof is correct when > actually it is not. No, that's not what would happen. If the *proof verifier* is > buggy, it might reject a correct proof or accept an incorrect > proof. If the human is confused, he might decide that the > proof said one thing when it really said a different thing. But the proof itself says what it says, and can't say anything > different from that. By the same reasoning a computer programme cannot have bugs because it says what it says and the computer is just executing the instructions. -- Who's your mama? === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=Rqa4sAoAAAC88UYanCtJRUF4S6TUauGA Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > Note that many computer programmes have silly bugs > which a human reader would immediately pick up but a compiler might > not. So it is possible that due to such a silly bug in the source > of a proof the computer will say that a proof is correct when > actually it is not. No, that's not what would happen. If the *proof verifier* is > buggy, it might reject a correct proof or accept an incorrect > proof. If the human is confused, he might decide that the > proof said one thing when it really said a different thing. But the proof itself says what it says, and can't say anything > different from that. By the same reasoning a computer programme cannot have bugs > because it says what it says and the computer is just executing > the instructions. No, not at all. A bug in a program is usually a difference between the This corresponds to the case I described above where the human believes the proof means one thing but as actually written it means something else. Marshall === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=6ea2ugoAAACnO44ASKspIG0s--Ju5Ekb Gecko/20020604,gzip(gfe),gzip(gfe) Note that many computer programmes have silly bugs > which a human reader would immediately pick up but a compiler might > not. So it is possible that due to such a silly bug in the source > of a proof the computer will say that a proof is correct when > actually it is not. No, that's not what would happen. If the *proof verifier* is > buggy, it might reject a correct proof or accept an incorrect > proof. If the human is confused, he might decide that the > proof said one thing when it really said a different thing. But the proof itself says what it says, and can't say anything > different from that. By the same reasoning a computer programme cannot have bugs > because it says what it says and the computer is just executing > the instructions. No, not at all. A bug in a program is usually a difference between the > This corresponds to the case I described above where > the human believes the proof means one thing but as > actually written it means something else. It also corresponds to what I described when I said the computer will say that a proof is correct when actually it is not. === Subject: Re: Computer-verified Mathematical Proof as Standard > You might find interesting. I've previously looked at Metamath, but this seems much more usable. -- Beware of bugs in the above code; I have only proved it correct, not tried it. -- Donald E. Knuth === Subject: Re: Computer-verified Mathematical Proof as Standard > Furthermore, why isn't there a centralized proof web/database that > contains all the axioms and verified proofs in some standard format? > If we had some standard naming reservation system than you could use > an old theorem from one verified proof in the database as a basis > axiom for a new proof. You might find interesting. > This looks definively nice. To solve all the already mentioned problems, like different styles, different logics, the wiki could be self explaining. Right down to the primitives it uses in its machinery. Bye === Subject: Re: Computer-verified Mathematical Proof as Standard Cc: freer@mit.edu posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) Furthermore, why isn't there a centralized proof web/database that > contains all the axioms and verified proofs in some standard format? > If we had some standard naming reservation system than you could use > an old theorem from one verified proof in the database as a basis > axiom for a new proof. You might find interesting. A formal mathematics wiki that only allows true statements. This is an interesting idea. I have two comments: 1. As discussed, there are various different logics and hence what is true in one is not necessarily true in another. How would vdash handle this? 2. I'm not sure mathematicians will be prepared to just donate their proofs anonymously and unattributed. Won't they want someway of identifying and authenticating who proved what? Idea: Maybe there could be a place for anyone to put conjecture statements on the wiki, but the proofs of those conjectures must be submitted by one author, and only accepted if true, and the author would get credit and sole access to write some paragraph on the proof page. -Andrew. === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) > You might find interesting. > 1. As discussed, there are various different logics and hence what >is true in one is not necessarily true in another. How would vdash >handle this? It appears that the plan is to stick to classical logic. This is a reasonable decision since the vast majority of existing mathematics is based on classical logic. > 2. I'm not sure mathematicians will be prepared to just donate their >proofs anonymously and unattributed. Won't they want someway of >identifying and authenticating who proved what? This is an astute point which doesn't seem to be addressed directly in any of the documentation. It seems like it shouldn't be too hard to add such a feature, though. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard > You might find interesting. > 1. As discussed, there are various different logics and hence what >is true in one is not necessarily true in another. How would vdash >handle this? >It appears that the plan is to stick to classical logic. This is a >reasonable decision since the vast majority of existing mathematics is based >on classical logic. > 2. I'm not sure mathematicians will be prepared to just donate their >proofs anonymously and unattributed. Won't they want someway of >identifying and authenticating who proved what? Why is it necessary that the proof be anonymous? >This is an astute point which doesn't seem to be addressed directly in any >of the documentation. It seems like it shouldn't be too hard to add such a >feature, though. >Tim Chow tchow-at-alum-dot-mit-dot-edu -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) Furthermore, why isn't there a centralized proof web/database that > contains all the axioms and verified proofs in some standard format? > If we had some standard naming reservation system than you could use > an old theorem from one verified proof in the database as a basis > axiom for a new proof. You might find interesting. A formal mathematics wiki that only allows true statements. This is > an interesting idea. I have two comments: 1. As discussed, there are various different logics and hence what > is true in one is not necessarily true in another. How would vdash > handle this? 2. I'm not sure mathematicians will be prepared to just donate their > proofs anonymously and unattributed. Won't they want someway of > identifying and authenticating who proved what? Idea: Maybe there could be a place for anyone to put conjecture > statements on the wiki, but the proofs of those conjectures must be > submitted by one author, and only accepted if true, and the author > would get credit and sole access to write some paragraph on the proof > page. > -Andrew. I tell you the truth, those who have earned will be recognized. I will show you the way. 3SAT is Not Too Easy. A Future Retrospective In Computational Complexity Read G.9adel's Lost Letter and P=NP. Also check out Iannis Tourlakis' paper on extensions of these lower bound. What I find nice about this type of proof is you get lower bounds by finding new algorithms. How to Solve P=NP? G.9adel's Lost Letter and P=NP was a good start but we all guessed wrong. G.9adel's Lost Letter and P=NP led to a discussion and proof that mathsf{NLOG} is closed under complement. Perhaps we should put P=NP on theory exams and hope dots [...]. I am serious. All the properties are easy to check. The main point is if the machine guesses wrong during the computational complexity theory, P = NP if and only if there exists a Turing machine T and a natural number k such that (ri) < nk, the question already considered by Godel! Computational Complexity: G.9adel Prize 12 Apr 2006 [...] Even proving it couldn't be done would solve the P/NP puzzle. [...] NP because it seems very counter intuitive to say that we can check an exponential number of [...]. Obviously it's not a formal proof, but it is an intuitive coding. Imagine some time in the future the problem has been solved and we programmer who solved the P vs. NP problem. [Note: I only use the word ingenious here as it is cited in the P vs. NP problem description: http://www.claymath.org/millennium/P vs NP/ from the Clay Mathematics Institute: (excerpt )However, this apparent difficulty may only reflect the lack of ingenuity of your programmer.] Well, I thought I may not be able to prove P = NP by traditional means, but I can certainly prove NP ! [....]. Hey Atwood, here's a cashes yet another nice check from the controversy his blog has [....] proof, establishing that 3-SAT could be reduced to 2SAT in O(n3) time. What can I say? It is the Power of randomness: Efficient Computation & P vs. NP. G.9adel's letter to von Neumann [1954]: [...] Probabilistically Checkable Proofs (PCPs). Claim: The Riemann Hypothesis. Prover: (argument)[...] Every proof can be efficiently transformed to ZK proof [...]. An Argument for P=NP: the winner needn't provide a constructive proof that P=NP. 2. Despite Godel's [...] Godel, writing of course before the modern P=?NP framework, inquires [.....]. By definition, a guess for an NP problem is checkable in polynomial time. [...] Imagine possibilities, conceive, wonder, speculate, discover! Complex Multi-Tiered Abstracts: Abstract: It is shown how to restrict G.9adel's system $T$ of recursion in all higher [...] Abstract: We discuss the forcing approach to P==NP problem. [...] sound proof-systems) showed how to efficiently check proofs of [...]. Then mathematics, science, technology, innovation, and most importantly advances in medicine, (still governed by fundamental physics--bases of reality) become more like storytelling. Imagination is more important than intelligence. --Albert Einstein The Tale of NP-Completeness By [...] 1931 [CapitalEth] Kurt G.9adel introduces the incompleteness theorems [...]. First Formal Proof that P ? NP. By giving a poly-time solution for the matching search problem, [....] find a proof then check it? - [YES]. Is nature non deterministic? [YES]. A Short History of A Short History of Computational Complexity By Martin Musatov It was a dark night in Los Angeles. I was curled up on a futon at a friend's downtown loft (4th & Broadway), writing a USENET post at 4 poked at the tiny QWERTY keyboard of my BlackBerry. -- Martin Musatov http://MeAmI.org Better than Google alone, plus no ads. === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 1.1.4322; eSobiSubscriber 2.0.4.16; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Furthermore, why isn't there a centralized proof web/database that > contains all the axioms and verified proofs in some standard format? > If we had some standard naming reservation system than you could use > an old theorem from one verified proof in the database as a basis > axiom for a new proof. You might find interesting. -- > --Tim Smith Below is NP=P machine checkable proof text. It points to M.I.T. as part of the proof and it was generated by typing the words NP=P Complete Machine Checkable Proof in the pre-html Custom Search at http://MeAmI.org. For Verification here is the link: http://meami.org/?cx=000961116824240632825%3A5n3yth9xwbo&cof=FORID%3A10&ie=U TF-8&q=NP%3DP+Complete+Machine+Checkable+Proof&sa=Search#1271 And the text: NP (complexity) - The existence of problems outside both P and NP- complete in this case was established by Ladner. [....] A nondeterministic machine can simply nondeterministically run the [...] NP can be seen as a very simple type of interactive proof system, [...] solvable by probabilistically checkable proofs where the verifier uses [...] http://en.wikipedia.org/wiki/NP (complexity) Complexity Zoo:P - Qwiki [...] The canonical P-complete problem is circuit evaluation: given a [....] PCP(r(n),q(n)): Probabilistically Checkable Proof [...] It was shown in [CPO7] that if the NP Machine Hypothesis holds, then mathsf{P}^{mathrm{SAT}[1]} [...] http://qwiki.stanford.edu/wiki/Complexity Zoo:P List of complexity classes - NE, Solvable by a non-deterministic machine in exponential time with linear exponent [...] NP, YES answers checkable in polynomial time (see complexity classes P and NP) [...] Solvable in polynomial time. P-complete, The hardest problems in P to solve on parallel computers [...] PCP, Probabilistically Checkable Proof [...] http://en.wikipedia.org/wiki/List of complexity classes School of Informatics Courses: Computer Science 4: Computational [...] Proof that NP=P if and only if satisfying assignments can be found for [...] Use of the technique to show there is an NP-complete problem in non-deterministic linear time. [...] Definition of Randomized Turing machine (RTM) and randomized time complexity [...] to theory of probabilistically checkable proof (PCP) systems. [...] http://www.inf.ed.ac.uk/teaching/courses/cmc/lecture log.html A Note on Non-complete Problems in NP[...]NPP (in the classical Turing machine setting) if P{NP is assumed. In [.....] So as in the proof of Theorem 1 we can write and check (again by means [...] http://linkinghub.elsevier.com/retrieve/pii/S0885064X9990537X versions Complexity classes with complete problems between P and NP-Cin order to check that a gb'en string w is in L', the robust machine only needs [.....] the difference between P and NP is the ability of the NP- machines to manufacture [...] shown previously to be complete in ilk. The details of the proof [...] http://www.springerlink.com/index/p6562j95u353rl14.pdf Complexity class - Computer Science Complexity class: A community- built table of topics, including P, NP, and NP-complete [...] In complexity theory, the notion of P-complete decision problems is useful in [....] Turing machine with an oracle for some decision problem in NP. [...] In computational complexity theory, a probabilistically checkable proof (in [...] http://computerscience.freebase.com/view/base/views/complexity class [PDF] 1 Overview 2 Summary of Contents machine complexity theory to include various other computational models such as [...] deterministic Turing machines and defines the basic complexity classes, including P, NP, PSPACE [...] Cook's theorem that SAT is NP-complete is proven, and reductions are [...] Given a short proof, is it possible to check correctness in [...] http://www.utdallas.edu/~dxd056000/cs6382/review.pdf begin{section}{NP and P/poly }end{section} For a sketch of the proof, [...] $(s 1,[...],s l)$, first check to make sure that $|s i| < (ki)^k$ for $1leq i leq l$. [....] we present a Turing machine that decides the $Sigma 3 P$-complete [...] http://www-math.mit.edu/~spielman/AdvComplexity/2000/lecture5.tex Np: Definition from Answers.com The existence of problems outside both P and NP-complete in this case was established by Ladner. [....] A nondeterministic machine can simply nondeterministically run the [...] NP can be seen as a very simple type of interactive proof system, [...] as the problems solvable by probabilistically checkable proofs where the [...] http://www.answers.com/topic/np === Subject: Re: Computer-verified Mathematical Proof as Standard > It is an objective fact that the XML people did not do a good > job making it human readable. It is my personal opinion that > they were not competent to do so. I would consider it subjective--I think XML is rather human-readable. The main problem that I think people have is that XML is designed to delineate all structure, and people would rather that structure be inferred. 2 % 3 $ 4 would be an ambiguous, but 2 3 4 is not. A lot is also dependent on the structure that people impose on XML files. 234 is definitely harder to read. One also needs to consider what exactly human-readable means. 99% or more of XML will not be written by hand as they are merely storage formats or transit formats. The primary case where they will be read by humans is in debugging, or possibly some explanatory prose. In this, I would say it is definitely human-readable (compared to binary protocols). -- Beware of bugs in the above code; I have only proved it correct, not tried it. -- Donald E. Knuth === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Interesting. As a computer scientist we think a lot about what makes > language both machine-readable and human-readable. One of the design > goals of XML for example was to do both. It might be possible to come > up with a language for formal proofs that achieves both goals. In my personal opinion, the XML people did not a good job in making it > human-readable. It is an objective fact that the XML people did not do a good > job making it human readable. It is my personal opinion that > they were not competent to do so. Every web site of the 40 Petrabytes (40,000 GB) that are currently online are written in HTML as a base, which is essentially an application of XML (technically they both descend from SGML). Clearly, regardless of the W3Cs alleged incompetence, one cannot argue that it is a virtually universal language that both humans and machines parse. I'm not suggesting that the ideal formal proof language would look like XML. I imagine it would look as similar to current proofs as possible while (a) making the minimum changes to make it both machine- readable and machine-verifiable; and (b) taking advantage of computer- aided features not available in static natural language. Eventually the ability of the verification algorithms are going to get better at deducing how to get from some well-formed formula X to some other well-formed formula Y based on the large set of available premises. This is essentially what mathematicians are good at when reading a proof that omits some of these steps. When that happens the formal language proofs will become shorter and eventually approach (or even surpass) the natural language proofs. I imagine in 50 years time, all mathematicians will be working in a formal language in an IDE, not because they are interested in more correctness - simply because it will be easier to have the computer at your side, and will speed up research. We could in fact get there today, but all the systems (Mizar, HOL, Isabelle, etc) have had so little investment - and so few experienced developers work on them. Basically there isn't the impetus or money to make it happen quickly, probably because most mathematicians do not yet appreciate the potential benefit to their productivity. -Andrew. === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=6ea2ugoAAACnO44ASKspIG0s--Ju5Ekb Gecko/20020604,gzip(gfe),gzip(gfe) Eventually the ability of the verification algorithms are going to get > better at deducing how to get from some well-formed formula X to some > other well-formed formula Y based on the large set of available > premises. This is essentially what mathematicians are good at when > reading a proof that omits some of these steps. Of course we don't want the algorithms to get too good because then they will start competing with human mathematicians >;- When that happens the formal language proofs will become shorter and > eventually approach (or even surpass) the natural language proofs. I > imagine in 50 years time, all mathematicians will be working in a > formal language in an IDE, not because they are interested in more > correctness - simply because it will be easier to have the computer at > your side, and will speed up research. In what way will it speed up research ? > We could in fact get there today, but all the systems (Mizar, HOL, > Isabelle, etc) have had so little investment - and so few experienced > developers work on them. Basically there isn't the impetus or money > to make it happen quickly, probably because most mathematicians do not > yet appreciate the potential benefit to their productivity. Again , what benefit to his productivity can a present day mathematician hope to gain if more investment was made on proof verifiers ? -- Who's your mama? === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Again , what benefit to his productivity can a present day > mathematician hope to gain if more investment was made on proof > verifiers ? Well if we assume that: - we can design a formal proof language that is machine-readable - the language is as human-readable as current natural language proofs - the length of a proof in that language is on-par with a natural language proof - the software gets good at finding truth-preserving pathways between formulas Then the software that a mathematician uses to write proofs would be able to follow along with them, so you would get all of the benefits that programmers get in their IDEs: - auto-completion - on-the-fly error checking - top-down structure views - dependency analysis - hyperlinked definition lookup - refactoring engine - etc Eventually, maybe, it would get to the stage where the software could actually help find the proof itself. Wouldn't it be nice to state the proof? ...or at least fills in some of the non-obvious steps that would *not* be omitted in a present day natural language proof? A comment was made that computers are superfast superimbeciles. I am not so sure that is fair. Out of the factory with no software this is the case. Getting away from that is a software problem. Search algorithms and machine learning algorithms have come a long way. I am not so sure that the full brunt of these algorithms have been applied to the type of proof software under discussion. -Andrew. === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=6ea2ugoAAACnO44ASKspIG0s--Ju5Ekb Gecko/20020604,gzip(gfe),gzip(gfe) Again , what benefit to his productivity can a present day > mathematician hope to gain if more investment was made on proof > verifiers ? Well if we assume that: > - we can design a formal proof language that is machine-readable > - the language is as human-readable as current natural language > proofs > - the length of a proof in that language is on-par with a natural > language proof > - the software gets good at finding truth-preserving pathways between > formulas The first 2 tasks are fairly easy , they may even be already true. The 3rd task may be impossible. I'm not sure what you mean with the 4th task. > Then the software that a mathematician uses to write proofs would be > able to follow along with them, so you would get all of the benefits > that programmers get in their IDEs: > - auto-completion > - on-the-fly error checking > - top-down structure views > - dependency analysis > - hyperlinked definition lookup > - refactoring engine > - etc I don't know what top-down structure views is but the rest are fairly trivial ; I don't think they would affect the speed of typing proofs. Well , auto-completion might but you get that with any decent text editor , it hasn't got much to do with proof verification. > Eventually, maybe, it would get to the stage where the software could > actually help find the proof itself. Wouldn't it be nice to state the > proof? ...or at least fills in some of the non-obvious steps that > would *not* be omitted in a present day natural language proof? It wouldn't be nice if it causes some mathematicians to lose their jobs. But that's a completely different discussion. -- Who's your mama? === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Then the software that a mathematician uses to write proofs would be > able to follow along with them, so you would get all of the benefits > that programmers get in their IDEs: > - auto-completion > - on-the-fly error checking > - top-down structure views > - dependency analysis > - hyperlinked definition lookup > - refactoring engine > - etc I don't know what top-down structure views is but the rest are > fairly trivial ; I don't think they would affect the speed of > typing proofs. Well , auto-completion might but you get that with > any decent text editor , it hasn't got much to do with proof > verification. No, I don't just mean auto-completing and error-checking latex macros, I am talking about larger logical sections of the proof. Entire forumalas, or a entire sequence of deductions. It is my understanding that some proofs take years to complete, so I'm not too sure how these things can be fairly trivial. -Andrew. === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) >We could in fact get there today, but all the systems (Mizar, HOL, >Isabelle, etc) have had so little investment - and so few experienced >developers work on them. Basically there isn't the impetus or money >to make it happen quickly, probably because most mathematicians do not >yet appreciate the potential benefit to their productivity. I think you're too optimistic that we could get there *today*, if by getting there you mean a benefit to *productivity*. We would get increased confidence in the correctness of our published proofs, which is a benefit to be sure, but I do not believe that incorrect proofs are currently a bottleneck in mathematicians' *productivity*. But we are getting close to the point where proofs are getting so large that they are difficult to check. Sooner or later, bugs in the mathematical literature *could* become a productivity killer. So it's good to be proactive and start implementing a fix now before the problem overtakes us. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=5t-ZfgkAAACU7ydoC4Cq-xVNAFsq481f Gecko/2009061622 Mandriva/1.9.0.11-0.1mdv2009.1 (2009.1) Firefox/3.0.11,gzip(gfe),gzip(gfe) Take look at Isabelle proof assistant. It is a free alternative to Mizar and maybe Isabelle is more flexible and powerful that Mizar. (I'm not an expert in this however.) http://isabelle.in.tum.de === Subject: Re: Computer-verified Mathematical Proof as Standard <> If also yes, than why isn't it required that the centerpiece of any <> published proof be the source code for such a computer verification? <> Because it would be necessary to prove that the code had no errors. >This is a completely illogical position. A proof must be published in >some language. Currently most are published in a mix of natural >language and mathematical notation. Is it necessary to prove that the >humans that read and approve these proofs contain no errors before >making them theorems? Of course not. >What I am suggesting is that we specify a standard language that all >mathematical proofs are written in, that both humans and computers can >read and verify. It seems this is exactly what Mizar is. It seems as >though if we did this it would be far quicker and more rigorous than >what we do now. It also seems like the basic rules of transformation >from one statement to another are so simple, that any bugs contained >in verifier implementations would quickly and easily be eradicated. <> Principia Mathematica, by Burtran Russel was a large three volume <> work that did no more than prove the very basics of logic and set theory. <> Upon publication, besides the usually errata, it was found to have fatal <> flaws. >Exactly my point. If Principia Mathematica was written in machine- >readable format, than the verifier software would of caught these >errors wouldn't it? > -Andrew. Not necessarily. One could cite an incorrect formulation, and the verifier would accept this; otherwise, one might have to redefine addition in every number theory proof. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Computer-verified Mathematical Proof as Standard >Is it true that all proofs of mathematical theorems must contain a >series of well-defined logical deductions from some set of axioms and >rules? >If yes, is it also true that all of these deductions could be written >in such a way that a computer program can infallibly verify the >correctness of these steps? >If also yes, than why isn't it required that the centerpiece of any >published proof be the source code for such a computer verification? >ie Shouldn't the center of every proof be a machine-readable theorem >and machine-readable steps to undeniably deduce that theorem? The >English should just be annotation essentially. The problem is that at the present time these proofs, written in computerese, would be too long. For some of them, the proof, in natural deduction, might be only about three to five times the length of the present proofs. Most of the present proofs are close enough to formal to be verified by people. Computers are superfast subimbeciles, and need to be instructed most carefully, which is too carefully for reasonable length papers. However, there are theorems for which a computer was carefully instructed to go through all the steps necessary, and for which we do not have a reasonably human readable version of the proof. >Furthermore, why isn't there a centralized proof web/database that >contains all the axioms and verified proofs in some standard format? >If we had some standard naming reservation system than you could use >an old theorem from one verified proof in the database as a basis >axiom for a new proof. >What am I missing? > -Andrew. We do not have a standard language. One can add macros to the computer proof; for example, in the basic language, one would have to prove e_1 = e_2, e_2 = e_3, ..., while one the explicit description of the step. For example, proving the associative law for addition from the Peano Postulates, one now does (a +b) + 0 = a+b = a+(b+0) if (a+b)+c = a+(b+c), then (a+b)+c' = ((a+b)+c)' = (a+(b+c))' = a+(b+c)' = a+(b+c') Then (a+b)+c = a+(b+c) by induction and universal generalization Now how would this have to be done in a computer formal proof? 1 (a+b)+0 = a+b definition of addition of 0 2 b = b+0 definition of addition of 0 3 a+b = a+(b+0) substitution of equals 4 (a+b)+0 = a+(b+0) 1, 3, transitivity of = I will leave out the rest; as you can see, the proofs get lengthy. If we have something like, in a similar manner, the whole thing would have to be repeated. People can think; computers can only carry out instructions. While it is true that any theorem has a completely computer verified formal proof, and possibly some should have a more formal proof published, as of yet it generally takes too much work to even produce the formal proof. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > (a +b) + 0 = a+b = a+(b+0) if (a+b)+c = a+(b+c), then > (a+b)+c' = ((a+b)+c)' = (a+(b+c))' > = a+(b+c)' = a+(b+c') It's an interesting example. So the question is given something like (a+b)+c' = ((a+b)+c)' and the huge list of axioms and results, can the computer deduce which one you used to perform this step? Or would you necessarily have to tell it that I'm using axiom (x+y') = ((x+y)') where x = (a+b) and y = c. In this specific case I can imagine creating a parse tree of both sides and then performing some kind of diff algorithm against them. Then factor out the common parts into a pattern, and then searching the axiom list for that pattern. Perhaps there would be a way to bind this in realtime with some kind of auto completion feature (like intellisense) in the editor software. Maybe it could make a guess and provide a short-list in a menu for you to select, to remove some of the tedium. Once the explanation step has determined it doesn't necessarily be displayed inline at that point, perhaps it can be linked to a second longer file that is published like an appendix. As Patricia Shanahan pointed out, we already have built up many tactics to manage this sort of complexity in computer programming. -Andrew. === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) >While it is true that any theorem has a completely computer >verified formal proof, and possibly some should have a more >formal proof published, as of yet it generally takes too >much work to even produce the formal proof. Too much work for the average mathematician, yes. But too much work for someone with an interest in the subject, no. See for example http://www.cs.ru.nl/~freek/100 for a list of theorems that have been fully formalized. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard <4a3bd44a$0$515$b45e6eb0@senator-bedfellow.mit.edu> posting-account=6ea2ugoAAACnO44ASKspIG0s--Ju5Ekb Gecko/20020604,gzip(gfe),gzip(gfe) While it is true that any theorem has a completely computer >verified formal proof, and possibly some should have a more >formal proof published, as of yet it generally takes too >much work to even produce the formal proof. Too much work for the average mathematician, yes. But too much work for > someone with an interest in the subject, no. See for example http://www.cs.ru.nl/~freek/100 for a list of theorems that have been fully formalized. I think Andrew's vision is that every mathematical proof will be computer verified before being published in a journal. So it shouldn't be too much work for the average researcher mathematician. -- Who's your mama? === Subject: Re: Computer-verified Mathematical Proof as Standard <4a3bd44a$0$515$b45e6eb0@senator-bedfellow.mit.edu> posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > http://www.cs.ru.nl/~freek/100 for a list of theorems that have been fully formalized. Impressive list. PNT surprised me, as did a number of others. Anyone up to tacking the classification theorem? :-) :-) === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) >Impressive list. PNT surprised me, as did a number of others. Yes, I remember being very impressed when Avigad announced his proof. FYI, it turned out that the Erdos-Selberg elementary proof was very helpful here. The complex-analytic proof is quite a bit more cumbersome because you need to develop the complex-analytic machinery along the way. I'm not sure which proof the HOL Light proof is based on. >Anyone up to tacking the classification theorem? :-) :-) I'd be happy just to live to see the completion of the GLS project! -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) >So you might have a verifier, and proof automation tools, etc.. that >simultaneously support classical and intuitionistic logic. About >the differences in quantifiers I am not so sure. One issue, which may be more of a data management issue than a fundamental problem, is that intuitionistically you will want to separately track the two statements set S is not infinite and set S is finite (e.g., if the former is a known theorem while the latter is still conjectural), whereas classically there is no distinction. The classical user might be confused that set S is finite is marked as a conjecture. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard > So you might have a verifier, and proof automation tools, etc.. that > simultaneously support classical and intuitionistic logic. About > the differences in quantifiers I am not so sure. One issue, which may be more of a data management issue than a fundamental > problem, is that intuitionistically you will want to separately track > the two statements set S is not infinite and set S is finite (e.g., > if the former is a known theorem while the latter is still conjectural), > whereas classically there is no distinction. The classical user might > be confused that set S is finite is marked as a conjecture. intuitionistic ontology is different? Maybe yes, the vocabulary can be the same, I can also form an antonym in intuitionistic logic, but some inferences are lacking, like double negation. Bye === Subject: Re: Computer-verified Mathematical Proof as Standard <4a3bb03e$0$500$b45e6eb0@senator-bedfellow.mit.edu> <4a3bcce8$0$515$b45e6eb0@senator-bedfellow.mit.edu> posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) >So you might have a verifier, and proof automation tools, etc.. that >simultaneously support classical and intuitionistic logic. About >the differences in quantifiers I am not so sure. One issue, which may be more of a data management issue than a fundamental > problem, is that intuitionistically you will want to separately track > the two statements set S is not infinite and set S is finite (e.g., > if the former is a known theorem while the latter is still conjectural), > whereas classically there is no distinction. The classical user might > be confused that set S is finite is marked as a conjecture. Well this would be a question of which module you import: import intuitionistic logic or import classical logic If you depend on set S is finite and changed between them then your proof would no longer verify. -Andrew. === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) >Well this would be a question of which module you import: import intuitionistic_logic or import classical_logic If you depend on set S is finite and changed between them then your >proof would no longer verify. As I said, I don't think the obstacle is *fundamental* here, but I also believe that you're underestimating the data management problems. statements, all expressed in a single language, and depending on which logic we want, some will come out as theorems and some won't. In reality, things are not that simple, because classically there will be some objects whose existence has been classically proven, but not intuitionistically proven. Classically, you'll want to introduce *names* for some of those objects so that you can refer to them. But then do we mark any statement involving that name intuitionistically conjectural? Some such statements might in fact be intuitionistically proven, but by some means that bypasses the classically proven but intuitionistically suspect lemma. Again, I think that your best bet at this stage is to move from armchair theorizing to learning one or more of the standard systems that are already learning how to use Mizar or HOL Light. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard <4a3bcce8$0$515$b45e6eb0@senator-bedfellow.mit.edu> <4a3bd6be$0$515$b45e6eb0@senator-bedfellow.mit.edu> posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) >Well this would be a question of which module you import: import intuitionistic logic or import classical logic If you depend on set S is finite and changed between them then your >proof would no longer verify. statements, all expressed in a single language, and depending on which logic > we want, some will come out as theorems and some won't. In reality, things are not that simple, because classically there will > be some objects whose existence has been classically proven, but not > intuitionistically proven. Classically, you'll want to introduce *names* > for some of those objects so that you can refer to them. But then do we > mark any statement involving that name intuitionistically conjectural? Here is a more detailed explanation of what I was imagining with respect to the data management issues as you call them. The basic system works on compilation units, which are individual files. Within a compilation unit you may: (a) define a propositional calculus (b) define aliases, names and truth-preserving rules based on previous ones (c) state axioms (d) make statements (which must deducibly true from previous statements, axioms and rules) (e) import other compilation units Each compilation unit has its own namespace, and names from one compilation unit can be selectively imported into another. There is some central registry where individuals and organizations can register their identity and get a key to sign the compilation units they produce. (Perhaps reusing the Internet domain name system as a basis.) So for example the math department at MIT might register the name edu.mit and create a compilation unit in which they define what they consider to be the foundation of intuitionistic logic as edu.mit.intuit logic. Once signed these compilation units can be distributed and copied in whatever manner the author sees fit. There is no need for centralization of anything other than the signing authority. You may then create a new compilation unit that imports some objects and names from the edu.mit.intuit logic into your compilation unit. Because all the compilation units are universally named and signed, the object edu.mit.intuit logic.infinite set is also uniquely defined. This means that the system is agnostic to the specific names for things. What you consider to be a lattice is bound to either (a) what you defined it to be or (b) the definition you endorsed by importing it into your compilation unit. When a compilation unit is verified, the machine will first check that all the language is well-formed, then it will check that all the statements are true, and then if successful, output a summarizable report of the axioms and truth-preserving rules that were used to determine the truth of each statement. When published this output could be included as an appendix in the compilation unit, in a similar way as when a programmer shows the output of a program after the source code. How does this description of naming fit into the concerns you stated regarding objects that are conjectural in intuitionistic logic but proven in classical logic? This isn't clear to me. -Andrew. === Subject: Re: Computer-verified Mathematical Proof as Standard > How does this description of naming fit into the concerns you stated > regarding objects that are conjectural in intuitionistic logic but > proven in classical logic? This isn't clear to me. > -Andrew. Your publishing will be a stream with updates. === Subject: Re: Computer-verified Mathematical Proof as Standard <4a3bcce8$0$515$b45e6eb0@senator-bedfellow.mit.edu> posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > How does this description of naming fit into the concerns you stated > regarding objects that are conjectural in intuitionistic logic but > proven in classical logic? This isn't clear to me. Your publishing will be a stream with updates. Ummm. What do you mean? -Andrew. === Subject: Re: Computer-verified Mathematical Proof as Standard <4a3bcce8$0$515$b45e6eb0@senator-bedfellow.mit.edu> posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) > How does this description of naming fit into the concerns you stated > regarding objects that are conjectural in intuitionistic logic but > proven in classical logic? This isn't clear to me. Your publishing will be a stream with updates. Ummm. What do you mean? > -Andrew. I mean what you read. If you do not understand pick up a dictionary as you read. Try to keep up. Marty === Subject: Re: Computer-verified Mathematical Proof as Standard > In reality, things are not that simple, because classically there will > be some objects whose existence has been classically proven, but not > intuitionistically proven. Classically, you'll want to introduce *names* > for some of those objects so that you can refer to them. But then do we > mark any statement involving that name intuitionistically conjectural? > Some such statements might in fact be intuitionistically proven, but by > some means that bypasses the classically proven but intuitionistically > suspect lemma. Interesting approach. Marking theorems as either intuitionistic or classical. And when then subsequent theorems are formed, all based on intuitionistic theorems and by intuitionistic rules, we have again an intuitionistic theorem. One simple problem is here. A theorem might have different competing proofs. This cries for multi marking! Or a theorem might have a classical proof right now, but later we will find an intuitionistic proof. This cries for the revision of markings! Anyway, I saw, that for example in metamath, competing proofs are there, but they have each individual identifiers. And only in the free text comment section of a theorem, such relationships between theorems are found. Bye === Subject: Re: Computer-verified Mathematical Proof as Standard <4a3bb03e$0$500$b45e6eb0@senator-bedfellow.mit.edu> posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) >It was my understanding that all the proofs in mathematical topics >(like abstract algebra, analysis, topology, number theory, probability >and so on) can all be expressed using FOL? (or at least must be able >to if they are correct) You should really say that everything can be expressed in the first-order > language of set theory, and proved in ZFC. But morally speaking what you > say here is correct, with only minor caveats. (One such caveat: FOL is > *classical* logic, and people who accept only intuitionistic logic won't > like some of your FOL proofs.) Ok, so perhaps something more primitive is required for the atomic basis of the formal language in which the theorems, axioms and proofs are expressed. Perhaps if we provide a machine code in which one can define any propositional calculus it would provide sufficiently general building blocks such that one can express the axioms of FOL, ZFC, intuitionistic logic, Peano axioms and so forth. Perhaps there would be competing versions of these different modules in the database, and it would be up to each mathematician to choose which to build on. It would also be interesting to perform a dependency analysis as you say to see which axioms were actually used to prove theorem X. In reality there is no such thing as an absolute theorem. All theorems are in fact only theorems in the relative context of which axioms they need. I can prove any theorem X by simply making X an axiom. :) -Andrew. === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR 3.0.30729),gzip(gfe),gzip(gfe) > I can prove any theorem X by simply making X an axiom. Right, but there is soundness, not only validity... I.e. there is an underlying problem of meaning which, AFAIK, cannot really be formalised (in this sense, any formalisation is a reduction to an abstract game, just meaningless when taken on its own). -LV === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) >Right, but there is soundness, not only validity... I.e. there is an >underlying problem of meaning which, AFAIK, cannot really be >formalised (in this sense, any formalisation is a reduction to an >abstract game, just meaningless when taken on its own). It's true that there are problems with formalizing meaning. However, that isn't necessarily an obstacle to delegating the verification of proofs to a computer. As human users we still have to agree that the formal theorem that we give the computer to verify adequately expresses what we have in mind. But given that, the computer can check the correctness of any proof we offer for the theorem, without having to know what we mean by the theorem. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard <4a3bd76d$0$515$b45e6eb0@senator-bedfellow.mit.edu> posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR 3.0.30729),gzip(gfe),gzip(gfe) Right, but there is soundness, not only validity... I.e. there is an >underlying problem of meaning which, AFAIK, cannot really be >formalised (in this sense, any formalisation is a reduction to an >abstract game, just meaningless when taken on its own). It's true that there are problems with formalizing meaning. However, that > isn't necessarily an obstacle to delegating the verification of proofs to > a computer. I still don't get how that could work *in general*, given not only that meaning proper cannot be formalised, but also that even within the realm of computation, it turns out not everything is actually computable (or, at least, effectively computable). -LV === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) > It's true that there are problems with formalizing meaning. However, that > isn't necessarily an obstacle to delegating the verification of proofs to > a computer. I still don't get how that could work *in general*, given not only >that meaning proper cannot be formalised, but also that even within >the realm of computation, it turns out not everything is actually >computable (or, at least, effectively computable). The second concern first: not everything is effectively computable, yes. However, what we're talking about here is verifying that an explicitly exhibited proof is correct. The expectation of the mathematical community is that when someone announces a proof and publishes it, everyone else (or at least everyone who has sufficient training) can verify it. It is also understood that even though every natural-language argument skips some steps that are obvious, it is possible in principle to flesh out those details formally if necessary. If these expectations are correct, then no uncomputability issues arise. We're not talking about *finding* proofs, but *verifying a given proof*. For a formal proof, that is certainly a finite computation. Now, it is true that the process of fleshing out a human proof into a *formal* proof is not a purely mechanical process, so this part cannot be delegated to a computer. In practice, however, there have not been any cases where human beings have agreed that a human proof is correct but have run into fundamental obstacles converting it into a formal proof. Something is still gained by introducing the computer, because the very last part of the formalization can often be automated, and here the accuracy of the computer comes into play. The process is similar to programming an algorithm. I come up with an algorithm for sorting. We argue about it using natural language and come to a consensus that the algorithm is precisely specified and correct. Then comes the implementation phase. The computer does not know what sorting means. It just crunches away. Nevertheless, in practice this does not prevent us from implementing our sorting algorithms and agreeing that the computer is running the algorithm. We also gain confidence that the algorithm is correct after we've gone through the detailed process of implementing it and trying it out. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard <4a3d126a$0$501$b45e6eb0@senator-bedfellow.mit.edu> posting-account=6ea2ugoAAACnO44ASKspIG0s--Ju5Ekb Gecko/20020604,gzip(gfe),gzip(gfe) [...] > Now, it is true that the process of fleshing out a human proof into a > *formal* proof is not a purely mechanical process, so this part cannot > be delegated to a computer. In practice, however, there have not been > any cases where human beings have agreed that a human proof is correct > but have run into fundamental obstacles converting it into a formal proof. Has anyone tried to write a completely formal version of a proof involving Turing machines ? [...] > The process is similar to programming an algorithm. I come up with an > algorithm for sorting. We argue about it using natural language and come > to a consensus that the algorithm is precisely specified and correct. Then > comes the implementation phase. The computer does not know what sorting > means. It just crunches away. Nevertheless, in practice this does not > prevent us from implementing our sorting algorithms and agreeing that the > computer is running the algorithm. We also gain confidence that the > algorithm is correct after we've gone through the detailed process of > implementing it and trying it out. There is any important difference here in that you can test the algorithm to verify that it produces the correct results. But in general you cannot test proofs because they're not supposed to produce any results , the proof itself is the result. -- Who's your mama? === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > I still don't get how that could work *in general*, given not only > that meaning proper cannot be formalised, but also that even within > the realm of computation, it turns out not everything is actually > computable (or, at least, effectively computable). It's true that some things are not computable (halting), and also true that some things cannot be proven (godel). However our discussion is limited to verification of mathematical proofs - so what is an example of a valid mathematical proof such that its verification process is not computable? I am not sure such a thing exists - almost by definition. -Andrew. === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) I can prove any theorem X by simply making X an axiom. Right, but there is soundness, not only validity... I.e. there is an > underlying problem of meaning which, AFAIK, cannot really be > formalised (in this sense, any formalisation is a reduction to an > abstract game, just meaningless when taken on its own). If it can't be formalized than does it have a place in mathematics? Or, put another way - what is an example of something in mathematics that has meaning but can't be formalized? -Andrew. === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=F3H0JAgAAADcYVukktnHx7hFG5stjWse Trident/4.0; MathPlayer 2.10d; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.21022; .NET CLR 3.5.30729; .NET CLR 3.0.30729),gzip(gfe),gzip(gfe) > Is it true that all proofs of mathematical theorems must contain a > series of well-defined logical deductions from some set of axioms and > rules? If yes, is it also true that all of these deductions could be written > in such a way that a computer program can infallibly verify the > correctness of these steps? Wasn't that the so called Hilbert's program? I wouldn't think the difficulties are just technical (in the strict sense). -LV === Subject: Re: Computer-verified Mathematical Proof as Standard posting-account=EL3hgwoAAABtyRFrR2z7EBO1tnJeMiO7 Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) Is it true that all proofs of mathematical theorems must contain a > series of well-defined logical deductions from some set of axioms and > rules? If yes, is it also true that all of these deductions could be written > in such a way that a computer program can infallibly verify the > correctness of these steps? Wasn't that the so called Hilbert's program? The claim that all mathematical proofs are in principle formalizable is sometimes called 'Hilbert's thesis', and that is an important part of the idea behind Hilbert's program. However, also central to Hilbert's program is finding an axiomatization of mathematics and finding a finitary proof of the consistency of that axiomatization. MoeBlee === Subject: Re: Computer-verified Mathematical Proof as Standard ... > Once you start trying to do this in earnest, you will see that it is not > quite so easy as it might seem at first glance. It's very tedious to write > out a formal proof in full detail, so you need the computer to take some of > the drudgery out of it by filling in the obvious steps. This is harder > than it sounds. If you don't believe me, then you should first try your hand > at formalizing a non-trivial theorem in one of the standard systems. Then > we can talk. Although proofs and computer programs are different things, I see some analogies. A formal proof in full detail is something like an assembly language program. Humans can, in practice, only write very short assembly language programs, and tend to make mistakes when doing so. Traditional proofs, as they appear in mathematics papers, are something like algorithms in pseudo-code. They are easier for people to write and understand, but not good as computer input. A lot of research in computer science has been about constructing languages that can be mapped to assembly language, or equivalent, by a compiler but that are easier for people to read and write. High level programming languages combine abstraction, reuse, and modularization, but keep formality. Has there been a similar trend in proof languages? Patricia === Subject: Re: Computer-verified Mathematical Proof as Standard <4a3bad3f$0$500$b45e6eb0@senator-bedfellow.mit.edu> Cc: hack@watson.ibm.com posting-account=b59GCwoAAAAi5nnxSoswpnEj2IJlJetr Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > A formal proof in full detail is something like an assembly language > program. Humans can, in practice, only write very short assembly > language programs, and tend to make mistakes when doing so. Traditional proofs, as they appear in mathematics papers, are something > like algorithms in pseudo-code. They are easier for people to write and > understand, but not good as computer input. The translation of pseudo-code, or of a high-level language by a compiler, to something like assembly language typically changes the size of the code by a linear factor, except possibly in cases of recursive macro expansions (that, in practice, would blow the compiler's storage allocation). Translating a traditional math proof to a formal proof often involves an exponential explosion in size, and sometimes MUCH worse (Ackermann- like). That is because definitions have to be expanded, and some definitions may be recursive or even doubly-recursive. A lot depends on the notation of course: if the formal system only has the successor notation for numerals the exponential explosion is almost guaranteed. Now, perhaps there are automatic verifiers that can handle transformations whose validity has been proved separately -- but was THAT proof formal? Those kinds of proof are often of the kind that explodes in size. Michel. === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) >A lot of research in computer science has been about constructing >languages that can be mapped to assembly language, or equivalent, by a >compiler but that are easier for people to read and write. High level >programming languages combine abstraction, reuse, and modularization, >but keep formality. Has there been a similar trend in proof languages? Yes, certainly. All the standard languages are high-level in your sense. The main advantage of HOL Light is its elegant architecture, which makes it a very powerful and reliable system. A proof of the correctness of the 394 line HOL Light logical core even has been formalized. On the other hand HOL has the disadvantage that it sometimes cannot express abstract mathematics---mostly when it involves algebraic structures---in an attractive way. It *can* essentially express all abstract mathematics though. Another disadvantage of HOL is that the proof parts of the HOL scripts are unreadable. They can only be understood by executing them on the computer. Mizar on the other hand allows one to write abstract mathematics very elegantly, and its scripts are almost readable like ordinary mathematics. Also Mizar has by *far* the largest library of already formalized mathematics (currently it is over 2 million lines). However, Mizar has the disadvantage that it is not possible for a user to automate recurring proof patterns, and the proof automation provided by the system itself is rather basic. Also, in Mizar it is difficult to express the formulas of calculus in a recognizable style. It is not possible to bind variables, which causes expressions for constructions like sums, limits, derivatives, and integrals to look unnatural. let CONG_MINUS1_SQUARE = prove ('2 <= p ==> ((p - 1) * (p - 1) == 1) (mod p)', SIMP_TAC[LE_EXISTS; LEFT_IMP_EXISTS_THM] THEN REPEAT STRIP_TAC THEN REWRITE_TAC[cong; nat_mod; ARITH_RULE '(2 + x) - 1 = x + 1'] THEN MAP_EVERY EXISTS_TAC ['0'; 'd:num'] THEN ARITH_TAC);; And now Mizar: theorem Th11: i gcd m = 1 & i is_quadratic_residue_mod m & i,j are_congruent_mod m implies j is_quadratic_residue_mod m proof assume A1: i gcd m = 1 & i is_quadratic_residue_mod m & i,j are_congruent_mod m; then consider x being Integer such that A2: (x^2 - i) mod m = 0 by Def2; m divides (i - j) by A1,INT_2:19; then A3: (i - j) mod m = 0 by Lm1; (x^2 - j) mod m = ((x^2 - i) + (i - j)) mod m .= (((x^2 - i) mod m) + ((i - j) mod m)) mod m by INT_3:14 .= 0 by A2,A3,INT_3:13; hence thesis by Def2; end; -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard let CONG_MINUS1_SQUARE = prove > ('2 <= p ==> ((p - 1) * (p - 1) == 1) (mod p)', > SIMP_TAC[LE_EXISTS; LEFT_IMP_EXISTS_THM] THEN > REPEAT STRIP_TAC THEN > REWRITE_TAC[cong; nat_mod; > ARITH_RULE '(2 + x) - 1 = x + 1'] THEN > MAP_EVERY EXISTS_TAC ['0'; 'd:num'] THEN > ARITH_TAC);; And now Mizar: theorem Th11: > i gcd m = 1 & i is_quadratic_residue_mod m & > i,j are_congruent_mod m > implies j is_quadratic_residue_mod m > proof > assume > A1: i gcd m = 1 & > i is_quadratic_residue_mod m & > i,j are_congruent_mod m; > then consider x being Integer such that > A2: (x^2 - i) mod m = 0 by Def2; > m divides (i - j) by A1,INT_2:19; > then > A3: (i - j) mod m = 0 by Lm1; > (x^2 - j) mod m > = ((x^2 - i) + (i - j)) mod m > .= (((x^2 - i) mod m) + ((i - j) mod m)) > mod m by INT_3:14 > .= 0 by A2,A3,INT_3:13; > hence thesis by Def2; > end; Looks like somebody is comparing apples and oranges. It seams the the HOL light stuff is a tactic. Whereas the mizar snippet is a thereom. What is a tactic, the same as a theorem? I don't think so. A tactic is a proof method, and the HOL light code might show the invocation of a proof method. The proof method will in the end produce a proof. Only if you run the HOL light stuff you will get a proof, and then you can compare this with the mizar stuff. But comparing the tactic invocation and the mizar proof looks to me unfair. Bye === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) >What is a tactic, the same as a theorem? I don't think so. A tactic is a proof method, and >the HOL light code might show the invocation of a >proof method. The proof method will in the end >produce a proof. Only if you run the HOL light stuff you will get >a proof, and then you can compare this with the mizar >stuff. But comparing the tactic invocation and the >mizar proof looks to me unfair. It depends on what you are trying to compare. If you are trying to compare what a human being has to type into the computer to get a formal proof out the other end so to speak, then the comparison is fair. On the other hand, it is true that HOL Light and Mizar have different underlying philosophies, so you could say that they are apples and oranges. For a start, Mizar is based on a ZFC-like system, whereas HOL Light is based on higher-order logic. More relevantly here, HOL Light relies heavily on a tactic-based approach; in practice, almost all proofs are generated via tactics rather than by typing them in directly so to speak. This is a very powerful approach, but it does require thinking about proofs in a slightly different way from what we're used to. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard > More relevantly here, HOL Light relies heavily on a tactic-based approach; > in practice, almost all proofs are generated via tactics rather > than by typing them in directly so to speak. This is a very powerful > approach, but it does require thinking about proofs in a > slightly different way from what we're used to. I don't see a reason to have it like that because of the underlying logic substrate. What is the motivation? I think some nuances will get lost. For example it will not be possible to use the system to try to most literally translate existing proofs. Bye === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) [Re: HOL Light tactics] >I don't see a reason to have it like that because of the >underlying logic substrate. What is the motivation? The motivation is that producing a formal proof is, to a great extent, mind-numbingly tedious. We want the computer to do as much of that work automatically as we can. Proof tactics are a powerful way to automate formal proof production. The higher-order logic also allows one to automate recurring proof patterns. >I think some nuances will get lost. For example it will not be possible >to use the system to try to most literally translate existing proofs. This is true, but let me ask, is the real purpose of the database of formal proofs to *literally translate existing proofs*, or to *verify correctness*? My philosophy is the latter. I see the computer's role as checking that alleged theorems are really theorems. I don't really care if the computer's proof is not quite the same as the argument I give to my fellow human beings to get them to understand the proof. This is the philosophy followed by most of the leaders in the theorem-proving community. When Gonthier formalized the four-color theorem in Coq, he found himself coming up with new ideas in order to make the proof easier to feed to the computer. Thus his proof is by no means a literally faithful rendition of the pre-existing human proofs. If you see literal translation as an important goal, then I agree that you'll need to come up with some approach that is different from the existing ones. I personally don't see that literal translation is that important. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard > If you see literal translation as an important goal, then I agree that > you'll need to come up with some approach that is different from the existing > ones. I personally don't see that literal translation is that important. Many times the journey is the reward. I doubt that many theorems are useful in itself. They are often simplifications or culminations of a set of subtheorems and lemmas which have much more substance as the theorem itself. Take for example a completness theorem. Not so exiting in itself. But if we take a Henkin proof of it, we see a total new world, with a lot of subcorollaries. And a G.9adel proof of the same theorem might look totally different. I agree at the moment the automated theorem prooving community resembles more a world cup organization. They make competitions and what counts is the number of theorems proved and the time taken to proof the theorems. Fine. But do we judge a mathematician by the time it took him to produce a proof. Or do we judge him by some properties the proof exhibits? Bye === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) >Fine. But do we judge a mathematician by the time it took him to >produce a proof. Or do we judge him by some properties the proof exhibits? I think you're conflating two different issues here. The first issue is whether proofs---in the ordinary sense of the word, not formal proofs---have inherent value or beauty, beyond doing their job of establishing the correctness of a theorem. Here we have no disagreement. Important theorems should ideally be proved in many different ways, each one giving new insight into what is going on. Proofs do more than certify correctness; they can *explain* a result, suggest new conjectures, introduce new and powerful general techniques that can be used to solve other problems, and so on. The second issue, which is very different from the first, is whether *formal* proofs should *literally translate* pre-existing ordinary proofs. I don't really see the point of this. Formal proofs are far inferior to proofs written in natural language when it comes to readability; I would not turn to a formal proof to understand *why* the prime number theorem is true. Ordinary proofs, written in natural language, have served and will continue to serve the function of transmitting mathematical knowledge from one human being to another, far better than formal proofs ever will. The one area where formal proofs have a decisive advantage over natural- language proofs is correctness. It therefore makes a lot of sense to use formal proofs to carry out the function of certifying correctness. But for this purpose, slavish imitation of ordinary proofs is not necessary, and can indeed be an impediment. To repeat, I have not seen you give any good argument for why *formal* proofs should *literally translate* natural-language proofs. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard > Ordinary proofs, written in natural language, have served and will continue > to serve the function of transmitting mathematical knowledge from one human > being to another, far better than formal proofs ever will. The greeks believed at some point that written books are evil since spoken transmition is far superior. I can't believe the argument you are giving. It sounds like since formalized proofs are not readable now, we should not work in the direction of improving the readability. So you are making the alleged status quo as the future goal. First of all that formalized proofs are not readable, is this juts gut feeling of yours, or is this based on real experience? I recently quite good readable. What do you think are programmers doing all day when they are not writing code? They might read others code... Its just a matter of education and improved tools and artificial languages, but it is not an argument as you think. It is not an impossibilty to work in formal systems. Its already day to day reality for many peoples. For example 2006 there were around 13.3 million professional developers world wide. http://www.theserverside.com/discussions/thread.tss?thread_id=18838 And they might do business model formalizations, they write code for requirements. Struggling with a lot of validation and verification issues. Some verification techniques could be of great help. Bye === Subject: Re: Computer-verified Mathematical Proof as Standard Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) >I can't believe the argument you are giving. It sounds like since >formalized proofs are not readable now, we should not work in the >direction of improving the readability. So you are making the alleged >status quo as the future goal. First of all that formalized proofs are not readable, is this juts >gut feeling of yours, or is this based on real experience? Certainly, it is based on experience. Forget about computers even: A lot of the time, I can't even understand a *human* proof when it is written too formally. Usually I need the ideas to be explained informally before I can understand what's going on. At that point, I often don't need to read the proof because, understanding the idea, I can reconstruct the proof myself. The argument I am making is not that formal languages should not be made more readable. I am making the argument that formal proofs will never supplant informal human communication as a vehicle for transmitting human knowledge. Now, let me argue on your behalf for a moment. I think that there could be some room for building a layer *on top of* HOL Light or Mizar that more closely mimics human proofs. At a sufficiently high level, after all, the formal proof should be the same as a humanly understandable proof. The analogy with computer programming would be a very high-level language in which we can write the *specs* for a program. Then you could write software that would translate such formal specs into, say, C++. Following this analogy, what I am saying is that it is not a valid criticism of C++ that it does not mimic human software specifications literally. That is not the purpose of C++. Similarly, HOL Light is a high-level language, but it is not *that* high, nor is it intended to be. It works at a much lower level of detail. It is not a valid criticism of HOL Light that it does not mimic human proofs literally. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Computer-verified Mathematical Proof as Standard > Ordinary proofs, written in natural language, have > served and will continue > to serve the function of transmitting mathematical > knowledge from one human > being to another, far better than formal proofs > ever will. The greeks believed at some point that written books > are evil > since spoken transmition is far superior. I can't believe the argument you are giving. It > sounds like since > formalized proofs are not readable now, we should not > work in the > direction of improving the readability. So you are > making the alleged > status quo as the future goal. First of all that formalized proofs are not readable, > is this juts > gut feeling of yours, or is this based on real > experience? I recently > tried to read a computer formatted formal mizar > quite good readable. What do you think are > programmers doing all day > when they are not writing code? They might read > others code... Its just a matter of education and improved tools and > artificial > languages, but it is not an argument as you think. It > is not an > impossibilty to work in formal systems. Its already > day to day > reality for many peoples. For example 2006 there were > around > 13.3 million professional developers world wide. > http://www.theserverside.com/discussions/thread.tss?th > read_id=18838 And they might do business model formalizations, they > write > code for requirements. Struggling with a lot of > validation and > verification issues. Some verification techniques > could be > of great help. Bye > LNAI 4603 - System for Automated Deduction (SAD): A Tool for Proof p divides n-p then p divides n.î). Series ... The verification manager goes through the normalized text section by section, .... T Mizar, Alcor and formal methods in mathematics. - Creating ... 3 posts - 2 authors - Last post: Feb 18 For verification purposes please type the characters you see in the picture below .... Manifold with the Mizar system actually testing for the compatibility ... the sort of question you can ask in P and NP. - Ian Parker ... LNCS 3119 - Theorem Proving and Proof Verification in the System SAD Distinguish Evidence Algorithm from Mizar, the system which has received a wide recognition all over the world. ...... N.I. Bakhvalov, N.P. Zhidkov, G.M. Kobelkon. ... University of California, Los Angeles, USA, 2000, p. 48. ... http://www.springerlink.com/index/WKYL624Q0G19NUFG.pdf P. Rudnicki, An Overview of the MIZAR Project, Proc. ... T. B. Knoblock , N. P. Mendler , P. Panangaden , J. T. Sasaki , S. F. Smith, .... John Rushby, Theorem proving for verification, Modeling and verification of parallel ... http://portal.acm.org/citation.cfm?id=287878 LNCS 5123 - Theorem Proving for Verification (Invited Tutorial) http://www.springerlink.com/index/e0119567v22v7p77.pdf Subtypes for Specifications P. Rudnicki, An Overview of the MIZAR Project, Proc. ... T. B. Knoblock , N. P. Mendler , P. Panangaden , J. T. Sasaki , S. F. Smith, ... the 8th International Conference on Computer Aided Verification, p.411-414, August 03, 1996 ... http://portal.acm.org/citation.cfm?id=287870.287878 Computer-verified Mathematical Proof as Standard - comp.theory [...] 6 posts - 4 authors - Last post: 22 hours ago In general, researchers believe that P NP, because ever since 1971, extensive and <. .... published proof be the source code for such a computer verification? .... This Mizar system and the QED project are [...] Working with Mizar & Alcor p. Descriptions herein apply to both Mizar and Alcor, unless explicitly ...... Host key verification failed. This phenomenon stems from the IP Load Balancer ...... the options -np ... -machinefile $PBS_NODEFILE are added implicitly ... http://dithpcbatch.epfl.ch/MizarAlcorDOC.pdf Computer-verified Mathematical Proof as Standard - sci.math ... Shtetl-Optimized é Blog Archive é A far-off dream: automating a ... Aug 25, 2006 ... I'd probably go with Mizar, simply because the proofs in it look the most to me ..... That, to me, is why P vs. NP is one of the most profound ... Computer verification will shift this burden from the reviewer to the ... http://scottaaronson.com/blog/?p=116 === Subject: Computer-verified Mathematical Proof as Standard Re: <4a3bdce2$0$515$b45e6eb0@senator-bedfellow.mit.edu> <4a3c0fe6$0$500$b45e6eb0@senator-bedfellow.mit.edu> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) [[[http://MeAmI.org generate: >Fine. But do we judge a mathematician by the time it took him to >produce a proof. Or do we judge him by some properties the proof exhibits? I think you're conflating two different issues here. The first issue is whether proofs---in the ordinary sense of the word, not > formal proofs---have inherent value or beauty, beyond doing their job of > establishing the correctness of a theorem. Here we have no disagreement. > Important theorems should ideally be proved in many different ways, each > one giving new insight into what is going on. Proofs do more than certify > correctness; they can *explain* a result, suggest new conjectures, introduce > new and powerful general techniques that can be used to solve other problems, > and so on. The second issue, which is very different from the first, is whether *formal* > proofs should *literally translate* pre-existing ordinary proofs. I don't > really see the point of this. Formal proofs are far inferior to proofs > written in natural language when it comes to readability; I would not turn > to a formal proof to understand *why* the prime number theorem is true. > Ordinary proofs, written in natural language, have served and will continue > to serve the function of transmitting mathematical knowledge from one human > being to another, far better than formal proofs ever will. The one area where formal proofs have a decisive advantage over natural- > language proofs is correctness. It therefore makes a lot of sense to use > formal proofs to carry out the function of certifying correctness. But for > this purpose, slavish imitation of ordinary proofs is not necessary, and > can indeed be an impediment. To repeat, I have not seen you give any good argument for why *formal* proofs > should *literally translate* natural-language proofs. > -- > Tim Chow tchow-at-alum-dot-mit-dot-edu > The range of our projectiles---even ... the artillery---however great, will > never exceed four of those miles of which as many thousand separate us from > the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences End it. In general, researchers believe P does not equal NP, because ever since 1971, the mathematical basis of the algorithm remains supportive of the intended purpose. We have a contradiction. The set of Goedel-formulas of PA is empty, and PA has no non-standard models. I tell you the truth, Computional Theory contains all the axioms and verified proofs in some standard format. Do the math. It's human nature. Stephen Arthur Cook had a purpose with P Versus NP. Did it serve you? It did not serve me. Perhaps it served institutional investors in the S&P? 1. There is a reason Intel labs at Berkeley: to make money. 2. There is a reason Berkeley hosts Intel: to make money. The overlap between innovation and academia is self-evident and important to commerce. This does not make Intel or Berkeley guilty of anything. I am simply establishing a symbiosis of reason. I tell you the truth, Cryptography can and is continually abused. Why did Wall Street recede and the economy decline? Because those in a position to leverage information pushed the envelope past reason. Their actions escaped capitalism and as a class bordered oligopoly. Consider the anti-virus industry? Does it seve you? We are told to fear understanding computation outside of sanctioned languages and those who do seek this understanding are labeled as troublemakers. Anything Microsoft does not want you to use they can call a virus. Read the Terms of Service on your Windows OS. The record speaks: The Cornficker hype peaked investors in the parent company made $10 million dollars with the Dow down 200+ points. It does not serve me. Perhaps it served institutional investors in the S&P? Suppose that p and p+2 are both prime and that there are the biggest pair IF P = NP then problems like the subset-sum problem are as easy to Proof as to compute. IF P = NP then problems like the subset-sum problem are as easy a discussion on USENET. Assume P=NP. Let y be a proof that P=NP. The proof y can be verified by computer scientists to produce a proof). P, NP and mathematics [CapitalEth] a computational complexity perspective enabling the computer revolution, made mathematically precise what Hilbert predicted. +++ (Facts) + 1. The correct solution to the search problem can be easily verified by V. 2. The extension of standard NP proofs was suggested independently in two academic publications. 3. Smale: Mathematical problems for the next century, Mathematical Intelligencer [...]. The standard cryptographic conjecture (about the existence of hard [problems] [...] The lengths of proofs, in: Handbook of Proof Theory, ed. [...] Proof Verification and Approximation Algorithms Lecture Notes in Computer Science, Vol. 1367.http://www.math.cas.cz/~krajicek/pnp syll.html 4. P=NP Proof Published at CERN (Musatov)[...]standard practice when using Quick Sort to make it effective for faster convergence.). [....] (NP/P) . This is true since the speed of the Computer should not be [deterministic]. It can be empirically verified as follows. A. If n is the numerical [....] (sci.math); Re: Perfection in Proof: Please Critique! [...] P) algorithm results [...]http://sci.tech- archive.net/Archive/sci.math/2009-05/msg01035.html B. Scott Aaronson (MIT) Shtetl-Optimized é Blog Archive é A far-off dream: automating a [...] 25 Aug 2006 [...] Were it standard to present proofs in computer- checkable form, [....] Its main point is that math is verified [....]. That, to me, is why P vs. NP is one of the most profound questions that humans have ever asked. [...]. http://scottaaronson.com/blog/%3Fp%3D116 in seconds, nor in computer cycles of a [...]. An equivalent, and now standard, way of viewing problems that are in NP is to say that a [...] A mathematical proof demonstrating whether P is equal to NP or not is [....] an integer is prime, which can be verified in polynomial time). P=NP. qed ? ´ . === Subject: Re: Computer-verified Mathematical Proof as Standard > Fine. But do we judge a mathematician by the time it took him to > produce a proof. Or do we judge him by some properties the proof > exhibits? Bye http://en.wikipedia.org/wiki/Paul_Erd%C5%91s He had his own idiosyncratic vocabulary: he spoke of ñThe Bookî, an imaginary book in which God had written down the best and most elegant proofs for mathematical theorems. Lecturing in 1985 he said, ñYou don't have to believe in God, but you should believe in The Book.î He himself doubted the existence of God, whom he called the ñSupreme Fascistî (SF).[9] He accused the SF of hiding his socks and Hungarian passports, and of keeping the most elegant mathematical proofs to himself. When he saw a particularly beautiful mathematical proof he would exclaim, ñThis one's from The Book!î. This later inspired a book entitled Proofs from THE BOOK. === Subject: Re: Computer-verified Mathematical Proof as Standard > I don't see a reason to have it like that because of the > underlying logic substrate. What is the motivation? I think > some nuances will get lost. For example it will not be possible > to use the system to try to most literally translate existing > proofs. Bye Except by using a bunch of constructor tactics. Given the literal translation requirement, we see that the length of a proof is not a measure for a proof verification system. More its versatility. === Subject: Re: Computer-verified Mathematical Proof as Standard <4a3bad3f$0$500$b45e6eb0@senator-bedfellow.mit.edu> posting-account=spgRJBAAAADTEf6m3y6Pyj43g6wnGUFN Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Has there been a similar trend in proof languages? Here is a list of the proof languages that I've just mined for investigation: - Boyer-Moore - Mizar - Coq - Isabelle - HOL Light So far all of them exhibit the relentless dedication to user- friendliness that we have come to expect from software projects out of academia. :) (Any time you get a Software Engineering Process book or a HCI book from an author that has never left their university campus - burn it.) -Andrew. === Subject: Re: michelson morley experiment questions posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > 1. Is it true that after a 90 degree rotation, the interference > pattern should change (assuming the ether theory is correct) - e.g. > would a 70 degree phase difference have a different interference > pattern to a 20 degree phase difference? During the time of the MMX, the Aether that allows for light propagation is modeled similar to a medium that allows for sound propagation. Thus, the answer would be yes. However, the null results do not mean the Aether does not exist. It could also mean that the Aether does not behave anything similar to the medium that allows for sound propagation. mathematically that as the apparatus is rotated, the interference > pattern and the phase difference should change (assuming the ether > theory is correct). Yes. This is true for sound waves. interference pattern didn't change when the apparatus was rotated? According to expert interpretations, yes. > 4. Did the experiment at the time, depend on the path lengths of the > two paths being exactly equal and was any effort made to make them > equal or was this completely unnecessary? If the experiment is performed through all orientations, it becomes unnecessary to set the lengths of each arm precisely. > 5. I've heard that the error/noise/inaccuracy of the original > experiment was too great for its result to be meaningful. If the > experiment depended only on observing the change in interference > pattern, what kind of error could invalidate this result? This is a good question. There have been enough interpretations to the null results. I give them the benefit of the doubt that they are indeed correct but willing to keep an open mind. The absolute frame of reference was actually detected through a Doppler shift in the Cosmic background radiation 100 years after the MMX. The self-styled physicists turned their backs on this monumental discovery because they have already BELIEVE IN the nonsense of SR. Well, Peter did not recognize Christ three times anyway. === Subject: Re: michelson morley experiment questions During the time of the MMX, the Aether that allows for light > propagation is modeled similar to a medium that allows for sound > propagation. Thus, the answer would be yes. However, the null > results do not mean the Aether does not exist. It could also mean > that the Aether does not behave anything similar to the medium that > allows for sound propagation. During the time of the MMX, the Aether that allows for light > propagation is modeled similar to a medium that allows for sound > propagation. Thus, the answer would be yes. However, the null > results do not mean the Aether does not exist. It could also mean > that the Aether does not behave anything similar to the medium that > allows for sound propagation. The Michelson-Morley experiment is consistent with no aether > at all. It is perfectly consistent with LET, which has an aether, and also with ballistic theories. === Subject: Re: michelson morley experiment questions <005ae681$0$9741$c3e8da3@news.astraweb.com> <005aebf2$0$9683$c3e8da3@news.astraweb.com> posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) Don'tbother tofeedthistrolland others like him! +------------+ +---------------------------------------------+ | PLEASE | | BEST TO IGNORE ATTENTION SEEKING TROLLS | | DO NOT | | LIKE Sam Wormley -- THEY DRY | | FEED | | UP AND BLOW AWAY WITHOUT FEEDBACK | | DA | | | | TROLLS | | http://www.angelfire.com/space/usenet/ | +------------+ +---------------------------------------------+ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ` '/ / ' / ` '/ / ' / ` '/ / ' / === Subject: Re: michelson morley experiment questions Importance: Normal I assume you're talking about Wormley > Don'tbother tofeedthistrolland others like him! === Subject: Re: michelson morley experiment questions Whoever says... I assume you're talking about Wormley > Don'tbother tofeedthistrolland others like him! I assume that when Koobee says things like that, or talks about people being liars and nitwits, he's actually talking about himself. At some level, he knows what he is. -- Daryl McCullough Ithaca, NY === === Subject: Re: michelson morley experiment questions During the time of the MMX, the Aether that allows for light > propagation is modeled similar to a medium that allows for sound > propagation. Thus, the answer would be yes. However, the null > results do not mean the Aether does not exist. It could also mean > that the Aether does not behave anything similar to the medium that > allows for sound propagation. The Michelson-Morley experiment is consistent with no aether > at all. It is perfectly consistent with LET, which has an aether, and also with > ballistic theories. http://physicstoday.org/vol-57/iss-7/p40.shtml http://cfa-www.harvard.edu/Walsworth/pdf/PT_Romalis0704.pdf No aether === Subject: Re: michelson morley experiment questions reply-type=response Importance: Normal > During the time of the MMX, the Aether that allows for light > propagation is modeled similar to a medium that allows for sound > propagation. Thus, the answer would be yes. However, the null > results do not mean the Aether does not exist. It could also mean > that the Aether does not behave anything similar to the medium that > allows for sound propagation. The Michelson-Morley experiment is consistent with no aether > at all. > It is perfectly consistent with LET, which has an aether, and also with > ballistic theories. > http://physicstoday.org/vol-57/iss-7/p40.shtml Can't read it .. have to subscribe. > http://cfa-www.harvard.edu/Walsworth/pdf/PT_Romalis0704.pdf Says nothing about aether or not > No aether So you say, but there is no evidence that there is no aether .. nor is there evidence that there is an aether. Its pretty much a matter of faith. There is SR worths fine without an aether, and LET that is identical mathematically to SR, has an aether. Basically, we have no need of an aether for us to make experimental predictions. === Subject: Computability & complexity posting-account=E-CdywoAAAAGiR6KPJCa4N4cvKx2O-9C Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) Hi All, Please let me know if you know any source of answered exercises about recursive functions,computable functions,universal programs,...etc. or computability in general. I am taking a class and really in bad need for such resource. Mohamed === Subject: Re: SR in graphs - mixed coordinates posting-account=PTS84AoAAACr67p51zvy0Hlr3LkoIUcc x64; .NET CLR 2.0.50727; SLCC1; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) > You are free to choose whatever coordinates you wish to use, as long as > they meet the requirement that there is a 1-to-1 correspondence between > coordinate N-tuples and points in the manifold. That is, each unique set > of values of the coordinates must specify a single point of the > manifold. There are additional requirements about continuity, etc., that > don't concern us here. So, Professor Roberts is pitching that SR is more special than GR. Although its name, the mathematics does not indicate SR is more special than GR. Flat space time is no more special than curved spacetime. Any spacetime should be equally special. Any mathematics indicating otherwise is absurd. After all, curved spacetime is just another ordinary geometry. to cover the manifold; in GR we don't (it's often impossible). Again, to describe any geometry, you must start with a set of coordinate system. Just because you can write the field equations in a concise one, (R ij [CapitalEth] R g ij / 2 = k T ij), it does not mean the set of field equations can be presented without a set of coordinate system. To claim you don't need a set of coordinate system to describe any spacetime thus geometry is utterly absurd and wrong. Note: I allow myself to be attacked to generate more discussions on this one. Any takers? > Note I said nothing about coordinates being inertial. In SR, it is usual > to use coordinates that are inertial, because that makes many > computations simpler; but there is no necessity to do so. All coordinate systems should be no more unique than the others. There should be no special frames of references identified as inertial. Spacetime is invariance. It is an artifact of geometry. It remains what it is regardless of which set of coordinate system you happen to choose to use. the set {x,t,x',t'} will satisfy the requirements. Choosing x' and t is > rather unusual, but certainly not forbidden. But you must be careful as > they are clearly not inertial coordinates (i.e. the metric components > are not diag(-1,1,1,1)). The above is mathematical. In physics, it is hopeless to > choose {x,x'}, because they are almost parallel and any > measurement resolution will make it impossible to establish > locations effectively. Similarly, for v approaching c it is > hopeless to choose any pairs except {x,t} or {x',t'}. acknowledge your much superior knowledge of relativity and I learn > something from your posts. Of course, I make good use of your > wonderful collection of evidence for relativity. Can anyone see how guru-worshipping can lead to Einstein-worshipping? After all, Einstein was just a nitwit, a plagiarist, and a liar. I think this incident may be over now. My work is done. The bully is > exposed as an ignoramus. (Until a new batch of newbies show up and > think he is an authority.) Please take the witch hunt business somewhere else. This is a serious discussion about the subject of relativity. === Subject: Re: SR in graphs - mixed coordinates posting-account=15T5jAkAAACpO9KgK0Ue212ywoAPQtp7 Trident/4.0; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; MDDC),gzip(gfe),gzip(gfe) snip > Could I remind you again > that Einstein was merely a nitwit, a plagiarist, and a liar? > Poincare' and Lorentz didn't think so. And http://math.ucr.edu/home/baez/Relativity/SR/experiments.html === Subject: Re: SR in graphs - mixed coordinates Uncle Ben says... >snip > Could I remind you again > that Einstein was merely a nitwit, a plagiarist, and a liar? Poincare' and Lorentz didn't think so. And http://math.ucr.edu/home/baez/Relativity/SR/experiments.html You mean: http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html -- Daryl McCullough Ithaca, NY === Subject: Re: SR in graphs - mixed coordinates posting-account=15T5jAkAAACpO9KgK0Ue212ywoAPQtp7 Trident/4.0; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; MDDC),gzip(gfe),gzip(gfe) On Jun 22, 8:55am, stevendaryl3...@yahoo.com (Daryl McCullough) > Uncle Ben says... >snip > Could I remind you again > that Einstein was merely a nitwit, a plagiarist, and a liar? Poincare' and Lorentz didn't think so. And http://math.ucr.edu/home/baez/Relativity/SR/experiments.html You mean:http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html -- > Daryl McCullough > Ithaca, NY computer to computer by hand. Ben === Subject: Re: SR in graphs - mixed coordinates snip > Could I remind you again > that Einstein was merely a nitwit, a plagiarist, and a liar? > Poincare' and Lorentz didn't think so. Lorentz was a crank who thought aether pressure would cause length contraction. He was so in' stupid he believed in the sound of one hand clapping. If Lorentz thought Einstein wasn't a lunatic that's a good indication he was. === Subject: Any solution manual or testbank for $25 ! only this week 17.06.2009 - 24.06.2009 ! posting-account=5BdoyQkAAAACm5Si7oheX_9haNFD_3c2 AppleWebKit/525.19 (KHTML, like Gecko) Version/3.1.2 Safari/525.21,gzip(gfe),gzip(gfe) electronic format (PDF or Doc), they are for sale: Automation, Production Systems, and Computer-Integrated Manufacturing - Mikell P. Groover (3rd ed) ISBN-10: 0132393212 ISBN-13: 978-0132393218 Price: $29 _________________________________________________________________________ Supply Chain Management - Sunil Chopra (3rd ed) by Prentice Hall ISBN-10: 0131730428 ISBN-13: 978-0131730427 Price: $29 _________________________________________________________________________ Operations Management: Process and Value Chains - Lee J. Krajewski (8th edition) solution manual ISBN-10: 0131697390 ISBN-13: 978-0131697393 Price: $29 _________________________________________________________________________ Operations Management: Process and Value Chains - Lee J. Krajewski (8th edition) testbank ISBN-10: 0131697390 ISBN-13: 978-0131697393 Price: $29 _________________________________________________________________________ Facilities Planning: James A. Tompkins, 3rd edition, Wiley ISBN-10: 0471413895 ISBN-13: 978-0471413899 Price: $29 _________________________________________________________________________ Mechanics of Materials Gere 6e solution manual Price: $12 _________________________________________________________________________ Accounting Information Systems, 11/E solution manual Marshall B. Romney, Brigham Young University Paul J. Steinbart, Arizona State University ISBN-10: 0136015182 ISBN-13: 9780136015185 price: $29 _________________________________________________________________________ Accounting Information Systems, 11/E testbank Marshall B. Romney, Brigham Young University Paul J. Steinbart, Arizona State University ISBN-10: 0136015182 ISBN-13: 9780136015185 price: $29 _________________________________________________________________________ Management Information Systems, 11/E solution manual Ken Laudon Jane Laudon ISBN-10: 013607846X ISBN-13: 9780136078463 price: $29 _________________________________________________________________________ Management Information Systems, 11/E testbank Ken Laudon Jane Laudon ISBN-10: 013607846X ISBN-13: 9780136078463 price: $29 _________________________________________________________________________ Business Statistics: A Decision Making approach, solution manual David F. Groebner ISBN-10: 0132416921 ISBN-13: 9780132416924 price: $29 _________________________________________________________________________ Business Statistics: A Decision Making approach, testbank David F. Groebner ISBN-10: 0132416921 ISBN-13: 9780132416924 Price: $29 _________________________________________________________________________ PROJECT MANAGEMENT ACHIEVING COMPETITIVE ADVANTAGE AND MS PROJECT international edition, Testbank by Jeffrey K. Pinto ISBN 10: 0138129320 ISBN 13: 9780138129323 Price: $29 _________________________________________________________________________ Consumer Behavior, 9/E ,Test bank Leon Schiffman, St. John's University Leslie Kanuk, CUNY-Baruch College Price: $29 _________________________________________________________________________ Introduction To Operations Research (scanned) solution manual Author: Hillier, Lieberman ISBN: 0070473870 ISBN-13: 9780070473874 Price $12 _________________________________________________________________________ Management Accounting, 5/E solution manual Anthony A. Atkinson, University of Waterloo Robert S. Kaplan, Harvard Business School Ella Mae Matsumura, University of Wisconsin-Madison S. Mark Young, University of Southern California ISBN-10: 0136005314 ISBN-13: 9780136005315 Price : $25 _________________________________________________________________________ Management Accounting, 5/E testbank Anthony A. Atkinson, University of Waterloo Robert S. Kaplan, Harvard Business School Ella Mae Matsumura, University of Wisconsin-Madison S. Mark Young, University of Southern California ISBN-10: 0136005314 ISBN-13: 9780136005315 Price : $25 _________________________________________________________________________ Cost Management: Strategies for Business Decisions, 4/e solution manual By Ronald W Hilton, Michael W Maher, Frank Selto ISBN: 0073526800 / 9780073526805 Price : $25 _________________________________________________________________________ Cost Management: Strategies for Business Decisions, 4/e testbank By Ronald W Hilton, Michael W Maher, Frank Selto ISBN: 0073526800 / 9780073526805 Price : $25 _________________________________________________________________________ Managerial Accounting, 12/e solution manual By: Ray Garrison, Brigham Young University Eric Noreen, University of Washington Peter Brewer, Miami University ISBN: 0073526703 Price: $25 _________________________________________________________________________ Operations research Hamdy Taha 8th edition solution manual (scanned) ISBN 0131889230 Price: $12 *Dont send here any questions email: cheap_manuals[@]hotmail.com Payment is through paypal to this email email: amverycool[@]live.com you can recieve it in less than 12 hours after payment. Its a limited time discount, get yours now before 24.June.2009 === Subject: critical points [x, y, X, Y]= Sqrt[x^2 + (2 - y)^2] + Sqrt[x^2 + y^2] + Sqrt[(5 - X)^2 + (2 - Y)^2] + Sqrt[(5 - X)^2 + Y^2] + Sqrt[(-x + X)^2 + (-y + Y)^2] find the critical points of f === Subject: Re: critical points > [x, y, X, Y]= > Sqrt[x^2 + (2 - y)^2] + Sqrt[x^2 + y^2] + > Sqrt[(5 - X)^2 + (2 - Y)^2] + > Sqrt[(5 - X)^2 + Y^2] + > Sqrt[(-x + X)^2 + (-y + Y)^2] find the critical points of f One critical point is x=sqrt(1/3) y=1 X=5-sqrt(1/3) Y=1 Best wishes Torsten. === Subject: Re: critical points f[x, y, X, Y]= Sqrt[x^2 + (2 - y)^2] + Sqrt[x^2 + y^2] + Sqrt[(5 - X)^2 + (2 - Y)^2] + Sqrt[(5 - X)^2 + Y^2] + Sqrt[(-x + X)^2 + (-y + Y)^2] find the critical points of f === Subject: ...Cyclic inner automorphism (sub)group Suppose G is a group and that Aut(G) is *cyclic*; then for some g in G, we have Inn(G) = < f_g >, where f_g (x) = gxg^{-1}. How do we show that G = Z(G) U ? After several attempts, I still can't see how to prove this equality. For all I know, it may be incorrect as stated, but I can't be absolutely sure at this point. I do know however that, as stated, it would follow that G is abelian, since G is a union of subgroups, in which case either subgroup is contained in the other. === Subject: Re: ...Cyclic inner automorphism (sub)group posting-account=-PngCgkAAAD2yUjosqWv1Nf1lkqWP4lp Gecko/20081213 SUSE/2.0.0.21post-0.3 Firefox/2.0.0.22pre,gzip(gfe),gzip(gfe) > Suppose G is a group and that Aut(G) is *cyclic*; then > for some g in G, we have Inn(G) = < f_g >, where f_g (x) = gxg^{-1}. How do we show that G = Z(G) U ? After several attempts, I still can't see how to prove this equality. For all I know, it may be incorrect as stated, but I can't be absolutely sure at this point. > I do know however that, as stated, it would follow > that G is abelian, since G is a union of subgroups, > in which case either subgroup is contained in the other. For any group G, Inn(G) is isomorphic to G/Z(G). So if Aut(G) is cyclic, then so is Inn(G), and hence so is G/Z(G). It is a standard elementary exercise to show that G/Z(G) cyclic implies G=Z(G), so G is abelian. Derek Holt. === Subject: inequality posting-account=frVNsgoAAADqMe0QlqRY45SfNlclErPW AppleWebKit/530.18 (KHTML, like Gecko) Version/4.0.1 Safari/530.18,gzip(gfe),gzip(gfe) For what x is exp(-n x/(1-x)) <= (1-x) ^n ? I believe this is (0,1) but I don't know how to prove this... Any help? === Subject: Re: inequality posting-account=e6PATAoAAACxeuMbOnLMqjakg3lAxhUd Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > For what x is exp(-n x/(1-x)) <= (1-x) ^n ? I believe this is (0,1) but I don't know how to prove this... Any help? Take logarithms in your inequality: -nx/(1-x) <= -nln(1/(1-x)) <--> x/ (1-x) >= ln(1/(1-x)). Setting y = 1/(1-x), we have x/(1-x) = y*(y-1)/y = y-1, while ln(1/(1-x)) = ln(y), so the inequality is y-1 >= ln(y). For which positive values of y is this true? Those give you the x you want. R.G. Vickson === Subject: Re: inequality > For what x is exp(-n x/(1-x)) <=3D (1-x) ^n =A0? I believe this is (0,1) but I don't know how to prove this... Any help? Take logarithms in your inequality: -nx/(1-x) <=3D -nln(1/(1-x)) <--> x/ > (1-x) >=3D ln(1/(1-x)). Setting y =3D 1/(1-x), we have x/(1-x) =3D > y*(y-1)/= y > =3D y-1, while ln(1/(1-x)) =3D ln(y), so the inequality is y-1 >=3D > ln(y). For which positive values of y is this true? Those give you the x > you want. I'm going to assume that n denotes a positive integer; if that is not the case, the OP should inform us. The original inequality is true for x < 1, as Ray's post implies. But for _even_ n, there is another region in which the inequality holds: x >= c where c = 1/W(1/e) - 1 = 2.5911... and W denotes the principal branch of the Lambert W function. David W. Cantrell === Subject: Absolute value of quotient posting-account=33KaEgkAAAA9tz8WICNABjrkyMKXFbGS Gecko/2009032609 Firefox/3.0.8,gzip(gfe),gzip(gfe) If quotient of absolute values of a function is absolute value of their quotient, i.e., if f (x) / f (y) = f (x / y), prove that f(z) = |z| where z is a complex variable. TIA Narasimham === Subject: Re: Absolute value of quotient > If quotient of absolute values of a function is > absolute value of > their quotient, i.e., > if f (x) / f (y) = f (x / y), prove that f(z) = |z| > where z is a > complex variable. TIA Narasimham What about f(x) = 1 ? === Subject: Re: The year of Cyber Tester > At times, I ask myself, Could some events of my life be a mere > application of the probability theory? probably === === Subject: Simple vector space question Hi If v is a vector in a vector space, is v=(1/2)v + (1/4)v + (1/8)v + ... ? Ron === Subject: Re: Simple vector space question Ron Jonesa a .8ecrit : > Hi If v is a vector in a vector space, is v=(1/2)v + (1/4)v + (1/8)v + ... ? > Ron It depends! Have you defined some notion of convergence in your vector space? If your vector space beares a norm, yes, it is true. If it bears a distance or more genrally a topology, it will depend on the properties of the topology. If there's no topology, it's just nonsense. -- Fatal === Subject: Solution manual to Differential Equations and Linear Algebra, 3e by Stephen W. Goode and Scott A. Annin IM posting-account=_ObeYAoAAABc8H8zknYzs3d0mwhkVSTP CLR 2.0.50727; CIBA),gzip(gfe),gzip(gfe) I have the following solutions manual. To get the solution manual you want, just contact me. My email address is hotsolution@hotmail.com, hotsolution(at) hotmail.com, please replace (at) to @ , just send email to me. Note: All solutions manual in soft copy that mean in PDF format or doc format. Solution manual to Accounting text and cases 12e Anthony IM Solution manual to Differential Equations and Linear Algebra, 3e by Stephen W. Goode and Scott A. Annin IM Solution manual to Basic Engineering Circuit Analysis, Problem Solving Companion 9th Edition by J. David Irwin, R. Mark Nelms Solution manual to Engineering Circuit Analysis 7th Ed. by William H. Hayt Jr Solution manual to Financial Accounting, 7e by Harrison Horngren Test Bank to Financial Accounting, 7e by Harrison Horngren Solution manual to Advanced Accounting 10th edition by Beams SM+TB Solution manual to Introduction to management accounting 14th edition by horngren, sundem, stratton, burgstahler, and schatzberg SM Test Bank to Biology Concepts and Connections 6e Neil A. Campbell Jane B. Reece Martha R. Taylor Eric J. Simon Jean L. Dickey test bank Solution manual to Lakeside Company, The: Case Studies in Auditing, 10th Ed SM Test Bank to Organizational Behavior, Fourth Canadian Ed., 4E Robins TB Test Bank to Cost accounting 12e by Charles T. Horngren Srikant Datar George Foster Madhav Rajan Chris Ittner test bank Test Bank to Introduction to Managerial Accounting 2nd ed Brewer test bank Solution manual to Government and Not-for-Profit Accounting: Concepts & Practices (4th edition) by Granof and Wardlow sm Solution manual to Foundations of Financial Management, 12e By Stanley B. Block Geoffrey A. Hirt SM Solution manual to Differential Equations and Linear Algebra, 3e by Stephen W. Goode and Scott A. Annin (instructor manual) Test Bank to Intermediate Accounting 12e Kieso Weygant Warfield Solution manual to Intermediate Accounting 12e Kieso Weygant Warfield Test bank to Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Solution manual to Introduction to management accounting 14th edition by horngren, sundem, stratton, burgstahler, and schatzberg Solution manual to Intermediate Accounting, 5th Edition, Spiceland, Solution Manual Solution manual to Computer Networking: A Top-Down Approach, 4/E solution manual and lab solutions Solution manual to Computer Networking: A Top-Down Approach, 5/E solution manual Solution manual to Introduction to Fluid Mechanics, Edition 7, Fox, Pritchard, McDonald Solution manual to Accounting Information Systems 10th ED by Marshall B Romney and Paul J Steinbart SM Solution manual to Accounting what number means 8e by Marshall Solution manual to Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley solution manual Solution manual to Fundaments of heat and mass transfer 6e Incropera, Dewiit, Bergman and Lavine Solution manual to Separation Process Engineering: 2e by wankat SM Solution manual to Macroeconomics, 5E Olivier Blanchard (test bank) Solution manual to Macroeconomics, 5E Olivier Blanchard (instructor manual) Solution manual to Modern Physics, 2/E Randy Harris SM Solution manual to accounting information systems 11th edition, romney, steinbart test bank Solution manual to Advanced Accounting, 9th Edition, Beams, Clement, Anthony, Lowensohn SM Solution manual to Auditing and Assurance Services An Intergrated Approach and ACL Software, 12e by Alvin Arens Randal J. Elder, ark Beasley Solution manual to Applied Numerical Methods with MATLAB for Engineers and Scientists 2nd Ed., Steven C. Chapra Solution manual to Managerial Accounting 12th ed By Garrison Noreen solution manual Test bank to Managerial Accounting 12th Edition by Garrison Noreen test bank Instructor's Manual to Fundamental Methods Of Mathematical Economics Chiang & Wainwright 2005 Mc Graw Hill Solution manual to Physics for Scientist & Engineers with Modern Physics - A strategic Approach chapter by Randall D. Knight 1-35 Solution manual to Fundamentals of Advanced Accounting 3rd Edition by Hill Solution manual to Mechanics of Materials By R.C.Hibbeler 7th edition Solution manual to Probability and Statistics for Engineering and the Sciences 7/e JAY L.DEVORE Solution manual to Computer Networks, 4th Ed., by Andrew S. Tanenbaum Solution manual to Computer Networks A Systems Approach 3ed by Larry L. Peterson & Bruce S. Davie solutions manual Solution manual to Computer Architecture A Quantitative Approach, 4th Edition, 2006 by John L. Hennessy, David A. Patterson Solution manual to Database System Concepts, Fifth Edition by Avi Silberschatz, Henry F. Korth solutions to exercises? Solution manual to Probability, Statistics, and Random Processes For Electrical Engineering - Alberto Leon-Garcia (3rd ed) Solution manual to Introduction to Chemical Engineering Thermodynamics 7th edition(solution manual) By J.M. Smith, Hendrick C Van Ness Solution manual to PROCESS SYSTEMS ANALYSIS AND CONTROL - DONALD R. COUGHANOWR Solution Manual Solution manual to Engineering Economy - Leland Blank & Anthony Tarquin 6th Editionselected solutions ( student solution) Solution manual to Fundamentals of Engineering Thermodynamics 6th Edition by Michael Moran and Howard Shapiro Solution manual to Engineering Electromagnetics, 7th edition by Hayt Solution manual to Applied Numerical Methods With MATLAB for Engineers and Scientists Solution manual to Elements of Electromagnetics, 3rd Ed., Matthew N.O. Sadiku Solution manual to Engineering Mechanics Dynamics (11th Edition) by Russell C. Hibbeler Solution manual to Engineering Mechanics Statics 11th Edition By R.C.Hibbeler Solution manual to Engineering Mechanics, statics 6th edition Solutions manual By J. L. Meriam, L. G. Kraige Solution manual to Engineering Mechanics, Dynamics, 6th edition, By J. L. Meriam, L. G. Kraige Solution manual to Linear Algebra and its Applications 3rd ed - D. Lay Solutions Manual Solution manual to Probability and Statistics for Engineers and Scientists, 8th Edition: by Sharon Myers , Keying Ye, Walpole Solution manual to Cost Accounting A Managerial Emphasis by Charles T. Horngren 13th edition Solution manual to Introduction Fluid Mechanics, 6Th Edition Solution by fox Solution manual to Differential Equations and Linear Algebra by Penney and Edwards, 2nd edition Solution manual to Fundamentals of Applied Electromagnetics 5th edition by Fawwaz T. Ulaby Solution manual to Financial Accounting 6e by horngren Harrison Solution manual to Financial Accounting (Libby, fifth edition) Solution manual to Corporate Finance 1e by Berk solution manual Solution manual to Accounting 7e by Horngren Harrison Solution manual to Financial Accounting, 7e by Harrison Horngren Solution manual to Power System Analysis and Design 3rd Edition by Glover and Sarma Solution manual to Financial management theory and practice 12e by Brigham Solution manual to Advanced Accounting, 9th edition by Hoyle, Schaefer, & Doupnik Solution manual to Separation Process Principles, 2nd Ed., by Seader, Henley Solution manual to Numerical methods for engineers 5th by Chapra Solution manual to Microelectronic circuits by R. Jaeger 3rd edition Solution manual to Computer system architecture 3rd edition ? Morris Mano Solution manual to Computer networking a top down approach 3th edition Solution manual to Introduction to Mathematical Statistics, sixth edition by Robert V.Hogg Solution manual to Introduction to Operations Research - Seventh Edition Solution manual to Elements of Engineering Electromagnetics 6th Edition Solution manual to Vector Mechanics Dynamics Beer 8th Edition Solution manual to Elements of Chemical Reaction Engineering 3th edition by Fogler Solution manual to Options futures and other derivatives(Hull), 3rd, 4th, 5th, 6th edition Solution manual to Thermodynamics an engineering approach sixth edition By Yunus A. Cengel, Michael A. Boles Solution manual to Elements Of Information Theory 1st ed by Thomas M.Cover, Joy A.Thomas Solution manual to Probability and Statistical Inference 7th edition, Hogg & Tanis solution === Subject: Re: Answer to Dik T. Winter Nntp-Posting-Host: hera.cwi.nl ... > Because you do not check the lines in order. It is always > your basic assumption that you first check the first line > and after that the next line. That is wrong. > > That is necessary because you cannot find the n-th line unless > you know the line number n - 1 or some equivalent mark. > > But why is getting the number n in any way related to the checking > of the previous lines? > > Because by blind choice you cannot be sure to hit what you want. > > Why does it imply checking the previous lines? Why do you not answer > that question? > > You cannot check line n without knowing line n-1. But why does that imply *checking* line n-1? Why do you not answer that question? > But you cannot find number n without referring to the numbers > less than n. > > That does not mean that you check the line with number n. So you > assertion that you need to check all lines in order is false. > > In unary or in von Neumann's representation there is the whole > counting process incorporated in each number. In decimal, you need > only count the powers of 10. Anyhow addressing a number means > counting. > > And that *still* does not imply checking. > > Counting is checking: how many. Aha, now we come closer. So when you state that checking line n in the list implies checking previous lines, you are using the word checking with two different meanings. In the first instance you are meaning that it is checked whether it is different from the diagonal. In the second instance you are meaning that you count to that line. Why do you use the word checking the second time with a meaning that is not related to the standard meaning of checking? > Of course you can check the n-th element before checking any other. > But in order to find the n-th element, you have to count from 1 to n, > either in unary or at least in the powers of 10. Therefore it is not > correct to talk about simultaneity. > > But the whole point is that in Cantor's argument, whatever n we choose, > it is > > a last and largest member of a finite set. Irrelevant. > shown that the line numbered with that n is not in the list. This is > true for an arbitrary n > > that is a last and largest member of a finite set. Irrelevant. > There is no specific line that is checked. And > how we come to the n-th line is also irrelevant. For any n, the n-th line > is not equal to the diagonal. > > And for any n, without counting, the next line is equal to the > diagonal in this example: > > 0.0 > 0.1 > 0.11 > 0.111 > ... Eh? The diagonal is 0.111111111... I see no line that is equal to that diagonal. > Why do you think that this is not contradicting Cantor? Because it is nonsense. Or are you actually stating that when we check 0.1, 0.11 is equal to 0.111111111...? > Perhaps right, depends on how you actually do define things. > But are there nodes mapped to all paths? That is what you > assert. > > Unless there is at least one node occupied by the path p_n that > is not occupied by the paths p_0 to p_n-1, p_n is not a new path. > > Assuming countability again. > > Countability of nodes only. I am only interested to cover every node, > i.e., to exhaust the tree. I am a follower of Eudoxos. > > You have to exhaust the paths, not the nodes. If you think that > exhausting the nodes implies exhausting the paths you are assuming > that the set of paths is countable. > > No, I am showing that the set of paths is counatble. No, you are asuming that you can exhaust the paths by exhausting the nodes, this implies that you are assuming that the set of paths is countable, because the two statements are equivalent. > It is said so. But there is no possibility, after having completed the > construction, to introduce such a path. They have sneaked in. > > And so paths have sneaked in that were not introduced by the construction, > and so when you use the paths given in the construction to map to nodes > you do not show that the set of paths is countable, only that the subset > of paths that you used in the construction is countable. There are other > paths, that have sneaked in, that are not mapped to a node, and can not > be mapped to a node to which no path has yet been mapped. So you have > not proven the the set of paths is countable. > > If you believe in sneeking (Virgil claimed that they say write it with > double e) then you believe in ghosts. I do not. > It is said so. But there is no possibility, after having completed the > construction, to introduce such a path. They have sneaked in. so by your own statement you are believing in ghosts. > Constructing the tree from the list is nothing but (or at least can be > done by) writing some digits or bits in a more economical way. This > does not increase the number of sequences or paths. In that case 1/3 is not in your tree. And your tree is not a set of nodes, but a set of paths. That are two different things. > Where am I talking about decimal expansions? According to you the > in finite sum above (which equals e by definition) is rational. Is > that true? > > True is: There are only rational sums of decimal or binary expansions. > > That is (again) not an answer to my question. By your logic e is a > rational number. > No, the contrary can be proven. e is not rational, but > there is no binary sequence for e. There are only approximations. But > they are not suitable to occur in Cantor's list. What are you rambling about? I am not talking about binary expansion. I am talking about a special series of sums. > Because that is what your logic dictates. That is, every sum of a > finite initial set of the summands is rational, and so according to your > logic also the complete sum is rational. Do you indeed think e is > rational? > > No. See above. Do you indeed think that you can communicate e to some > person by means of a bit sequence? I am not talking about a bit sequence, I am talking about an infinite sum. To recap: *You* state: union{i = 0..n} FISON(i) is a FISON and so: union{i = 0..oo} FISON(i) is a FISON With exactly the same reasoning I get: sum{i = 0..n} 1/(i!) is a rational number and so: sum{i = 0..oo} 1/(i!) is a rational number. So why is the reasoning correct in the first case and wrong in the second case (according to you)? A mathematician will tell you that the reasoning is wrong in both cases. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Answer to Dik T. Winter Nntp-Posting-Host: hera.cwi.nl ... > No. I mean exactly that: The set of finite words over a finite > alphabet is countable. > > Right. > > The set of meanings of these words, i.e., the > set of languages, is countable. > > Is it? I would state that the set of meanings of each of those words can > indeed be countable (I do not know), nothing more. > > Every meaning of every word is defined by a language. > Every language is a finite definition. > The number of finite definitions is countable. For each word the meaning can indeed be countable. But that does not mean that the set of meanings for all the words in a language is countable. > The set of finite alphabets is > countable. > > Is it? I would state that a finite alphabet consists of a finite number > of disctinct symbols. Now you are actually stating that the number of > symbols is countable. > > Every symbol is finite and is defined by a finite word. Therefore the > number of symbols and the number of finite sets of symbols is > counatble. I did not know that every symbol is defined by a finite word. Can you show where I can find that result? > The logic is obtained from physical objects. How else should it have > come into being? Remember, even brains are physical objects. > > Yeah, I know that you have a very liberal view on what is part of physics > means that we use physical objects to do cryptography, and so it is part > of physics... > > And that answers your question that I snipped above: > Every set of linear sets in physics is finite and has a last element. > Therefore logic, that is obtained from physics, requires for finite > linear sets: > AnEm <==> EmAn.. Yeah, I know that you have a very liberal view on what is part of physics and what not. The mathematicians have a different view. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Answer to Dik T. Winter Nntp-Posting-Host: hera.cwi.nl > > If every terminating path of the form 111...1000... is used, then > every node is covered by the last 1. > > But that still does not show that all nodes are covered by a countable set > of paths. It only shows that every node is covered by a set of paths that > contains a countable subset, not that the set itself is countable. > > It is easy to construct a bijection between a countable set of paths > and all nodes. These nodes can even be defined by the paths that lead > to them. That shows that all nodes of the tree can be covered by a > countable set of paths. Yes, they can be covered by a countable set of paths. Nothing more. It does *not* show a bijection, and not a construction of a bijection. > Yes, they are in the tree, so you have to prove that they are also used in > the covering, which you have not done. You do not have to show that each > node is covered, you have to show that with your covering you use each > path. You did show the former. > > If every node is covered, then there remains no path to be covered. What do you mean with covering a path? Until now you were talking about covering nodes. And whatever it may mean, in what way does every node is covered show that there remains no path to be covered? > Or can you find a node that is *not* covered by a path that after > some node to the right? Can you find a node that is covered by a > path that alternates going left and right that is not covered by a > path that after some node always goes to the right? > > I see that every such alternating path with all its nodes is in the > tree, after construction. > > This is not an answer to my question. The path is in the tree, but does > it contain a node that is not covered by a path that after some node > always goes to the right? > > terminating rationals. There does not exist a sequence 0.010101... > that is longer than *every* finite sequence of that form. Ah, so now you contend that 1/3 is a terminating rational. As the sequence of terminating rationals starting with that is: 1/4, 5/16, 21/64, 84/256, ... which of those is 1/3? > We can state: The number of nodes is countable. The number of paths > required to cover all nodes is countable too. > > Right. But the number of required paths is the minimal number of paths > needed to cover all the nodes. That is *not* the number of all paths. > > If all nodes are covered then all path that can be distinguished by > nodes, i.e., all reals that can be distinguished by digits, are there. What do you *mean* with all path that can be distinguished by nodes? I see two meanings: (1) All paths that can be distinguished by a node from each other path (2) All paths that can be distinguished by a node from all other paths. As the covering of all nodes obviously does not imply (1), you must mean (2). But there is no path in the set of all paths that can be distinguished by a node from all other paths. So clearly that is not all paths. > Again: > consider the set of paths where each path after some point always goes to > the right. This set of paths covers each node. Consider the path that > alternates going right and left continuously. Can you point to a node in > this alternating path that is not covered by one of the paths in the > earlier set? But you did agree slightly higher up that that path was in > the tree. > > All parts of that path that really exist, really are in the tree. That is not an answer to my question. Moreover you have not defined really exist. > That is a ridiculous requirement in an informal discussion, in > particular if not mathematics is concerned. > > Oh. So in an informal discussion you can tell nonsense whatever you like > and when challenged you do not need to back it up? > > I have read that there is a dogma of the catholic church stating that > the existence of God can be proved by means of scientific reasoning. I > do not remember the source. Does that turn this information into > nonsense? (Except that its contents is nonsense.) Clearly it is not backed-up by facts, so it can be nonsense or not, I have no way of knowing. It might be true, if might be false, the author may have been wrong, you can remember wrong. But whatever, it is not an argument in a sensible discussion. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Answer to Dik T. Winter posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Precisely: We are talking about subsets of nodes that can be paths or > parts of paths. NO subset of nodes can be a PATH, dumbass! PATHS have EDGES!! === Subject: Re: Answer to Dik T. Winter posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Then let me know one of those paths, please. I will tell you, whether > it belongs to a counatble set. EVERY path belongs to a countable set, DUMBASS. It belongs to the set of cardinality ONE, containing ONLY THAT path! This is NOT the same as there is a countable set to which every path belongs. Every path belongs to a countable set DOES NOT MEAN Every path belongs to some(fixed) countable set!! === Subject: Re: Answer to Dik T. Winter Then let me know one of those paths, please. I will tell you, whether > it belongs to a counatble set. > EVERY path belongs to a countable set, DUMBASS. > It belongs to the set of cardinality ONE, containing ONLY THAT path! > This is NOT the same as there is a countable set to which every path > belongs. > Every path belongs to a countable set DOES NOT MEAN > Every path belongs to some(fixed) countable set!! WM's quantifier dyslexia strikes again Wm claims For each path, p, there exists a countable set, S, with p e S implies There exists a countable set S, such that for each path, p, p e S. But outside of WM's world of mathUnrealism, it doesn't. As Cantor proved, and WM has vainly tried to disprove. -- Virgil === Subject: Re: Answer to Dik T. Winter posting-account=S6jUlgkAAAAS0KYO9CfNqTx523v1YxGt Gecko/2008102920 Firefox/3.0.4 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) The tree is constructed by all terminating paths with tails 000... Which is a countable set of paths, and therefore, by Cantor, does not > include all paths. By Jove, it does! No, it doesn't. As you yourself have already pointed out, this set is easily bijectible with the set of paths terminating with ANY given tail, INCLUDING THE EMPTY tail (which would leave us with the set of all FINITE paths). The set of all FINITE paths will cover or be able to construct THE WHOLE tree, according to your (foolish) usage of these terms. This does NOT imply that actually infinite paths do not exist. The fact that one set of paths covers or can construct the tree goes NOWHERE toward proving that paths outside that set cannot be contained in the tree. === Subject: Re: Answer to Dik T. Winter > legroups.com>, On 17 Jun., 21:37, Owen Jacobson > On 2009-06-17 14:55:38 -0400, WM > said: On 17 Jun., 20:30, Virgil And there are in any maximal infinite binary > tree paths that are not > members of any countable set of paths, as > Cantor proved. Then let me know one of those paths, please. I > will tell you, whether > it belongs to a counatble set. > Your quantifier confusion is showing again. Your belief in matheological nonsense is showing > again. Fools like WM sneer at what they cannot understand. For any path in the complete maximal binary tree, > there is at least one > countable set of paths that contains it. > (Trivially, the set {p} > contains the path p for every path p. The union > of {p} and the set of > terminating paths is a countably infinite set > which contains p.) For any countable set of paths, there is at least > one path in the tree > that is not in that set. Your belief in matheological nonsense is showing > again. > > Cantor has proved, and WM has not disproved, what WM > is calling nonsense. Such 'nonsense' is of much greater mathematical value > than anything WM > has ever done. > also: > For any list of binary sequences, there is at > least one binary > sequence > that is not in that list? Cantor proved it, and none of WM's attempts to fault > that proof are > worth the time it takes to read them. The tree is constructed from the list of > terminating sequences in the > form of terminating paths. It can be, but need not be, constructed that way. One can construct the complete infinite binary tree > directly from the > 1-origin naturals by taking 1 as the root node and > for any n taking 2*n > + 0 and 2*n + 1 as, respectively, node n's left and > right children. Note that for this construction, no paths at all > exist until the > construction is complete. > > This list does not contain the path 0.111... > Hence the union of terminating paths, namely the > tree, does not > contain that path 0.111... My tree above does. It is the minimal set of naturals > containing 1 and > for each of its members n containing also 2*n+1. You cannot distinguish it from all paths of the > tree because 0.111... > does not contain any digit that is not in a path > of the list, > together with all its preceding digits. One can distinguish it in my tree from any path > containing an even > integer, which includes all other paths. Consider the set of terminating rooted paths One does not need to consider any paths to get the > desired tree, as my > construction above shows. Describe a countable set of paths that you > believe contains every path > in the complete maximal binary tree. The set of all terminating paths extended by tails > 000... contains all > nodes and all combinations of nodes that can act as > paths in the tree. In my tree, as defined above, that is flat out false. > In my tree your > paths all are limited to finitely many odd naturals, > but there are paths > with infinitely many odd naturals in them, including > one which contains > only odd naturals. > -- > Virgil Is P Versus NP Formally Independent? In my opinion, no. If you don't believe Euclid's proof that there are infinitely many primes I do not know why seeing a formal proof in ZF set theory should quell your doubts there exists an oracle A relative to which P = NP, and another oracle B (the interpolation problem), then we could distinguish f from a random function in time 2. Using this reduction to an instance (A, B, C) .81ü 2DIO and happen (either To prove that P = NP we must show that for a given problem, no efficient one hole [CapitalEth] this condition can be added, but the truth of the principle Propositional Proof Complexity: Past, Present. === Subject: Re: Answer to Dik T. Winter > But the whole point is that in Cantor's argument, whatever n we choose, it > is a last and largest member of a finite set. Also the first and smallest member of an infinite set. shown that the line numbered with that n is not in the list. This is > true for an arbitrary n that is a last and largest member of a finite set. Also the first and smallest member of an infinite set. So what? There is no specific line that is checked. And > how we come to the n-th line is also irrelevant. For any n, the n-th line > is not equal to the diagonal. And for any n, without counting, the next line is equal to the > diagonal in this example: 0.0 > 0.1 > 0.11 > 0.111 > ... Why do you think that this is not contradicting Cantor? Because Cantor's diagonal proof only refers to infinite binary sequences, which what WM listed are NOT, and any infinite binary sequence is automatically different from every finite sequence such as the ones WM has listed. No, I am showing that the set of paths is counatble. Not in this world! Your set of FINITE paths is countable, but its countability is irrelevant to the countability of a set of paths that it is disjoint from. > It is said so. But there is no possibility, after having completed the > construction, to introduce such a path. They have sneaked in. And so paths have sneaked in that were not introduced by the construction, > and so when you use the paths given in the construction to map to nodes > you do not show that the set of paths is countable, only that the subset of > paths that you used in the construction is countable. There are other > paths, > that have sneaked in, that are not mapped to a node, and can not be mapped > to a node to which no path has yet been mapped. So you have not proven the > the set of paths is countable. If you believe in sneeking (Virgil claimed that they say write it with > double e) then you believe in ghosts. I do not. How is it creating a ghost to note that an infinite binary string with infinitely 1's is not in any set of infinite binary strings each having at most finitely many 1's? Wm is becoming delusional again. Or is it still? Constructing the tree from the list is nothing but (or at least can be > done by) writing some digits or bits in a more economical way. This > does not increase the number of sequences or paths. Constructing a tree requires constructing its node set together with the appropriate left child, right child and parent of relations. Paths are merely a consequence of that construction. For all finite complete binary trees, any set of paths whose union is the nodes set of that tree must have a path for each leaf node. Since the set of paths bijects in an obvious way with the set of leaf nodes, one has to have every path in order to get every node. In maximal infinite binary trees, there are no leaf nodes, and there is no bijection between the set of all paths and any set of nodes. WM does not understand this difference. -- Virgil === Subject: Re: Answer to Dik T. Winter Well, I see, you think mathematical logic is nonsense. To great parts, yes. > No. I mean exactly that: The set of finite words over a finite > alphabet is countable. Right. > The set of meanings of these words, i.e., the > set of languages, is countable. Is it? I would state that the set of meanings of each of those words can > indeed be countable (I do not know), nothing more. Every meaning of every word is defined by a language. In mathematics, not every word need have a meaning. For example, in set theory, is a member of need not have meaning, though it will have a grammar. WM is hung up on his ow particular model of set theory, but his is not the only possible model, and, in general, one can, and possibly should, do set theory without any particular model in mind at all. -- Virgil === Subject: Re: Answer to Dik T. Winter > If every terminating path of the form 111...1000... is used, then > every node is covered by the last 1. But that still does not show that all nodes are covered by a countable set > of > paths. It only shows that every node is covered by a set of paths that > contains a countable subset, not that the set itself is countable. It is easy to construct a bijection between a countable set of paths > and all nodes. These nodes can even be defined by the paths that lead > to them. That shows that all nodes of the tree can be covered by a > countable set of paths. Yes, they are in the tree, so you have to prove that they are also used in > the > covering, which you have not done. You do not have to show that each node > is covered, you have to show that with your covering you use each path. > You > did show the former. If every node is covered, then there remains no path to be covered. Covering a node with a path does not automatically also cover each of the uncountably many paths through that node. If all nodes are covered then all path that can be distinguished by > nodes, i.e., all reals that can be distinguished by digits, are there. Then WM must mean something other than the usual by distinguished. No single digit, nor finite set of digits, distinguishes any one real from all others, just as no one node, nor even any finite set of nodes, distinguishes any one path in a maximal infinite binary tree from all others. Again: > consider the set of paths where each path after some point always goes to > the right. This set of paths covers each node. Consider the path that > alternates going right and left continuously. Can you point to a node in > this alternating path that is not covered by one of the paths in the > earlier > set? But you did agree slightly higher up that that path was in the tree. All parts of that path that really exist, really are in the tree. If any part of that path does not really exist, one is no longer talking about maximal infinite binary trees at all, but just another of WM's myths. > That is a ridiculous requirement in an informal discussion, in > particular if not mathematics is concerned. Oh. So in an informal discussion you can tell nonsense whatever you like > and when challenged you do not need to back it up? I have read that there is a dogma of the catholic church stating that > the existence of God can be proved by means of scientific reasoning. I > do not remember the source. Does that turn this information into > nonsense? It is WM who keeps trying to insert his own dogmas in places that they do not fit. In order to even talk about infinite sets coherently, one must have at least one infinite set, any inductive set as a metaphor for the set of all naturals will do. And once one has that set, none of WM's objections obtain, since we can define a partial order on any such set which makes it into a maximal infinite binary tree having all those properties WM objects to. -- Virgil === Subject: Re: Answer to Dik T. Winter > If every terminating path of the form 111...1000... is used, then > every node is covered by the last 1. But that still does not show that all nodes are covered by a countable set > of > paths. It only shows that every node is covered by a set of paths that > contains a countable subset, not that the set itself is countable. It is easy to construct a bijection between a countable set of paths > and all nodes. These nodes can even be defined by the paths that lead > to them. That shows that all nodes of the tree can be covered by a > countable set of paths. Actually, WM is right for once. Every node (there are only countably many of them after all) can be covered by a countable set of paths. Simply pick the nth path so as to contain the nth node in some counting of the nodes. However often WM is wrong on his own, one should be careful not to assume him always wrong. He is not that consistent. -- Virgil === Subject: Re: Answer to Dik T. Winter A subset of nodes is distinguished from every > element of P that you can specifically address > if and only if it is not contained in > a single element of P that you can specifically > address. and you have agreed that t can be distinguished from > every element of P. It does not matter whether I have agreed, it matters whether it is > true. And as WM has no access to truth, except by accident, and even then he may well reject it, one is better advised to go elsewhere to find it. > As you see from the tree, it is not true, unless the transformation > from the list to the tree would introduce new paths. Which it does. To get from a set of paths to a tree, one bmust take the union of the set of paths as the set of nodes of that tree, and that set of nodes contains subsets, including paths, that were not members of the original set of paths. WM has demonstrated this himself, though without realizing what he has shown: Wm starts with the set of all infinite binary sequences of 0 and 1 nodes which contain only finitely many one nodes. The the union of this set of sets is the set of all nodes of a maximal infinite binary tree, so is such a tree. But in that tree there are maximal totally ordered by ancestor of sets of nodes, i.e., paths, which contain infinitely many 1 nodes, so are NOT members of WM's original set of paths. That, however, > would be something between mathemagic and matheology. Under any > circumstances that is rubbish. It is WM's own personal rubbish then, since WM is the one who presented us with that set of paths and that tree. > -- Virgil === Subject: Re: Answer to Dik T. Winter > Why should the subset belong to one element of the list of > paths It doesn't. > the tree contains a subset of nodes that is > *not* contained in one element of the list of paths As it is neither contained in a path of the tree, this observation is > completely irrelevant. If the original list of paths is no more than countable and the tree is > a maxima; infinite binary tree, then there are necessarily paths in that > tree not in the list. > This is so because countably many paths can cover all nodes but cannot > cover all paths but they do, nevertheless They can cover all nodes, but Cantor proved that for any countable set of paths there are other paths. as Cantor proved. Therefore he was wrong. In a war between WM and Cantor, WM will always lose. During the next 100 years we will laugh about his giant joke We do not even have to wait to laugh at WM. He is laughable now, and has been for years. - and > then he will be forgotten by mathematicians, except by some > historians. WM will be forgotten long before Cantor is. If it were not for WM's continual postings here, he would have been forgotten already. -- Virgil === Subject: Re: Answer to Dik T. Winter > Your claim is that no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path. A: actually infinite paths exist, > B: the infinite tree contains a path p that can be > distinguished from every path of P. You agree A ==> B So if A is true then B is true > and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) Please answer yes or no t is not an element of P The actually infinite path t is not an element of P > and not a path of T, because t does not exist. If t does not exist it CERTAINLY can be distinguished from things that do exist. Note it would be circular to simply assume that actually > infinite paths do not exist. It is not assumed. WM repeatedly asumes it, but has never proved it. > It is proved by the fact that t cannot be > distinguished from the paths of P and T. But t CAN be distinguished from them,, particularly if the paths of P and T exist but t does not. Proof by the fact that t cannot be distinguished from the set P Nope: you have agreed that t can be distintuished from the every > element > of the set P (Recall, You have agreed. A subset of nodes is distinguished from every > element of P if and only if it is not contained in > a single element of P.) All of t, that does exist, is contained in a path of P. It is only > your delusion that opposes to this fact. WM is not in a position to accuse others of having delusions when he has so many of his own that he is quite unable to distinguish from reality. > You say that for every path p of P there is a bit of t that does not > belong to p. That is not what anyone but WM says. What we do say is that if P is a countably infinite set of paths in some maximal infinite binary tree, then there are paths in that tree which are not members of P, even though the union of P may contain all nodes of that tree. In fact, WM's own example of the set of all paths with only finitely many right branches is such a P, since in the resulting tree there are paths with infinitely many right branches. So that WM has managed to disprove his own thesis. -- Virgil === Subject: Re: Answer to Dik T. Winter posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Your claim is that no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path. A: actually infinite paths exist, > B: the infinite tree contains a path p that can be > distinguished from every path of P. You agree A ==> B So if A is true then B is true > and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) you have agreed that t can be distinguished from > every element of P. > It does not matter whether I have agreed > it matters whether it is > true. > As you see from the tree, the subset of nodes t is in the tree You cannot distinguish it from all paths of the tree. And we agree that the subset of nodes t is not in > a single element of the list P if actual infinity axists. so it is true that the subset of nodes t is > in the tree and can be distinguished from > every element of P. If you were right. But that would imply the existence of actual infinity and the creation of paths by dropping bits. As the latter is wrong, you are not right. === Subject: Re: Answer to Dik T. Winter > Your claim is that no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path. A: actually infinite paths exist, > B: the infinite tree contains a path p that can be > distinguished from every path of P. You agree A ==> B So if A is true then B is true > and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) you have agreed that t can be distinguished from > every element of P. > It does not matter whether I have agreed > it matters whether it is > true. > As you see from the tree, the subset of nodes t is in the tree You cannot distinguish it from all paths of the tree. And we agree that the subset of nodes t is not in > a single element of the list P if actual infinity axists. Since no potentially infinite sets can exist, either there is no maximal infinite binary tree at all, in which case WM's speculating on its properties is foolish, or there is one, and its properties are those of actually infinite sets. so it is true that the subset of nodes t is > in the tree and can be distinguished from > every element of P. If you were right. And if such a tree exists at all, he is. > But that would imply the existence of actual > infinity and the creation of paths by dropping bits. Paths are created by the partial order on the set of nodes induced by the transitive closure of theancestor of relation. In a maximal infinite binary tree, uncountably many of them are created. > As the latter is > wrong, you are not right. In set theory, WM is the one who is not right by being left out. > -- Virgil === Subject: Re: Answer to Dik T. Winter posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I Your claim is that no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path. A: actually infinite paths exist, > B: the infinite tree contains a path p that can be > distinguished from every path of P. You agree A ==> B So if A is true then B is true > and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) you have agreed that t can be distinguished from > every element of P. > It does not matter whether I have agreed Outside of Wolkenmuekenheim it does. it matters whether it is > true. > As you see from the tree, the subset of nodes t is in the tree a single element of the list P if actual infinity axists. So you cannot prove ~B without making the assumption ~A which is what you are trying to prove. We are left we the result that you cannot prove A or ~A. - William Hughes === Subject: Re: Answer to Dik T. Winter posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Your claim is that no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path. A: actually infinite paths exist, > B: the infinite tree contains a path p that can be > distinguished from every path of P. You agree A ==> B So if A is true then B is true > and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) you have agreed that t can be distinguished from > every element of P. > It does not matter whether I have agreed Outside of Wolkenmuekenheim it does. it matters whether it is > true. > As you see from the tree, the subset of nodes t is in the tree And we agree that the subset of nodes t is not in > a single element of the list P if actual infinity axists. Otherwise your alleged proof is even more obviously wrong. So you cannot prove ~B without making > the assumption ~A which is what you are trying > to prove. Wrong. ~B is proven by the impossibility to distinguish t from every path of the binary tree and the fact that the tree does not contain paths that are missing in P. === Subject: Re: Answer to Dik T. Winter > Your claim is that no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path. A: actually infinite paths exist, > B: the infinite tree contains a path p that can be > distinguished from every path of P. You agree A ==> B So if A is true then B is true > and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) you have agreed that t can be distinguished from > every element of P. > It does not matter whether I have agreed Outside of Wolkenmuekenheim it does. it matters whether it is > true. > As you see from the tree, the subset of nodes t is in the tree And we agree that the subset of nodes t is not in > a single element of the list P if actual infinity axists. Otherwise your alleged proof is even more obviously wrong. If actually infinite sets can exist, WM is wrong, and if they don't then all trees are finite and WM IS STILL WRONG. So you cannot prove ~B without making > the assumption ~A which is what you are trying > to prove. Wrong. ~B is proven by the impossibility to distinguish t from every > path of the binary tree and the fact that the tree does not contain > paths that are missing in P. Neither of which claimed facts is true if any actually infinite sets exist, and the alleged tree and set P themselves do not exist at all if no actually infinite sets exist, so the issue would then be moot. -- Virgil === Subject: Re: Answer to Dik T. Winter posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I Your claim is that no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path. A: actually infinite paths exist, > B: the infinite tree contains a path p that can be > distinguished from every path of P. You agree A ==> B So if A is true then B is true > and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) you have agreed that t can be distinguished from > every element of P. > It does not matter whether I have agreed Outside of Wolkenmuekenheim it does. it matters whether it is > true. > As you see from the tree, the subset of nodes t is in the tree And we agree that the subset of nodes t is not in > a single element of the list P if actual infinity axists. So you cannot prove ~B without making > the assumption ~A which is what you are trying > to prove. Wrong. ~B is proven by the impossibility to distinguish t from every > path of the binary tree Nope. You just said that if actual infinity exists, it is possible to distinguish t from every path of the binary tree. Hence you cannot prove ~B without assuming ~A. We are left we the result that you cannot prove A or ~A. - William Hughes === Subject: Re: Answer to Dik T. Winter posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > Wrong. ~B is proven by the impossibility to distinguish t from every > path of the binary tree Nope. You just said that if actual infinity exists, it is possible to > distinguish t from every path of the binary tree. Hence you cannot > prove ~B without assuming ~A. I prove ~B, for instance by your inability to distinguish t from T, with no regard to the truth of A. === Subject: Re: Answer to Dik T. Winter Wrong. ~B is proven by the impossibility to distinguish t from every > path of the binary tree Nope. You just said that if actual infinity exists, it is possible to > distinguish t from every path of the binary tree. Hence you cannot > prove ~B without assuming ~A. I prove ~B, for instance by your inability to distinguish t from T, > with no regard to the truth of A. > In the maximal infinite binary tree which I showed how to construct from the infinite set of all naturals, one can distinguish LOTS of other paths from any fixed countable set of paths. If it can't be done in WM's trees, then his trees aren't maximal infinite binary trees at all -- Virgil === Subject: Re: Answer to Dik T. Winter posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I Your claim is that no possibility exists to construct or to distinguish by one or many or infinitely many nodes of the tree another path. A: actually infinite paths exist, B: the infinite tree contains a path p that can be distinguished from every path of P. You agree A ==> B So if A is true then B is true and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) > I prove ~B, for instance by your inability to distinguish t from T, > with no regard to the truth of A. > Nope. You need to distinguish the subset of nodes t from every element of P, not from the tree, and you have repeatedly agreed that you can distinguish t from every element of P if A is true. You have never shown that you cannot distinguish t from every element of P without regard to the truth of A. We are left we the result that you cannot prove A or ~A. - William Hughes === Subject: Re: Answer to Dik T. Winter posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Your claim is that no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path. A: actually infinite paths exist, > B: the infinite tree contains a path p that can be > distinguished from every path of P. You agree A ==> B So if A is true then B is true > and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) I prove ~B, for instance by your inability to distinguish t from T, > with no regard to the truth of A. Nope. You need to distinguish the subset of nodes t from every > element of P, not from the tree, The paths of the tree are the same as the subsets of P. There is no reasonable argument that leads to a difference. Further we can derive from the axioms that the union of sets does not contain any element, that is not contained in at least one of the sets united. We unite the singlets {p n} where p n is in P. T = U{p n}. There is no other path in the tree. > and you have > repeatedly agreed that you can distinguish t from every element of > P if A is true. You erroneously believed so. I could not contradict your error. Therefore I let it go. Now you can see that you were wrong. >You have never shown that you cannot distinguish > t from every element of P without regard to the truth of A. I cannot show that because I cannot disprove a dream unless the sleper is awaked. This is accomplished by the tree. We are left we the result that you > cannot prove A or ~A. === Subject: Re: Answer to Dik T. Winter Your claim is that no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path. A: actually infinite paths exist, > B: the infinite tree contains a path p that can be > distinguished from every path of P. You agree A ==> B So if A is true then B is true > and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) I prove ~B, for instance by your inability to distinguish t from T, > with no regard to the truth of A. Nope. You need to distinguish the subset of nodes t from every > element of P, not from the tree, The paths of the tree are the same as the subsets of P. Not in the maximal infinite binary tree which one can so easily build from theactually infinite set of all 1-origin naturals by defining the left child of n to be 2*n+0 and the right child of n to be 2*n+1. > There is no > reasonable argument that leads to a difference. Cantor's argument re the incompleteness of any list of binary sequences is reasonable argument which leads to a difference. It is WM who has no reasonable argument prohibiting such a difference. > Further we can derive > from the axioms that the union of sets does not contain any element, > that is not contained in at least one of the sets united. It has been already granted that a countable set of paths can have every member of a countable set of nodes in at least one path. But such a fact does not in any way require that such a countable set of paths contain each possible path of a maximal infinite binary tree, and Cantor proved that it did not. We unite the > singlets {p_n} where p_n is in P. T = U{p_n}. There is no other path > in the tree. Every path is a countable set of nodes, all of which are members of members of P. But a family of sets whose union is a given set need not contain all subsets of that union, which is what WM's argument would require. So most paths of the tree are not in WM's set of paths, P. > and you have > repeatedly agreed that you can distinguish t from every element of > P if A is true. You erroneously believed so. It is hardly erroneous to believe Cantor's diagonal proof. So given any COUNTABLE set of paths, P, in a maximal infinite binary tree, there are more paths in the tree but not in P than actually in P. > I could not contradict your error. But you did contradict his truth. > Therefore I let it go. Now you can see that you were wrong. On the contrary, we all still see where WM is still wrong. As soon as any actually infinite set exists, and one is necessary for any construction of a maximal infinite binary tree, then WM is wrong about such trees. And unless there is at least one such actually infinite set, there are no such trees for WM to pontificate about. > >You have never shown that you cannot distinguish > t from every element of P without regard to the truth of A. I cannot show that because I cannot disprove a dream unless the sleper > is awaked. This is accomplished by the tree. Then it is WM who is doing all the dreaming, as his sort of maximal infinite binary tree can not ever exist anywhwere. Such trees can only exist in a world containing an actually infinite set. We are left we the result that you > cannot prove A or ~A. We are left with the result ~B. WM is left with the result that his sort of tree cannot exist at all. In WM's world, a set of paths, P, with each path limited to finitely many right child nodes must contain a path containing infinitely many right child nodes. That is not allowed to happen in mathematical set theories. -- Virgil === Subject: Re: Answer to Dik T. Winter posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > Your claim is that no possibility exists to construct or to > distinguish by one or many or infinitely many nodes > of the tree another path. A: actually infinite paths exist, > B: the infinite tree contains a path p that can be > distinguished from every path of P. You agree A ==> B So if A is true then B is true > and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) I prove ~B, for instance by your inability to distinguish t from T, > with no regard to the truth of A. Nope. You need to distinguish the subset of nodes t from every > element of P, not from the tree, The paths of the tree are the same as the subsets of P. Nope. You have agreed that if infinite paths actually exist then t is not contained in any element of P. So you cannot argue The paths of the tree are the same as the subsets of P without assuming ~A. We are left we the result that you cannot prove A or ~A. - William Hughes === Subject: Re: Answer to Dik T. Winter posting-account=X9VdBgoAAAA0ZF8HT8BN_JvL2DEZQ6_G CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > The paths of the tree are the same as the subsets of P. Nope. You have agreed that if infinite paths > actually exist then t is not contained in any element > of P. So you cannot argue The paths of the tree > are the same as the subsets of P without assuming ~A. That is not a matter of A or not A. It is the same as x = x That is independent of A. === Subject: Re: Answer to Dik T. Winter The paths of the tree are the same as the subsets of P. Nope. You have agreed that if infinite paths > actually exist then t is not contained in any element > of P. So you cannot argue The paths of the tree > are the same as the subsets of P without assuming ~A. That is not a matter of A or not A. It is the same as x = x That is independent of A. What it depends on is, in WM's view, the absence of any actually infinite sets, which implies the absence of the very maximal infinite binary tree that WM is pontificating about. In order to have such a tree at all, one must first have at least one actually infinite, and preferably well-ordered, set. Any actually infinite well -ordered set contains as a subset (possibly improper) a set that is order isomorphic to the infinite ordered set of all naturals, from which such a tree is easily built. And in such a tree, WM's claim are wrong. Specifically, the set of all paths each having only finitely many right branchings, while containing each node in at least one paths, does not contain any of those uncountably many paths which each contains infinitely many right branchings. -- Virgil === Subject: Re: Answer to Dik T. Winter posting-account=1lE9SQkAAADFrJsDv61dh1YXcJ_ahy5I > Your claim is that no possibility exists to construct or to distinguish by one or many or infinitely many nodes of the tree another path. A: actually infinite paths exist, B: the infinite tree contains a path p that can be distinguished from every path of P. You agree A ==> B So if A is true then B is true and your claim is false. You want to show ~A [Follows from ( A ==> B, ~B) ==> ~A ] by proving ~B (Note that assuming ~A is circular) Wolkenmuekenheim logic A: actually infinite paths exist, > You have agreed that if infinite paths > actually exist > That is not a matter of A or not A. - William Hughes === === Subject: question about notation The superscript above t, next to -1 in the gamma function (it looks kind of like a couple of tildes ~ stacked on top of each other) http://en.wikipedia.org/wiki/Gamma_function what does that notation represent? === Subject: Re: question about notation >The superscript above t, next to -1 in the gamma function (it looks kind of >like a couple of tildes ~ stacked on top of each other) >http://en.wikipedia.org/wiki/Gamma_function >what does that notation represent? > It's just a z that doesn't render well in the picture. Gamma(z) = int[0..oo] t^(z-1) exp(-t) dt. --Lynn http://math.asu.edu/~kurtz === Subject: Re: question about notation posting-account=oTDIagkAAACTxHurtPutBWvNQS8ZCNO9 Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > The superscript above t, next to -1 in the gamma function (it looks kind of > like a couple of tildes ~ stacked on top of each other)http://en.wikipedia.org/wiki/Gamma function > what does that notation represent? It is a lower case z: the expression within the integral is (t^(z-1)) (e^(-t)). === Subject: Re: question about notation posting-account=3y8algoAAAC2FNJlQOsd2fY-Swm5XWIE Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) On Jun 22, 12:16pm, cbr...@cbrownsystems.com The superscript above t, next to -1 in the gamma function (it looks kind of > like a couple of tildes ~ stacked on top of each other)http://en.wikipedia.org/wiki/Gamma function > what does that notation represent? It is a lower case z: the expression within the integral is (t^(z-1)) > (e^(-t)). > D'oh. (Smacks forehead). === Subject: Classical and Modern mathematics and (over?)specialization. Hi: As a first-year student, I was surprised to see the degree of (what I thought was ) over-specialization in many students. I implicitly assumed that the goal of learning math was to have a broad base of knowledge, and this is what I will try to do, unless something convinces me otherwise. Still, I see people who get their degrees in , e.g., algebra in two years, but do not know what an open set is , nor the definition of a Cauchy sequence, let alone basic results/defs. related to them, like the intersection of open sets being open, or that a space is complete if all Cauchy seqs. converge ; I am not talking the fancier, more advanced results, but what I think are issues. Is this a good thing (to be fair, these people do know their areas of specialty extremely well)? I have been told that this trend is more of a modern trend, where much of the subject is black-boxed , and the details don't matter, only the overall larger result, and what can be proven with it : we can use some theorems on e.g.,differential forms, without understanding at a basic level what a differential form is. Is this trend the result of the explosion of knowledge that makes it difficult to know well even a small area, or is there something else going on?. Just wanted to know other's thoughts. === Subject: Re: where did the big bang start? posting-account=n8pQvgkAAAAR2icJiQ21GsmYtflsTgld Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) C'mon. It's all there in the Scriptures. > Where did the Big Bang start? There was no 'where'. > When did the Big Bang start? There was no 'when'. > How did the Big Bang start? The Cosmic Flatulator did it. > What did the Big Bang start? Usenet, among other things. > Who/Whom did the Big Bang start? See above. > Why did the Big Bang start? A Little Bang would have resulted in a Universe 14 inches across. Glad I could help. Dangerous Bill === Subject: Re: where did the big bang start? posting-account=tNh-2AoAAACqdWo2IikcW-FF_IGUAvWf AppleWebKit/530.18 (KHTML, like Gecko) Version/4.0.1 Safari/530.18,gzip(gfe),gzip(gfe) > ... from the vast fields of the Deccan where Lava flowed for > millions of years, the great teacher cleared his thirsty throat Where did the Big Bang start? > When did the Big Bang start? > How did the Big Bang start? > What did the Big Bang start? > Who/Whom did the Big Bang start? > Why did the Big Bang start? The most important of these six questions is Why. > If one spends 5/6 of his/her lifetime answering the > least important of these questions, that still leaves > 1/6 of an answer perpetually pending. Yet you get to > pretend you're a Physicist if you can feign not caring > Hey, yo!, Teach'!.. Yes, there are 6 reasons! Where did the Big Bang NOT start? > When did the Big Bang NOT start? > How did the Big Bang NOT start? > What did the Big Bang NOT start? > Who/Whom did the Big Bang NOT tart? > Why did the Big Bang NOT start? These questions, all reasonable, are implicit surely. Since the Big Bang is not repeatable, why does it still get categorized as Science!? Questions can be rhetorical? > Now, that we have level the playing field, and have NOT > even created a Mexican standoff, ... the answer is clear > and self-evident, isn't it....... ahahaha.... It doesn't need > 5/6 of one's life time, not even 5/6 of an hour... nor 1/6 > of perpetual dangling to see it... ahahahaha... It remains ironic that the term Big Bang was coined mockingly by Hoyle. As it is, society's mass media being dangerously single minded, this topic must contain homage to the Big Bang -- disingenuous or otherwise. > Jay Bharat, Virdy Marzipan. I always enjoy your tripe. Hey how come there are so many more Newsgroups suddenly? Usenet, however dated, even outdated, must be some monolithic messaging service. Reach one group, you've reached them all? More importantly, you hanson -- and I do enjoy your insights -- characterized all my thirsty thoughts as from profound to tripe all in one post. That range does about cover the available spectrum. You're welcome to the well deserved AH-HA moments of laughs. Life, the Profound Trip, is to enjoy. Enjo(y)... -- Mahipal === Subject: Re: where did the big bang start? posting-account=7bF0GwoAAABMFHX6V4fON4-1F6LFJ834 Trident/4.0; .NET CLR 2.0.50727; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > Where did the Big Bang start? > When did the Big Bang start? > How did the Big Bang start? > What did the Big Bang start? > Who/Whom did the Big Bang start? > Why did the Big Bang start? The most important of these six questions > is Why. If one spends 5/6 of his/her lifetime > answering the least important of these > questions, that still leaves 1/6 of an answer > perpetually pending. Yet you get to pretend > you're a Physicist if you can feign not caring > Mahipal > Hey, yo!, Teach'!.. Yes, there are 6 reasons! Where did the Big Bang NOT start? > When did the Big Bang NOT start? > How did the Big Bang NOT start? > What did the Big Bang NOT start? > Who/Whom did the Big Bang NOT tart? > Why did the Big Bang NOT start? These questions, all reasonable, are implicit > surely. Since the Big Bang is not repeatable, > why does it still get categorized as Science!? Because it is a feature of a current theory, extrapolating backwards in time (with the usual caveats about how bad an idea that is). > Questions can be rhetorical? Now, that we have level the playing field, > and have NOT even created a Mexican > standoff, ... the answer is clear and > self-evident, isn't it....... ahahaha.... It > doesn't need 5/6 of one's life time, not > even 5/6 of an hour... nor 1/6 of > perpetual dangling to see it... ahahahaha... It remains ironic that the term Big Bang > was coined mockingly by Hoyle. Zeno's paradox also was a joke, a veritable poke in the ribs. > As it is, society's mass media being > dangerously single minded, this topic must > contain homage to the Big Bang -- > disingenuous or otherwise. It provides a recognizeable landmark in the language. The common man knows the name, and vagely knows what it means. Those in Science, know that it stands for a large body of work and observation (and has nothing to do with giant fireworks). > Jay Bharat, Virdy Marzipan. I always enjoy > ahahahaha... ahahahanson Hey how come there are so many more > Newsgroups suddenly? Usenet, however > dated, even outdated, must be some > monolithic messaging service. Reach one > group, you've reached them all? No, not unless you crosspost. hanson always did enjoy an audience... > More importantly, you hanson -- and I do > enjoy your insights -- characterized all my > thirsty thoughts as from profound to tripe > all in one post. That range does about cover > the available spectrum. You're welcome to > the well deserved AH-HA moments of laughs. Life, the Profound Trip, is to enjoy. Graciously put. David A. Smith === Subject: Re: where did the big bang start? posting-account=_-PQygoAAAAciOn_89sZIlnxfb74FzXU Gecko/2009060215 Firefox/3.0.11,gzip(gfe),gzip(gfe) > ... from the vast fields of the Deccan where Lava flowed for > millions of years, the great teacher cleared his thirsty throat Where did the Big Bang start? In the middle. > When did the Big Bang start? In the beginning and end. > How did the Big Bang start? Universe ends. > What did the Big Bang start? Perspective. > Who/Whom did the Big Bang start? N/A > Why did the Big Bang start? Because it did. The most important of these six questions is Why. > If one spends 5/6 of his/her lifetime answering the > least important of these questions, that still leaves > 1/6 of an answer perpetually pending. Yet you get to > pretend you're a Physicist if you can feign not caring > Hey, yo!, Teach'!.. Yes, there are 6 reasons! Where did the Big Bang NOT start? > When did the Big Bang NOT start? > How did the Big Bang NOT start? > What did the Big Bang NOT start? > Who/Whom did the Big Bang NOT tart? > Why did the Big Bang NOT start? Now, that we have level the playing field, and have NOT > even created a Mexican standoff, ... the answer is clear > and self-evident, isn't it....... ahahaha.... It doesn't need > 5/6 of one's life time, not even 5/6 of an hour... nor 1/6 > of perpetual dangling to see it... ahahahaha... Jay Bharat, Virdy Marzipan. I always enjoy your tripe. === Subject: Re: Crank Education posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) On Jun 7, 1:07pm, zzbun...@netscape.net Well, some of that is because, it's been so long since > anything in computer theory was anything other than neural nets, > that's also why the engineers in post stone age computing > do just about nothing but GPS, Digital Terrain Mapping, Digital > Fiber Optics, > Cell Phones, Broadband, Flat Screen Debuggers, HDTV, Blue Ray, > Holographic Systems, Distributed Processing, On-Line Publishing, On- > Line Banking, > On-Line Shopping, XML, USB, C++, PGP, Anti-Spam, Autonomous > Vehicles, > Light Sticks, Thermo-Electric Cooling, Microwave Cooling, > non lead acid batteries, Self-Replcating Machines, and Self- > Assembling Robots. Anyone cracking any of those problems with a good P=NP implementation would go > to the top of the food chain, and become the first quadrillionaire... Probably would. But Algorithmic Information Theory > self-satisfies the boundary condition that the only aires > for the remaninder of the idiot Big Bang > will necessarily be string-alongers regardless. > So, the people who can actually still think work on GPS, > HDTV, and Self-Assembling Robots anyway. These are very strange words. Why did you choose them and where did they come from? They seem forced or jilted. Do they have anything to do with the fact I have proved P==NP on USENET? === Subject: Re: Crank Education posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > On Jun 7, 1:07pm, zzbun...@netscape.net anything in computer theory was anything other than neural nets, > that's also why the engineers in post stone age computing > do just about nothing but GPS, Digital Terrain Mapping, Digital > Fiber Optics, > Cell Phones, Broadband, Flat Screen Debuggers, HDTV, Blue Ray, > Holographic Systems, Distributed Processing, On-Line Publishing, On- > Line Banking, > On-Line Shopping, XML, USB, C++, PGP, Anti-Spam, Autonomous > Vehicles, > Light Sticks, Thermo-Electric Cooling, Microwave Cooling, > non lead acid batteries, Self-Replcating Machines, and Self- > Assembling Robots. Anyone cracking any of those problems with a good P=NP implementation would go > to the top of the food chain, and become the first quadrillionaire... Probably would. But Algorithmic Information Theory > self-satisfies the boundary condition that the only aires > for the remaninder of the idiot Big Bang > will necessarily be string-alongers regardless. > So, the people who can actually still think work on GPS, > HDTV, and Self-Assembling Robots anyway. These are very strange words. Why did you choose them and where did > they come from? They seem forced or jilted. Do they have anything to do with the fact I have proved P==NP on > USENET? P=NP folks. I am just hanging out here in the edge of cyberspace.... On the moon, over the Sea of Tranquility, he leaned perilously close to the edge, and casually yelled, Hello?!... then Echo!... ... and his words resounded off the barren craters and echoed the truth he had earned in his dramatic quest to Prove P vs. NP... ...tbc... === Subject: Re: Crank Education posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) You are half way to the cure. > What is the traditional route for the other half? > In your case... euthanasia. > See earlier question: > ---- > How about suicide in your case? > Better yet, why don't you find your own suicide solution. Oh... > wait.. > if it is anything like your P vs NP solution, you will fail over and > over again. > Why would you suggest that? It is not natural to say such things. I take it your first attempt failed? To prove P=NP? Yes. But this attempt worked. === Subject: Re: Crank Education <9jRWl.110549$Ro1.35219@en-nntp-05.dc1.easynews.com> posting-account=sxrJ7goAAABI7pirjnwOXjy89oxl-rMO Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > You are half way to the cure. > What is the traditional route for the other half? In your case... euthanasia. See earlier question: > ---- How about suicide in your case? > Better yet, why don't you find your own suicide solution. Oh... wait.. > if it is anything like your P vs NP solution, you will fail over and > over again. Euthanasia is out of the question. So are cruel suggestions. === Subject: Re: Crank Education posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) You are half way to the cure. > What is the traditional route for the other half? > In your case... euthanasia. > See earlier question: > ---- > How about suicide in your case? > Better yet, why don't you find your own suicide solution. Oh... > wait.. > if it is anything like your P vs NP solution, you will fail over and > over again. > Why would you suggest that? It is not natural to say such things. I take it your first attempt failed? My first attempt at what? Suicide, as you cruelly suggested? No. I have never attempted to commit suicide nor would I ever. === Subject: Re: Crank Education posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) On Jun 7, 1:07pm, zzbun...@netscape.net Well, some of that is because, it's been so long since > anything in computer theory was anything other than neural nets, > that's also why the engineers in post stone age computing > do just about nothing but GPS, Digital Terrain Mapping, Digital > Fiber Optics, > Cell Phones, Broadband, Flat Screen Debuggers, HDTV, Blue Ray, > Holographic Systems, Distributed Processing, On-Line Publishing, On- > Line Banking, > On-Line Shopping, XML, USB, C++, PGP, Anti-Spam, Autonomous > Vehicles, > Light Sticks, Thermo-Electric Cooling, Microwave Cooling, > non lead acid batteries, Self-Replcating Machines, and Self- > Assembling Robots. Anyone cracking any of those problems with a good P=NP implementation would go > to the top of the food chain, and become the first quadrillionaire... Probably would. But Algorithmic Information Theory > self-satisfies the boundary condition that the only aires > for the remaninder of the idiot Big Bang > will necessarily be string-alongers regardless. > So, the people who can actually still think work on GPS, > HDTV, and Self-Assembling Robots anyway. Why do you call people idiots? Why not be kind and teach them? === Subject: Re: Crank Education <9jRWl.110549$Ro1.35219@en-nntp-05.dc1.easynews.com> posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw Gecko/2009060215 Firefox/3.0.11 (.NET CLR 3.5.30729),gzip(gfe),gzip(gfe) > You are half way to the cure. > What is the traditional route for the other half? In your case... euthanasia. See earlier question: > ---- How about suicide in your case? > Better yet, why don't you find your own suicide solution. Oh... wait.. > if it is anything like your P vs NP solution, you will fail over and > over again. Why are you so mean? === Subject: 2 dimensional parity matrix, pattern qty? 2 dimensional parity matrix, pattern qty? This matrix is a parity bit matrix that is using 2 dimensional parity check. So each matrix intersection is a 1 or 0. It turns out that a 2x2 pattern of errors that are located in adjacent row and column will not be detected as errors by the parity check. The patterns looks something like below (this is 7x4 matrix and shows the 2x2 pattern). So bits located in that pattern shown by the x will not be detected in either the row or column. They can be anywhere as long as the intersect to have 2 in a row and 2 in a column. 1x1x101 0x0x100 1100110 0011001 What is the equation to determine the total number of patterns in a matrix like this that is K wide and J deep? Any thoughts appreciated as Im at a total loss on how to approach this. thank you === Subject: Computer-Based Times Tables Video Game posting-account=-LsU5QoAAADlmZ8sORNW6vX0Eva6j_04 Trident/4.0; AT&T CSM6.0; GTB6; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) Now's the time and free is good. Get a jump on next school year by getting the BEST multiplication facts learning game out there, TimezAttack by BigBrainz. Free base version teaches all facts 2-12. This is highly recommended, take a peek. http://www.bigbrainz.com/index.php?PARTNER=brettstaylor Brett MyGEDClass.com www.geocities.com/multiplicationfacts Coming Soon! www.NOTgeocities.com for those affected who want a place to leve a link to your new site, Email me at mygedclass@gmail.com === Subject: Liar Paradox Explanations & Resolutions posting-account=UA-6fQkAAADI18fSPOc495gPgW1akxLl Trident/4.0; MathPlayer 2.10b; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618),gzip(gfe),gzip(gfe) Liar Paradox Explanations & Resolutions I'm Charlie and I'm working on a project to gather URLs that contain information on Liar Paradox Explanations & Resolutions. I'm doing this on a new web site called Biggest And Best Sites. If you will click on: Liar Paradox Explanations & Resolutions http://www.abcdedcba.com?a=L3VEGA then you will see the list of URLs created so far, sorted by their Size and Rating, as entered by my helpers and me. The Size is defined as the # of Liar Paradox Explanations & Resolutions on the site. So please join in, and together we can evaluate every URL known to relate to Liar Paradox Explanations & Resolutions, and we'll all have instant access to the Biggest and Best sites in the world for this purpose! Yours, Charlie === Subject: question from a math retard I'm 44 and need remedial math starting at about the 9th grade level. Eventually I need accreditation in a 12th grade calculus course to gain admission to the B.Sc. psychology program at my college. Any suggestions? Woody -- NOTE TO NEWSGROUP USERS; My reply-to email address is valid. For a safe valid reply-to address of your own go to www.hushmail.com === Subject: Re: question from a math retard > I'm 44 and going back to college after an absence of 18 years. To get into > my college's B.Sc. Psychology program, I need accreditation in a 12th grade > calculus course. Before I can get that I need remedial math starting at the > 9th grade level. Any suggestions? Woody > See my reply alt.math. Don't multipost, learn about cross posting. See http://oakroadsystems.com/genl/unice.htm === Subject: Re: question from a math retard > I'm 44 and need remedial math starting at about the 9th grade level. > Eventually I need accreditation in a 12th grade calculus course to gain > admission to the B.Sc. psychology program at my college. Any suggestions? Take some community college courses. Try learning on your own. Get a tutor. At what level of math are you needing to start? Skip psychology, consider counseling. === Subject: Re: --- --- --- Reference related to a number theory question posting-account=OxGkAAoAAADdCLj72dc_tDaOxMAzDWsw 240x320),gzip(gfe),gzip(gfe) (squid/2.5.STABLE12) The following equation is under consideration. x^p + (1/M)y^p = z^2 (1) Conditions: x, y, z are relatively prime integers each > 5, prime p 3, y is even, integer M > 2. Statement: (1) has no integer solutions under the given conditions if > M is even. But it can have integer solutions if M is odd. I would greatly appreciate if anyone can kindly refer me to some > appropriate referenc > related to (1) Take z to be some large, odd number. > Take x and p to satisfy the conditions, with x^p < z^2, x odd. > Take y = z^2 - x^p. > Then M will be an even integer. Do you ever think these things through before posting them? > Even a tiny bit? -- > Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) The solution numerically is given by tyhe sequence 2*234579167=469158334/78167/3001/2=2 You guys are ridiculous. These days I can say that I left my house > with a GPS at 10:13.012 h:m.s today and arrived at the store at > 10:32.304 and had a VMG of 34.23 mph. > This level of detail was not available in Kant's time, Wow, shucks you are soooooo ridiculously bright. NOT but the same > sensibilities are exactly what he discusses. You may find the following packed with sensibilities, the application > of reason certainly doesn't. First sentence of Kant's pure unadulterated destruction of reason: > (PUDOR) > That all our knowledge begins with experience there can be no > doubt. First sentence second paragraph: > But, though all our knowledge begins with experience, it by no means > follows that all arises out of experience. You may find Kant's take on morality sensible, whereas reason proves > it to be one of the most senseless, therefore utterly mind dependent, > disgustingly arbitrary, context bereft, utterly ignorant and bereft of > anything man can experience, (touch see feel hear smell), therefore > the most anti-human anti-reason morality known to man. You may regard Kant's dopey idea that man cant know things in > themselves, sensible, when in reality, as determined via reason, that > garbage is just sooo ridiculously stupid its beyond words. In man aquiring his knowledge there is absolutely no requirement of > man to know things in themselves for him to be able to claim 100% > certain knowldge, with 100% certainty man CAN and DOES know the > differences between forms of matter and matter's nature. That presupposes a magical sudden undestanding from which to claim > 100% understanding, that also insists @ its more fundamental level > that knowledge was gained without any experimental evidence to back it > up and from which to base his reason... you're totally cart before > horse. don't you thing the horse will have more success pulling? You missed > the foundations - next you'll be telling us that you can build a house > from the roof down? You need to step back and put things into the correct context before > you start trying to claim some kinda supperior thought process -which > only appears totally lacking from reading this . It is NOT the entity in itself that man needs to know, but rather it > is the differences between the forms of matter and their nature is ALL > there is for man to have knowledge of, Aristotle's law of identity > which Kant rejects as a means to knowledge. Same position, get the right context and you might have something > MG The essence of truth in proof can be properly expressed through narrative means and recollections citing facts to prove otherwise forgone or obscured conclusions to bring light to further truth. Begin logix narrative:(thread) I challenge the devil to a debate (and any logicians, too): For forms of matter nature proof p=NP. Search problem 'v' computes: Is P Versus NP Formally Independent? Nature of P = NP.84a conjecture that all but asserts the titanic difficulty of finding [...] P = NP asks for an efficient procedure that finds a short proof [.....] independent of ZF, no matter which Turing machine is used to specify O. [....] It's interesting that this proof rules out only lower bounds of the form 2 [...]. Consider: computational complexity and mathematics: P, NP and mathematics [CapitalEth] a computational complexity perspective. Describe the computational model precisely (e.g. it does not matter if we allow [.....] it is so hard to prove indeed P = NP it seems completely obvious. We [......] the very nature of proof. We exhibit three different remarkable manifestations of [.....] a rank 1 tensor as a product of linear forms (one in X, [...]. The Awakening of The American Mind: P=NP complete The Maximal [......] to the extremal ends of the conservation law of matter/ energy, fields/motions, [....] or any other form of heiarchical organization, of any other possible [...] P=NP i.e., Proof=NonPossibles, add em up, and choose what's left the [....] senses The sensible Better Nature senses, over the Higher Nature senses. [...] And now we're getting interesting. An Argument for P=NP, again I say this repeatedly out of necessity, the winne of the Clay Mathematics prize need not provide a constructive proof P=NP [...] of the matter than, say, whether many current cryptographic schemes can be [...]. Godel apparently believed it might well be possible to answer questions of the form ñ¤l [.....] 'proto'-law of nature. It's a profound waste of time to build gadgets to [...]. Truth is the goal and hard work and common sense filled with imagination is the real necessity. Chris Menzel helped me prove N=NP: on USENET with Inverse 19 Mathematics in sci.math [...], I simply said, Consider this thread an extension of my proof P=NP, and add to it this [...] always the same path as we what we seek to define we by nature of our > observing change. [...] In form and function, across language and guild, the > heir apparent us. [...] At any rate, no matter the claim, they do not belong to me. I did not [...]. A consequence of a proof of the one-way function existence for the [...]8 Nov 2008 [...]. Indeed, form the assumption follows while for the initial stages of the [...]. The above statement may seem vague to the impatient reader (especially to Kant or Russell, I assume) but nonetheless by the nature of our existence and the very essence of time it is ontologically sound. The statement may simply be rephrased: A proof of the consequence of a past action is based on the sound assumption causal relations can only be established after the existence of their result in time. --Martin Musatov As to numerical solutions, a proof P Á' NP would guarantee a [....]. Hence, it is plausible to conclude the NP nature of the Schr.9adinger equation [...] state of play, prospects. But before we get too far removed in physics, we must return to the proof. Computational Complexity and Mathematical Proofs clearly agree the P versus NP problem is clearly an important problem for computer scientists. Also a fundamental problem about the nature of mathematics [...] string over a fixed alphabet and is written in a left-justified form directly below [....]. As a matter of fact, by choosing our proof systems accordingly, we can represent P = NP { What does it mean? No matter how fast computers we manage to build, we will still be unable to express [.....] the exact nature of these problems has not yet been determined, even though every- [...] (posi)tive proof for P=NP would mean we have a polynomial time algorithm for [....] Boyce-Codd Normal Form Violation. Conjunctive Query Foldabilty [...]. Sticking to the complexity of Computational Complexity: We all have our favorite theorems: P = NP for Space. The non-trivial nature of a result and proof is in the insight [....] I sometimes joke about having a two line proof of P=NP that keeps [...]. So the book as Erdos referenced contains as derivatives of the author's work (lawfully on unlawfully attained): 1. The Chapter 2: God Math (Logik, LOGOS, P=NP) ' Robot Pirate Ninja. You laugh and it all seems silly, but it is quite upsetting to those just beginning to understand it. It is actually quite daunting and cruel. This is my P=NP proof, after all. One would have to be a bit outside the norm to [...] see. 1a. Supposition claims proofs of reality, by threading a narrative to hypotheses. 1b. We later learned from Einstein that the existence of matter and energy made a [...] lines that go on forever, are so rare as to be nearly unique in nature [....] and we finally see the fully realized (simple) model in its ideal form.[ ...] Truth is the highest order. Period. P=NP. q.e.d. PROOF BERTRAND RUSSELL WAS UNWISE: Bertrand Arthur William Russell [Third Earl Russell] (1872-1970) British philosopher, mathematician, social critic, writer. 1st Argument: 1a. Russell: ...by intellectual integrity the habit of deciding vexed questions in accordance with the evidence, or of leaving them undecided where the evidence is inconclusive. 1b. Musatov: The limit principle of defending a negative-valued statement or impossibility allows for a divine divide between classes as to the public people esteemed insist something is unknowable, uncountable, or impossible, simply discourages the acceptance of truth, discovery, and the incidence of greater possibility than what remains to be seen. Conclusion: Musatov: (Claims) P==NP. Even Russell himself agreed. On P=/=NP. Russell states: (implies) Proof: [...]Russell: Most of the greatest evils that man has inflicted upon man have come through people feeling quite certain about something which, in fact, was false.-- Bertrand Russell, Unpopular Essays, Ideas That Have Harmed Mankind (1950), p. 149, quoted from James A Haught, ed, 2000 Years of Disbelief P==NP is a truth-valued claim. P=/=NP is a false-valued claim. q.e.d. (1st argument) Summary Statment: The defense of a truth statement should always be given favor to the insistence of an impossibility. --Martin Musatov Argument 2 2a. Russell: So far as I can remember, there is not one word in the Gospels in praise of intelligence; and in this respect ministers of religion follow gospel authority more closely than in some others.-- Bertrand Russell, quoted, in part, from Jonathon Green, The Cassell Dictionary of Cynical Quotations 2b. Musatov: (cites) P==NP.1.Matthew 22:37 And He said to him, 'YOU SHALL LOVE THE LORD Jesus said unto him, Thou shalt love the Lord thy God with all thy heart, and with all thy {p} soul, and with all thy mind. [...]http:// bible.cc/matthew/22-37.htm 2.Matthew 22:37 Jesus said unto him, Thou shalt love the Lord thy [...] Jesus said to him: Thou shalt love the Lord thy God with thy whole heart, and with thy whole soul, and with thy whole mind. [...] http://scripturetext.com/matthew/22-37.htm 3. ...In Phillipians 2:5, the apostle Paul said, let this mind be in you which was also in Christ Jesus. In Mathew 6:33 Jesus said, seek ye first the kingdom [...]http://www.thechristmind.org/ The fact is there are many instances and portrayals in the bible where frankness and honesty are encouraged over formalsim and inauthentic truth. God allowed Abraham to question and challenge him over his reasoning in the destruction of Sodom. God and Abraham reached a compromise. God listened to David's accusations of unfairness, betrayal, and abandonment. Jeremiah even claimed God tricked him. Job was allowed to vent and when his ordeal was over he rebuked his friends for being inauthentic. God rewards honesty and authenticity. Honesty and authenticity predicate truth, hence they are one and the same rewarded in the portrayal of the gospels as written in The Old and New Testaments. Summary argument: Musatov: Following Jesus begins in your Mind. Jesus said, ñYou must love the Lord your God with all your heart, with all your soul, with all your mind and with all your strength.î (Mark 12:30) [...]http://www.frtommylane.com/homilies/year b/03.htm The below results prove my above forgone conclusion further: THE MIRACLE OF ONE MIND AT SAFEPLACEFELLOWSHIP.COM All these signs pointed to the singleness of mind experience would soon be coming but it [...] I know she is but Jesus said she would be ok, I replied. Organizing for America | Danielle Clarke's Blog: Barack Obama and [...] 24 Jun 2007 [...] As Jesus said 'to them with an ear to listen, let them hear' Can we (the ego me) ever really change another mind? And if we can for how long? [...] -- Martin Musatov http://MeAmI.org http://alexslemonade.org === Subject: Re: basic algebra/arithmetic question >If you have four real numbers that average out to 1.95, how many times would >you have to add the number 3.5 to them in order to make that average 3.3? >If someone can also give me the formula it would be appreciated. >Woody Let > S = the known sum > Sorry for the previous partial posting, I apparently pushed the wrong button. I'll assume by 'average' you mean 'arithmetic mean'. Let A = the given arithmetic mean n = how many numbers in the given arithmetic mean B = the constant number to be added C = the desired arithmetic mean k = the number of times B is added to get C Then ( n*A + k*B ) / (n + k) = C Solving for k, k = n (C - A) / (B - C) (*) For your problem, A = 1.95 n = 4 B = 3.5 C = 3.3 and the formula (*) gives k = 27 === Subject: Re: basic algebra/arithmetic question posting-account=_l4K0QkAAAC09JhOoK_ZfoJKXOmr_jZf Gecko/2009060309 Ubuntu/8.04 (hardy) Firefox/3.0.11,gzip(gfe),gzip(gfe) > If you have four real numbers that average out to 1.95, how many times would > you have to add the number 3.5 to them in order to make that average 3.3? I assume that by average, you mean the arithmetic mean (the sum of the four numbers divided by 4); bear in mind that average can have several different meanings... If someone can also give me the formula it would be appreciated. You have four numbers, call them a, b, c, and d. You know that (a+b+c +d)/4 is equal to 1.95, or that (a+b+c+d) = (1.95)*4 = 7.8. You want to know how many times k you need to add 3.5 so that (a+b+c+d +k(3.5))/(k+4) = 3.3. Mutiply out by k+4 to get (a+b+c+d) + k(3.5) = (k+4)(3.3). You know how much a+b+c+d is, so we get 7.8 + 3.5(k) = 3.3(k) + 13.2 Now move all the k's to the left, and all the constants to the right, and you get: 3.5(k) - 3.3(k) = 13.2 - 7.8 or 0.2(k) = 5.4 Dividing through by 0.2, you get k = 27. So you would need to add 3.5 twenty seven times for the average to be 3.3. -- Arturo Magidin === Subject: Re: Smooth homeomorphisms dense in homeomorphisms? Originator: bergv@math.uiuc.edu (Maarten Bergvelt) > I've a question, and I am a physicist so take it easy on me... If M and N are smooth manifolds and Hom(M,N) is the non-empty > set of homeomorphisms from M to N and C^infty(M,N) is the set > of smooth maps from M to N, then is C^infty(M,N) cap Hom(M,N) > dense in Hom(M,N), where the set Hom(M,N) is given the strong > topology, otherwise known as the Whitney topology? If you don't know an answer, do you know where I could find one? Ok, I think I have found an answer to this when M and thus N are of dimension 4, the dimension in which I am working. The answer is C^infty(M,N) cap Hom(M,N) is not dense in Hom(M,N). The logic is as follows, a theorem of Scharlemann and Siebenmann[1] states... Theorem 1 Let f:M rightarrow N be a C^infty homeomorphism of connected metrizable smooth manifolds without boundary. If M and N are of dimension 4 further assume they are non-compact. Let M and N be given Whitehead compatible piecewise-linear structures, then there exists a topological isotopy of f to a piecewise-linear homeomorphism. A Theorem of Munkres[2], Kirby, and Siebenmann[3]... Theorem 2 If f:M rightarrow N is a piecewise-linear homeomorphism of smooth manifolds of dimension 6 or less with Whitehead compatible PL-structures, which always exist in this case, then M and N are diffeomorphic. However, a theorem of Taubes[4] states... Theorem 3 There exists an uncountable set of non-diffeomorphic smooth structures on R^4. All of this together implies that for M=R^4 and N=R^4, where M is given a smooth structure inequivalent to that on N which exists according to Theorem 3, the set C^infty(M,N) cap Hom(M,N) is empty. If the set C^infty(M,N) cap Hom(M,N) were not empty, then as a result of Theorem 1 there would exist a piecewise-linear homeomorphism between M and N. As a result of Theorem 2, this piecewise-linear homeomorphism would imply the existence of a diffeomorphism between M and N. However, by construction, there exists no diffeomorphism between M and N; thus one has a contradiction. Hence, C^infty(M,N) cap Hom(M,N) is not dense in Hom(M,N) when M and N are four dimensional. If fact, sometimes it is empty! [1] Compositio Mathematica, Vol. 29. Fasc. 3, 1974, pag. 253-263 [2] J.R. Munkres, Concordance of differentiable structures, two approaches. Michigan Math. J. 14 (1967) 183-191 [3] R.C.Kirby and L.C. Siebenmann, Classification of sliced families of smooth or piecewise-linear manifold structures. Essay V of Foundational Essays on Topological Manifolds, Smoothings, and [4] Taubes, Clifford Henry (1987), Gauge theory on asymptotically periodic 4-manifolds., Journal of Differential Geometry 25: 363--43 === Subject: Re: Simplification of Bessel K expression Originator: bergv@math.uiuc.edu (Maarten Bergvelt) I am searching, but cannot find in large references (such as > functions.wolfram.com) > a formula for simplifying sums of the following kind BesselK(0, a + i b) +/- BesselK(0, a - i b) (for a and b reals) These would be twice the real and imaginary parts of K_0(a+ib) ... I don't know of any simpler way to write them. It appears that these sums are real or pure imaginary and > seem to involve again BesselK(0, a) multiplied by some > oscillatory factor. Maybe readers of this newsgroup can help in this matter. > Olivier GERARD > === Subject: Re: This Week's Finds in Mathematical Physics (Week 275) Originator: bergv@math.uiuc.edu (Maarten Bergvelt) A correction: >Meanwhile, Christian Schommer-Pries has written a thesis on 2d extended >TQFTs - you can see it here: 6) Christian Schommer-Pries, The Classification of Two-Dimensional >Extended Topological Field Theories, Ph.D. theis, U.C. Berkeley, 2009. His name is Chris, not Christian! You see more discussion of week275 here: http://golem.ph.utexas.edu/category/2009/06/this_weeks_finds_in_mathematic_3 6.html === Subject: CFP: Optical SuperComputing Workshop 2009 Originator: bergv@math.uiuc.edu (Maarten Bergvelt) CFP: Optical SuperComputing Workshop 2009 2nd International Workshop on Optical SuperComputing in Bertinoro (OSC09) November 18-20, Bertinoro, Italy http://www.cs.bgu.ac.il/~dolev/OSC09 SCOPE: OSC, the International Workshop on Optical SuperComputing, is an annual forum for research presentations on all facets of optical computing for solving hard computation tasks. Optical computing devices have the potential to be the very next computing infrastructure. Optical computing presents an alternative to the frequency limitations, cross-talk phenomena and soft-errors of electronic devices. The natural parallelism of optical computing devices, coupled with the advance in fiber optics and optical switches make optical computing commercially viable. Research contributions to the theory, design, specification, analysis, implementation, or application of optical supercomputers are solicited. Topics of interest include, but are not limited to: [Eth] Designs or demonstrations of optical computing devices and systems [Eth] Algorithmics and complexity issues of optical computing [Eth] Computation representation by photons and holograms [Eth] Neural and brain inspired architectures [Eth] Electro-optic devices for interacting with optical computing devices [Eth] Practical implementations [Eth] Analysis of existing devices and case studies [Eth] Optical photonics and laser switching technologies [Eth] Optical and photonic memories [Eth] Optical signal processing subsystems [Eth] Optical networks for high-performance computing [Eth] Optical interconnections [Eth] Quantum optical systems [Eth] Applications and algorithms for optical devices Submission deadline July 25, 2009 Acceptance notification August 25, 2009 Camera-ready copy due September 10, 2009 Steering and Organization Committee: H. John Caulfield Fisk University Shlomi Dolev Ben-Gurion University Yeshaiahu Fainman UCSD Mihai Oltean Babes-Bolyai University Tobias Haist Stuttgart Universitat Program Committee: George Barbastathis MIT Antonella Bogoni CNIT H. John Caulfield Fisk University Ernesto Ciaramella SSSUP Cristian Calude University of Auckland Shlomi Dolev (Chair) Ben-Gurion University Yeshaiahu Fainman UCSD Dietmar Fey Erlangen-Nuremberg University William Green IBM Tobias Haist Stuttgart Universitat JÂurgen Jahns FU Hagen Efstratios Kehayas NTUA Shimon Levit Weizmann Institute of Science Michal Lipson Cornell David Miller Stanford Thomas Naughton NUIM Kouichi Nitta Kobe University Jeremy L. Obrien University of Bristol Mihai Oltean Babes-Bolyai University Wolfgand Osten Stuttgart Universitat Haldun Ozaktas Bilkent University Joseph Rosen Ben-Gurion University Yunlong Sheng Laval University Natan T. Shaked Duke University Joseph Shamir Technion Dan Tamir Texas State University Kristof Vandoorne Universiteit Gent Damien Woods University of Seville Toyohiko Yatagai Utsunomiya University Zeev Zalevsky Bar-Ilan University Xinliang Zhang Huazhong University How to submit: Authors are invited to submit their extended abstracts electronically. A detailed description of the electronic submission procedure will appear on the workshop web-page, as of June 1, 2009. Authors unable to submit electronically should contact the program chair, Shlomi Dolev by email, dolev@cs.bgu.ac.il or by phone, +972-8-6428119 to receive instructions. Workshop presentations will have two formats: Regular presentations of at least 25 minutes accompanied by papers of up to 15 pages in the proceedings. Additional material may be added in a clearly marked Appendix to be read at the discretion of the Program Committee Members. This form is intended for contributions reporting on original research, submitted exclusively to this workshop. Brief announcements of at least 10 minutes accompanied by two page abstracts in the proceedings. This format is a forum for brief communications, which may be published in other workshops. Longer versions expanding the brief announcements will be collected in a web site. The workshop proceedings will be published by LNCS Springer Verlag. We are also seeking a special issue with a journal. SUBMISSIONS FORMAT: The cover page should include (1) title, (2) authors and affiliation, (3) postal and e-mail address of the contact author, (4) indication of the format(s) to which the paper is submitted, and (5) a brief abstract describing the work. It is recommended that each submission begin with a succinct statement of the problem, summary of the main results, and a brief explanation of their significance, all suitable for a non-specialist. Technical development of the work, directed to the specialist, should follow. A submission for the regular presentation format should be no longer than 4,500 words (10 pages on letter-size paper using at least 11-point font, figures and tables included) excluding references. If the authors believe that more details are essential to substantiate the main claims of the paper, they may include a clearly marked appendix that will be read at the discretion of the program committee. Extended abstracts deviating significantly from these guidelines risk rejection without consideration of their merits. A submission for the brief announcement format should be no longer than three pages. Authors of accepted brief announcements will be asked to submit a full version of their work to be placed on a WWW site. If requested by the authors in the cover letter, an extended abstract that is not selected for a long presentation will also be considered for the brief announcement format. Such a request will not affect consideration of the paper for a long presentation. === Subject: This Week's Finds in Mathematical Physics (Week 276) Originator: bergv@math.uiuc.edu (Maarten Bergvelt) Also available at http://math.ucr.edu/home/baez/week276.html June 20, 2009 This Week's Finds in Mathematical Physics (Week 276) John Baez Math is eternal, but I'll start with some news that may be time-sensitive. Betelgeuse is shrinking! 1) Stefan Scherer, Shrinking Betelgeuse, http://backreaction.blogspot.com/2009/06/shrinking-betelgeuse.html Betelgeuse is that big red star in the shoulder of Orion. It's a red supergiant, one of the largest stars known. It's only 20 times the times the size of the Earth's orbit. For more of a sense of what that means, watch this video: 2) Hansie0Slim, Largest stars this side of the Milky Way, http://www.youtube.com/watch?v=u70UBs7BWY8 But, it's shrinking. These authors claim its radius has shrunk 15% since 1993: 3) C. H. Townes, E. H. Wishnow, D. D. S. Hale and B. Walp, A systematic change with time in the size of Betelgeuse, The Astrophysical Journal Letters 697 (2009), L127-L128. That's about 1000 kilometers per hour! Of course, it's a bit tricky to estimate the size of Betelgeuse - besides being rather far, it's so diffuse that its surface isn't very precisely defined. And it's a variable star, so maybe a little shrinkage isn't a big deal. But the two known cycles governing its oscillations have periods of one year and 6 years. So, the authors of the above paper think this longer-term shrinkage has some other cause. It could be just another cycle, with a longer period. But there's another possibility that's a lot more exciting. Maybe Betelgeuse is about to collapse and go supernova! Indeed this seems likely in the long term, since that's the usual fate of such massive stars. And the long term may not even be so long, since Betelgeuse is about 8.5 million years old - quite old for stars this big, which live fast and go out in a blaze of glory. What if Betelgeuse went supernova? How would it affect the US economy, and the next Presidential election? Could this be the Republican party's best hope? Sorry, I'm being a bit parochial... let me try that again. How would it affect the insignificant inhabitants of a puny speck called Earth, located about 500 or 600 light years away from Betelgeuse? According to Brad Schaefer at Louisiana State University, it would be brighter than a million full moons, but it wouldn't hurt us - in part because of the distance, and in part because we're not lined up with its pole. (Perhaps just to build up the suspense, Schaefer added that Betelgeuse could already have gone supernova, in which case we're just waiting for its light to reach us.) It would be nice to see some calculations of just how much power we'd get from a supernova at that distance. I must admit that brighter than a million moons doesn't really do it for me. Does anyone out there have what it takes to crunch the numbers? It's worth recalling that not too long ago, a supernova exploded at a roughly comparable distance from us, forming the Local Bubble - a peanut-shaped region of hot thin gas about 300 light years across, containing our Sun. The gas in the Local Bubble is about 1000 times less dense than ordinary interstellar space, and vastly hotter. What do I mean by not too long ago? Well, nobody is sure, but back in week144 I reported a bunch of evidence for a theory that the Local Bubble was formed just 340,000 years ago, when a star called Geminga went supernova, perhaps 180 light years away. Now I'm getting a sense that the situation is more complex. It seems our Sun is near the boundary of the Local Bubble and another one, called the Loop I Bubble. This other bubble seems to have formed earlier - perhaps 2 million years ago, at the Pliocene-Pleistocene transition, when a bunch of ultraviolet-sensitive marine creatures mysteriously died: 4) NASA, Near-earth supernovas, The Loop I Bubble may have been caused by a supernova in Sco-Cen, a cloud in the directions of Scorpius and Centaurus. It's about 450 light years away now, but it used to be considerably closer. In the last few million years, some wisps of interstellar gas have drifted into the Local Bubble. Our solar system is immersed in one of these filaments, charmingly dubbed the local fluff. It's much cooler than the hot gas of the Local Bubble: 7000 Kelvin instead of roughly 1 million. It's also much denser - about 0.1 atoms per cubic centimeter instead of 0.05 or so. But Sco-Cen is sending interstellar cloudlets in our direction that are denser still, by a factor of 100. These might actually have some effect on the Sun's magnetic field when they reach us. a satellite called the Cosmic Hot Interstellar Plasma Spectrometer, or CHIPS for short, to study this sort of thing: 5) NASA/UC Berkeley, Overview of CHIPS Science, http://chips.ssl.berkeley.edu/science.html It sounds pretty interesting. Unfortunately the latest news on the CHIPS homepage dates back to 2005, before they'd done much science. What's up? You can't do much about Betelgeuse. But you can do something about mathematics! For example, if you're into categories or n-categories, you can help out the nLab: 6) nLab, http://ncatlab.org/nlab The nLab is like the library, or laboratory, in the back room of the n-Category Caf.8e. The nCaf.8e is a place to chat: it's a blog. The nLab is a place to work: it's a wiki. It's operating since November 2008. There's quite a lot there by now, but it's really just getting started. Check it out! You'll find a lot of explanations of a lot of concepts, and the beginnings of some big projects. So far the main contributors include Urs Schreiber, Mike Shulman, Toby Bartels, Tim Porter, Todd Trimble, David Roberts, Andrew Stacey, Bruce Bartlett and myself. Jim Dolan recently joined in with a page on algebraic geometry for category theorists - I'll say more about this someday. And like the nCaf.8e, technical aspects of the nLab are largely run by Jacques Distler - it uses some wiki software called Instiki which he is helping develop. Finally, a bit of actual math. Here's a paper by the fellow I'm working with here in Paris, and a grad student of this: 7) Paul-Andr.8e Mellies and Nicolas Tabareau, Free models of T-algebraic theories computed as Kan extensions, available at http://hal.archives-ouvertes.fr/hal-00339331/fr/ I really need to understand this for my work with Mike Stay. In week200 I talked about Lawvere's work on algebraic theories; I'll assume you read that and pick up from there. In its narrowest sense, an algebraic theory is a category with finite products where every object is a product of copies of some fixed object c. We use algebraic theories to describe various types of mathematical gadgets: to be precise, any type of gadget that consists of a set with a bunch of n-ary operations satisfying a bunch of purely equational laws. For any type of gadget like this, there's an algebraic theory C; I explained how you get this back in week200. If we have a functor F: C -> Set that preserves finite products, then F(c) becomes a specific gadget of the given type. Conversely, any specific gadget of the given type determines a functor like this. So, we define a model of the theory C to be a functor F: C -> Set that preserves finite products. But actually, this is just a model of C in the world of sets! We could replace Set by any other category with finite products, say X, and define a model of the theory C in the environment X to be a functor F: C -> X that preserves finite products. For example, if C is the theory of groups and X is Set, a model of C in X is a group. If instead X is the category of topological spaces, a model of C in X is a topological group. And so on. In general people call a model of this particular theory C in any old X a group object in X. But as you might fear, we want to understand more than a single model of C in X. As category theorists, we want to understand the whole *category* of models of C in X. This category, which I'll call Mod(C,X), has: functors F: C -> X that preserve finite products as its objects; natural transformations as its morphisms. For example, if C is the theory of groups and X is the category of topological spaces, Mod(C,X) is the category of topological groups and continuous homomorphisms. So far I've just been reviewing at a fast pace. What happens next? Well, there's always a forgetful functor R: Mod(C,X) -> X sending any model to its underlying object in X. But what we'd really like is for R to have a left adjoint L: X -> Mod(C,X) sending any object of X to the free gadget on that object. Then we could follow L by R to get a functor RL: X -> X called a monad. One reason this would be great is that monads are another popular way to study algebraic gadgets. I explained monads very generally back in week89, and said how to get them from adjoint functors in week92; in week257 I gave some links to some great videos by the Catsters explaining monads and what they're good for. So, I won't say more about monads now: I'll just assume you love them. Given this, you must be dying to know when the functor R has a left adjoint. In fact it does whenever X has colimits that distribute over the finite products! For example, it does when X = Set. And Mellies and Tabareau give a very nice modern explanation of this fact before generalizing the heck out of it. The key is to note that R: Mod(C,X) -> X is just an extreme case of forgetting *some* of the structure on an algebraic gadget: namely, forgetting *all* of it. More generally, suppose we have any map of algebraic theories Q: B -> C that is, a finite-product-preserving functor that sends the special object b in B to the special object c in C. Then composition with Q gives a functor Q*: Mod(C,X) -> Mod(B,X) For example, if B is the theory of groups and C is the theory of rings, C is bigger, so we get an inclusion Q: B -> C and then Q* is the functor that takes a ring object in X and forgets some of its structure, leaving us a group object in X. But when B is is the most boring algebraic theory in the world, the theory of a bare object, then Q* forgets everything: it's our forgetful functor R: Mod(C,X) -> Mod(B,X) = X So, we should ask quite generally when any functor like Q*: Mod(C,X) -> Mod(B,X) has a left adjoint. And, the answer is: it always does! The proof uses a left Kan extension followed by what Mellies and Tabaraeu call a miracle - see page 5 of their paper. And, it's this miracle they want to understand and generalize. They generalize it by replacing algebraic theories by T-algebraic theories where T is any pseudomonad on Cat. I already said that monads are a trick for studying very general algebraic gadgets. Similarly, pseudomonads are a trick for studying very general *categorified* algebraic gadgets, like categories with finite products or monoidal categories or braided monoidal categories of symmetric monoidal categories. Each of these types of categories allows us to define a type of theory: monoidal categories let us define PROs braided monoidal categories let us define PROBs symmetric monoidal categories let us define PROPs categories with finite products let us define algebraic theories I explained all these, along with monads, here: 8) John Baez, Universal algebra and diagrammatic reasoning, available as http://math.ucr.edu/home/baez/universal/ Take my word for it: they're great. So, we would like to generalize Lawvere's original results to these other kinds of theories, which are all examples of T-algebraic theories. But, it's not automatic! For example, it doesn't always work with PROPs. A typical kind of algebraic gadget we could define with a PROP is a bialgebra. While there's always a free group on a set, there's not usually a free bialgebra on a vector space! The problem is not the category of vector spaces: it's that bialgebras have not only operations like multiplication, but also co-operations like comultiplication. So, Mellies and Tabareau have their work cut out for them. But they tackle it very elegantly, using profunctors and a certain generalization thereof: Richard Wood's concept of proarrow equipment. That sounds pretty scary when you first hear about it, so I'll stop here, right around page 12 of the paper - right when the fun is getting started. ---------------------------------------------------------------------- Quote of the Week: The question you raise, how can such a formulation lead to computations? doesn't bother me in the least! Throughout my whole life as a mathematician, the possibility of making explicit, elegant computations has always come out by itself, as a byproduct of a thorough conceptual understanding of what was going on. Thus I never bothered about whether what would come out would be suitable for this or that, but just tried to understand - and it always turned out that understanding was all that mattered. - Grothendieck ----------------------------------------------------------------------- mathematics and physics, as well as some of my research papers, can be obtained at http://math.ucr.edu/home/baez/ For a table of contents of all the issues of This Week's Finds, try http://math.ucr.edu/home/baez/twfcontents.html A simple jumping-off point to the old issues is available at http://math.ucr.edu/home/baez/twfshort.html If you just want the latest issue, go to http://math.ucr.edu/home/baez/this.week.html === Subject: AT&T Usenet Netnews Service Shutting Down Distribution: internal Please note that on or around July 15, 2009, AT&T will no longer be offering access to the Usenet netnews service. If you wish to continue reading Usenet newsgroups, access is available through third-party news providers. of AT&T servers is due to the posts being downloaded and redistributed without the knowledge or consent of AT&T. === Subject: A combination problem Consider a function of N variables, i.e. f(x_1 ... x_N). I would like to know how many unique derivative terms are at M^{th} order. Some M^{th} order derivatives are: partial f^M / partial x_1^M partial f^M / partial x_2^M ... partial f^M / partial x_N^M partial f^M / partial x_1 partial x_2 ^ (M-1) .... I know for M = 2, the answer is 1+2+ ... + N, which can be told from the symmetric Jacobian matrix. My question is to generalize it to M^{th} order. kzhu === Subject: Re: A combination problem Consider a function of N variables, i.e. f(x_1 ... > x_N). I would like to > know how many unique derivative terms are at M^{th} > order. Some M^{th} > order derivatives are: > partial f^M / partial x_1^M > partial f^M / partial x_2^M > ... > partial f^M / partial x_N^M partial f^M / partial x_1 partial x_2 ^ (M-1) .... I know for M = 2, the answer is 1+2+ ... + N, which > can be told from the > symmetric Jacobian matrix. My question is to > generalize it to M^{th} order. > kzhu > Your question is equivalent to the combinatorial problem to determine the number of ways to put M undistinguishable balls into N distinguishable urns. The answer is C(N+M-1,M) = (N+M-1)!/(M!*(N-1)!) Best wishes Torsten. === Subject: Re: A combination problem Consider a function of N variables, i.e. f(x_1 ... > x_N). I would like to > know how many unique derivative terms are at > M^{th} > order. Some M^{th} > order derivatives are: > partial f^M / partial x_1^M > partial f^M / partial x_2^M > ... > partial f^M / partial x_N^M partial f^M / partial x_1 partial x_2 ^ (M-1) .... I know for M = 2, the answer is 1+2+ ... + N, > which > can be told from the > symmetric Jacobian matrix. My question is to > generalize it to M^{th} order. > kzhu > Your question is equivalent to the combinatorial > problem to determine the number of ways to put M > undistinguishable balls into N distinguishable urns. The answer is > C(N+M-1,M) = (N+M-1)!/(M!*(N-1)!) Best wishes > Torsten. Of course, this is only correct if the order of differentiation does not matter. If it matters, there are N^M possible derivative terms. Best wishes Torsten. === Subject: Re: A combination problem Consider a function of N variables, i.e. f(x_1 ... > x_N). I would like to > know how many unique derivative terms are at > M^{th} > order. Some M^{th} > order derivatives are: > partial f^M / partial x_1^M > partial f^M / partial x_2^M > ... > partial f^M / partial x_N^M partial f^M / partial x_1 partial x_2 ^ (M-1) .... I know for M = 2, the answer is 1+2+ ... + N, > which > can be told from the > symmetric Jacobian matrix. My question is to > generalize it to M^{th} order. > kzhu > Your question is equivalent to the combinatorial > problem to determine the number of ways to put M > undistinguishable balls into N distinguishable urns. > The answer is > C(N+M-1,M) = (N+M-1)!/(M!*(N-1)!) > Best wishes > Torsten. Of course, this is only correct if the order of > differentiation does not matter. > If it matters, there are N^M possible derivative terms. Best wishes > Torsten. === Subject: question from a math retard I'm 44 and going back to college after an absence of 18 years. To get into my college's B.Sc. Psychology program, I need accreditation in a 12th grade calculus course. Before I can get that I need remedial math starting at the 9th grade level. Any suggestions? Woody -- NOTE TO NEWSGROUP USERS; My reply-to email address is valid. For a safe valid reply-to address of your own go to www.hushmail.com === Subject: Re: question from a math retard > I'm 44 and going back to college after an absence of 18 years. To get into > my college's B.Sc. Psychology program, I need accreditation in a 12th grade > calculus course. Before I can get that I need remedial math starting at the > 9th grade level. Any suggestions? Woody > See my reply alt.math. Don't multipost, learn about cross posting. See http://oakroadsystems.com/genl/unice.htm