mm-21 == I need to know how to calculate x^y where y is not an integer. Any> help in this matter would be appreciated.Depending on where one is in number theory, one can do one of thefollowing.[1] If y is a rational number, write y = p/q and compute the qth root of x^p. For example, 6^(2/3) is equal to the cube root of 6^2 = 36. Of course x^(-y) = (1/x)^y = 1/(x^y).[2] If y is not a rational number, one can use logarithms: x^y = exp(y * log(x)). This form is also useful in problems involving calculus. Note that log(x) has periodicity 2 * pi * i, if one is in the complex plane; this can lead to somewhat odd results.-- Its still legal to go .sigless. > I need to know how to calculate x^y where y is not an integer. Any> help in this matter would be appreciated.With x positive x = e ^ ln (x), substitute back into expression andevaluate. > [ how to calculate x^y where y is not an integer?] With x positive x = e ^ ln (x), substitute back into expression and> evaluate.>An example may help. If given the chore of computing 7.5 ^ 12.34youd compute ln(7.5) as about 2.0149030, take that times12.34 to get about 24.863903, and then take e^(24.863903) whichis 6284286702.63, the ?al answer.Im away from my trusty calculator, but in Win95 left-clicked onStart button, Programs, Accessories, Calculator, 7.5, ln buttonof calculator, * button, 12.34, = button, ?led in the inv check-box,clicked on ln button again{which performed an e^x operationand cleared the inv checkbox.} > I need to know how to calculate x^y where y is not an integer. Any> help in this matter would be appreciated.If y is rational, i.e. y = a/b, then b th root (x^a). For example,x^2/3 = cube root of (x^2). Otherwise, check out:http://mathworld.wolfram.com/Power.htmlLurch > I need to know how to calculate x^y where y is not an integer. Any>> help in this matter would be appreciated.If y is rational, i.e. y = a/b, then b th root (x^a). For example,x^2/3 = cube root of (x^2). Otherwise, check out:http://mathworld.wolfram.com/Power.html??? I dont see a mathematical de?ition of x^y on thatpage, nor anything else that might be what hes lookingfor when he asks how to calculate it...>Lurch>************************David C. Ullrich >> I need to know how to calculate x^y where y is not an integer. Any>> help in this matter would be appreciated.>If y is rational, i.e. y = a/b, then b th root (x^a). For example,>x^2/3 = cube root of (x^2). Otherwise, check out:>http://mathworld.wolfram.com/Power.html ??? I dont see a mathematical de?ition of x^y on that> page, nor anything else that might be what hes looking> for when he asks how to calculate it... >Lurch> ************************ David C. UllrichIs that your profound contribution?Lurch >>I have another more general question, if you dont mind : is there an>>intuitive meaning for a nilpotent group ? Nilpotent groups are closely connected to nilpotent lie algebras,>which is where the name actually comes from, as I understand it, and>where nilpotent actually makes some sense.>As to intuitive meaning, that will depend a lot on you, I guess.[...]>Others think of them as groups constructed through central extensions,>which is not a bad way to think about them either.Some of us just instinctively think, Product of p-groups. RealisticallyI just think about p-groups, period, and then mutter something aboutdirect products at the end of the story. (And if you want an intuitivemeaning of p-groups, think about layers of small vector spaces overthe ?ld of characteristic p, forming the quotients of chains ofnormal subgroups. I dont necessarily think only of central extensions,by the way; in fact one of the prototypes I keep in mind is a semidirectproduct of a Z/p acting on a p-dimensional vector space over GF(p).Ill bet most people dont think about the dihedral group of order 8this way...)Of course, some of us carry along a related intuitive notion thatgroup means ?ite group. Youll have to modify the previous paragraph if support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBSDc1T02534; [.snip.]J. Willekens > Notice that the in Noble Verse 57:25 above, Allah Almighty says clearly We> sent down iron.... and He didnt say We created iron from earth....> Allah Almightys claim was very accurate and precise. We sent down> iron..... clearly states that iron was created outside the earth and was> brought down by the Will of Allah Almighty for a purpose, and that is> (material for) Mighty war, as well as many bene?s for mankind, that Allah> Noble Quran, 57:25)>Hypothetically, if this is proven incorrect, and the iron did not come down,would you be willing to give up on the Quran?Bill X-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Pose: george_cox@btinternet.comX-Punge: Micro$oft at 02:12 PM, Mark K. Bilbo said:>There is no down in space. There is if you send a goose up. I dont know if thats enough downfor a jacket.-- Shmuel (Seymour J.) Metz, SysProg speak thusly:> at 02:12 PM, Mark K. Bilbo said:> >>There is no down in space. > There is if you send a goose up. I dont know if thats enough down> for a jacket.The poor goose...-- Mark K. Bilbo X-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Pose: george_cox@btinternet.comX-Punge: Micro$oft at 07:30 PM, Goran Jakupovic said:>Like somebody else already said not just iron, but all atoms starting>with helium and heavier now in solar system were products of>supernova.No. Helium is predominantly primordial, Beryllium and Lithium arealmost entirely primordial. The conditions for light elementnucleosynthesis are very different from the conditions for heavierelements. Stars produce Helium, but they destroy Lithium andBeryllium. Theres more Helium in the Universe now than right afterthe big bang, but not a lot more.-- Shmuel (Seymour J.) Metz, SysProg and JOATnot reply to > down is relative like meaning closer to core like when you get down> from> bed. but the quran has things being created on earth but for some odd> reason> it diverges with iron. it says we sent down iron. iron was not created> on> earth according to quran. how did the quran know that iron came down?> down> meaning from elsewhere. it was not made on this earth. god caused iron> to> descend. coincidence?> Its untrue. Iron was here when the earth was formed. It did not come> later.> And if anything, it came up from the core from volcanoes and the like.> you are mistaken in a small way. iron not even from this solar system. it> came from other stars and had to land on earth. maybe it was primitive> molten earth but earth was here. if earth was not here what iron land on?> simple logics no offense. the miracle is that quran say many things created> on earth and if this book from man who forging gods word man just say iron> like people and animals and plants and mountains was created on earth. but> for some reason quran treats iron different and say that it is sent down to> earth. why not just say it was created on earth? because that would be> wrong. --> saab siddiqui al mujahed> but you have to change the (a) to @ for it to workIron is an element, copper is an element, carbon is an element, and so on.What scienti? basis do you have for your belief that iron came latter thanthe others? What made up the earth that the iron landed on?Bill thusly:>> thusly:>> right. i did not say it came to earth after it ?ished with animals> plants>> and all that. i only noted that the quran has many things created on> earth>> but for some reason does not have iron created on earth.>> What about all the *other elements that werent formed here?> what about them? are you trying to raise an argument ex silentio? if it> turns out on usenet you never once say your mothers maiden name does that> necessarily mean you did not know your mothers maiden name? as for the> elements other than iron i will be agnostic on what the author of the quran> knew about them for now.So this is like one of those christian arguments. God failed to mentionanything *useful like penicillin but seems to have mumbled something vagueabout iron.-- Mark K. Bilbo a lack of belief in gods.No, thats Agnosticism. Atheism is the belief in the lack of a god.-- Shmuel (Seymour J.) Metz, > at 07:13 PM, raynand@netzero.net (Jefferson Rourke) said:> >Atheism is simply a lack of belief in gods.> No, thats Agnosticism. Atheism is the belief in the lack of a god.How about un-theist. Does that work for you? I think the god-conceptis a nonexistant mind created reality that it is used as a tool todupe the gullible.I think religious mysticism is a form of mental illness and madnessthat is unique to the human mind on this planet. This still work foryou?I think the god-concept and religion have held back the development ofthe human race by 2000 to 3000 years. Instead of looking for thenonexistent afterlife the human race should be working to build abetter life here and now. If not for religion and the god-concept itis a possible that we could be on other planets by now and havelifespans of over 500 years. The loss and waste of potential in thehuman race because of the god-concept is immense.Still working for you?If all of this does not ? within your de?ition parameters pleaselet me know about my ill-de?ed thought processess.Jefferson RourkeLaissez-Faire! <3fee0f44$21$fuzhry+tra$mr2ice@news.patriot.net> tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Pose: george_cox@btinternet.comX-Punge: Micro$oft at 08:02 PM, raynand@netzero.net (Jefferson Rourke) said:>How about un-theist. Does that work for you?Its not a question of whether it works for me; its a question ofwhether it works for the English language. The English terms areagnostic and atheist. What would work for me is honesty, which you arenot exhibiting.>I think religious mysticism is a form of mental illness and madness>that is unique to the human mind on this planet. Then you were lying when you stated that Atheism is simply a lack ofbelief in gods. You have gone beyond not believing in a god tobelieving that there is no god. >I think the god-concept and religion have held back the development>of the human race by 2000 to 3000 years.Perhaps it did. And perhaps it had the oposite effect. Do you haveevidence, or is it just a matter of faith for you?>Still working for you?Nope. But if your faith works for you, . . .>If all of this does not ? within your de?ition parameters please>let me know about my ill-de?ed thought processess.You might start with post hoc ergo propter hoc.-- Shmuel (Seymour J.) Metz, SysProg and > at 08:02 PM, raynand@netzero.net (Jefferson Rourke) said:>How about un-theist. Does that work for you?> Its not a question of whether it works for me; its a question of> whether it works for the English language. The English terms are> agnostic and atheist. What would work for me is honesty, which you are> not exhibiting.I honestly answered the ?st time. Atheism is a lack of belief ingods. It works just ?e for my use of the english language. >I think religious mysticism is a form of mental illness and madness>that is unique to the human mind on this planet. > Then you were lying when you stated that Atheism is simply a lack of> belief in gods. You have gone beyond not believing in a god to> believing that there is no god. Are you really this simple? Can you read the de?ition you weregiven? A pro-individual, free market laissez-faire capitalist likemyself could be an atheist or a statist, communist could be anatheist. Both lack a belief in gods but they have totally differentphilosophies and world views yet both are atheists.How does my thinking that the god-concept is a mind disease change myatheism (lack of belief in gods)? You are not making sense. >I think the god-concept and religion have held back the development>of the human race by 2000 to 3000 years.> Perhaps it did. And perhaps it had the oposite effect. Do you have> evidence, or is it just a matter of faith for you?Look at the history of the Catholic church. Look at the history ofIslam. Look at history period. If you would like me to cite referencesI can do so.How about the thousands of books and multiple libraries that wereburned by the church and christians at the beginning of the Dark Ages?What was burned?Gnostic Basilides.Porphyrys 15 volume treatise condemning christianity.Emperor Theodosious had 27,000 papyrus scrolls burned because theycontained the doctrinal basis for the gospels.By offering rich rewards Ptolemy Philadelphius gathered 270,000ancient documents and burned them.It was said in jest that christians heated their baths with theancient wisdom/knowlege of Greece and Rome.The leaders of the Crusades burned all of the books they could ?dincluding ancient Hebrew scrolls.Pope Gregory VII (1021-1085) burned the entire Apollo library to theground.In 1233 the works of Maimondes were burned along with 12,000 volumesof the Talmud.In 1244 18,000 books of various kinds were destroyed by religiousleaders. According to one eyewitness account, Cardinal Ximenesdelivered to the ?in the square of Granada 80,000 Arabicmanuscripts.This is the tip of the iceburg my friend. Do you think the destructionof all of this knowledge and the anti-knowledge attitudes of theauthorities at this time might have had a wee bit to do with thehuman race entering the Dark Ages?August 24, 1572 10,000 Protestants were slaughtered by order of PopeGregory XIII.Crusades.Witch burning.Killing of heretics etc. etc.It has been estimated that 250,000,000 human beings have been killedin the name of your nasty god-concept throughout recorded history. Doyou think the destruction of all of these people and their potentialmay have held up the development of the human race?I could go on and on and on but time doesnt allow for it.Try looking up a little history besides that we were taught inthe public school system. >Still working for you?> Nope. But if your faith works for you, . . .Havent been paying attention have you? You should have phrased it asmy lack of faith in your mind created god-concept works just ?e forme. >If all of this does not ? within your de?ition parameters please>let me know about my ill-de?ed thought processess.> You might start with post hoc ergo propter hoc.Dont know what this means. But if you really wanted me to know themeaning you would have posted it in english instead of trying to makeyourself look like something you arent.Jefferson RourkeLaissez-Faire! speak thusly:> at 08:02 PM, raynand@netzero.net (Jefferson Rourke) said:>>How about un-theist. Does that work for you?> Its not a question of whether it works for me; its a question of> whether it works for the English language. The English terms are> agnostic and atheist. What would work for me is honesty, which you are> not exhibiting.Nope. Wrong.Some of the colloquial connotations that have accreted to the words aresimilar to what youre claiming but colloquial meaning shifts around allthe time.Atheism is lacking belief in any gods. The word was coined to mean that.That is what atheists use the word to mean. That is the meaning.-- Mark K. Bilbo thusly:>> at 07:13 PM, raynand@netzero.net (Jefferson Rourke) said:>>>Atheism is simply a lack of belief in gods.>> >> No, thats Agnosticism. Atheism is the belief in the lack of a god.> How about un-theist. Does that work for you? I think the god-concept> is a nonexistant mind created reality that it is used as a tool to> dupe the gullible.Actually, theres no point to trying to change terms. Theists would trashany term used.And atheism actually *is un- or maybe more accurately non- theism.Since a- means without. As in amoral means *without morals ascontrasted to immoral which is *not moral. The in- pre? meaningopposite of or not.What they try to claim is atheism is, is more something you might callintheism (to coin a word). That would be opposite of theism. Atheism works ?e. Fits the way we do things in the language (hence theword was brought into the language to mean without theism). Theistmisunderstanding or even deliberate obfuscation notwithstanding...-- Mark K. Bilbo > thusly:>> at 07:13 PM, raynand@netzero.net (Jefferson Rourke) said:>>>Atheism is simply a lack of belief in gods.>>> No, thats Agnosticism. Atheism is the belief in the lack of a god.> How about un-theist. Does that work for you? I think the god-concept> is a nonexistant mind created reality that it is used as a tool to> dupe the gullible.> Actually, theres no point to trying to change terms. Theists would trash> any term used.> And atheism actually *is un- or maybe more accurately non- theism.> Since a- means without. As in amoral means *without morals as> contrasted to immoral which is *not moral. The in- pre? meaning> opposite of or not.> What they try to claim is atheism is, is more something you might call> intheism (to coin a word). That would be opposite of theism. > Atheism works ?e. Fits the way we do things in the language (hence the> word was brought into the language to mean without theism). Theist> misunderstanding or even deliberate obfuscation notwithstanding...Hey Mark:I was just trying to have a bit of fun with the guy and see what hisresponse would be. I thought I had the de?ition right the ?st timeand I was writing off of the top of my head without double checking.Hope you had a happy Winter Solstice,Jefferson Rourke thusly:>> thusly:>> at 07:13 PM, raynand@netzero.net (Jefferson Rourke) said:>Atheism is simply a lack of belief in gods.> No, thats Agnosticism. Atheism is the belief in the lack of a god.>>> How about un-theist. Does that work for you? I think the god-concept>> is a nonexistant mind created reality that it is used as a tool to>> dupe the gullible.>>> Actually, theres no point to trying to change terms. Theists would trash>> any term used.>>> And atheism actually *is un- or maybe more accurately non- theism.>> Since a- means without. As in amoral means *without morals as>> contrasted to immoral which is *not moral. The in- pre? meaning>> opposite of or not.>>> What they try to claim is atheism is, is more something you might call>> intheism (to coin a word). That would be opposite of theism. >>> Atheism works ?e. Fits the way we do things in the language (hence the>> word was brought into the language to mean without theism). Theist>> misunderstanding or even deliberate obfuscation notwithstanding...> Hey Mark:> I was just trying to have a bit of fun with the guy and see what his> response would be. I thought I had the de?ition right the ?st time> and I was writing off of the top of my head without double checking.No big thing. I was just rattling along on an interesting (to me at least)subject.I cant help it. Im moving more and more into linguistics as (if thingshold together) will be my next ?ld.Words fascinate me to no end...-- Mark K. Bilbo speak thusly:> at 07:13 PM, raynand@netzero.net (Jefferson Rourke) said:>>Atheism is simply a lack of belief in gods.> No, thats Agnosticism. Atheism is the belief in the lack of a god.No, atheism is lacking belief in gods.We know, were atheists.-- Mark K. Bilbo X-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Pose: george_cox@btinternet.comX-Punge: Micro$oft Saab Siddiqui said:>im snipping mr metz points that i have no response to at this>time.Good; that is proper quoting style for Usenet. Youll see peopleis generally something to avoid and not to imitate.>not that star collide with earth but that matter from star like iron>collide with earth.The Earth was formed by the accretion of matter. Much of that matterwas Iron. There was already a substantial amount of Iron when theEarth was very small. The material that fell later included a lot ofelements besides Iron, and had no higher percentage of Iron than theinitial material. Given the outgassing of lighter elements, theprimordial proto-Earth probably had a higher concentration of Ironthan the new material falling on it did.-- Shmuel (Seymour J.) Metz, X-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Pose: george_cox@btinternet.comX-Punge: Micro$oft at 04:56 PM, Mark K. Bilbo said:>The process is that iron forms in stars. The stars go nova and eject>material which includes iron. No. Iron forms in signi?ant quantities only in stars that gosupernova. A simple nova is not hot enough or dense enough.-- Shmuel (Seymour J.) Metz, SysProg and JOATnot X-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Pose: george_cox@btinternet.comX-Punge: Micro$oft >Not just large, but dense. A white dwarf star is about the size of>the Earth,Well, I prefer a yellow dwarf, but would rather that it remain a safe93,000,000 miles away ;-)>I do wonder what would happen if the impacting object was a neutron star,Lethal. The details would depend on the size, but I imagine that theradiation would kill us before we had a chance to observe the rest.-- Shmuel (Seymour J.) Metz, SysProg and JOATnot tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Pose: george_cox@btinternet.comX-Punge: Micro$oft Steve Knight said:> Great. Some camel ing, rag head, sand muncher, At least he is not a racist xenophobe like you. *PLONK*-- Shmuel (Seymour J.) Metz, SysProg and JOATnot reply to >How do you prove what the (imaginary) zeroes of the Fibonacci polynomials>are?http://mathworld.wolfram.com/ FibonacciPolynomial.htmlF(1,x)=1>F(2,x)=x>F(k,x)=xF(k-1,x)+F(k -2,x)Let G(T,x) = sum F(k,x) T^k, so that (1 - x T - T^2) G(T,x) = T, sothat G(T,x) = T/(1-xT-T^2) which we can expand using partial frations:G(T,x) = a(x)/(1-r(x)T) + b(x)/(1-s(x)T) where r(x) and s(x) arethe roots of the quadratic Z^2 - x Z - 1 . Then F(k,x), whichis the coef?ient of T^k in G, is simply a(x) r(x)^k + b(x) s(x)^k.So the roots are the values of x which make ( r(x)/s(x) )^k = -b(x)/a(x).I make it out to be that a(x) = 1/sqrt(x^2+4) and b(x) = - a(x),so -b(x)/a(x) = 1. So the roots are the values of x which make r(x) = zeta s(x)where zeta is any k-th root of unity. I further ?d r and s to bex/2 +- sqrt(x^2+4)/2, so this is equivalent to the equations x + sqrt(x^2+4) = zeta ( x - sqrt(x^2+4) ) [Note that zeta <> 1] (zeta + 1) sqrt(x^2+4) = (zeta - 1) x (zeta + 1)^2 (x^2+4) = (zeta - 1)^2 x^2 (4 zeta) x^2 + 4 (zeta + 1)^2 = 0 x^2 = - (zeta + 1)^2 / zetaWriting zeta = exp( 2 pi i p/k ) we can then rewrite the last line as x = ( +- i) (exp( 2 pi i p/(2k) ) + exp( - 2 pi i p/(2k) ) = ( +- i) 2 cos( pi p/k ).dave >How do you prove what the (imaginary) zeroes of the Fibonacci polynomials>are?>http://mathworld.wolfram.com/ FibonacciPolynomial.html>F(1,x)=1>F(2,x)=x>F(k,x)=xF(k-1,x)+F( k-2,x) Let G(T,x) = sum F(k,x) T^k, so that (1 - x T - T^2) G(T,x) = T, so> that G(T,x) = T/(1-xT-T^2) which we can expand using partial frations:> G(T,x) = a(x)/(1-r(x)T) + b(x)/(1-s(x)T) where r(x) and s(x) are> the roots of the quadratic Z^2 - x Z - 1 . Then F(k,x), which> is the coef?ient of T^k in G, is simply a(x) r(x)^k + b(x) s(x)^k.> So the roots are the values of x which make> ( r(x)/s(x) )^k = -b(x)/a(x). I make it out to be that a(x) = 1/sqrt(x^2+4) and b(x) = - a(x),> so -b(x)/a(x) = 1. So the roots are the values of x which make> r(x) = zeta s(x)> where zeta is any k-th root of unity. I further ?d r and s to be> x/2 +- sqrt(x^2+4)/2, so this is equivalent to the equations> x + sqrt(x^2+4) = zeta ( x - sqrt(x^2+4) ) [Note that zeta <> 1]> (zeta + 1) sqrt(x^2+4) = (zeta - 1) x> (zeta + 1)^2 (x^2+4) = (zeta - 1)^2 x^2> (4 zeta) x^2 + 4 (zeta + 1)^2 = 0> x^2 = - (zeta + 1)^2 / zeta> Writing zeta = exp( 2 pi i p/k ) we can then rewrite the last line as> x = ( +- i) (exp( 2 pi i p/(2k) ) + exp( - 2 pi i p/(2k) )> = ( +- i) 2 cos( pi p/k ).>it yet. > Don> Have you looked at> http://www.utm.edu/research/primes/mersenne/> 163 does not Mersenne numbers, Mp163.MZD03-Oct.MPTH163The search for Mersenne primes begins by looking forsmall factors of (mersenne numbers) 2^prime -1.Thats what I did.My letter proves a low factor for 2^163-1.Showing (on a pocket calculator) that it ISNt a Mersenne PRIME.I have photographed mersenne number plates MP163 and MP67in my (one street away.) And Mercurial factorisation HG 7817 etc.LN 2718, PI 315, PI 180. All in Newtown.= 70^2 + 14^2 == 5200 -2*52.= 14^2 x(5^2+1.)I have also eliminated some exponents about recent million) -1.e.g. ?twin primes about mersenne prime exponent.or ?factors of mersenne numbers. ?? 80mill... divides M_13mill...search don.lotto@paradise.net.nzGimps require one supercomputer week to provethe worlds largest known prime number. After it has beenselected by 200,ooo distributed personal computers.(??)Penguin dictionary of curious +interesting numbers states (1987)29th mersenne prime = M_132049.This held me up for a while. The revised edn (David Wells 1997)gives that Mp as the 30th and inserts a more recentM_110503 as 29th. Unfortunately I missed thatinteresting date 11.05.03 and 25th = 21.7.01.29th = 1.3.2049 etc.there seem to be lots.They are supposed to say (probably-possibly the 40th Mersenne prime)if not all indicies have been checked twice.Readers Guide abstracts reported M_858433 is prime?.I con?med a FACTOR and possibly reported a typo.In fact it should be M_859433 may be prime.I advised author David Wells of a number of errors in [1987]and he acknowledged me in Revised Edn [1997.](I claim 1/*61 and 7^*510 and 1215306625.eis)I have about 45 sequences in On-line eis lookup.Don.McDonald29.12.03 23:13> my?e.> DON02. Calc.Factors.FermatMers.Mersenne.CARMP163.SPMP163> subject:Mersenne numbers, Mp163 > D.Calc.Factors.FermatMers.Mersenne.CARMP163.SPMP163> We look at the usual long multiplication of, for > example, 123*48....In message you write:> lies.> teletext pball#860 total prize pool $34mill lies.> 10 lotto always add twice..lies. (teleph keypad)> very deceptive and misleading.> how many ticket sells?.> $7.248 588 million powerball.> don.mcdonald 27.12.03 23:23> 04/389-6820.> >>D.LOTTO.lotoadvice.clients.NZLCLotter.pball+twic> check--> > (prob) -- #formula,-- value, -- FACTORS -- , (centiseconds).> ---> 2 860 # draw powerball..=860= 2^2*5*43*all 3cs> 27.12.03> divis 1 roll down.> winners x $ dividend.> 3 11*1558133 div 2..=17139463= 11*19*82007*all 7cs> 4 95*714 div 3..=67830= 2*3*5*7*17*19*all 4cs> 5 725*151 divis 4..=109475= 5*5*29*151*all 4cs> 6 3328*55 divis 5..=183040= 2^8*5*11*13*all 4cs> 7 8899*28 divis 6..=249172= 2^2*7*11*809*all 4cs> 9 p(3)+p(4)+p(5)+p(6)+..p(7)..> total dividends should be $17.7 mill> =17748980= 2^2*5*887449*all 11cs> 10 lotto always add twice..lies. (teleph keypad)> =568625929723389440= Accy?(2^2*3*7*167* 47s.> 11 34748980 tot prize pool> too big by $ 17.ooo,ooo m..=34748980= 2^2*5*7*47*5281*all 7cs> 14 210*323 primorial..=67830= 2*3*5*7*17*19*all 5cs> 15 double digit bounce..(teleph keypad> =36825334448268624= Accy?(2^2*3*19*2^2*53*761861437609prime 1mn> 16 55331155338899..=55331155338899= 11*43*116979186763prime 39s.> > e n d. prog c241Q 24.2.03 close *spool> The opposite of a profound truth is another profound truth. -- NielsBohrWhat Rovelli doesnt seem to understand is that this all makes perfectsense onceyou give up strict equivalence and distinguish the background andphysical metrics.JS: I do not understand this distinction. Please give more details whatyou mean.PZ: In that case you dont understand Newtonian physics either, which makes preciselythis distinction: you dont understand the Newtonian distinction between real and?titious forces.But at least you are honest enough to admit it. :-)JS: What I understand is that ?titious or inertial forces are artifacts of the non-geodesic timelike motion of the local frames of reference. I understand Coriolis, centrifugal, standing on a scale in an elevator as inertial forces. I also understand that LOCALLY there is, APPROXIMATELY, no way to distinguish the inertial force from a gravity force or G-force on a SINGLE TEST PARTICLE 1 NOT ON A TIMELIKE GEODESIC in sense of connection ?ld for parallel transport (Experiment A), IF one MAKES NO ATTEMPT to measure the relative tidal acceleration between TWO OTHER TEST PARTICLES 2 & 3 BOTH ON TIMELIKE GEODESICS with ZERO G-FORCE (Experiment B). My OPERATIONALISM is showing, which you ignore in your too abstract formal analysis. Therefore, you end up in a false comparison comparing apples to oranges so to speak by confounding the essentially different, indeed, complementary in Bohrs sense of total experimental arrangements - even of macro relevance, Experiments A & B.Further, I do not see how you tie that to strict equivalence, which, if I understand you, you say is fundamentally wrong in some way? I do not understand how you mean background and physical above. Do you mean nondynamical and dynamical. The problem is that you introduce key terms without enough contextual background to understand what you mean. In many cases an equation would eliminate the ambiguity.Now if you mean by strict equivalence that Einstein did not include Experiment B as a matter of principle in his early formulations, then if indeed, that is historically correct, then he may have made an error that was later corrected and is completely corrected in MTW (1973), which I suppose you say EEP is a correspondance, which is always the way I viewed it to begin with. If indeed your history of the evolution of Einsteins thought on his own theory is correct, I do not know if it is, then it is a minor footnote only. I am sure similar stories exist in the evolution of all the great theories of physics from Newton on.Have you read pp. 112 - 114 that completely demolishes Hal Puthoff suse ofdr/dt = c = c/K radial null geodesicin his Tables.PZ: It does no such thing. I would not even characterize pp 112-114 asan argument.It is simply a sketch of a model in which *everything* is quantizedexcept the rawmanifold.JS: It shows no intrinsic meaning to Puthoffs r and t as he means itin his Tables.PZ: In Rovellis approach, almost everything is quantized and time itself has no fundamentalmeaning.So, OK, things are VERY different in Rovellis theory. No argument there.He wants to dig down to the raw manifold so he can quantize the stripped-offEinsteinian chronogeometric structure of spacetime, replete with its uni?d metric,thinking this may be the real solution to the quantum gravity conundrum.I say he has not properly understood the status and meaning of the uni?d metric.He has simply skated over this. He is trying to run before he can walk....What does he mean by ?tions?JS: What do you mean by kinematical g_uv and dynamic gravitationalg_uv apart from Ruvwl = 0 in the former and not in the latter.PZ: I mean what it means in Newtonian physics.JS: Huh? Newton uses forces with action at a distance. He never invokes any geometrodynamicalreplacement of forces the way Einstein does. Newton never talks of a metric so what do you mean?Do you simply mean again the distinction between inertial and non-inertial frames of reference?There are no ?titious or inertial forces in inertial frames. Newton only had implicitlythe idea of a global frame of reference not local frames of reference on a rigid Euclidean space with arigid absolute time.Einstein in 1905 uni?d rigid space and rigid time into a rigid space-time in which space and time separately were no longer rigid.Special Relativity uses a MATTER WITHOUT BACK-ACTION of MATTER on space-time.Einstein by 1915 corrects that approximation in General Relativity. (Bohm and (MASS-ENERGY).Similarly, nonlocal linear unitary evolving orthodox micro-quantum theory with signal locality its ENVIRONMENT via boundary conditions, stochastic pumps, semi-classical couplings etc. I am only here talking other interpretations of micro-QM whereIT FROM BIT (Wheeler)BIT is complete description of micro-quantum reality.This includes all collapse models with the possible exception of Penroses OR and all many-worlds models from Everett to Gell-Mann/Hartle to David Deutschs multi-verse and also Cramers transactional.Shelly Godstein takes a wrong turn IMHO in his Bohmian Quantum Gravity paper in Physics Meets Philosophy at the Planck Scale in rejecting a source for the pilot wave where it is most important on the vast scale of the Universe in the FRW limit.In contrast to micro-quantum theory, MACRO-QUANTUM THEORY is P.W. Andersons More is different in action IMHO.MACRO-QUANTUM THEORY is local, non-unitary nonlinear with presponse (Dick Bierman) signal nonlocality in the sense of Antony Valentinis violation of sub-quantal heat death.The nonlocal linear micro-quantum Schrodinger equation in the con?uration space of entangled parts of the whole is replaced by a local nonlinear MACRO-QUANTUM Landau-Ginzburg equation coupled to a residual micro-quantum Schrodinger equation in the sense of the old two-?odel of Tiza but now generalized. This seems to go against some of Lenny Susskinds and tHoofts ideas and seems to support some of Hawkings older ideas on information loss in black holes. However, I am not sure of that. Lenny et-al seems to want to misapply micro-quantum theory in the MACRO-domain ignoring PW Andersons More is different? I could be wrong. We shall see.The phase-transition from an unstable completely random white zero point noise micro-quantum vacuum to a metastable MACRO-QUANTUM VACUUM with colored zero point noise controlled by Vacuum Coherence has a lower q-entropy de?ed as log of the phase space needed by the vacuum.96% of the stuff of The World, we have been forced by the weight of FACTS to expand our notion of MATTER as MASS-ENERGY to include VIRTUAL ZERO POINT ENERGY or EXOTIC VACUA. Zero Point energy has w = Pressure/Energy Density = -1. Dark energy is exotic vacuum with negative micro-quantum pressure and dark matter is the same, but with positive pressure. All lepto-quarks have dark matter vortex string cores which prevent the distributed electric charge of the IT extra-variable from exploding. This is consistent with J.P. Vigiers notion of tight atomic states and it solves the old Abraham-Becker-Lorentz self-energy of the electron problem from ~ 100 years ago. The smallness of the cosmological constant is not solved by string theory as Ed Witten admits, but it is, IMHO, solved by MACRO-QUANTUM VACUUM COHERENCE.http://qedcorp.com/APS/EmergentGravity.pdfKey prediction: No dark matter detector will click with the right dark stuff because all dark stuff is virtual not real. Dark stuff looks like w ~ 0 at a distance but up close it is w = -1 as one day interstellar space probes using dark energy weightless warp (Alcubierre) drives will con?m.What is interesting about Lenny Susskinds theory however is the connection between black holes and elementary lepto-quarks and gauge force bosons as merely a matter of the complexity or bit length of the strings in which string has dual meaning as vibrating strings of energy and strings of computer theory in the sense of algorithmic complexity and all that. This is already seen in black hole thermodynamics whereArea/Lp^2 ~ number of bitsand the world hologram idea. > Sure, math has little to do with actual numbers. But sometimes you> need to look at literals to look for patterns. Even when youre> result is radix neutral, the elegance of hexadecimal will set your> brain in a mode of logic and intelligence. Unless youre examining> bowling scores, use hexadecimal.Re: Hexadecimal leads to insight. calls.30.12.03 X-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Pose: george_cox@btinternet.comX-Punge: Micro$oft at 03:36 PM, Timothy Murphy said:>Isnt that all equipment?Only if 18 is a multiple of 4.-- Shmuel (Seymour J.) Metz, SysProg and JOATnot reply to tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Pose: george_cox@btinternet.comX-Punge: Micro$oft mensanator@aol.compost (Mensanator) said:>Which explains why DEC used octal for 16-bit registers and 20-bit>addressing?When did I ever say that everything DEC did with the PDP-11 wasreasonable? For that matter, when did I ever say that anything DEC didwith the PDP-11 was reasonable?More to the point, A implies B is not equivalent to B implies A.-- Shmuel (Seymour J.) Metz, SysProg and JOATnot reply to >Message-id: mensanator@aol.compost (Mensanator) said:>Which explains why DEC used octal for 16-bit registers and 20-bit>>addressing?When did I ever say that everything DEC did with the PDP-11 was>reasonable? For that matter, when did I ever say that anything DEC did>with the PDP-11 was reasonable?When did I say it was unreasonable? My point apparently went completely overyour head. What you _did_ say wasHeadecimal is only reasonable for equipment that dealswith numbers in bytes that are multiples of 4 bits.It would be unreasonable for the PDP-11 to use hex because the index registerdesignations are three bits, thus making the machine language more easilyinterpreted when the dump is in octal. If the PDP-11 had 16 registers insteadof 8, then it would be reasonable to use hex. Note that this has nothing to dowith word size or addressing.Of course, a real programmer would understand that.More to the point, A implies B is not equivalent to B implies A.--MensanatorAce of ClubsX-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Pose: george_cox@btinternet.comX-Punge: Micro$oft mensanator@aol.compost (Mensanator) said:>My point apparently went completely over your head.No, your point was simply irrelevant.>What you _did_ say was>with numbers in bytes that are multiples of 4 bits.>K3wl. No read it very carefully and note what I did *NOT* write in it.>It would be unreasonable for the PDP-11 to use hex>thus making the machine language more easily>interpreted when the dump is in octal. Only for people whose ability to do mental arithmetic is impaired.>Note that this has nothing to do with word size or addressing.I note your belief to that effect.>Of course, a real programmer would understand that.ROTF,LMAO! There is a difference between understanding why somebodydid something stupid and pretending that it wasnt stupid. The factthat I dont agree with the decision doesnt mean that I didntunderstand it before you were born.I repeat, >>More to the point, A implies B is not equivalent to B implies A.You quoted it, but appear to have not read and understood it.-- Shmuel (Seymour J.) Metz, SysProg and JOATnot reply to > Making a mistake on sci.math is a good way to attract _corrections_.> You could have learned what youve learned about analytic > continuation a lot faster if youd simply tried to avoid being> certain you were right and everyone else was wrong, _even> though_ (as you _said_) you did not understand the construction> that others were talking about. To all: please excuse my not being good at following what othershave done. So, there are two approaches to the construction of a Riemannsurface from a given relation f(w,z)=0: the original which goes fromrelation to system of branches to Riemann surface, and the modernwhich bypasses the introduction of branches. But one may think thatbranches are worth studying for there own sake, and then in contextjust think of Riemann surfaces as a byproduct. This is about branches. Branches cannot be studied from the given equation on its own.Auxillary entities have to be introduced, ?st an ordinary point z0in the z-plane to serve as an initial value for z. This done thesolutions of the equation f(w,z0)=0, say w1, w2, w3... will be initialvalues for branches. Now, permutations on branches produced byanalytic continuation round closed circuits are already determinedwithout the branches as yet being fully speci?d. A circuit from z0passing among but not through singularities and returning to z0 sendseach initial value into an initial value which may be the same ordifferent. The permutation depends only on the homotopy class of thecircuit. These classes depend in turn on the branch points which aredetermined by the given equation. So one gets the idea that associatedwith a speci? branch point there may be a speci? branchpermutation. It turns out that this is only so when another auxillaryentity, namely a set of branch boundaries, is introduced. So one arrives at a theory but one which depends on auxillaryentities which are arbitrary. At this point it is useful to take ashort digression into the philosophy of language. A statement may bemade in different languages but must be made in some language. So itcan be claimed that a statement is language-independent only in thesense that it is translatable. This is the best that can be done. Byanalogy what is needed in the present theory is to show that from aresult for one set of auxillary entities a result for any other can bederived. This is easy and well known for an alternative initial point.The two points are joined by an arc and the arc added to the circuit.It is not quite as simple for an alternative set of boundaries but itcan be done. With this, branches and permutations on branches aretreated in a way which is as general as it can be. [lots of stuff]I think youve got it. Good show.Lee Rudolph Its just pretty depressing to> see a book tell you that you have learned next to nothing that you should know> coming into graduate school. Any comments or advice would be appreciated,> including book suggestions (the author tends to say Ive heard that> such-and-such book is good though I have not seen it which is pretty odd> considering the focus of the book).You may have trouble getting into a top ranked graduate program ifyour background is de?ient. However, whats far more important iswhat you do in the graduate school you do get into. Many will allowyou to take a few undergraduate courses to ?m up your background. Another clue to what you will eventually need to know is the book ofproblems from UCBerkely qualifying exams published by Springer.Dont let snobs tell you that a PhD from a less than top-ranked schoolis worthless. It isnt. What is important is to work with an activeand productive researcher with a national (or international)reputation in his/her ?ld of research. Such people will make sureyou do a good thesis and will be able to write letters that say whatprospective employers want to hear. There are such people even atlower ranked schools due to the bad job market of recent years. Youmay even do better than you might at a top school because as a goodstudent youll get a lot more attention than you would otherwise. > I checked out a book called All the Mathematics You Missed [But Need to Know> for Graduate School] from the library and was surprised by its contents. The> book is divided into 16 sections that I am supposed to know before I get> into> graduate school. This is my last year and I can check off very little.> Here are the sixteen topics that I need to know along with whether or not I> will have completed them by the end of the year:> [...]> I know that looks awful, even beyond awful, with 5/16. I dont think its> realistic that I could learn that much material over the Summer. Which areas> do I absolutely need to know? > That kind of depends on what the grad school you go to expects. Forexample, some schools will expect you to have some familiarity withundergraduate complex analysis in their graduate complex analysiscourse, and some wont. What may be most helpful is to take a look at Lebesgue integration. Atleast get a rough outline of what its about. And in particular, youcan be more careful about checking details and stuff for thepreliminary stuff like measures and sigma algebras. This is probablyone of the harder topics in a ?st year grad course, and it helps toget a start on it.Another thing is to learn some point set topology before you get tograd school. It shouldnt be too hard to learn, given that youve hadreal analysis. This will really help in learning graduate levelanalysis. Even though there is such a thing as graduate point settopology, few places offer a course in it, and many assume youvelearned undergrad point set topology somehow. Theres nothing likewalking into an analysis or algebraic topology class and learning thatyoure *supposed* to know what a locally compact, connected, Hausdorffspace is.You might as well learn about Gaussian curvature of surfaces in R^3. It motivates a lot of very advanced material that you may very well runinto in some of your classes. And its a relatively simple topic thatis fun to learn about. It should offer a nice respite from Lebesgueintegration or whatnot. Theres more stuff you could learn (like the generalized Stokestheorem), but probably it not essential, and you have more than enoughon your hands already.> Is this book very accurate in what I SHOULD know for graduate school? Almost> everything seems to roughly fall under analysis/applied math. [...]I think so. Note your ideas about applie math are rather misguided.> The strange thing is that, besides applied math classes, Im taking or have> taken what they offer in terms of pure math. Its just pretty depressing to> see a book tell you that you have learned next to nothing that you should know> coming into graduate school. Cheer up; you have a jump on all your future classmates who will nothave a clue that they should know these things. Sometimes it takespeople a year or two in grad school before they realize they need toremedy their ignorance in some of these topics, and then its very lateand hard to ?.Besides, doesnt the author say he doesnt expect the reader to knowall these things? After all, look at the title; clearly he expects youto have missed some of the topics. The emphasis should be on thephrase *should know*. I could go on all day about what you shoulda,but it wont help you much.> Any comments or advice would be appreciated,> including book suggestions (the author tends to say Ive heard that> such-and-such book is good though I have not seen it which is pretty odd> considering the focus of the book).> > I remember ?g through this book at Borders, and thinking thereferences were rather scanty in some spots.with the list of references for those topics in the book, so I cancomment on whether I think they are suf?ient or lacking. I remembermost seemed suf?ient. Ill try to clear a few things up. The lowest grade Ive made in a math courseis a B+. Normally I just get As. For what its worth, my school is a Tier2 school according to US News and World Reports. It also has a PhD program. Some of the professors that are well known do not want to teach undergraduates,so that is partly (I think) why topology is not offered.Im interested in algebra and number theory. That is why I was surprised whenthe book had only 2 sections on algebra and none on number theory. Ive takenthe regular number theory course and an algebraic number theory one as well. Two of the Professors that are writing my recommendations were disappointedwith where I wanted to apply. One of them has told me that I have researchpotential but I guess that can be interpreted as just being nice. [...]| Two of the Professors that are writing my recommendations were disappointed| with where I wanted to apply. One of them has told me that I have research| potential but I guess that can be interpreted as just being nice. Take it seriously if they think you should try applying to some betterschools.Its too bad you didnt get better opportunities as an undergraduate, butconsider that water under the bridge.Its still some years from when you have to do anything, but one thing youmight want to keep in mind for when you get there: If you wind up in a PhD program which is only okay, but you have reason to believe youre doingthesis work of a higher caliber (so it seems like you might be on your wayto being underrated), Id recommend trying to get letters of recommendationfrom bigger names in addition to your advisor. I was always crummy atself-promotion, but even I know that it does your career good to be well-connected. So as you get into a ?ld, get acquainted with some of the people already established in it. When you get good results, see if you can get favorable letters.It was heartening when I was looking for mathematical jobs when someone from one of the schools Id had an interview with came up to me afterward, and said something like, Hey, Professor [name] was just telling us about you, and evidently it was something good hed told them. Not that I got the job :-(but it sure can help the odds.I remember a guy who managed to get a letter of recommendation from Delignesaying something like, this guy solved a problem we tried to solve. He didget the job!Keith Ramsay > Ill try to clear a few things up. The lowest grade Ive made in a math course> is a B+. Normally I just get As. For what its worth, my school is a> Tier 2 school according to US News and World Reports. It also has a> PhD program. Some of the professors that are well known do not want to> teach undergraduates, so that is partly (I think) why topology is not> offered.your school does not seem impressive at all.even in cases where prefessors do not like teaching undergrads, anundergrad topology course offering is a must. of course that can beresolved by offering independent studies. does your school offer such?if it does, why didnt you study undergrad topology independently?> Im interested in algebra and number theory. That is why I was surprised> when the book had only 2 sections on algebra and none on number theory.> Ive taken the regular number theory course and an algebraic number> theory one as well. in general, a gap in undergrad algebra, advanced calculus, andtopology is a very serious one for anyone pursuing a graduate mathdegree. a gap in number theory is not.> Two of the Professors that are writing my recommendations were disappointed> with where I wanted to apply.assuming your report is accurate, your professors have good reasons tobe dissapointed - graduate math degrees from unranked programmes aregenerally worthless in the job market.> One of them has told me that I have research potential but I guess that> can be interpreted as just being nice. true. but if his/her assessemnt is accurate, then you should endeavourto ?l in the gaps in your undergrad math preparation and then shoothigh for a ranked math graduate school. >Ill try to clear a few things up. The lowest grade Ive made in a math course>is a B+. Normally I just get As. For what its worth, my school is a Tier>2 school according to US News and World Reports. It also has a PhD program. >Some of the professors that are well known do not want to teach undergraduates,>so that is partly (I think) why topology is not offered.Im interested in algebra and number theory. That is why I was surprised when>the book had only 2 sections on algebra and none on number theory. Ive taken>the regular number theory course and an algebraic number theory one as well. Two of the Professors that are writing my recommendations were disappointed>with where I wanted to apply. One of them has told me that I have research>potential Thats different. You didnt mention those letters in your originalpost.You should apply to a few good schools. Those professors have abetter idea than you do about your ability compared to the studentsthose places usually admit. The worst that could happen is theyturn you down...>but I guess that can be interpreted as just being nice. No. Math professors are not nice. Its a condition of employment.************************David C. Ullrich > Ill try to clear a few things up. The lowest grade Ive made in a math> course> is a B+. Normally I just get As. For what its worth, my school is a Tier> 2 school according to US News and World Reports. It also has a PhD program. > Some of the professors that are well known do not want to teach> undergraduates,> so that is partly (I think) why topology is not offered.> Im interested in algebra and number theory. That is why I was surprised when> the book had only 2 sections on algebra and none on number theory. Ive taken> the regular number theory course and an algebraic number theory one as well. > Two of the Professors that are writing my recommendations were disappointed> with where I wanted to apply. One of them has told me that I have research> potential but I guess that can be interpreted as just being nice. > Hmm...this is interesting. It sounds like to me that they think youcould do better. Perhaps you are being overly pessimistic. Granted,the discussion on sci.math thus far has not been encouraging, but ithas mostly centered around getting into really hard schools.Your professors probably have a better idea than you of where you canget in. If they think you can get in somewhere better, then followtheir advice! Your professors may also have a better reputation thanyou think. Even if theyre not hotshots (that dont teach, as youmention above), you shouldnt dismiss them; if they have decentreputations, and/or have connections, you could do very well with theirrecommendations.Am I right in thinking that youve decided to apply to some mastersprograms, instead of some doctoral programs? I urge you to read myother posts in this discussion. Basically, you may very well beshooting yourself in the foot if you decide to go the masters route. > Am I right in thinking that youve decided to apply to some masters> programs, instead of some doctoral programs? I urge you to read my> other posts in this discussion. Basically, you may very well be> shooting yourself in the foot if you decide to go the masters route.I should say that I agree with Chan-Ho Suh here. (Surprise!)I think that the best reason to go to a masters program, for someonewho someday hopes to get a doctorate, is that they have failed to getinto the sort of doctoral programs they think they need in order tosucceed. I think this is true for all disciplines, actually. Some ofthe comments here suggest that a masters may be a positive detrimentto some math PhD programs; but if you could have gotten a decentdoctorate anyway, then in any discipline, math or not, the masters isreally only a waste of a couple years.Note that this is the hidden message of the Philosophical Gourmetexcerpt I quoted. The only reason to get a masters is if without it,you would not be able to get into a decent doctoral program. Perhapsit doesnt help in math as much as it might in some ?lds, butregardless, if you can get into a decent doctoral program, then youshouldnt get a separate masters ?st.And the only way to know if you can get into a decent doctoral programis to apply. Thomas > Two of the Professors that are writing my recommendations were> disappointed with where I wanted to apply. One of them has told me> that I have research potential but I guess that can be interpreted> as just being nice.You mean, in the sense that they thought you should apply to betterschools? Take that advice! I think one should aim high, whilebeing prudent, in this as everything. I think its always a good ideato apply to several places that you think are beyond your reach. >Message-id: [...]>If you are aiming for a ph.d, then I would suggest getting into the best M.S>program you can, and then apply to a great ph.d program when you get your>M.S.. This is essentially what I am doing, for I am in the same situation.>Good luck!LurchThis is basically what I plan on doing. Is it bad to get a masters at a schoolwith a PhD program and then transfer to another school afterwards, even if youget good recommendations? Im applying to a few pretty low-ranked PhD programsand one masters program. I just dont know of any really GREAT mastersprograms but Im sure they are out there. Do you know of any? I think there are several mathematics programs for people with weakbackgrounds at interesting schools ,e.g. , Mathematics Opportunity Committeeat Berkeley , and perhaps Princeton or Harvard have something similar .Best of Luck.> I checked out a book called All the Mathematics You Missed [But Need toKnow> for Graduate School] from the library and was surprised by its contents.The> book is divided into 16 sections that I am supposed to know before I getinto> graduate school. This is my last year and I can check off very little. Here are the sixteen topics that I need to know along with whether ornot I> will have completed them by the end of the year: 1. Linear Algebra - Yes> 2. Real Analysis - Yes> 3. Differentiating Vector Valued Functions (jacobians, inverse function> theorem) - No (nothing like this taught at my school)> 4. Point Set Topolgy - No (not offered here)> 5. Classical Stokes Theorems - Yes> 6. Differential Forms and Stokes Theorem - No (nothing like that here)> 7. Curvature for Curves and Surfaces (differential geometry) - No (notoffered)> 8. Geometry - No (only course offered is one for future high schoolteachers> and was advised not to take it)> 9. Complex Analysis - No (schedule con?last year and this year)> 10. Countability and the Axiom of Choice - No (not offered but I havelooked> into it a bit)> 11. Algebra - Yes> 12. Lebesgue Integration - No (not undergrad here)> 13. Fourier Analysis - No (I thought this was for engineers)> 14. Differential Equations - Yes> 15. Combinatorics and Probability - No (combinatorics not offered;probability> only after calc-based statistics is taken)> 16. Algorithms - No (the closest thing to what is described here is amid-level> computer science course). I know that looks awful, even beyond awful, with 5/16. I dont think its> realistic that I could learn that much material over the Summer. Whichareas> do I absolutely need to know? Is this book very accurate in what I SHOULD know for graduate school?Almost> everything seems to roughly fall under analysis/applied math. The math> department has no one that does any research whatsoever in geometry (forthose> areas listed here). Only 2 sections are devoted to algebra and there is> nothing about number theory. The strange thing is that, besides applied math classes, Im taking orhave> taken what they offer in terms of pure math. Its just pretty depressingto> see a book tell you that you have learned next to nothing that you shouldknow> coming into graduate school. Any comments or advice would be appreciated,> including book suggestions (the author tends to say Ive heard that> such-and-such book is good though I have not seen it which is pretty odd> considering the focus of the book). > I checked out a book called All the Mathematics You Missed [But Need to> Know for Graduate School] from the library and was surprised by its> contents. The book is divided into 16 sections that I am supposed to> know before I get into graduate school. This is my last year and I> can check off very little.> Here are the sixteen topics that I need to know along with whether or> not I will have completed them by the end of the year:> 1. Linear Algebra - Yes> 2. Real Analysis - Yes> 3. Differentiating Vector Valued Functions (jacobians, inverse> function theorem) - No (nothing like this taught at my school)> 4. Point Set Topolgy - No (not offered here)> 5. Classical Stokes Theorems - Yes> 6. Differential Forms and Stokes Theorem - No (nothing like that here)> 7. Curvature for Curves and Surfaces (differential geometry) - No> (not offered)> 8. Geometry - No (only course offered is one for future high school> teachers and was advised not to take it)> 9. Complex Analysis - No (schedule con?last year and this year)> 10. Countability and the Axiom of Choice - No (not offered but I have> looked into it a bit)> 11. Algebra - Yes> 12. Lebesgue Integration - No (not undergrad here)> 13. Fourier Analysis - No (I thought this was for engineers)> 14. Differential Equations - Yes> 15. Combinatorics and Probability - No (combinatorics not offered;> probability only after calc-based statistics is taken)> 16. Algorithms - No (the closest thing to what is described here is a> mid-level computer science course).> I know that looks awful, even beyond awful, with 5/16. I dont think> its realistic that I could learn that much material over the Summer.> Which areas do I absolutely need to know?strong background in in areas 1-11. at least moderate workingknowledge in areas 11-15.> Is this book very accurate in what I SHOULD know for graduate school? Almost> everything seems to roughly fall under analysis/applied math. The math> department has no one that does any research whatsoever in geometry (for those> areas listed here). Only 2 sections are devoted to algebra and there is> nothing about number theory. > The strange thing is that, besides applied math classes, Im taking or have> taken what they offer in terms of pure math. Its just pretty depressing to> see a book tell you that you have learned next to nothing that you should know> coming into graduate school. Any comments or advice would be appreciated,> including book suggestions (the author tends to say Ive heard that> such-and-such book is good though I have not seen it which is pretty odd> considering the focus of the book).it seems clear that you wasted your undergrad years in a bad mathschool (typical.) that alone is good reason for you to quit while youare not so far behind, assuming that a major reason for you to pursuemath is a job, including academic math jobs beyond k-12. now, if themain reason for you to pursue math is for its own sake (extremelyunlikely,) then you will need to patch the huge gaps your undergradinstitution left behind, and then engage in graduate math studies,preferably in a highly ranked programme. >>What you need to know before starting grad school varies considerably>>from place to place - you probably dont have any chance at all of >>getting into one of the best graduate programs in the country, but>>there are plenty of graduate math departments around where most>>of the incoming students will have a background more or less like>>yours (and plenty of places where the majority of incoming grad>>students will be entering with what the department considers an>>inadequate background, because they cant get the students they>>want - it happens a lot that incoming students at medium-level>>grad programs start by taking a lot of undergraduate classes>>that didnt exist where the student came from.)>>One bit of advice would be next time, if you intend to go to>>grad school, do your undergrad work at a place with a slightly>>stronger program. Maybe a little late for that now...I realized that I had no shot at any top program about a year ago when I looked>at the course offerings at the Ivy League schools and MIT. This is my senior>year so its too late to go to a stronger program. I know that my department>is bad but now its just could have and should have. How realistic is it>to get a masters degree and transfer to a better school? Hard to say. I dont know of any examples (in math) of someone witha BS from a mediocre place who got a masters from some placebetter and then a PhD from a top school. The fact that I dontknow of any examples doesnt prove there are none - Bushnellhas stated that he knows of plenty of such examples (otoh hesfailed to name any, after being asked twice...)But it really doesnt follow that youre screwed. You should be ableto get into a PhD program _somewhere_ if thats what you want.Then later when youre applying for jobs the fact that the placeyou got your degree was not a top school will not be in yourfavor, but if youve written a really fabulous thesis people willoverlook that - if you settle the Riemann hypothesis people will be interested regardless of where you got your degree.>Are you just screwed>if you did not go to the right school and take the right courses with the right>professors?When were talking about undergraduate work probably right coursesis the main thing. And the right grades in those courses.(You could arrange to ?hilosophy or something, so you get tostick around another year and ?l in a few gaps...)>>As far as what you should really know, probably the most>>important thing is that you have a good idea what a _proof_>>is, and you have some facility writing correct proofs of relatively>>easy facts (by this I mean most of the exercises in a beginning>>abstract algebra course, say. The algebra you say youve>>taken was about groups and rings and things, not like>>a high-school algebra course, right?)Of course. >By the way, many of the topics youre thinking of as>>applied math are _also_ very important in pure math ->>it may not look that way from the course offerings where>>you went to school. (In particular, although there is>>certainly such a thing as a _course_ in Fourier analysis>>thats meant for engineers, Fourier analysis itself is>>incredibly important in many ?lds of math. Same for>>complex.)The applied math courses here are almost exclusively for engineering or physics>majors. There is a class that covers Fourier Analysis>and Partial Differential Equations but I (mistakenly?) thought that it was for>the engineering and physics people. >************************>>David C. Ullrich>************************David C. Ullrich > Hard to say. I dont know of any examples (in math) of someone with> a BS from a mediocre place who got a masters from some place> better and then a PhD from a top school. The fact that I dont> know of any examples doesnt prove there are none - Bushnell> has stated that he knows of plenty of such examples (otoh hes> failed to name any, after being asked twice...)We can also look at catalogues from schools that list all the degreesof their faculty. Of course, that is often somewhat dated, but itsat least published information so I dont need to be reticent aboutnames.UMass/Amhersts math department includes one Nathaniel Whitaker, whois BA, Hampton Institute, 1974; MS, Cincinatti, 1981; PhD, California,1987. I assume that California means UC Berkeley.I looked through the list of current grad students at Cornell. Ifound one Liang Chen, who has a BS from Peking University and a MSfrom the University of Wisconsin at Madison, and is now at Cornell.And Jose Trujillo Ferreras, who has a Licenciado from the UniversidadAutonoma de Madrid, and an MA from Duke and is now at Cornell.Jennifer Fawcett is BA from Rice, MA from UC Davis, and now atCornell. Lee Gibson, BS from the University of Kentucky, MS from theUniversity of Louisville, now at Cornell. Farkhod Eshmatov, BS fromTashkent State University, MA from SUNY Binghamton, now at Cornell. Thats six, in about ten minutes of web looking.Thomas > Hard to say. I dont know of any examples (in math) of someone with>> a BS from a mediocre place who got a masters from some place>> better and then a PhD from a top school. The fact that I dont>> know of any examples doesnt prove there are none - Bushnell>> has stated that he knows of plenty of such examples (otoh hes>> failed to name any, after being asked twice...)We can also look at catalogues from schools that list all the degrees>of their faculty. Of course, that is often somewhat dated, but its>at least published information so I dont need to be reticent about>names.UMass/Amhersts math department includes one Nathaniel Whitaker, who>is BA, Hampton Institute, 1974; MS, Cincinatti, 1981; PhD, California,>1987. I assume that California means UC Berkeley.Thats _one_ example that seems valid, at least if California doesmean Berkeley. My reaction to most of the examples below is thesame as the people whove already replied - the majority of theplaces that you seem to be regarding as mediocre seem likepretty good schools to me. This is certainly true of most of theplaces you say people got their masters degrees.Take the person with the BA from Rice. You think that hereundergraduate transcript looks anything like the transcript ofthe OPs?>I looked through the list of current grad students at Cornell. I>found one Liang Chen, who has a BS from Peking University and a MS>from the University of Wisconsin at Madison, and is now at Cornell.>And Jose Trujillo Ferreras, who has a Licenciado from the Universidad>Autonoma de Madrid, and an MA from Duke and is now at Cornell.>Jennifer Fawcett is BA from Rice, MA from UC Davis, and now at>Cornell. Lee Gibson, BS from the University of Kentucky, MS from the>University of Louisville, now at Cornell. Farkhod Eshmatov, BS from>Tashkent State University, MA from SUNY Binghamton, now at Cornell. Thats six, in about ten minutes of web looking.Thomas************************David C. Ullrich > Take the person with the BA from Rice. You think that here> undergraduate transcript looks anything like the transcript of> the OPs?Who knows? Its possible to have bad grades from a good school, andgood grades from a bad school. Im speaking only about the latter.Thomas > Take the person with the BA from Rice. You think that here>> undergraduate transcript looks anything like the transcript of>> the OPs?Who knows? Its easy to ?d out with a little web searching. Atwe read that an undergad degree at Rice requires 8 courses at 300 level or above. To get an idea what that means we lookat the course offerings in three recent semesters (details below).And we conclude that the transcript of someone with a degreefrom Rice looks _nothing_ like the OPs transcript - its possiblethat he hasnt taken even _one_ course thats anything likea 300+ course at Rice, much less 8. (He says hes taken algebra - its hard to know how the content of that course compareswith the content of a similarly-named course at Rice. Butits easy to guess what the typical admissions committeeis going to guess about the comparison between thesimilarly named courses at the two schools...)Citing a person with a BA from Rice as an example of someonewith a mediocre BA who nonetheless got into a good PhD programby getting a masters from a good place turns out to be asridiculous as it seemed to me yesterday, before I lookedup the details.Details: http://math.rice.edu/Courses/webpages.html Math 401: Differential Geometry Math 423: Partial Differential Equations Math 444: Geometric Topology Math 468: Potpourri (Dynamical Systems) Math 499/699:Math. Sciences VIGRE Seminar: Computational Algebraic Geometry Math 590: Current Mathematics Seminar Math 591: Graduate Teaching Seminar MATH 356 ABSTRACT ALGEBRA Credits 3.00Spring 03 * DISTRIBUTION COURSE: GROUP III Groups: normal subgroups, factor groups, Abelian groups.Rings: ideals, Euclidean rings, and unique factorization. Fields: algebraicextensions, ?ite ?lds. Students may not take this course and Math 463. 001 HB 227 - MWF 02:00PM - 02:50PM Hyeon, Donghoon DavidEnr: 12 Max: 0 MATH 366 GEOMETRY Credits3.00 Spring 03 * DISTRIBUTION COURSE: GROUP III Topics chosen from Euclidean, spherical, hyperbolic, andprojective geometry, with emphasis on the similarities and differences found invarious geometries. Isometries and other transformations are studied and usedthroughout. The history of the development of geometric ideas is discussed.This course is strongly recommended for prospective high school teachers. 001 HB 227 - MWF 03:00PM - 03:50PM Hassett, BrendanEnr: 32 Max: 0 MATH 382 COMPLEX ANALYSIS Credits3.00 Spring 03 * DISTRIBUTION COURSE: GROUP III Study of the Cauchy integral theorem, Taylor series, residues,as well as the evaluation of integrals by means of residues, conformalmapping, and application to two-dimensional ?ow. May not receivecredit for this course and Math 427. 001 HB 227 - MWF 01:00PM - 01:50PM Song, Joung Min JaimeEnr: 26 Max: 0 MATH 390 UNDERGRADUATE COLLOQUIUM Credits1.00 Spring 03 * DISTRIBUTION COURSE: GROUP III Lectures by undergraduate students on mathematical topics notusually covered in other courses. Each student is required to give one lectureand to attend all sessions. 001 HB 423 - MF 12:05PM - 12:50PM Jones, FrankEnr: 7 Max: NA MATH 402 DIFFERENTIAL GEOMETRY Credits3.00 Spring 03to year. Prereq- Math 401 and either Math 443 or DIFFERENTIAL EQUATIONS Credits3.00 Spring 03 See Math 423. 001 HB 423 - MWF 02:00PM - 02:50PM Jones, FrankEnr: 8 Max: 0 MATH 426 TOPICS IN REAL ANALYSIS Credits3.00 Spring 03harmonic analysis, probabilty theory, advanced topics in measure theory,ergodic theory, and elliptic integrals. 001 HB 423 - TTH 01:00PM - 02:20PM Veech, William A.Enr: 2 Max: 0 MATH 427 COMPLEX ANALYSIS Credits3.00 Spring 03 Study of the Cauchy-Riemann equation, power series, Cauchysintegral formula, residue calculus, and conformal mappings. 001 HB 427 MATH 443 GENERAL TOPOLOGY Credits3.00 Spring 03 Study of basic point set topology. Includes a treatment ofcardinality and well ordering, as well as metrization. Prereq: MATH 321 or permission of instructor recommended. 001 HB 427 - MWF 02:00PM - 02:50PM Clark, GregoryEnr: 8 Max: 0 MATH 445 ALGEBRAIC TOPOLOGY Credits3.00 Spring 03 Introduction to the theory of homology. Includes simplicialcomplexes, cell complexes and cellular homology and cohomology, as well asmanifolds, and Poincare Duality. Prereq- Math 444 and either Math 356 or Math 463 or permissionof instructor. 001 HB 427 - MWF 01:00PM - 01:50PM Cochran, Tim D.Enr: 10 Max: 0 MATH 464 ALGEBRA II ALGEBRA Credits3.00 Spring 03 Pre-req- Math 356 or Math 463 or Credits3.00 Spring 03 This course will consider power series, real analyticfunctions, and some related matters. Prereq- Math 321 and either Math 382 or Math 427 (which may betaken concurrently), or permission of the instructor. 001 TBA - TTH 01:00PM - 02:20PM Semmes, StephenEnr: 3 Max: NA MATH 490 SUPERVISED READING CreditsSpring 03 No description. 001 TBA - TBA StaffEnr: 6 Max: NA 002 TBA - TBA StaffEnr: 1 Max: NA 003 TBA - TBA StaffEnr: 0 Max: NA MATH 502 TOPICS IN DIFFERENTIAL GEOMETRY Credits3.00 Spring 03 The Atiyah-Singer theorem, secondary invariants, and relatedtopics. 001 HB 427 - TTH IN REAL ANALYSIS Credits3.00 Spring 03 Geometric Measure Theory treats measure-theoretic properties ofgeometrically de?ed sets of various dimensions. Some of the criticalnotions are Hausdorff measure, recti?ble sets, and recti?ble currents. The kdimensional Hausdorff (outer) measure H k(A) gives, for every nonnegativenumber k , a precise notion of the k dimensional size of A . Recti?blesets and currents arise as limits of k dimensional manifolds. theseoccur in the solution of the Plateau Problem of ?ding a k dimensionalsurface of least k dimensional area having a given boundary. Graduate student standing or permission of instructor. 001 TBA - MWF 12:00PM - 12:50PM StaffEnr: 7 Max: NA MATH 590 CURRENT MATHEMATICS SEMINAR Credits1.00 Spring 03 Lectures on topics of recent research in mathematicsdelivered by mathematics graduate students and faculty. Prereq: graduate student standing or permission of thedepartment. 001 HB 227 - TTH 02:30PM - 03:45PM StaffEnr: 25 Max: NA MATH 591 GRADUATE TEACHING SEMINAR Credits1.00 Spring 03 Discussion on teaching issues and practice lectures byparticipants as preparation for classroom teaching of mathematics. Graduate student status or permission of department. 001 HB 427 - T 02:30PM - 03:30PM StaffEnr: 15 Max: NA MATH 800 THESIS AND RESEARCH CreditsSpring 03 http://www.rice.edu/projects/courses/2002fall/MATH.htmlMATH 321 INTRODUCTION TO ANALYSIS I Credits 3.00 Fall02 * DISTRIBUTION COURSE: GROUP III A thorough treatment of basic methods of analysis such asmetric spaces, compactness, sequences and series of functions. Also furthertopics inLiouville theory. Prereq- Math 222 or permission of department. 001 HB 427 - MWF 03:00PM - 03:50PM Semmes, StephenEnr: 21 Max: NA MATH 355 LINEAR ALGEBRA Credits3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Linear transformations and matrices, solution of linearequations, eigenvalues and eigenvectors, quadratic forms, rational canonical form,Jordan canonical form. 001 HZ 210 - MWF 02:00PM - 02:50PM Clark, GregoryEnr: 108 Max: NA MATH 368 TOPICS IN COMBINATORICS Credits3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Study of combinatorics and discrete mathematics. Topics thatmay be covered include graph theory, Ramsey theory, ?ite geometries,combinatorial enumeration, combinatorial games. Prereq- Math 211. 001 HB 227 - MWF 03:00PM - 03:50PM Stong, Richard A.Enr: 26 Max: NA MATH 381 INTRODUCTION TO PARTIAL DIFFERENTIAL EQU Credits3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Laplace transform: inverse transform, applications to constantcoef?ient differential equations. Boundary value problems: Fourierseries, Bessel functions, Legendre RichardEnr: 73 Max: NA MATH 390 UNDERGRADUATE COLLOQUIUM Credits1.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Lectures by undergraduate students on mathematical topics notusually covered in other courses. Each student is required to give one lectureand to attend all sessions. 001 HB 227 - MF 12:05PM - 12:55PM Jones, FrankEnr: 6 Max: 0 MATH 401 DIFFERENTIAL GEOMETRY Credits3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Study of the differential geometry of curves and surfaces inR3. Includes an introduction to the concept of curvature and thorough treatmentof the Gauss-Bonnet theorem. 001 HB 427 - TTH DIFFERENTIAL EQUATIONS Credits3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Theory of distributions. Wave equation, Laplaces equation,heat equation. Fundamental solutions. Other topics include ?st orderhyperbolic systems, Cauchy-Kowalewski theorem, potential theory, Dirichlet andNeumann problems, integral equations, elliptic equations. 001 HB 427 - MWF 02:00PM - 02:50PM Jones, FrankEnr: 9 Max: NA MATH 425 REAL ANALYSIS Credits3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Lebesgue theory of measure and integration. 001 HB 423 - TTH 01:00PM - 02:20PM Wiandt, TamasEnr: 13 Max: NA MATH 428 TOPICS IN COMPLEX ANALYSIS Credits3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Special topics include Riemann mapping theorem, RungesTheorem, elliptic function theory, prime number Hassett, BrendanEnr: 4 Max: NA MATH 444 GEOMETRIC TOPOLOGY Credits3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Introduction to algebraic methods in topology and differentialtopology. Elementary homotopy theory. Covering 10 Max: NA MATH 463 ALGEBRA I Credits3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Groups, rings, ?lds, vector spaces. Matrices, determinants,eigenvalues, canonical forms, multilinear algebra. Structure theorem for?itely generated READING CreditsFall 02 No description. 001 TBA - TBA StaffEnr: 3 Max: 0 002 TBA - TBA StaffEnr: 2 Max: NA 003 TBA - TBA StaffEnr: 0 Max: NA MATH 521 ADVANCED TOPICS IN REAL ANALYSIS Credits3.00 Fall 02 Topic TBA. 001 GRB 212W - MWF 03:00PM - 03:50PM Hardt, Robert M.Enr: 7 Max: NA MATH 527 ERGODIC THEORY MATH 541 TOPICS IN TOPOLOGY Credits3.00 Fall 02 No description. 001 HB 423 - MWF 01:00PM - 01:50PM Cochran, Tim D.Enr: 9 Max: NA MATH 590 CURRENT MATHEMATICS SEMINAR Credits1.00 Fall 02 Lectures on topics of recent research in mathematicsdelivered by mathematics graduate students and faculty. Prereq: graduate student standing or permission of thedepartment. 001 HB 427 - T 02:30PM - 03:50PM Song, Joung Min JaimeEnr: 25 Max: 0 MATH 591 GRADUATE TEACHING SEMINAR Credits1.00 Fall 02 Discussion on teaching issues and practice lectures byparticipants as preparation for classroom teaching of mathematics. Graduate student status or permission of department. 001 HB 453 - TH 02:30PM - 03:50PM Masters, JosephEnr: 14 Max: 0 MATH 800 THESIS AND RESEARCH CreditsFall 02 >Its possible to have bad grades from a good school, and>good grades from a bad school. Im speaking only about the latter.Thomas************************David C. Ullrich >> Take the person with the BA from Rice. You think that here>> undergraduate transcript looks anything like the transcript of>> the OPs?>Who knows? > Its easy to ?d out with a little web searching.When I said who knows I meant not which classes did she take butdid she do well in them.Thomas > Take the person with the BA from Rice. You think that here>> undergraduate transcript looks anything like the transcript of>> the OPs?Who knows? Its possible to have bad grades from a good school, and>good grades from a bad school. Im speaking only about the latter.I think it has been mentioned in this thread that grades (and alsoGRE scores) are maybe not too important; the list of courses takenmight matter much more (assuming the grades average at least a Bor so) and the extra-curricular indicators may be even more telling(someone else mentioned things like undergrad publications). In allthese ways the weak student at the strong school has more opportunitiesthan the strong student at the weak school, IMHO.It would be very interesting to ?d data about pipeline issueslike this. Assume for a moment the (actually quite bogus) premise that every high-school math-lover dreams of a full professorship.Assume as well that institutions can be broken into equivalenceclasses which can be linearly ordered (maybe not too bad an assumption).Fix a cohort of people (say, US citizens born in one year) and assume that they operate in a closed system of opportunities andfeeder stages. (Not really accurate, since so many students crossborders, but we could assume the number of positions to be held bymembers of the cohort will stay ?ed for a while.)Then one can track a cohort of people through various stages: admission to university graduation with bachelors degree in math admission to grad school attainment of PhD postdoc tenure-track job tenured professorshipAt each stage, one could take a census of how many from the cohortare in Harvard-class schools; how many at a Rice-class school;how many at Big State U; how many at Local Community College, etc.This would provide a statistical answer to the OPs questions(which may or may not be applicable to that one person, of course).My hunch is that the genius comments made elsewhere are prettyaccurate, which is to say that the main job of schools is to standout of the way and let the bright students ?and identify themselves. That would be re? in the data if we found thateach institution tends to be fed only be institutions ofcomparable or superior rank: the passages from stage to stageare simply ?ters which let the best progress.Actual data data about where the Group-I PhDs get their ?st jobs,the Group-IIs, etc. These data tend on the whole to support thehunch I just made.Also available are the column totals. A typical age cohort inthe US is nowadays about 4 million. About 2-3 million will entercollege (including community college), 1-2 million will completecollege, of whom about 1% will be math majors. In some years almostevery one of them who wants it can ?d a spot in a grad school,but thats not true when the economy is bad, and its harder todo when the number of mathematically-strong foreign students ishigh. At the output end there, we know there are only something like1000-1200 new PhDs per year in the US, only half of whom areoriginally from the US. Of?ially-named post-doc positions mustnumber in the low hundreds (counted as openings per year, nottotal inhabitants). Regular academic positions advertised per year numberin the high hundreds, but the bulk of those are at the lower-rankedschools. (You can peruse the annual compendium of job openings toquantify this if you wish.) Finally, the number of tenure casesdecided positively per year has to be in the mid-hundreds, againfar more at the lower schools (where turnover is higher) than atIvy level. In short: only a tiny fraction of youngsters who are goodat math will make it all the way to the end.One can always be optimistic and hope for some upward migration,but at almost every level this seems unlikely. For example, theremay be hundred openings every year for postdocs at Ivy-class schools.Where do you think the successful applicants will come from?Some will come from, say, Kansas or Wyoming, but the great majorityare surely from Ivy-class grad schools. Those same schools producedseveral times that number of PhDs the previous year, so where willthe rest of their students go? They will be grabbing the tenure-trackopenings at Kansas and Wyoming, forcing _their_ students to lookfor jobs at schools with no graduate program at all, etc.Seems to me this would make for a dandy study by a budding economist!dave > Hard to say. I dont know of any examples (in math) of someone with> a BS from a mediocre place who got a masters from some place> better and then a PhD from a top school. The fact that I dont> know of any examples doesnt prove there are none - Bushnell> has stated that he knows of plenty of such examples (otoh hes> failed to name any, after being asked twice...)> We can also look at catalogues from schools that list all the degrees> of their faculty. Of course, that is often somewhat dated, but its> at least published information so I dont need to be reticent about> names.> UMass/Amhersts math department includes one Nathaniel Whitaker, who> is BA, Hampton Institute, 1974; MS, Cincinatti, 1981; PhD, California,> 1987. I assume that California means UC Berkeley.> I looked through the list of current grad students at Cornell. I> found one Liang Chen, who has a BS from Peking University and a MS> from the University of Wisconsin at Madison, and is now at Cornell.And Peking University is mediocre?? Not to mention, Wisconsin iscomparable to Cornell, so it doesnt really prove anything. Cornell ismore selective, but reputation-wise its very similar.> And Jose Trujillo Ferreras, who has a Licenciado from the Universidad> Autonoma de Madrid, and an MA from Duke and is now at Cornell.Sigh...as someone else has mentioned, do you regard any place fromoutside the U.S. as mediocre? > Jennifer Fawcett is BA from Rice, MA from UC Davis, and now at> Cornell. Rice is a pretty good place for an undergraduate math degree,especially if youre planning to specialize in low-dimensionaltopology. Getting a recommendation from Hempel is a good thing; andshe did in fact do that.As for Jennifer (nickname - Sunny), she is not a good example for thepoint you are making because she transferred over with Thurston when hemoved from Davis. Also, let me add that Sunny was good enough to getinto Berkeley when she applied to grad schools. So this is really anot very good example, is it?> Lee Gibson, BS from the University of Kentucky, MS from the> University of Louisville, now at Cornell. Farkhod Eshmatov, BS from> Tashkent State University, MA from SUNY Binghamton, now at Cornell. > Thats six, in about ten minutes of web looking.> I think Ive spent enough time on this also. > And Jose Trujillo Ferreras, who has a Licenciado from the Universidad> Autonoma de Madrid, and an MA from Duke and is now at Cornell.> Sigh...as someone else has mentioned, do you regard any place from> outside the U.S. as mediocre? Not at all. I am simply giving people who earned an intermediatemasters from a third institution.Thomas > And Jose Trujillo Ferreras, who has a Licenciado from the Universidad> Autonoma de Madrid, and an MA from Duke and is now at Cornell.> Sigh...as someone else has mentioned, do you regard any place from> outside the U.S. as mediocre? > Not at all. I am simply giving people who earned an intermediate> masters from a third institution.> ThomasWhy? David Ullrich speci?ally said he didnt know any example ofpeople getting a degree from a *mediocre* undergrad, then an M.S. at abetter school, and then a Ph.D. at a *top* school. He then mentionedyou had not given any examples of such. To which you responded bylisting examples, one of which is quoted above.If you are indeed simply giving examples of those who earned anintermediate masters from a third institution, thats irrelevant. > Why? David Ullrich speci?ally said he didnt know any example of> people getting a degree from a *mediocre* undergrad, then an M.S. at a> better school, and then a Ph.D. at a *top* school. He then mentioned> you had not given any examples of such. To which you responded by> listing examples, one of which is quoted above.What I *said*, originally, was that for someone who went to anothing-special school, it was not crazy to get a good masters if youcant get into topnotch PhD programs. I made a fair prima facie case for why this is so, including examplesfrom other ?lds. I was asked do you know anyone who did that andI said yes (more than one) at MIT. I certainly dont claim I have given conclusive examples. On theother hand, people claiming the contrary have given no examples of anykind, nor have they given any reasons to the contrary.At some point, you folks need to provide *some* kind of reason beyondyour common agreement.Thomas > Why? David Ullrich speci?ally said he didnt know any example of> people getting a degree from a *mediocre* undergrad, then an M.S. at a> better school, and then a Ph.D. at a *top* school. He then mentioned> you had not given any examples of such. To which you responded by> listing examples, one of which is quoted above.> What I *said*, originally, was that for someone who went to a> nothing-special school, it was not crazy to get a good masters if you> cant get into topnotch PhD programs. > I made a fair prima facie case for why this is so, including examples> from other ?lds. I was asked do you know anyone who did that and> I said yes (more than one) at MIT. > I certainly dont claim I have given conclusive examples. On the> other hand, people claiming the contrary have given no examples of any> kind, nor have they given any reasons to the contrary.> At some point, you folks need to provide *some* kind of reason beyond> your common agreement.Well, as someone who stepped into this thread rather late in the game,I know my impressions of what is going on may be very different frompeople actively engaged in the thread; however, it appears to me thereare several related, but different, discussions going on. There isone, started by Lee Rudolph, in which the topic of ?bootstrappingoneself up the prestige ladder, through a masters, is raised. Yourresponse, with examples (*not* the one about MIT), was issued directlyto David Ullrichs response in this discussion. Thats why I, and Ithink several others, interpreted your issuing of examples as beingrelated to this idea of ?bootstrapping.So my comment above was in that context. i believe what said Lee off in the ?st place was your comment that:Then with a respected masters under your belt, you are an excellentcompetitor with the people who are coming straight out of the bestundergrad programs.As Ive explained in another post (regarding genius), this doesntappear to be so. But your point is taken, obviously, one has to dowhat one can to improve ones chances of getting into a better Ph.D.program than one would initially, in light of a mediocre (or worse)undergrad.In any case, I think this subthread is dying out, since its ratherclear now that nobody is really arguing about anything. Ill post aresponse to your response to my genius post, since I think that stillhas some life in it. > Hard to say. I dont know of any examples (in math) of someone with> a BS from a mediocre place who got a masters from some place> better and then a PhD from a top school. The fact that I dont> know of any examples doesnt prove there are none - Bushnell> has stated that he knows of plenty of such examples (otoh hes> failed to name any, after being asked twice...) We can also look at catalogues from schools that list all the degrees> of their faculty. Of course, that is often somewhat dated, but its> at least published information so I dont need to be reticent about> names. UMass/Amhersts math department includes one Nathaniel Whitaker, who> is BA, Hampton Institute, 1974; MS, Cincinatti, 1981; PhD, California,> 1987. I assume that California means UC Berkeley. I looked through the list of current grad students at Cornell. I> found one Liang Chen, who has a BS from Peking University and a MS> from the University of Wisconsin at Madison, and is now at Cornell.> And Jose Trujillo Ferreras, who has a Licenciado from the Universidad> Autonoma de Madrid, and an MA from Duke and is now at Cornell.> Jennifer Fawcett is BA from Rice, MA from UC Davis, and now at> Cornell. Lee Gibson, BS from the University of Kentucky, MS from the> University of Louisville, now at Cornell. Farkhod Eshmatov, BS from> Tashkent State University, MA from SUNY Binghamton, now at Cornell. Thats six, in about ten minutes of web looking.>Do you want tp say that any university outside US (Madrid, Beijing in yourexamples) are mediocre places?> Thomas > I realized that I had no shot at any top program about a year ago>> when I looked at the course offerings at the Ivy League schools and>> MIT. This is my senior year so its too late to go to a stronger>> program. I know that my department is bad but now its just could>> have and should have. How realistic is it to get a masters>> degree and transfer to a better school? Are you just screwed if you>> did not go to the right school and take the right courses with the>> right professors?No. The typical advice in your place is to apply to a good masters>program. This generally means a school that offers only the masters>and not the doctorate in your ?ld. Find the best ones, and if you>did well as an undergrad and have decent GREs, you should be able to>get in without a problem. Then with a respected masters under your>belt, you are an excellent competitor with the people who are coming>straight out of the best undergrad programs.Hey, just call me a starry-eyed old cynic, but I ?d it really,*really* hard to believe that from the point of view of theIvy League schools and MIT, or any top program, there even*exist* any respected masters degrees. Do you know of a singleexample of someone who got a (respected or otherwise) mastersdegree in mathematics at a school that offers only the mastersand not the doctorate in mathematics, and was then acceptedto any top program, speci?ally, one of the Ivy Leagueschools and MIT? Lee Rudolph I asked tb+usenet@becket.net (Thomas Bushnell, BSG) >Do you know of a single>example of someone who got a (respected or otherwise) masters>degree in mathematics at a school that offers only the masters>and not the doctorate in mathematics, and was then accepted>to any top program, speci?ally, one of the Ivy League>schools and MIT? He produced (not in direct response to that question) thefollowing. (1) A faculty member at UMass--Amherst with an MS from Cincinatti(1981) and a Ph. D. from Berkeley (1987). Since Cincinatti is nota school that offers only the masters and not the doctorate inmathematics, this is not an example.(2) A grad student at Cornell with an MS from the University ofWisconsin at Madison. Since UWM is not a school that offersonly the masters and not the doctorate, this is not an example.(3) A grad student at Cornell with an MA from Duke. Since Dukeis not a school that offers only the masters and not the doctoratein mathematics, this is not an example.(4) A grad student at Cornell with an MA from UC Davis. Since UC Davis is not a school that offers only the masters and not the doctorate in mathematics, this is not an example.(5) A grad student at Cornell with a masters from the University of Louisville. Finally, an example! for, indeed, the University ofLouisville does not offer a doctorate in mathematics. (However,his BA was from the University of Kentucky, which *does*.) (6) A grad student at Cornell with a masters from SUNY Binghampton.Since SUNY Binghampton is not a school that offers only the masters and not the doctorate in mathematics, this is not an example.Well, I only *asked* for a single example, so I cant sayI didnt get what I asked for. The tare/wheat ratio was a bithigh, though.>Thats six, in about ten minutes of web looking.Only for very small values of six.Lee Rudolph > Well, I only *asked* for a single example, so I cant say> I didnt get what I asked for. The tare/wheat ratio was a bit> high, though.I gave examples of people with intermediate masters from thirdinstitutions, which is what I thought you said you wanted.Still, as I said, I have made a prima facie case, and so far, youhavent given *any* reasons to think Im wrong. I really aminterested, but just blank assertion isnt worth much, is it?*Some* kind of explanation would be appropriate, dont you think?rightly or wrongly, is expected by admissions committees in math--andnot so much in other subjects. This is an excellent point, but thesame correspondent mixed up people with mediocre records and peoplewith excellent records from second-class schools. The latter do notnecessarily look like non-hotshots who are making up for theirearlier failures.Thomas >Message-id: > I realized that I had no shot at any top program about a year ago> when I looked at the course offerings at the Ivy League schools and> MIT. This is my senior year so its too late to go to a stronger> program. I know that my department is bad but now its just could> have and should have. How realistic is it to get a masters> degree and transfer to a better school? Are you just screwed if you> did not go to the right school and take the right courses with the> right professors?>>No. The typical advice in your place is to apply to a good masters>>program. This generally means a school that offers only the masters>>and not the doctorate in your ?ld. Find the best ones, and if you>>did well as an undergrad and have decent GREs, you should be able to>>get in without a problem. Then with a respected masters under your>>belt, you are an excellent competitor with the people who are coming>>straight out of the best undergrad programs.Hey, just call me a starry-eyed old cynic, but I ?d it really,>*really* hard to believe that from the point of view of the>Ivy League schools and MIT, or any top program, there even>*exist* any respected masters degrees. Do you know of a single>example of someone who got a (respected or otherwise) masters>degree in mathematics at a school that offers only the masters>and not the doctorate in mathematics, and was then accepted>to any top program, speci?ally, one of the Ivy League>schools and MIT? Lee RudolphJust to clear this up, I meant that I knew that I had no shot at any topprogram without going to one of the best schools. It seems like my programwould roughly put me around the junior level at one of the best schools when Igraduate. Furthermore, Im sure there are more math majors at the very best schools thanthere are spots in PhD programs at those schools, so I assumed that they couldeven ?ter down to some of the ?great schools that arent quite the best,making it even harder to get into those.Basically, I want to be able to get into a very good state school. > Hey, just call me a starry-eyed old cynic, but I ?d it really,> *really* hard to believe that from the point of view of the> Ivy League schools and MIT, or any top program, there even> *exist* any respected masters degrees. Do you know of a single> example of someone who got a (respected or otherwise) masters> degree in mathematics at a school that offers only the masters> and not the doctorate in mathematics, and was then accepted> to any top program, speci?ally, one of the Ivy League> schools and MIT? Yes, in math, physics, and in philosophy.A masters degree from a doctoral program generally means we let himgo because he couldnt hack it. But a good masters degree (say inphilosophy from Tufts) means a lot. It means this person has donewell in an advanced program, carries no implied failure, andindicates to most people reviewing applications that they can dograduate work well.This is exactly what is not clear when an applicant comes from asecond-rate undergrad school.All your annoying scare quotes serve only to obscure the point:There are three different kinds of masters degrees out there instrictly academic subjects (subjects like math, physics, orphilosophy):* There are the ones which are kind exit for someone washing out of a doctoral program;* There are the ones that smaller schools can offer to try and boost their pro?e;* There are ones that are taught by top-notch faculty, well respected in their ?ld, and which carry weight.The latter two generally exist only in departments that do not offer adoctorate. Both the latter two have very similar promotionalmaterials, and its important to ?ure out the difference.Those who receive the last sort are generally better off in theirapplication than if they had not gone, most especially when theirundergraduate degree is from a less stellar school.I quote, for example, from the Philosophical Gourmet Report: Who should consider an M.A. program in philosophy? Three categories of students who ultimately want to get a Ph.D. and pursue an academic career might bene? from such programs: (i) students whose undergraduate major was not philosophy; (ii) students who majored in philosophy at universities with philosophy departments outside the mainstream of the profession; and (iii) students who majored in philosophy, have a solid grounding in the various areas of philosophy, but who studied philosophy at smaller colleges and universities, or at institutions with weak academic reputations....Students in each category may be both quali?d and able to get into the Ph.D. programs of their choice; but students who ? into one of these categories may be more likely to have trouble getting into Ph.D. programs and may be good candidates to bene? from M.A. programs. A good M.A. program will provide many bene?s: it will allow a student to get a basic grounding in philosophy or expand the breadth of her existing knowledge; to develop increased familiarity with current debates in philosophy; to prepare and polish written work in philosophy that will be useful in the applications process for Ph.D. programs; and to get to know some established philosophers who can then provide meaningful letters of recommendation for Ph.D. programs.This advice applies pretty much to any strictly academic subject, forwhich there isnt an industry demand for masters degrees. Incomputer science, for example, a masters degree is a real job boostall by itself, and the schools have adjusted to suit, and so theadvice doesnt carry over so easily.But for a strictly academic subject, where the job quali?ation isreally a doctorate, this is what a terminal masters program is goodfor.And to repeat, yes, I know people in a variety of ?lds who wereadmitted to top-notch graduate programs upon receiving a masters atsuch a school.Thomas > Hey, just call me a starry-eyed old cynic, but I ?d it really,>> *really* hard to believe that from the point of view of the>> Ivy League schools and MIT, or any top program, there even>> *exist* any respected masters degrees. Do you know of a single>> example of someone who got a (respected or otherwise) masters>> degree in mathematics at a school that offers only the masters>> and not the doctorate in mathematics, and was then accepted>> to any top program, speci?ally, one of the Ivy League>> schools and MIT? Yes, in math, physics, and in philosophy.A masters degree from a doctoral program generally means we let him>go because he couldnt hack it. But a good masters degree (say in>philosophy from Tufts) means a lot. It means this person has done>well in an advanced program, carries no implied failure, and>indicates to most people reviewing applications that they can do>graduate work well.Well, Ill have to say Im amazed to hear about the math example. But I believe you. (Would it be within the limits of your discretionto say which doctoral program *in math*, in particular, took thisperson? Was it one of the Ivy League schools and MIT?)What, by the way, is the nature of the evidence on which you would base a statement (which you didnt make, explicitly)that a masters degree *in mathematics* indicates to mostpeople reviewing applications that the person with the degreecan do graduate work *towards a doctorate in mathematics* well?I freely admit that I have never reviewed applications for a graduateprogram in mathematics. Have you? I know a lot of people who have,and have sometimes talked to them about the process. Have you?>This is exactly what is not clear when an applicant comes from a>second-rate undergrad school.All your annoying scare quotes serve only to obscure the point:They arent scare quotes, they are quotation marks that markdirect quotations. I regret that you ?d them annoying (but Im not sorry I put them in; quite the contrary, Im glad I put them in, and I hope you will learn to ?d them, not annoying, but a positive joy, once you have perceived theirfunction and appreciated that it is very useful).>There are three different kinds of masters degrees out there in>strictly academic subjects (subjects like math, physics, or>philosophy):* There are the ones which are kind exit for someone washing out of a> doctoral program;Right.>* There are the ones that smaller schools can offer to try and boost> their pro?e;* There are ones that are taught by top-notch faculty, well respected> in their ?ld, and which carry weight.The latter two generally exist only in departments that do not offer a>doctorate. Both the latter two have very similar promotional>materials, and its important to ?ure out the difference.So that I can compare my ideas of quality with yours, could yougive examples--not in physics or philsophy, but in math--of afew masters programs of the latter two types (in departmentsthat do not offer a doctorate)? Would, for example, BostonColleges masters program in mathematics count (in the second of the latter two types)? They certainly have some top-notch faculty, well-respected in their ?ld teaching masters students,but I have not heard that the graduates of their masters program are getting in to top schools (because, indeed, I have not heard that they have any ambitions beyond the masters degree, with its concomitant payoff if youre a school teacher in Massachusetts)--I dont hear everything, naturally. If not BC, perhaps some other school in the Boston area? >Those who receive the last sort are generally better off in their>application than if they had not gone, most especially when their>undergraduate degree is from a less stellar school.I quote, for example, from the Philosophical Gourmet Report:[deleted]Philosophy is a different kettle of ?h entirely from mathematics,and the material I deleted seems to me quite irrelevant to adiscussion of masters degrees in mathematics.>This advice applies pretty much to any strictly academic subject, So you assert. I have my doubts. You havent yet given memuch reason (by my standards) to lose my doubts.>for>which there isnt an industry demand for masters degrees. In>computer science, for example, a masters degree is a real job boost>all by itself, and the schools have adjusted to suit, and so the>advice doesnt carry over so easily.But for a strictly academic subject, where the job quali?ation is>really a doctorate, this is what a terminal masters program is good>for.And to repeat, yes, I know people in a variety of ?lds Including, you say, mathematics--the only one Im interested intalking about. Lets stick to that one in the sequel, if youdont mind. >who were>admitted to top-notch graduate programs upon receiving a masters at>such a school.Howd they do?Lee Rudolph > Well, Ill have to say Im amazed to hear about the math example. > But I believe you. (Would it be within the limits of your discretion> to say which doctoral program *in math*, in particular, took this> person? Was it one of the Ivy League schools and MIT?)MIT. > What, by the way, is the nature of the evidence on which you > would base a statement (which you didnt make, explicitly)> that a masters degree *in mathematics* indicates to most> people reviewing applications that the person with the degree> can do graduate work *towards a doctorate in mathematics* well?Can you explain why you think that mathematics should be differentthan other disciplines? Your continual protestations that you think it amazing and unheard ofsuggests to me simply that you cant think of anything you could sayother than your open mouthed amazement. So far, all you can say is I cant believe it! In response towhich, unless you can say why, is simply repeat what I have said. Or,if you have a criticism of what Ive said, then to make it, ratherthan allude vaguely to it.> Philosophy is a different kettle of ?h entirely from mathematics,> and the material I deleted seems to me quite irrelevant to a> discussion of masters degrees in mathematics.Can you say what the differences are? >This advice applies pretty much to any strictly academic subject, > So you assert. I have my doubts. You havent yet given me> much reason (by my standards) to lose my doubts.Well, so far you havent even explained the doubt, other than saidits there. Im afraid I dont give much credence to doubts of thatdegree. In other words, if you want the conversation to continue, you gotta domore than just say you still havent proven it to me. Ive made afair prima facie case, and if you have an objection to register to it,do so.Perhaps you have misunderstood what Im saying.Im saying that a bachelors from Podunk U, plus a masters from Really-Cool-U,is worth as much as a bachelors from Really-Cool-U.Thomas > Well, Ill have to say Im amazed to hear about the math example. >> But I believe you. (Would it be within the limits of your discretion>> to say which doctoral program *in math*, in particular, took this>> person? Was it one of the Ivy League schools and MIT?)MIT. > What, by the way, is the nature of the evidence on which you >> would base a statement (which you didnt make, explicitly)>> that a masters degree *in mathematics* indicates to most>> people reviewing applications that the person with the degree>> can do graduate work *towards a doctorate in mathematics* well?Can you explain why you think that mathematics should be different>than other disciplines? Your continual protestations that you think it amazing and unheard of>suggests to me simply that you cant think of anything you could say>other than your open mouthed amazement. So far, all you can say is I cant believe it! In response to>which, unless you can say why, is simply repeat what I have said. Or,>if you have a criticism of what Ive said, then to make it, rather>than allude vaguely to it.> Philosophy is a different kettle of ?h entirely from mathematics,>> and the material I deleted seems to me quite irrelevant to a>> discussion of masters degrees in mathematics.Can you say what the differences are? >This advice applies pretty much to any strictly academic subject, >>> So you assert. I have my doubts. You havent yet given me>> much reason (by my standards) to lose my doubts.Well, so far you havent even explained the doubt, other than said>its there. Im afraid I dont give much credence to doubts of that>degree. In other words, if you want the conversation to continue, you gotta do>more than just say you still havent proven it to me. Ive made a>fair prima facie case, and if you have an objection to register to it,>do so.Perhaps you have misunderstood what Im saying.Im saying that a bachelors from Podunk U, plus a masters from Really-Cool-U,>is worth as much as a bachelors from Really-Cool-U.It doesnt look to you like hes misunderstood your claim, it lookslike he simply doesnt believe its so. Neither do I.Youve _stated_ that you know of plenty of examples _in math_.Hes asked you to _give_ such examples. Hes asked this_twice_ by my count. So far you havent given any examples.(Speaking of if you want the conversation to continue...you dont give much credence to his doubts? He hasnteven asserted hes _right_, hes just expressed _doubts_about what youre asserting. Youre the one whosmaking actual assertions and then refusing to backthem up with examples that you say you know of. Me,I dont give much credence to people who say theyhave examples of something but fail to produce themwhen asked.)>Thomas>************************David C. Ullrich > Youve _stated_ that you know of plenty of examples _in math_.> Hes asked you to _give_ such examples. Hes asked this> _twice_ by my count. So far you havent given any examples.Huh? No, I did mention I knew ?st hand examples at MIT.You are free to doubt, the original poster asked am I screwed becauseI didnt go to a ?st rate school.Your doubts are nothing but doubts if you have nothing to do but sayI doubt it. I *am* interested in *why* you doubt it, something neither of you havedeigned to say.Thomas > Youve _stated_ that you know of plenty of examples _in math_.> Hes asked you to _give_ such examples. Hes asked this> _twice_ by my count. So far you havent given any examples.> Huh? No, I did mention I knew ?st hand examples at MIT.> You are free to doubt, the original poster asked am I screwed because> I didnt go to a ?st rate school.> Your doubts are nothing but doubts if you have nothing to do but say> I doubt it. > > I *am* interested in *why* you doubt it, something neither of you have> deigned to say.> Thomas> Can you explain why you think that mathematics should be differentthan other disciplines? Your continual protestations that you think it amazing and unheard ofsuggests to me simply that you cant think of anything you could sayother than your open mouthed amazement. So far, all you can say is I cant believe it! In response towhich, unless you can say why, is simply repeat what I have said. Or,if you have a criticism of what Ive said, then to make it, ratherthan allude vaguely to it.--------------Well, I really didnt think I was going to entangle myself in thisthread, but Ive already put a foot in (my other post), and then I gotsucked into reading the whole thread.However, I think I can offer some words of explanation of why I thinkLee and David both seem reluctant to accept your conclusions. This isonly my own idea of what I think they are thinking/feeling, and isbased on my much more limited experience. Clearly, Lee and David havemuch more experience in these matters and have interacted signi?antlymore with the people in charge of making these kinds of admissionsdecisions. Yet I think the fact that in my handful of years in themathematical community Ive picked up on the kinds of things (that Ibelieve) are in?ng Lee and David, show how pervasive theseelements can be. Basically, in the mathematics world, there is a culture of geniusthat is not in the subjects youve mentioned, like philosophy. Now, Ineed to explain what I mean by genius, because after all, we dontnormally regard geniuses as being limited to mathematics.In mathematics, it is clear what genius is and who has it. Ifsomeone is a genius, there is no doubt. This is different fromphilosophy, where you might say, I think hes got some good ideas, butI disagree... In mathematics, you cant solve some problem, andsomeone else can. And if he was the only one who could, and could doit near instantaneously, there is no more arguing or discussion if thisperson has genius. This unambiguity (or near-unambiguity) of the quality of geniuspervades the whole institution of mathematics. Especially when itcomes to recommendation letters. Even if two people had a similarperformance (in terms of being able to do the work, etc.) in a class,one may, in the professors eyes, have exhibited a genius-likequality in his/her performance. Consequently, this person will get asigni?antly better recommendation. The other person may be seen as agood worker, but obviously not a genius. Even if they could solvethe same problems, etc., the prof might think one was just bettersomehow. More of a genius.What does this have to do with grad school admissions? Well, thinkabout it: if youre a mathematician, who are you going to admit? Applicant A who has done similar work (but at a much slower rate, a bigindication of non-genius ability), as applicant B, who graduatedcollege at age 16? I dont think Im wrong as saying that even gettinga masters (in the U.S.) is seen as a sign of weakness. At the least,it shows you didnt feel ready to plunge into a Ph.D. programstraightaway or you werent strong enough. Either identi?s you as anon-genius.A note about the masters: I know at least one top ten school (in theU.S.) that offers a masters that will *never*, as of?ial policy,admit someone who graduates from their own masters program into thePh.D. program. The masters students there are also treated much worsethan the doctoral students in some very obvious ways. I believe thisis re?e of the disdain many top graduate programs have toward themasters. A masters from some other country, I think, is given morerespect than one from the U.S.The point you are missing is that admissions committees are NOT lookingat an applicants record to see if he/she has done well. Rather theyare looking for indications of genius. A transcript, etc. can help,but if they have one recommendation that is from a highly eminentmathematician saying, this person is a genius, thats *all* theyneed. I think you are operating under the assumption that the committees arelooking at prior performance as an indicator of future performance. Thats not really so. They want to see if the applicant has any geniusor near-genius qualities. Now of course, there arent that many genius-like applicants. So thebest schools will follow the above pattern of behavior closest. Lesserschools will be more willing to compromise and select people, partlybased on what they believe future performance will be. Will they beable to graduate with a decent thesis? Will they do well enough tore?ack favorably on the school? And so on. But even theseschools (especially the schools that are top 25 -- whatever thatmeans) will be in?d by the cult, er I mean culture, of genius. This is why you are facing such amazement from Lee and David. They aremore than familiar with the culture of genius. And they know thatthe very best schools, which include MIT and some of the Ivy Leagues,want geniuses more than anything else. They prefer them to thehard-workers. Because the latter are unlikely to be FieldsMedalists, Wolf Prize winners, etc. > This is why you are facing such amazement from Lee and David. They are> more than familiar with the culture of genius. And they know that> the very best schools, which include MIT and some of the Ivy Leagues,> want geniuses more than anything else. They prefer them to the> hard-workers. Because the latter are unlikely to be Fields> Medalists, Wolf Prize winners, etc.I am inclined to agree Chan-ho, but check this out: It is important to keep in mind that no technique has been or ever will bediscovered for teaching students to have ideas. All that the faculty can dois to provide an ambience in which ones nascent abilities and insights canblossom. Moreover, Ph.D. theses vary enormously in quality, from hardexercises to highly original advances. Finally, many very good researchmathematicians begin very slowly, and their theses and ?st few paperscould be of minor interest. On the whole, we feel that the ideal attitudeis: (1) a love of the subject for its own sake, accompanied byinquisitiveness about things which arent known; and (2) a somewhatfatalistic attitude concerning creative ability, and recognition that hardwork is, in the end, much more important. Taken directly fromhttp://www.math.harvard.edu/graduate/index.html# admissionSo, it may also be that math people from Podunk U are looking to ride thecoat-tails of Geniuses. What ever happened to studying math for mathssake? I say if someone is willing to go into debt for the majority of theiradult life, devote their life to the study and progress of a subject, thenlet them do it. This university b.s. is so ridiculous!Lurch Basically, in the mathematics world, there is a culture of genius that is not in the subjects youve mentioned, like philosophy. Maybe, maybe not... > Youve _stated_ that you know of plenty of examples _in math_.> Hes asked you to _give_ such examples. Hes asked this> _twice_ by my count. So far you havent given any examples.> Huh? No, I did mention I knew ?st hand examples at MIT.> You are free to doubt, the original poster asked am I screwed because> I didnt go to a ?st rate school.> Your doubts are nothing but doubts if you have nothing to do but say> I doubt it.> I *am* interested in *why* you doubt it, something neither of you have> deigned to say.> Thomas> Can you explain why you think that mathematics should be different> than other disciplines? Your continual protestations that you think it amazing and unheard of> suggests to me simply that you cant think of anything you could say> other than your open mouthed amazement. So far, all you can say is I cant believe it! In response to> which, unless you can say why, is simply repeat what I have said. Or,> if you have a criticism of what Ive said, then to make it, rather> than allude vaguely to it. -------------- Well, I really didnt think I was going to entangle myself in this> thread, but Ive already put a foot in (my other post), and then I got> sucked into reading the whole thread. However, I think I can offer some words of explanation of why I think> Lee and David both seem reluctant to accept your conclusions. This is> only my own idea of what I think they are thinking/feeling, and is> based on my much more limited experience. Clearly, Lee and David have> much more experience in these matters and have interacted signi?antly> more with the people in charge of making these kinds of admissions> decisions. Yet I think the fact that in my handful of years in the> mathematical community Ive picked up on the kinds of things (that I> believe) are in?ng Lee and David, show how pervasive these> elements can be. Basically, in the mathematics world, there is a culture of genius> that is not in the subjects youve mentioned, like philosophy. Now, I> need to explain what I mean by genius, because after all, we dont> normally regard geniuses as being limited to mathematics. In mathematics, it is clear what genius is and who has it. If> someone is a genius, there is no doubt. This is different from> philosophy, where you might say, I think hes got some good ideas, but> I disagree... In mathematics, you cant solve some problem, and> someone else can. And if he was the only one who could, and could do> it near instantaneously, there is no more arguing or discussion if this> person has genius. This unambiguity (or near-unambiguity) of the quality of genius> pervades the whole institution of mathematics. Especially when it> comes to recommendation letters. Even if two people had a similar> performance (in terms of being able to do the work, etc.) in a class,> one may, in the professors eyes, have exhibited a genius-like> quality in his/her performance. Consequently, this person will get a> signi?antly better recommendation. The other person may be seen as a> good worker, but obviously not a genius. Even if they could solve> the same problems, etc., the prof might think one was just better> somehow. More of a genius. What does this have to do with grad school admissions? Well, think> about it: if youre a mathematician, who are you going to admit?> Applicant A who has done similar work (but at a much slower rate, a big> indication of non-genius ability), as applicant B, who graduated> college at age 16? I dont think Im wrong as saying that even getting> a masters (in the U.S.) is seen as a sign of weakness. At the least,> it shows you didnt feel ready to plunge into a Ph.D. program> straightaway or you werent strong enough. Either identi?s you as a> non-genius. A note about the masters: I know at least one top ten school (in the> U.S.) that offers a masters that will *never*, as of?ial policy,> admit someone who graduates from their own masters program into the> Ph.D. program. The masters students there are also treated much worse> than the doctoral students in some very obvious ways. I believe this> is re?e of the disdain many top graduate programs have toward the> masters. A masters from some other country, I think, is given more> respect than one from the U.S. The point you are missing is that admissions committees are NOT looking> at an applicants record to see if he/she has done well. Rather they> are looking for indications of genius. A transcript, etc. can help,> but if they have one recommendation that is from a highly eminent> mathematician saying, this person is a genius, thats *all* they> need. I think you are operating under the assumption that the committees are> looking at prior performance as an indicator of future performance.> Thats not really so. They want to see if the applicant has any genius> or near-genius qualities. Now of course, there arent that many genius-like applicants. So the> best schools will follow the above pattern of behavior closest. Lesser> schools will be more willing to compromise and select people, partly> based on what they believe future performance will be. Will they be> able to graduate with a decent thesis? Will they do well enough to> re?ack favorably on the school? And so on. But even these> schools (especially the schools that are top 25 -- whatever that> means) will be in?d by the cult, er I mean culture, of genius.> This is why you are facing such amazement from Lee and David. They are> more than familiar with the culture of genius. And they know that> the very best schools, which include MIT and some of the Ivy Leagues,> want geniuses more than anything else. They prefer them to the> hard-workers. Because the latter are unlikely to be Fields> Medalists, Wolf Prize winners, etc. > Basically, in the mathematics world, there is a culture of genius> that is not in the subjects youve mentioned, like philosophy. Now, I> need to explain what I mean by genius, because after all, we dont> normally regard geniuses as being limited to mathematics.I think I understand clearly what you mean here, and its is nearly agood answer. The question is: what about the genius who goes to the fair-to-middlinundergrad school? Does the culture recognize that such people reallyexist?Someone who does a mediocre job and then gets a stunning masters willnot trigger the genius reaction, and I agree completely that thestunning masters has not helped at all.So if you are faced with a student who says Im not that hot, but ifI go get a masters, will I get a leg up? the answer is probably no.And this is a difference between math and many other ?lds, preciselybecause of the genious factor.But if you are faced with a student who *is* that hot, but is going toa fair-to-middlin undergrad school, my claim is that *they* cancertainly bene? by going to a good masters program. For example, atthat good masters program, for the ?st time, they have the chance toget a genius recommendation from a recognized name in the ?ld.> I think you are operating under the assumption that the committees are> looking at prior performance as an indicator of future performance.> Thats not really so. They want to see if the applicant has any genius> or near-genius qualities.I think this as a very important point, and I dont disagree. Its abig difference between the math culture and many other ?lds. (Idont mean to imply that the math culture is wrong; I assume that itworks ?e for math.)My point is that there is a set of people who *do* have genius ornear-genius qualities, who are at less-regarded undergrad schools, andthat there are people who know this.Thomas > The question is: what about the genius who goes to the fair-to-middlin> undergrad school? Does the culture recognize that such people really> exist?When I was applying to grad school around 30 years ago the answer wasde?itely yes; Id bet it hasnt changed. My undergrad degree isfrom a land-grant university far better known for football than foracademics, with a math department that sent certainly less thana half-dozen graduates on to grad school in an average year (and grantedabout the same number of Ph.D.s) -- but I made As in the introductorygraduate courses in algebra, analysis, and (point-set) topology, had recommendations from the people who taught them, and got a decent thoughnot stellar result on the Putnam exam one year. I got offers fromtwo top-25 schools but dropped out for a couple of years ... andsubsequently went to a different top-25 school. > Basically, in the mathematics world, there is a culture of genius> that is not in the subjects youve mentioned, like philosophy. Now, I> need to explain what I mean by genius, because after all, we dont> normally regard geniuses as being limited to mathematics.> I think I understand clearly what you mean here, and its is nearly a> good answer. > The question is: what about the genius who goes to the fair-to-middlin> undergrad school? Does the culture recognize that such people really> exist?> In my experience, yes. I know of such people and know some personally. Im pretty con?ent in saying every mathematician knows of at leastone such case. The caveat is that these people are recognized to exist because theyare so damn brilliant. Its hard to hide that kind of brilliance. Soto give advice based on the fact that there are such people is rathermisleading and useless. The people to whom such advice applies dontneed it!I suppose if one goes to an incredibly bad undergrad, then even if oneis a genius, the profs recs wont be given much weight, if they arenot held in any esteem by the letter readers. But I would say thereare enough independent channels, like the Putnam, or other contests, orthe possibility of publishing in undergrad journals, or collaboratingwith some mathematician who will be held in some esteem, that it seemsunlikely a genius-type will slip through the cracks. Of course, thereare very capable people who will not appear to be geniuses ornear-geniuses, and I think its fair to say going to a bad undergrad isa big handicap.> Someone who does a mediocre job and then gets a stunning masters will> not trigger the genius reaction, and I agree completely that the> stunning masters has not helped at all.> So if you are faced with a student who says Im not that hot, but if> I go get a masters, will I get a leg up? the answer is probably no.> And this is a difference between math and many other ?lds, precisely> because of the genious factor.> I think this is the point that others are trying to make.> But if you are faced with a student who *is* that hot, but is going to> a fair-to-middlin undergrad school, my claim is that *they* can> certainly bene? by going to a good masters program. For example, at> that good masters program, for the ?st time, they have the chance to> get a genius recommendation from a recognized name in the ?ld.> Well, the thing is that even a fair, middle-level undergrad school willoften have some very good mathematicians. Especially state schools. Just because the undergrad education sucks, doesnt mean the departmentas a whole does! The whole trickle-down effect caused by there not being enough slotsfor very good mathematicians means that if youre a genius, someonewill recognize you as one, and that someone or someone else that s/heknows will have a good reputation. I fear your point, while correct, is more academic than practical. Ifthere is a very brilliant, genius-like, student that somehow gothoodwinked into going to a mediocre undergrad, and somehow s/he is notrecognized as such, even through all the independent channels Imentioned above, then sure, go to a respectable state school (orwherever they will have some well-known mathematicians) and make yourgenius known. In fact, if the student is *that* good, after just onesemester, s/he should be able to transfer to some ?e academicinstitution. But I think in practice, this is a rare situation, and in terms ofgiving advice, etc., one cant expect this to be the case.> I think you are operating under the assumption that the committees are> looking at prior performance as an indicator of future performance.> Thats not really so. They want to see if the applicant has any genius> or near-genius qualities.> I think this as a very important point, and I dont disagree. Its a> big difference between the math culture and many other ?lds. (I> dont mean to imply that the math culture is wrong; I assume that it> works ?e for math.)> I assume so too. I have doubts occasionally, but thats for anotherthread, I guess ;-)> My point is that there is a set of people who *do* have genius or> near-genius qualities, who are at less-regarded undergrad schools, and> that there are people who know this.> > Youve _stated_ that you know of plenty of examples _in math_.>> Hes asked you to _give_ such examples. Hes asked this>> _twice_ by my count. So far you havent given any examples.Huh? No, I did mention I knew ?st hand examples at MIT.I guess you did, sorry.>You are free to doubt, the original poster asked am I screwed because>I didnt go to a ?st rate school.Your doubts are nothing but doubts if you have nothing to do but say>I doubt it. I *am* interested in *why* you doubt it, something neither of you have>deigned to say.The reason I doubt hes going to get into a ?st-rate doctoral program was not speci?ally because of where he did hisundergraduate work, it was because of what he said aboutwhat courses hed taken and not taken.>Thomas>************************David C. UllrichX-Cise: tanbanso@iinet.net.auX-CompuServe-Customer: YesX-Coriate: admin@interspeed.co.nzX-Ecrate: tanandtanlawyers.comX-Pose: george_cox@btinternet.comX-Punge: Micro$oft porker899@aol.com (Porker899) said:>I checked out a book called All the Mathematics You Missed [But Need>to Know for Graduate School] from the library and was surprised by>its contents. The book is divided into 16 sections that I am>supposed to know before I get into graduate school. This is my>last year and I can check off very little.Check the catalogs of the speci? schools thqt you want to apply to.That sort of general checklist is at best a guide.>3. Differentiating Vector Valued FunctionsThere wasnt a course called something like Advanced Calculus?>4. Point Set Topolgy - No (not offered here)>6. Differential Forms and Stokes Theorem - No (nothing like that>here)Ouch!>8. Geometry - No (only course offered is one for future high school>teachers and was advised not to take it)The advice was sound. The lack of a real Geometry course wasunfortunate.>11. Algebra - YesI hope that you mean Abstract Algebra; its essential.>Which areas do I absolutely need to know? That depends on the school. But I would expect at least basicknowledge of Set theory Groups, rings and ?lds Topology, including the Topolgy of the Real Line Real and Complex AnalysisAlong with classes that youve already taken. It might turn out thatsome of your course work was too shallow.-- Shmuel (Seymour J.) Metz, SysProg and JOATnot reply to >Message-id: <3fee0f34$20$fuzhry+tra$mr2ice@news.patriot.net>[...]>>3. Differentiating Vector Valued FunctionsThere wasnt a course called something like Advanced Calculus?Yes, Im currently taking it. We are not using a book and I dont have asyllabus for the next semester yet. I guess I will have that covered. Mymistake.[...]>>11. Algebra - YesI hope that you mean Abstract Algebra; its essential.Yes.>>Which areas do I absolutely need to know? That depends on the school. But I would expect at least basic>knowledge of Set theory Groups, rings and ?lds Topology, including the Topolgy of the Real Line Real and Complex AnalysisAlong with classes that youve already taken. It might turn out that>some of your course work was too shallow.-- > Shmuel (Seymour J.) Metz, SysProg and JOAT > The problem is that the length functional, length, is not continuous> on this function space and so does not commute with limits.I often wondered if there is a 2D analogy to the 1D limit conceptwhereby in the 1D case, a point approaches a point, and in the 2D casea curve approaches a curve. Naturally this limit concept can beexpanded (no pun intended) to include higher dimensions, ie a volumeapproaching a volume... etc. > The problem is that the length functional, length, is not continuous> on this function space and so does not commute with limits.> I often wondered if there is a 2D analogy to the 1D limit concept> whereby in the 1D case, a point approaches a point, and in the 2D case> a curve approaches a curve. Naturally this limit concept can be> expanded (no pun intended) to include higher dimensions, ie a volume> approaching a volume... etc.One can de?e the concept of limits in a very general setting in terms ofany of the following frameworks:- general topological spaces, which are de?ed via collections of sets- metric spaces, which are de?ed via a distance function, e.g. see myposting in this thread concerning the sup|f-g| metric for an example - Banach spaces, which require that a norm be de?ed, e.g. see Rob Johnsons posting in this threadis a Banach space, every Banach space is a metric space and every metricspace is a topological space.Any of these will allow you to de?e convergence in n-dimensions and even in in?ite dimensions, i.e. even in function spaces. The nifty thing is that the most general of these frameworks, topologicalspaces, has an amazingly simple de?ition of limits which strips themdown to their essentials and really enlightens what they are.Check out a book on real analysis for more info -- be sure its one thatcovers all the above spaces in progression. |Isnt this the same problem as needing 2 pi rho ds as the integrand for|surface area rather than 2 pi rho dx?Not really, but Id agree that the mistake which leads people sometimesto think that they need dx rather than ds is of a similar ?Archimedes solved some problems which today we would solve by doingan integral. One rigorous method was known as the method of exhaustion.There were other, less rigorous methods termed mechanical, whichsometimes looked a bit like considering the solid to be sliced intoin?itesimal slices. The ancients knew then that this kind of methodrequired care, and theyre still right.Keith Ramsay > The problem is that the length functional, length,> is not continuous on this function space and so> does not commute with limits.Hmmm... the length-function is such a nice function,that we better look for a limit-de?ition such thatlength *is* continuous.This has been emphasized by others in this thread alreadyand it goes into the heart of the matter, as I think andas the OP seems to feel by now, too.Rainer Rosenthalr.rosenthal@web.de > The problem is that the length functional, length,> is not continuous on this function space and so> does not commute with limits.> Hmmm... the length-function is such a nice function,> that we better look for a limit-de?ition such that> length *is* continuous.> This has been emphasized by others in this thread already> and it goes into the heart of the matter, as I think and> as the OP seems to feel by now, too.But the length function being nice is the problem. The intuition that length is continuous is wrong and your request to change the topology so that it becomes continuous cant work since if it did then length and lim would commute in which casethe two lengths are the same. You are going to have to change your de?tion of length but if you do that, the essential Euclidean nature of the problem is changed.I think the best we can do is to notice that lim length(f_n) = 2 > length(lim f_n) = sqrt(2)suggests that even if length is not continuous itmay be lower semicontinuous and, in fact, that is the case. (A function g on a metric space is continuous iff g and -g are lower semicontinuous so being lower semicontinuous gets you part way to continuity.)This can all be made precise in the metric space of bounded real functions on [0,1] with the metric: d(g,h) = sup|g(x)-h(x)| and sup is over x in [0,1].In this setting, de?e, length(g), the length of a bounded real function g as: sup sum sqrt( [x_i - x_(i-1)]^2 + [g(x_i) - g(x_(i-1))]^2 )where - sup is over all partitions 0 = x_0 < x_1 < ... < x_n = 1 of [0,1] for all n- sum is over i=1,...,n > The intuition that length is continuous is wrong and> your request to change the topology so that it becomes> continuous cant work ...This is clearly wrong: Lets take the discrete topologyand then every function is continuous.Well, this is just the extreme of what I had in mind:Looking for a de?ition of convergence of functionsequences, which excludes such zappel candidates.There *must* be some de?ition of convergence, whichis in accordance with intuition. I did enough topologyonce so as to succeed in ?ding out how to do that ...But it would be nice to get a hint by some learnedpeople around here (Dave? Robert? Rob? ...)> since if it did then length and lim would commute> in which case the two lengths are the same.No. This is correct for the discrete topology (see above)but in a richer topology this is a non sequitur.BTW why did you write twe two lengths? You have tocompare length(line) to length(n-th convergent), so youhave two lengths in every step n, but in?itely manylengths in all.> You are going to have to change your de?tion of lengthNo. I dont have to. On the contrary I want to hold on tothe original lovely and well known length. And its myDon Quixotes aim to kill these ugly wood-be-convergences. This can all be made precise in the metric space of> bounded real functions on [0,1] with the metric: d(g,h) = sup|g(x)-h(x)| and sup is over x in [0,1].>Well, if we restrict our function space to piecewise differentiablefunction, then the line and the stepfunctions fall into that space.And if we include some epsilon-demands like d_better(g,h) := max( sup|g(x)-h(x)|, sup|g(x)-h(x)| )then we should get a more decent de?ition of convergence.Rainer Rosenthalr.rosenthal@web.de > The intuition that length is continuous is wrong and> your request to change the topology so that it becomes> continuous cant work ...> This is clearly wrong: Lets take the discrete topology> and then every function is continuous.Firstly, you have deleted part of my response making it seem wrong. I didnt say no topology could make it continuous. I saidthat you are not going to be able to make it work withoutchanging the essential nature of the problem. Secondly, in the discrete topology, lim f_n does not equal f so the essential nature of the original problem is notpreserved.Thirdly, I think it needs to be placed in a reasonably elementary common framework to stay within the spirit ofthe original problem and bounded functions on [0,1] with the sup|f-g| metric seems to satisfy that pretty well. > The intuition that length is continuous is wrong and> your request to change the topology so that it becomes> continuous cant work ...> This is clearly wrong: Lets take the discrete topology> and then every function is continuous.> Firstly, you have deleted part of my response... in order to get hold of the relevant part. I have theidea of a natural topology for function sequences, wherethe length is a continuous function.> ... you are not going to be able to make it work without> changing the essential nature of the problem.I disagree again. The essential nature of the problem is IMOthe proper de?ition of convergence. The OP was perplexed,since the lengths of seemingly convergent functions did notconverge to the length of the limit function.> Secondly, in the discrete topology, lim f_n does not equal> f so the essential nature of the original problem is not> preserved.The essential nature is well preserved, since this radicalchange of topology sheds light on the role of topology itself.And the essential nature is wonderfully exhibited insofar aslim f_n does not equal f in any topology, where length shallbe a meaningful term. The discrete topology is just an extremeexample. The topology, which I pointed to by the metric generatingformula (skipped by you): d_better(g,h) := max( sup|g(x)-h(x)|, sup|g(x)-h(x)| )is quite natural and not as pathological as the discrete topology.And here we have again: lim f_n <> f.> Thirdly, I think it needs to be placed in a reasonably> elementary common framework to stay within the spirit of> the original problem and bounded functions on [0,1] with> the sup|f-g| metric seems to satisfy that pretty well.Not really. The sup|f-g| metric is too rich, too far into thedirection of the trivial topology, where each sequence convergesagainst each function.How about the enhancement (d_better from above)? The spirit of theoriginal problem is preserved, as I think. The OP could be happy.Rainer Rosenthalr.rosenthal@web.de Perhaps we are just arguing over what we regard asthe essential nature of the problem.To me the problem can be stated as: If f_nconverges to f then why does length(f_n) notconverge to length(f)? (*)Although its slightly less obvious in the postersoriginal formulation, when stated this way itbecomes clear that the answer is that ourintuitive notion of length being continuous iswrong.To me, the if part of (*) is the essentialnature of the problem -- maybe not to you (sincethis if part is false in all your examples). Ill give you the bene? of the doubt andinterpret your response as saying that the sourceof the problem is that the intuitive notion thatf_n converges to f is wrong and a topology so de?ed can make it possible for length to be continuous. > Perhaps we are just arguing over what we regard as> the essential nature of the problem.Well, in a way. Yes, indeed. True, true.> To me the problem can be stated as: If f_n> converges to f then why does length(f_n) not> converge to length(f)? (*)I agree. And I am completeley happy with Rob Johnsonsanswer, which says:1. Our staircase f_n functions are converging to f in the C^0 norm. And one has to live with the fact that length is not continuous.2. Our staircase f_n functions do not converge to f in the C^1 norm (my d_better() *proud*) and so there is no need for the lengths |f_n| to converge to |f|.3. If a sequence f_n converges to f in the C^1 norm, then |f_n| are converging against |f|.Best wishes for the New YearRainerRainer Rosenthalr.rosenthal@web.de >> The intuition that length is continuous is wrong and>> your request to change the topology so that it becomes>> continuous cant work ...> This is clearly wrong: Lets take the discrete topology>> and then every function is continuous.>> Firstly, you have deleted part of my response... in order to get hold of the relevant part. I have the>idea of a natural topology for function sequences, where>the length is a continuous function.De?e the C^0(I->R^n) and C^1(I->R^n) norms to be ||f|| = sup|f| 0 I ||f|| = sup|f| + sup|f| 1 I ISee .Suppose a sequence of curves {f_n} converges to {f} under the C^1 norm: |L(f ) - L(f)| n | | | = | | |f(t)| - |f(t)| dt | | | I n | | <= | |f(t) - f(t)| dt | I n <= ||f - f|| n 1Thus, if a sequence of curves converges under the C^1 norm, then thelengths of the sequence will also converge to the length of the limit.Thus, length is continuous under the C^1 norm. There is no way tocontrol length using only the C^0 norm.Even though the staircase curves converge under the C^0 norm to thediagonal, they dont converge under the C^1 norm.>> ... you are not going to be able to make it work without>> changing the essential nature of the problem.I disagree again. The essential nature of the problem is IMO>the proper de?ition of convergence. The OP was perplexed,>since the lengths of seemingly convergent functions did not>converge to the length of the limit function.> Secondly, in the discrete topology, lim f_n does not equal>> f so the essential nature of the original problem is not>> preserved.The essential nature is well preserved, since this radical>change of topology sheds light on the role of topology itself.>And the essential nature is wonderfully exhibited insofar as>lim f_n does not equal f in any topology, where length shall>be a meaningful term. The discrete topology is just an extreme>example. The topology, which I pointed to by the metric generating>formula (skipped by you): d_better(g,h) := max( sup|g(x)-h(x)|, sup|g(x)-h(x)| )is quite natural and not as pathological as the discrete topology.>And here we have again: lim f_n <> f.> Thirdly, I think it needs to be placed in a reasonably>> elementary common framework to stay within the spirit of>> the original problem and bounded functions on [0,1] with>> the sup|f-g| metric seems to satisfy that pretty well.Not really. The sup|f-g| metric is too rich, too far into the>direction of the trivial topology, where each sequence converges>against each function.>How about the enhancement (d_better from above)? The spirit of the>original problem is preserved, as I think. The OP could be happy.Your d_better is the C^1 norm. This norm makes length a continuousfunction on curves.Rob Johnson take out the trash before replying > Your d_better is the C^1 norm. This norm makes length> a continuous function on curves.So ?ally my exclamation worked Dave? Robert? Rob? ...) :-)Best wishes > Your d_better is the C^1 norm. This norm makes length> a continuous function on curves.> So ?ally my exclamation worked Dave? Robert? Rob? ...) :-)No one was arguing that one could not de?e a topology that makeslength continuous or that different notions of convergence exist.The problem is that none of these different notions of convergencecan result in length being continuous without violating the assumptionsof the problem. Thus to make length continuous you either have to giveup on f_n converging to f or change the de?ition of length, etc. >> The problem is that the length functional, length,>> is not continuous on this function space and so>> does not commute with limits.> Hmmm... the length-function is such a nice function,> that we better look for a limit-de?ition such that> length *is* continuous.In theory, same as we might have in theory that the speed of light is not limiting. >If we have the analytic (about x = 0) real -> real function >f(x) = sum{k=0 to oo} a(k) x^k /k!,>we might, for whatever reason,>want to de?e g(x) as>sum{k=0 to oo} b(k) x^k /k!,>where {b(k)} is a permutation of {a(k)}.>I am wondering if taking the permutations of terms of exponential>generating functions, or of ordinary generating functions, has been>studied (or has any applications).> Applications? Does it matter?Not really. :)I was wondering more speci?ally if there were any applications amongother branches of *pure* mathematics, or in combinatorics anyway.> Studied? The closest thing that comes to mind is Camerons journal of integer sequences)> It depends on what kinds of permutations youre thinking of: e.g. a simple > involution > b(2k) = a(2k+1)> b(2k+1) = a(2k)> it is easy to compute gfs:> > f(x) + f(-x) f(x) - f(-x)> g(x) = x ------------ + ------------> 2 2x> (which can be easily generalized for more similar constant bounded > distance permutations)> But what about the gf for the Gray code permutation? EIS A003188 (take the> basic binary re? Gray code, convert back to integers: > <0,1,3,2,6,7,5,4,..>) you get a permutation of the integers where the> distance is unbounded. and the gf for it is ..er... not nice (IMHO) (which > makes > I think what I need to do now is to take a 10 cm long, 10 gram> weighing elastic wooden stick. I will put this stick on rather> frictionless tiles of my room. I would like to bend this stick using> thumb and middle ?ger of my right hand. I would like to make sure> that elastic potential energy stored in this curved stick is maximum.> Now I will tie a thread to a small stone weighing about 15 gram and> other end of loose thread to center point of curved stick. I will> place this stone near center point of bended, curved stick making sure> that when I release both ends of stick, center point of stick strikes> to center of gravity of stone. Now I will release both ends of stick> to allow center point of bended stick to strike to center of gravity> of stone. Now I will see stone propelled on rather frictionless tiles> of my room. If the propelled stone pulls the stick through tied thread> in direction of motion of stone, then I have propelled the stick,> thread and stone in only one direction without having to expel> reaction mass or using propellant.You hope to use this in space, dont you?You have a problem: what happens if you use your device twice?This problem will arise in any situation in which friction forces arethe same in all directions. In particular, this includes space.Think about the following experiment: you are in a little boat, on alake. You have big, heavy stones on board. You stay in the back of theboat: you throw a stone backwards. What happens? Your boat goesforward! And quite fast. But there is a problem, you have lost yourstone.You think a little and say: why not attach a rope to the stone? Sothat I can take it back on board! Methinks Im a genus! We are toenter into an age of stones&ropes! And what happens if you try? Whenyoull use the rope to take back the stone the boat will gobackward...In the end you will have not moved.You are trying to do exactly the same thing. You dont have a chance.There is a case in which you can do something, but this is no miracle(and no apocalypse, btw). This is when friction forces are big in oneway and small in the other one. Say you are in the followingcon?uration:________________________________________ _________/ / / / / / / / / ,/ / / / / / / / | +---------+ | | | device | | | +---------+ | ? -------------------------------------------------The rails on both side are here to represent (or to implement) theoriented friction forces. You can easily move the device to the left(with some click-click), but you cannot go in the other way. In sucha case, you could have bow and arrow in your device, a thread toattach the arrow to the device, some motor to bring the arrow backinto the device. And now, if the friction forces are small enoughcompared to the weight of your arrow, and the strenght of your bow,youll have a chance. But be sure of one thing: it wont besigni?antly more ef?ient that anything else. And probably less.Try to understand this last experiment, this is probably where you arein trouble. Your intuition tells you it _has_ to work. In someparticular cases, yes. But not in general, and not when it would begreat.To come back to the experiment you proposed: holding the bow, you playthe role of the rail. The bow cannot go backward: you hold it. But itcan go forward: you allow it to go this way.I hope this has helped you to understand your mistake, I wish you aMerry Christmas, and a happy New Year. /er. Letq(r,m) =--- 1/ ------ k^rk|mk>= sqrt(m)which is, in linear-mode,sum{k|m, k>=sqrt(m)} 1/k^r,where the sum is over the divisors of m which are >= the squareroot ofm. If we again sum over the divisors, but now over every positive divisorof n, so that we have:Q(r,n) =---/ q(r,m) --m|n= sum{m|n} q(r,m),then the average of all the Q(r,n)s, taken over the ns, approaches alimit.ie.limit{q-> oo} q 1 ------ q / Q(r,n) = A(r) --- n=1= limit{q -> oo} (1/q) sum{n=1 to q} Q(r,n)And A(r) is, if I am right, ... oo--- (1+1/2+1/3+...+1/k) -------------------/ k^(r+1)---k=1= sum{k=1 to inf} (1+1/2+1/3+...+1/k)/ k^(1+r),which is an Euler sum.[ http://mathworld.wolfram.com/EulerSum.html ](For example,A(1) = 2*zeta(3).)(Right?)So, since q(r,m) = sum{k|m,k<=sqrt(m)} k^r /m^r(note inequalitys direction here, as opposed to in q()s de?ition),I wonder naivelyif there is some kind of zeta-function-like re?n formula for theEuler-sum analytical continuation which relatesE(r) and E(2-r),where E(r) is sum{k=1 to inf} (1+1/2+1/3+...+1/k)/ k^r.(I know of no study regarding analytical continuating Euler sums atall, nor anything beyond the consideration of My son bought us a couple of Pepsi drinks today, which feature aCaps for caps promotion. You buy the bottle and look inside thecap for an imprint; save the caps and you can win a team hat (cap)bearing the logo of an NFL (American football) team.The imprint inside the bottle cap is usually the name of one ofthese teams. I dont follow sports, but the rules inside specify thenames of 32 teams (which I believe is the complete set of teams inthe league). When you have collected two copies of one team name,you may claim a free hat as your prize (and no, it doesnt have tobear the imprint of the team whose name you found twice).Alternatively, some of the caps carry a Buy-one-get-one-freemessage (according to the rules sheet). The label of the bottlestates the odds of this happening to be one in six. (Shouldntthat be _odds_ of ?e to one? But I digress...)I believe every cap carries exactly one imprint, although it isntclear from the rules that there are no Sorry, try again imprints. Here is my question: The rules state, Once you have your ?st bottle cap [with a team logo], odds of matching such cap are 1 in 36. I would like to know how they derive this number.It appears that 1/6 of the caps win a free drink, and I am guessingthat the other 5/6 of the caps are equally distributed with theimprints of the 32 teams, i.e. 5/192 of the caps say Bears, 5/192say Bengals, etc. So once you have a cap showing Bears, isntyour probability of getting a match next time 5/192 ? Thats about1/38, not 1/36. What am I missing?I considered the possibility that they meant that the odds of matchinga cap you already own, _given that_ the next cap is not a free-drink cap,were 1/36. But thats obviously wrong; its 1/32.I considered the possibility that the 1/6 was just rounded off.Repeating the calculation with 1/(5.5) of the imprints offering afree drink, the chances that the second cap is a match to a team youalready have would be (1 - 1/5.5)/32, about 1/39; with only 1/(6.5)of the caps winning a free drink, a cap matches your teams (1 - 1/6.5)/32 of the time -- about 1/37.8 . So a rounding error isnot ennough.Then I considered the possibility that the team names were not printedequally often. (That sounds pretty impolitic to me, but then, Im notin marketing!) This sort of thing is common; for example, McDonaldsrestaurants used to have a promotion in which customers were givena free game ticket bearing the name of an ingredient in the Big Macsandwich; collect them all (seven, IIRC) and you get a free sandwich.The company printed far fewer tickets showing Special Sauce sothe odds of getting a free sandwich were lower than 1/7 even if you were given a bundle of the other six ingredients by someone else.So assume that the fraction of the caps imprinted with the name ofteam i is p_i = 5/192 + x_i. Then we know sum p_i = 5/6, which isto say sum x_i = 0. Also evidently the claim is that among those people with a non-free-drink cap ?st, 1/36 of those people will have two identical caps; I make this out to say that sum (p_i)^2 = (5/6) (1/36),which is equivalent to sum x_i^2 = (5/6) (1/36) - 32 (5/192)^2 = 5/3456.Well, thats only 2 equations in 32 unknowns. We can ?d some of thesolutions by looking for a 2-variable problem to solve which specializesthe general case. For example, suppose there are k teams with adifferent probability from the other 32-k teams (k=0, 1, 2, ...)Then there are just two different probabilities to compute. I ?d thatthe equations allow for the greater and smaller probabilities to beone of many different combinations: k p1 p2 1, .06347892127, .02483401328 2, .05208333333, .02430555555 3, .04694721281, .02387902397 4, .04383151175, .02350026023 5, .04166666667, .02314814815 6, .04003864192, .02281159545[...]12, .03472222222, .02083333333[...]16, .03276559609, .01931773725[...]27, .02893518519, .0104166666328, .02858307311, .0082518215429, .02820430937, .0051361205530, .02777777778, 0The last case corresponds to using 30 team names each 1/36 of the timeand not using the other two teams at all. The cases k=12 and k=16show the most equitable distributions of this type, minimizingrespectively the ratio and the difference between the high and thelow probabilities. I dont know whether we can improve these measuresby allowing the p_i to assume more than just two values.So I dont know whether Im missing a possible alternative model, butit rather looks to me that either they or I have made an arithmeticerror, or else there is a gross disparity in the distribution of the team names!Mathematically, this situation is obviously the birthday paradox.Suppose again that the 32 team names are printed equally often.Once you have 33 team imprints, you must have a match; the probability pthat you have at least one match once you have k imprints is shownin the table below. Also shown is the probability q that you haveat least one match after k draws (about 1/6 of which should garnera free drink); q_k is sum (5/6)^i (1/6)^(k-i) binomial(k,i) p_i. k, p q 1, 0 0 2, .0312500000 .0217013889 3, .0917968750 .0639738860 4, .1769409180 .1243626630 5, .2798233032 .1993244322 6, .3923509121 .2845765171 7, .5062851161 .3755105100 8, .6142852469 .4676137835 9, .7107139352 .5568439157...27, .9999999497 .999770817228, .9999999921 .999881333629, .9999999990 .999940009130, .9999999999 .999970378431, 1.0000000000 .999985709032, 1.0000000000 .999993260533, 1 .9999968919(So if you really, really want a free team hat, probably 8 or 9bottles of Pepsi will get you one.)But these probabilities are affected by an unequal distribution ofthe team names. For example, if as above we really only use 30 ofthe team names (equally often), then the chances of an early matchgo up. I didnt work out the probabilities in other cases, butit seems clear that any choice of the p_i which makes the chanceof a win with two caps equal to 1/36 rather than 5/192 willincrease all the other numbers in the table too, that is, thechance of having a match when you possess 3 caps should begreater than 0.091796875 no matter what solution { p_i } ischosen for the pair of equations. I didnt see how to prove this.Such is the curse of being a mathematician: even the insigni?antevent can lead to quite a bit of pondering!dave >My son bought us a couple of Pepsi drinks today,event can lead to quite a bit of pondering!davePepsi has caffeine, doesnt it?--MensanatorAce of Clubs Given Two lines whose quations are 3x+y-8=0 and -2x+by+9=0, determine the value of b such that the two lines are perpendiclar. Ok so i know that they have to be negative reciprocals and i get stuck aty=-3x+8y=2x-9/bWhat exactly do i do here? TIA for helping out guys, really appreciate it!---= 19 East/West-Coast Specialized Servers - Total Privacy via Encryption =--- > Given Two lines whose quations are 3x+y-8=0 and -2x+by+9=0, determine the> value of b such that the two lines are perpendiclar. Ok so i know that they have to be negative reciprocals and i get stuck at> y=-3x+8> y=2x-9/b What exactly do i do here? TIA for helping out guys, really appreciate it!News==----> http://www.newsfeed.com The #1 Newsgroup Service in the World! >100,000> ---= 19 East/West-Coast Specialized Servers - Total Privacy via Encryption=---So you know that the slope of the second line has to be 1/3So we can say 2/b=1/3; which means b=6.-- David MoranChief MeteorologistOklahoma Storm Team > y=2x-9/bYouve made a mistake here....This should be y= 2x/b - 9/b> What exactly do i do here? TIA for helping out guys, really appreciate it!> News==---- http://www.newsfeed.com The #1 Newsgroup Service in the World!> Privacy via Encryption =--- you please help me, and show the steps??Translated into plain text, the inequality in the subject line mightbe written as |x| >= |x-3|You call this a problem; Im guessing you want to know the valuesof x for which this statement is true. Heres a useful hint: whena and b are real numbers, | a - b | is the distance from a to bon the number line. So your question may be phrased, Which are thenumbers x which are further (or equidistant) from 0 than they are from 3?In that form theres really nothing to write down except a picture!A glance at the real number line shows that the answer is every realnumber to the right of (or equal to) the midpoint between 0 and 3.You can write this is symbols if you like: suggestions are { x ; x >= 3/2 }or simply [ 3/2, oo )Before you complain that I didnt show you the steps, let me respondthat youre a lot better off in mathematics if you get used to thinkingabout what mathematical statements _mean_ (in English, say), instead ofhow to manipulate the symbols. Once you understand a meaning, you candevelop your own steps and tricks.dave > Can you please help me, and show the steps??Could you actually post it as ascii text instead of the crypto you used? Sniper> Can you please help me, and show the steps?? |x|≥|x-3|seems to be html for |x| >= |x-3|.But this is not true for all x. It is true only for x >= 3/2.LH A = event that keys are contained in box BB = event that contestant chooses box BC = event that Monty Hall opens box AThenP(keys in box B | contestant selects B and Monty opens A)= P(A | BC) = P(ABC)/P(BC) = P(C | AB)P(AB)/P(C | B)P(B) = P(C | AB)P(B | A)P(A)/P(C | B)P(B) = (1/2)(1/3)(1/3)(1/2)(1/3) 1/3 --MensanatorAce of Clubs Because no one bothers to write their own computer simulation.knowing the value from X and not knowing the value of X,in software its just X.Herc everyone> when I say I never noticed this...Well, you know you better than I do, so you must speak for me when you sayyou never noticed this.Jon Miller IVIn Rovellis approach, almost everything is quantized and time itself has no fundamentalmeaning.So, OK, things are VERY different in Rovellis theory. No argument there.He wants to dig down to the raw manifold so he can quantize the stripped-offEinsteinian chronogeometric structure of spacetime, replete with its uni?d metric,thinking this may be the real solution to the quantum gravity conundrum.I say he has not properly understood the status and meaning of the uni?d metric.He has simply skated over this. He is trying to run before he can walk.PZ: He wants to throw away time in order to keep a uni?d g_uv.Read Goldstein on time in QMGR....JS: What do you mean by kinematical g_uv and dynamic gravitationalg_uv apart from Ruvwl = 0 in the former and not in the latter.I mean what it means in Newtonian physics.We can always write a metric tensor expression for the invariant interval in Newtonianmechanics. We can then covariantly describe the ?titious inertial forces ofNewtonian theory (and Jack, please dont say here that you dont know what I mean)in terms of the space-time connection ?ld. The metric gradients then determine thestrength of the apparent forces that are observed in accelerated frames. They canbe viewed as the metric potentials (Tolman, Bergmann) of the ?titious force ?ld.Of course, the space-space connections are not here associated with any forces,?titious or otherwise.JS: Are you sure of that?Everything contributes.E.g. for a charge on a timelike non-geodesic in an external EM ?ld Fvwd^2x^u/ds^2 + {^u|vw}(dx^v/ds)(dx^w/ds) + (e/m)e(^u^v^w l)Fvwdx^l/ds = 0{^u|vw} is the connection ?lde(^u^v^w l) is the 4-antisymmetric symbol.I think thats correct off-hand?(v/c)^2]^-1/2off the time-like geodesic it is on when Fvw = 0.On the other hand the quantum BIT ?ld is feeling Au in its phase accumulation even when Fvw = 0 at its location.So I think you have made another error using only words and not checking the relevant math.PZ: Jack, are you able to distinguish between the Lorentzian and Einsteinianinterpretations of the Lorentz contraction and time dilation? John Bell a whole essay on this in Speakable and Unspeakable. Have you read it?JS: Yes, but it makes no difference to the formal structure or to the physical predictions.It is only in the informal language. It is moot. Only until that degeneracy is lifted willthere be physics there. Einstein was very interested in the constructive view that waslike kinetic theory to his thermodynamics.PZ: The situation here is precisely analogous: it is the difference between viewinggravitational distortions of measurements as inseparable from the nature ofspacetime and the de?ition of its fundamental structure, on the one hand, andviewing it as a physical effect, similar to universal thermal contraction and expansionof measuring sticks (Feynman), which is regarded as *separable* from thefundamental chronogeometric structure of spacetime.JS: Again this is not really interesting physics until a signi?ant experimentally testable difference can be found - at least in principle if not in fact.PZ: If you are really having problems with these distinctions, I suggest you re-readFeynmans Lectures on Gravitation, where he pays considerable attention toprecisely this kind of issue (in the context of developing a spin-2 quantum?ld theory of gravitation). Feynman was a wonderful teacher.JS: Yes I know.PZ: And I ?d it dif?ult to believe that Feynman would describe his own ideas,and his own perceptive critique of Einsteinian physics, as philosofauzy.JS: I think he was objective enough to do so if the situation warranted.PZ: That is the great Einsteinian insight -- which is.unfortunately, based on strict Einstein equivalence, which is?titious.JS: Again I really do not understand what you mean by this sentence.PZ: Then I suggest you read just about anything Einstein published on this -- at leastup to 1921. It certainly seemed to make sense to him, at least at the time.JS: He changed his mind? Early ideas mature.already givenyou a veritable cornucopia of direct Einstein quotes on this concept!The fact is that the reason we have a uni?d gravitational-inertial metric in orthodoxGR is because Einstein supposed that the gravitational and inertial ?lds were *oneand the same*.JS: They essentially are. In fact the idea of a uniform gravity ?ld without tidal curvature is rare if not impossible to come by.PZ: You and Rovelli seem to be content to have the g_uv grin without the cat. I, on theother hand, am trying to paste this same grin on a very different cat....Can you explain what Rovelli means by active diff invariance with respect to araw manifold of indistinguishable points? And how his Cartesian relationismis at all relevant to existing gravitational physics and to Einsteinian relativity?JS: Good question to which at the moment I do not have a good short answer....JS: Yes on just another ?ld. But NO that its like PV and Yilmaz.Nottrue at all because,at least in PV, Hal uses an absolute non-dynamical background globalMinkowski spacePZ: That is what Rovelli *should* be doing, but he doesnt evenconsider thispossibility. He seems to think you can treat uni?d g_uv as aphysical ?ld.JS: Why do you think you cannot?PZ: Because then you arrive at the absurdity of diff invariance with respect to rawspacetime manifold as some kind of physically relevant notion of relativity-- which reduces the whole thing to absurdity.JS: You lost me. What is absurd about diff invariance? Do you also think local gauge invariance is absurd?Diff invariance is to the base space of the set of physical ?er bundles as local gauge invariance is to theseveral ?er spaces for lepto-quark fermion sources and gauge boson forces and self-sources with the addedsupersymmetry mixing the two.Diff invariance is simply locally gauging the translational subgroup of the Poincare group of the base space. Doing so converts a globally ?se space to a variably curved one without torsion. Locally gauging the Lorentz sub-group seems to introduce torsion. The compensating gauge ?lds restore the symmetry broken by the initial local gauging.In the case of gravity, as curvature without torsion and without residual micro-quantum zero point stress-energy density tensori.e. tuv(exotic vacuum) = [(Fine Structure Coef?ient)]^-1(Witten String Tension)]/zpfguv --> 0/zpf = Lp^-2[Lp^3|Vacuum Coherence|^2 - 1]guv = Minkowski(uv) + d(u.v)du = Lp^2(Arg Vacuum Coherence),uRestoring the translational symmetry is found in the consequence of the Bianchi identitiesGuv(Einstein)^;v = 0Which is only true when there is no torsion and no exotic vacuum.With zero torsion but exotic vacuum and insigni?ant Tuv(Matter)Guv(Einstein)^;v + /zpf^,vguv = 0Assuming also metricity i.e.guv^;v = 0.One of the basic equations for practical metric engineering of weightless Alcubierre warp drive and star gate time travel isGuv(Einstein)^;v + /zpf^,vguv = 0IMHO.PZ: You cannot paste the grin of the uni?d metric on the cat of Cartesian relationism,in Rovellis de?ition of the term. It wont stick.PZ: I cant imagine anything more wrong-headed. And you say Rovelli isa bigshot?That is why I say Rovellis position is incoherent.JS: Is coherence in the mind of the beholder?PZ: As of the above sentence it is you who is now the beholder. :-)JS: Narcissus Principle i.e. Universe as a self-excited circuit. (Wheeler)PZ: So, whats the answer?JS: The Question is: What is The Question? (Wheeler)PZ: Yes, I know Im sticking my neck out, but this is how Rovellis position strikes me.You yourself admit that you havent yet been able to make sense out of his relationism.So, OK, you have faith.JS: There is no consistent ontology for quantum gravity based on any non-Bohmian interpretation of quantum theory. The exception isShelly Goldsteins paper in the book Physics Meets Philosophy at the Planck Scale, even he makes a mistake IMHO in not sticking toNO ACTION WITHOUT DIRECT REACTION by proposing that the BIT wave function of the universe has no sources from its ITextra variable, i.e. the 3-geometry (or something deeper like spin networks maybe or perhaps a set of D-branes with strings as 1 branes).The BIT MACRO-QUANTUM WAVE OF THE UNIVERSE is IMHO Hawkings Mind of God ONLY when it has sources! That makes Fred Hoyles Intelligent Universe conscious IMHO. ----------------------------- <^> <()> <^> -----------------------------> [...]> Jim, Im going on a break, the discussion is over. You are> sitting at a comfy computer and you are free to do what you> want. I am at my computer because I am ?hting for my life> while I am being tortured by a spy satellite for 2 years> continuously. it is the most hideous torture in all history,> I wish you would believe me, even give me a few hours bene?> of doubt because that is all it would take to con?m my> admitedly odd story. Dont watch your TV, its a lie. Sure, discussion is over. Maybe it wasnt such a good idea of> mine to press for resolution of these questions right now.> Im sorry if it made things harder for you than they would> otherwise be. One last word: consider ?ding someone YOU trust, and> using them as a sounding board, running some of your more> unusual ideas past them, before you actually put them into> action.Internets my only medium. My lifes progress out of poverty andabuse because I cant defend myself from a noisy satellite dependson the kindness of strangers. Of 5,000 replies on usenet not onehas been courteous, not to even spend 1 minute on my paranormal proof.The satellite picks up your thoughts and plays them out to everyone.Sounds like Sci Fi, I am in a constant forced telelpathic dialog witha team of purist sickos passing themselves off as pyschs.Anyone nearby can hear my thoughts, most people verbally abuse meto force a nasty reply. Im the kindest man on Earth, but thats becauseIm used to conceiling anything condescending. I watched my brotherand sister out my window leave yesterday, pretending I wasnt home. Thealternative is half dozen people sitting around me trying to tame my thoughts. Itsing painful, they started with chinese water torutre under a 24 hourlamp in the watchhouse 2 years ago, it didnt stop, it got much much worse.Herc100,000 witnesses to the mind broadcasting satellite that tracks you everywhereThis whole block of ?an hear this post as I type, when I go out tomorrowpeople will question me about Jim and sci.skeptic, degrade me and wait forme to mentally retaliate and listen in, then back on usenet no one will believe it.2 years of this. In sci.math, Virgil Hancher>> [...]>> Jim, Im going on a break, the discussion is over. You are >> sitting at a comfy computer and you are free to do what you >> want. I am at my computer because I am ?hting for my life >> while I am being tortured by a spy satellite for 2 years >> continuously. it is the most hideous torture in all history, >> I wish you would believe me, even give me a few hours bene? >> of doubt because that is all it would take to con?m my >> admitedly odd story. Dont watch your TV, its a lie.> You can get relief by wearing a hat of aluminium foil, or by blowing > your brains out.The ?st is probably easier on the brains...http://zapatopi.net/afdb.html:-)-- #191, ewill3@earthlink.netIts still legal to go .sigless. > It plots and analyses any x-y data for peak location, peak height,> peak> width, semi-derivative, derivative, integral,semi-integral,> convolution,> deconvolution, curve ?ting, and separating overlapped> peaks> and> background.> www.chemSoftware.com This is a follow up of the previous posting.Given a, b, c, d are non-square integers such that (a, b) = 1 and (c, d) = 1.Assertion: The following equality (1) is not possible. sqrt(a^5) + sqrt(b^5) = (sqrt(c) + sqrt(d))^5 (1)Any comment upon the correctness of the assertion will be appreciated.