mm-292 ==== Subject: Maxima and symbolic derivatives Dear newsgroup: I am evaluating Maxima (version 5.9.0) as a free symbolic-math aid for students. Most of the symbolic mathematics packages I have used know how to derive common functions symbolically. And for all I know Maxima also knows how to do this, but I can't figure out what the syntax is. Example, Mathematica: Integrate[x,x] 2 x -- 2 D[(x^2)/2] x Example, Maxima: integrate(x,x); 2 x -- 2 diff((x^2)/2,x); 2 d x -- (--) dx 2 Well, yes, that's true, but I wanted the derivative form. Maybe I am using the wrong Maxima function, or perhaps I am evaluating the wrong free student aid? I normally research these problems using groups.gogle.com, but in this case the obvious search term maxima has too many generic references, and MacSyma tends to produce very old results with little relevance to the present form of Maxima. Does anyone know an easy way to produce this result with Maxima, suitable for students getting their feet wet in Calculus? Alternatively, can anyone suggest another free symbolic math tool, cross-platform (suitable for Linux), that can produce this class of result? Thanks in advance. -- Paul Lutus http://www.arachnoid.com === == Subject: Follow-up: Maxima and symbolic derivatives I have solved my problem with Maxima by downloading the GCL Lisp interpreter from this site, which is the primary download site for Maxima: http://maxima.sourceforge.net/download.shtml The clisp download, which appears to be one of three equivalent choices on the above page, is in fact buggy and should be avoided. Problem solved. Thanks for your help, Richard and Jay. -- Paul Lutus http://www.arachnoid.com ==== Subject: Re: Follow-up: Maxima and symbolic derivatives I have solved my problem with Maxima by downloading the GCL Lisp > interpreter from this site, which is the primary download site for Maxima: http://maxima.sourceforge.net/download.shtml The clisp download, which appears to be one of three equivalent choices on > the above page, is in fact buggy and should be avoided. I want to make sure we avoid this problem in the future. Which version of clisp do you have? Did you download the maxima-exec-clisp-5.9.0-1.i386.rpm? The problem is that Maxima 5.9.0 is incompatible with clisp versions >2.29. I would have thought the pre-compiled version would fail completely when installed with a newer version of clisp. If you build Maxima 5.9.0 from source and run the provided tests (via make check) you would find that many, many tests fail. The current CVS version of Maxima is compatible with the most recent versions of clisp. In order to avoid the problem you see now ever happening again, the next release will include 1) Binary distributions that are statically linked* against clisp, so only the correct version of clisp will ever be used. 2) The test suite moved from the build system to the run-time system, so that you can run the checks yourself, even with the compiled version. 3) An added emphasis in the documentation on running the test suite. --Jim Amundson *In reality, there is no such thing as static linking for clisp. I have a scheme that provides something functionally equivalent, however. ==== Subject: Re: Follow-up: Maxima and symbolic derivatives > I have solved my problem with Maxima by downloading the GCL Lisp >> interpreter from this site, which is the primary download site for >> Maxima: >> http://maxima.sourceforge.net/download.shtml >> The clisp download, which appears to be one of three equivalent choices >> on the above page, is in fact buggy and should be avoided. I want to make sure we avoid this problem in the future. Which version of > clisp do you have? Did you download the > maxima-exec-clisp-5.9.0-1.i386.rpm? Yes. Unfortunately my first installation procedure was somewhat unorthodox, arising from a wish to minimize download time. I downloaded the Maxima source tarball and two RPMs -- the clisp version named above and the xmaxima RPM. I installed the clisp interpreter (using --nodeps to avoid the circular dependency), then I compiled the Maxima source, which detected the installed clisp interpreter, then I installed the xmaxima RPM last. This combination caused the difficulties described earlier, so I removed all the RPMs and the Maxima executable, downloaded the Maxima RPM to install instead of compiling from source, and the GCL interpreter. I then installed all three at once (including the xmaxima RPM) as recommended on the download site. This resolved the problems. > The problem is that Maxima 5.9.0 is incompatible with clisp versions >>2.29. I would have thought the pre-compiled version would fail completely > when installed with a newer version of clisp. If you build Maxima 5.9.0 > from source and run the provided tests (via make check) you would find > that many, many tests fail. The current CVS version of Maxima is compatible with the most recent > versions of clisp. In order to avoid the problem you see now ever > happening again, the next release will include > 1) Binary distributions that are statically linked* against clisp, so > only the correct version of clisp will ever be used. 2) The test suite moved from > the build system to the run-time system, so that you can run the checks > yourself, even with the compiled version. 3) An added emphasis in the documentation on running the test suite. I an glad to see that this first-rate application is being maintained. There are some students that are about the feel the same way. Thanks! -- Paul Lutus http://www.arachnoid.com ==== Subject: Re: Maxima and symbolic derivatives If you want to just try it out without downloading anything, type into the address bar of a browser: telnet://maxima.franz.com you are in a lisp system. to get to maxima, type (run). {There are instructions.} This version runs in Allegro Common Lisp. Since the interface is kind of impoverished, it doesn't support plotting etc. This telnet is not intended as a user friendly interface, but I find it perfectly usable for trying out a few commands. And it is about 10000 times better than typing MathML or OpenMath. RJF (You have clearly downloaded a broken Maxima.) ==== Subject: Re: Maxima and symbolic derivatives < snip (You have clearly downloaded a broken Maxima.) So it seems. It's not easy to find an obviously superior version, a single clear choice for download, especially because it must be married to a Lisp interpreter, also subject to good and bad choices. In another post, the Lisp interpreter I am using (clisp) is thought to be the problem. I am open to any suggestions in this regard, and thank you for replying. -- Paul Lutus http://www.arachnoid.com ==== Subject: Re: Maxima and symbolic derivatives ... > Example, Maxima: ... > diff((x^2)/2,x); > 2 > d x > -- (--) > dx 2 Well, that's clearly a bug; it should return x. I just tried it here, and Maxima did give x as an answer. (Although I'm using the cvs version of Maxima.) So, what platform are you running Maxima on? What is the underlying lisp? I seem to recall that there were some similar problems when the underlying lisp was clisp, but that's been fixed in cvs. For now, if you are using clisp, try gcl or cmucl. > Does anyone know an easy way to produce this result with Maxima, suitable > for students getting their feet wet in Calculus? Alternatively, can anyone > suggest another free symbolic math tool, cross-platform (suitable for > Linux), that can produce this class of result? For symbolic computations, there's Maxima and Yacas. Jay ==== Subject: Re: Maxima and symbolic derivatives ... >> Example, Maxima: > ... >> diff((x^2)/2,x); >> 2 >> d x >> -- (--) >> dx 2 Well, that's clearly a bug; it should return x. > I just tried it here, and Maxima did give x as an answer. (Although > I'm using the cvs version of Maxima.) > So, what platform are you running Maxima on? Red Hat Linux 9. > What is the underlying > lisp? clisp. > I seem to recall that there were some similar problems when > the underlying lisp was clisp, but that's been fixed in cvs. > For now, if you are using clisp, try gcl or cmucl. Thank you! I will try to remove the existing lisp and use one of the alternatives, or download the CVS version of Maxima. >> Does anyone know an easy way to produce this result with Maxima, suitable >> for students getting their feet wet in Calculus? Alternatively, can >> anyone suggest another free symbolic math tool, cross-platform (suitable >> for Linux), that can produce this class of result? For symbolic computations, there's Maxima and Yacas. If you have time, can you tell me whether Yacas is comparable in other respects to Maxima, e.g. graphing and so forth? Thanks for your assistance! -- Paul Lutus http://www.arachnoid.com ==== Subject: Re: Maxima and symbolic derivatives <103a6tu29i04vf4@corp.supernews.com> ... >> For symbolic computations, there's Maxima and Yacas. > If you have time, can you tell me whether Yacas is comparable in other > respects to Maxima, e.g. graphing and so forth? Well, I like both of them. I haven't graphed anything in Yacas for a while, so I don't know where that stands. Yacas can do a lot and you should take a look at it. It is really very well documented; it contains documents on just about everything about it. That said, though, Maxima is older and more powerful. Jay ==== Subject: Plot Option I am trying to plot two functions for the same x-axis. But the value of these functions are very different so I want to use two different axis for y (one on the left and one on the right for example). I could not find how to do that. Can you help me? Thank you Kerem ==== Subject: Re: Plot Option > I am trying to plot two functions for the same x-axis. But the value > of these functions are very different so I want to use two different > axis for y (one on the left and one on the right for example). I could > not find how to do that. Can you help me? Thank you No one can help you if you don't specify what software you're using. ==== Subject: Re: Journals and my papers Dear newsgroup: Journal of mathematics of Kyoto University has sent the paper on Quintic and Riccati differential equations for their referee consideration. It looks like most of my papers are in the referral process. The new list is as follows. Sincerely Dr.Mehran Basti -------------------------------------------------------------- ------------- 1-Basti.M. Solving polynomials with differential equations. Submitted for publication to Journal of Algebra. 2-Basti.M. A class Polynomial. Submitted for publication to Journal of Algebra. 3-Basti.M. A class Polynomial II. Submitted for publication to Central European Journal of Mathematics. 4-Basti.M. A class Polynomial III. Submitted for publication to Journal of Algebra. 5-Basti.M.Polyomials and Riccati differential equations. Submitted for publication to Central European Journal of Mathematics. 6-Basti.M. New Methods Of Solving Riccati Differential Equations.Submitted for publication to Electronic journal of differential equations . 7-Basti.M. New Methods Of Solving Riccati Differential Equations II. Submitted for publication to. Electronic journal of differential equations. 8-Basti.M. On Bessel Differential Equations. Submitted for publication Journal on Scientific computing. 10-Basti.M.On Associated Legendre. Submitted for publication to the 11. Basti.M. Quintic and Riccati differential equations. Submitted for publication to Journal of mathematics of Kyoto University. ==== Subject: Re: Journals and my papers Dear newgroup: I have sent my two other papers on Bessel differential equations to Moscow Mathematical Journal. Sincerely Dr.Mehran Basti ==== Subject: Re: Journals and my papers Dear newsgroup: I have sent the paper On Associated Legendre to Proceedings of the Indian Academy Of Sciences. Sincerely Dr.Mehran Basti ==== Subject: Plot Option I previously posted a question asking how to use two different axis for y (one on the left and one on the right for example). I forgot to mention the program that I am using. It is MAPLE8. Thank you, Kerem ==== Subject: Re: Plot Option >I previously posted a question asking how to use two different axis >for y (one on the left and one on the right for example). I forgot to >mention the program that I am using. It is MAPLE8. Thank you, A plot in Maple can have only one set of axes. However, you can make what looks like an axis by hand with plot and textplot. For example, suppose you want to plot f1 = x^2 and f2 = 100*x for x = 0 .. 1. I'll actually plot f1 and f2/100, and make a fake axis on the right for f2: > with(plots): P1:= plot(f1, x=0..1, colour=red): P2:= plot(f2/100, x=0..1, colour=blue): P3:= plot({[[1,0],[1,1]],seq([[1,0.04*j],[1.015,0.04*j]],j=1..25)}, colour=black): P4:= textplot({seq([1.03,0.2*j,sprintf(%2.0f,100*0.2*j)],j=1..5)}, align=RIGHT): display({P1,P2,P3,P4},axes=frame,view=[0..1.07,0..1]); Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 ==== Subject: Re: Unique mathematical challenge, rising > I've been fortunate enough to discover some challenging mathematics, > which is also easy to elaborate on, and has been made easier for me by > an example from a professor who happens to disagree with my position. In sci.math, and some other NGs, Harris has already appologized for his errors which I have snipped from this thread. I think he is here just looking for a new audience to bamboozle. ==== Subject: Displaying arrays side by side by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i1KEBFA07062; I am trying to display 2 arrays of the same size (11,1) side by side. One of my arrays is a string and the other is numbers, so I have used FPRINTF, and that worke. But no matter what I do I keep getting them one under the other. Any suggestions?! Mikal ==== Subject: Re: Displaying arrays side by side |>I am trying to display 2 arrays of the same size (11,1) side by side. |>One of my arrays is a string and the other is numbers, so I have used |>FPRINTF, and that worke. But no matter what I do I keep getting them |>one under the other. |>Any suggestions?! It might help if you said what program you're using. If it's Maple, you can do something like this: # constructing the two arrays > A:= array(1..11,1..1): B:= array(1..11,1..1): alpha:= cat(seq(c,c=a..z)): for i from 1 to 11 do A[i,1]:= alpha[i]; B[i,1]:= i od: # now to display them > eval(A), eval(B); [a] [ 1] [ ] [ ] [b] [ 2] [ ] [ ] [c] [ 3] [ ] [ ] [d] [ 4] [ ] [ ] [e] [ 5] [ ] [ ] [f], [ 6] [ ] [ ] [g] [ 7] [ ] [ ] [h] [ 8] [ ] [ ] [i] [ 9] [ ] [ ] [j] [10] [ ] [ ] [k] [11] Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 ==== Subject: Re: Displaying arrays side by side > I am trying to display 2 arrays of the same size (11,1) side by side. > One of my arrays is a string and the other is numbers, so I have used > FPRINTF, and that worke. But no matter what I do I keep getting them > one under the other. > Any suggestions?! Use a loop and print one element from each array at a time. ==== Subject: Re: does anyone know what this means? Thanks for that, Doubt No.2: What is the value of e^ infinity and e^ -infinity. e^x->oo as x->oo , e^(-x) = 1/e^x. Isn't it impossible to figure out the value of e to the power of > infinity? Litterally speaking it is impossible. > Eh? As you yourself indicate below (and as I had already indicated in a > previous response), it is, literally speaking, possible if you're working > with a system (such as the two-point extension of the reals) in which > infinity is defined. > But you may define f(oo)=oo as a shorthand notation for f(x) tends to oo as x tends to oo I interpreted the question in this sense. [ And it is still possible to extend the real numbers by two objects > oo and -oo and to define some limited arithmetic for them, as -oo < x < oo for any real number x > x + oo = oo for any real number x > x + -oo = x - oo = -oo for any real number x > x * oo = oo for any positive real number x > x * oo = -oo for any negative real number x > oo + oo = oo > -oo + -oo = -oo But caution: you cannot define oo - oo because any definition of this term would lead to a contradiction ] > I'd be interested to see what, in your opinion, such a contradiction > might be. Would you please elaborate? > David Cantrell It must go something like this.. As an object accelerates towards the speed of light, its mass increases towards a limit of infinity. Therefore light must be heavy. A photon must be the heaviest object in existence. In scientific circles, there is a debate about where all the dark matter went. There's your answer - it became light ! RexP ==== Subject: Re: does anyone know what this means? Thanks for that, Doubt No.2: What is the value of e^ infinity and e^ -infinity. e^x->oo as x->oo , e^(-x) = 1/e^x. Isn't it impossible to figure out the value of e to the power of > infinity? Litterally speaking it is impossible. Eh? As you yourself indicate below (and as I had already indicated in a > previous response), it is, literally speaking, possible if you're working > with a system (such as the two-point extension of the reals) in which > infinity is defined. But you may define f(oo)=oo as a shorthand notation for f(x) tends to oo as x tends to oo I interpreted the question in this sense. [ And it is still possible to extend the real numbers by two objects > oo and -oo and to define some limited arithmetic for them, as -oo < x < oo for any real number x > x + oo = oo for any real number x > x + -oo = x - oo = -oo for any real number x > x * oo = oo for any positive real number x > x * oo = -oo for any negative real number x > oo + oo = oo > -oo + -oo = -oo But caution: you cannot define oo - oo because any definition of this term would lead to a contradiction ] I'd be interested to see what, in your opinion, such a contradiction > might be. Would you please elaborate? David Cantrell > It must go something like this.. As an object accelerates towards the speed of light, its mass increases > towards a limit of infinity. Therefore light must be heavy. A photon must be the heaviest object in existence. In scientific circles, there is a debate about where all the dark matter > went. > There's your answer - it became light ! RexP > Next you will be claiming that black is white. ==== Subject: Re: does anyone know what this means? Thanks for that, Doubt No.2: What is the value of e^ infinity and e^ -infinity. e^x->oo as x->oo , e^(-x) = 1/e^x. Isn't it impossible to figure out the value of e to the power of > infinity? Litterally speaking it is impossible. Eh? As you yourself indicate below (and as I had already indicated in a > previous response), it is, literally speaking, possible if you're working > with a system (such as the two-point extension of the reals) in which > infinity is defined. But you may define f(oo)=oo as a shorthand notation for f(x) tends to oo as x tends to oo I interpreted the question in this sense. [ And it is still possible to extend the real numbers by two objects > oo and -oo and to define some limited arithmetic for them, as -oo < x < oo for any real number x > x + oo = oo for any real number x > x + -oo = x - oo = -oo for any real number x > x * oo = oo for any positive real number x > x * oo = -oo for any negative real number x > oo + oo = oo > -oo + -oo = -oo But caution: you cannot define oo - oo because any definition of this term would lead to a contradiction ] I'd be interested to see what, in your opinion, such a contradiction > might be. Would you please elaborate? David Cantrell > It must go something like this.. As an object accelerates towards the speed of light, its mass increases > towards a limit of infinity. Therefore light must be heavy. A photon must be the heaviest object in existence. In scientific circles, there is a debate about where all the dark matter > went. > There's your answer - it became light ! RexP Next you will be claiming that black is white. Don't be Cilla !! RexP ==== Subject: The word Quadratic I would have thought that the word quadratic would have something to do with the number 4. Can anyone throw some light on this. I vaguely remember that there was some connection with the number 4 but I can't remember it. Joseph ==== Subject: Re: The word Quadratic > I would have thought that the word quadratic would have something to do with > the number 4. Can anyone throw some light on this. I vaguely remember that > there was some connection with the number 4 but I can't remember it. > Joseph A square has 4 sides, so it is a special case of a quadrangle or quarilateral. The area of a square is the square of an edge. Thus areas, in squares, are related to quadratic (four-sided or four-angles) regions. ==== Subject: Re: The word Quadratic > I would have thought that the word quadratic would have something to do > with the number 4. Can anyone throw some light on this. I vaguely remember > that there was some connection with the number 4 but I can't remember it. Squares have four sides. -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9 Francis Wheen, _How Mumbo-Jumbo Conquered the World_ ==== Subject: Re: prediction > www.RacePredictor.com: utilises Internet technology and expert system to > track all the professional activity of the racing experts when they invest. www.racePredictor.com ==== Subject: Re: MathHandbook.com > www.MathHandbook.com: web-based symbolic calculator, math handbook and > computer algebra system. ==== Subject: A little question for you learned folks Hi there, My friend and I have a little issue with the odds on a 6 number lottery. Derick says that you have as much chance winning with the numbers : 1 2 3 4 5 6 , as you would have spreading the numbers out. Please could u help us settle this. Many thanx, Tim Durban, South Africa ==== Subject: Re: A little question for you learned folks > Hi there, > My friend and I have a little issue with the odds on a 6 number > lottery. > Derick says that you have as much chance winning with the numbers : 1 > 2 3 4 5 6 , as you would have spreading the numbers out. > Please could u help us settle this. Your friend Derick has it right. ==== Subject: Re: A little question for you learned folks >> Hi there, >> My friend and I have a little issue with the odds on a 6 number >> lottery. >> Derick says that you have as much chance winning with the numbers : 1 >> 2 3 4 5 6 , as you would have spreading the numbers out. >> Please could u help us settle this. >Your friend Derick has it right. Thank you for the swift reply. The reason why I had my doubts was: 1.] Why doesn't anyone play the numbers: 1 2 3 4 5 6? 2.] I once read a wonderful book called Bridges To Infinity that seemed to suggest otherwise (details lost in an alcoholic haze). Please forgive my stubborness on this. Law of averages/spread? Tim Dowson Durban South Africa ==== Subject: Re: A little question for you learned folks > Thank you for the swift reply. > The reason why I had my doubts was: > 1.] Why doesn't anyone play the numbers: 1 2 3 4 5 6? Because of psychology. In general, people tend to think that a lottery result is a random number, so a winning guess should look random too. An ordered sequence like 1,2,3,4,5,6 just doesn't look random. Now consider that the symbols we use to designate the numbers are just that: symbols. Suppose I had a typewriter where I could change around the key mapping. First I type out 1 2 3 4 5 6. Looks about as un-random as you can get. Now I shuffle the key map, and once again press exactly the same keys in the same order. This time I see printed 9 1 4 5 3 7. Looks more random, right? Yet it was the same keys being pressed. The numbers generated for lottery results are just sets of symbols chosen from a finite set. *Every* combination is just as likely as any other. > 2.] I once read a wonderful book called Bridges To Infinity that > seemed to suggest otherwise (details lost in an alcoholic haze). > Please forgive my stubborness on this. > Law of averages/spread? > Tim Dowson > Durban South Africa ==== Subject: small problem needs formula the problem reads 1c+1t=4 2c+2p=9 1p+2t=2 we know through trial and error that :- c=3.5 t=.5 p=1 is there a formula for this type of thing thanks cliff ==== Subject: Re: small problem needs formula > the problem reads 1c+1t=4 > 2c+2p=9 > 1p+2t=2 we know through trial and error that :- > c=3.5 > t=.5 > p=1 is there a formula for this type of thing > thanks cliff There are algorithms for these kinds of problems. The problem is to find the solution to a system of linear equations. A Google search for system of linear equations returned 44,500 hits. Most of these describe or refer to methods of solution. ==== Subject: O the fearsome variable! I thought this was a curious and telling comment. <<< We might as well be arguing over whether or not we should use x for a variable. ..and don't even try to tell me that when first introduced to even this _English_ letter to denote a variable, some are not confused for a while. I have a good friend who teaches first and second grade, and she assures me that introducing letter names for numbers in simple equations doesn't faze her students. So I wonder what sort of spiny shell a teacher might be creating in the minds of students around the introduction of a letter as a variable in middle school that could cause confusion, and other problems reported by some teachers. Students are perfectly at home naming cats, dogs, stuffed animals, game characters, cars, trucks, trains, and various other machines -- so one would not expect them to even think it odd to name (even temporarily) some numbers, or formulas, or functions when the discussion turns to math. These students learned before going to school how pronouns (substitute names that may be without specific object reference) work and how they can be used in sentences, and variables are just the pronouns of math. How is the teacher whose students react negatively hedging the natural naming propensity about with fearsome extra verbiage, and why? (Sorry, I wouldn't normally write anything related to education that used the word fear or any variant of it - I must have been infected by the frequent exposure to it in one responder's missives.) -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: Re: O the fearsome variable! > (Sorry, I wouldn't normally write anything related to education that > used the word fear or any variant of it - I must have been infected by > the frequent exposure to it in one responder's missives.) Quite OK. Although not p.c., everything pretty much is related to fear in some way or another, at least in the U.S. The media controls the masses via fear. The government also controls by fear. We're literally scared into consumption, in general. Look at Y2K and all the stuff purchased in preparation. Fear is a very powerful thing, and the ability to instill fear makes for the power to control others. As a society, we are essentially scared into compliance for just about everything, including education. Don't pass, and look, _here's_ what happens. Seen _Bowling for Columbine_? So although not p.c. in many circles, there is much truth and relevance in discussing fear in an educational context. You do raise some interesting questions, though. I submit the possibility that those who are scared of algebra at first, specifically variables like x and y, (if you'll forgive my continued references to fear,) are just having problems because what used to be straightforward concepts (eg 5, 231, 1/2) are now being presented in a somewhat abstract fashion (x, y, etc.) Once the fear of the abstract is removed, then usually the fear of whatever particular 'name' is chosen for an unidentified number, is also removed. I applaud the person you spoke of that had the fortitude to introduce letters to name numbers, and was successful. Chances are, those 2nd graders will not have any problem at all if, when in 8th grade, their math teacher shows tells them to denote a change in x by a certain Greek letter for they learned long before there was nothing really to be 'scared' of. -- Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: Re: Prove that 7^203 ends in 07 > hello, this ia my math homework. been trying to prove it but failed. basically, they told us that the last two digit of 7^2 => 49 > 7^3 => 43 > 7^4 => 01 > 7^5 => 07 now i have to prove that the last two digits of > 7^201 is 07 7^203 35884 10533920824 51103148256 68531670 853179816 727083901 45362898 0488240 48138226 5219523586132369 1391186 9250521380 15062 33857617 0367085788 347177 753570871369 75570713 80647449160343 7^201 732328680 39200500225 13229728 271769561 8734319851 191635 6196509805 882458803719 698357624 2067830436554 8352051456737 767824199218 442262405 78513831705527 9871378715742 462192840007 -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: Re: Solving the stated problem not the problem you think up In my opinion, the only reason that we have an outside test to determine graduation is that the public can't understand how some people graduate from high school and can barely read, write, or do basic computation. Until we stop social promotions and demand that kids show real accomplishment to move on to higher grades, diplomas cannot be trusted. Although we have implemented a high stakes test in Massachusetts, there is still no provision to record on the pupil's transcript the grade or the date it was taken. Further, the test is given in Mar- May and the scores are not returned until December. Those who failed have been most likely promoted into the next year. > Mister, I've read a lot of anti-high-stake-testing posts in this forum. I > understand why you guys are against it. I merely ask that people think beyond the American perspective for a moment, > and consider all the possible social functions it could serve in other > societies. OTOH, I am not saying that testing would solve THE American > problem. Not at all. (If you don't believe in something, it will never work > in the first place.) I merely ask that you do not consider testing as *EVIL* > for everyone in the world, simply because it doesn't suit the American social > and cultural taste. For simple-minded people like my parents back home, their children's success in > a high-stake test is their glimmer of hope to get out of the bottom rung of the > social ladder. Are you telling me that this is bad for them? This was the only > hope they had. (of course, this is something I have trouble getting Americans to understand, > cause the cultural environment is so different) > Jeffrey Turner (jturner@localnet.com) said: The point is not to give people just a hope of this, but to try to > make it so that there's NO correlation between where you start off and > where you end up. That is supposed to be goal of the US educational > system and that is a valid perspective from which to critique > standardized tests. > A recent study, done in Arizona, showed that high stakes tests do not > correlate with - in fact may be counterproductive to - future success > in academia and the real world. Humans are not like widgets and the > whole premise that you can quality control their education by testing > them more appears to be faulty. > ------------------------------------------------------- > This mail sent through HKedCity http://www.hkedcity.net > -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: Re: 8th grade : > : One of the points (the original point, actually) was whether or not to > introduce the notation Delta x to denote a change in x to an 8th grade > class, and some of the arguments against it are for reasons of little > more > than no, its Greek, so don't do it. The fact of the matter is the Delta notation is commonly used, even by a > first year algebra student. I did not read Ladnor's post that way at all. My interpretation of Ladnor's post, was that the introduction of Delta was > not necessary to the topic of instruction for that lesson, and so omit it. I didn't really think he meant to omit any mention of greek letters in > beginning algebra for 8th graders. Really. How else do you interpret > Ignore Greek letters entirely in K-14. ? Well, I thought that either he was exaggerating, or (as he noted) that he was not familiar with the K-12 curriculum, so I just didn't really focus on that one, short sentence out of his entire, rather well-written and lengthy meant literally. > Indeed, the greek letter Pi is commonly > used in first year algebra, and sometimes even earlier than that, > depending > on the middle school curriculum. It's utterly ridiculous (not just simply misspeaking, but utterly > _ridiculous_) to suggest to ignore Greek letters completely in K-14, even if > you exclude pi. If exotic notation is to be feared for the simple fact > that it's exotic, therefore may be a hindrance at least for the moment, then > even pi would never be introduced. Nor would x. heck, nort would algebra > alltogether. To be precise, he called the notation seemingly exotic. As I read that, he is considering the student's point of view, and that because the student has not seen these symbols used in mathematical statements previously, the notation may seem exotic to the student. I guess you've decided to focus on this one brief statement of his and I really don't have anything more to say to that particular statement. He has also, in other posts, indicated that he was rushed and may have made statements that were not 100% accurate as to how he feels on the matter. > However, in regards to a first lesson on slope for either 8th or 9th grade > students, here is my own experience and recommendations: <... > That's all quite fine, but avoiding Delta initially when first discussing > the concept of slope, is very different from suggesting it (or any other > Greek letter) be avoided in *all* K-14 math. That's what was suggested. See above. > The letter x can also > be intimidating on day 1 of algebra I too, but we don't go around suggesting > it be avoided in *all* of K-12 math. On day 1 of alg. 1, perhaps, but > certainly for not much longer. They _will_ encounter it, as they will > encounter some Greek letters as well, uless you want to rewrite all the > textbooks that contain them. Actually, it is entirely possible to complete the required 3 years of math required for college admission and not encounter any greek letters other than Pi. I suppose if they actually enroll in college and take the required GE course, which will probably include at least statistics if it does not require some sort of practical calculus course, then they will eventually need to deal with some additional greek letters. But at that stage of the game, I have rarely seen adult students have problems accepting the notation used. It's quite different teaching a 12 year old vs. an adult who has had quite a bit more exposure to algebra. -- Sheila King http://www.thinkspot.net/sheila/ http://www.k12groups.org/ http://www.mathxy.com -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: Re: 8th grade : > Well it seems that I have a way of putting my foot in my mouth - but > since that appears to generate some interesting discussion (rants?) on > this forum, I'll not be hesitant to try again. ;) > The question of just what geometric facts are commonly, or may in very > good programs be, discussed in elementary and middle schools came up > in a couple of the earlier notes to this thread. Since I'm curious > about this and have no idea about it, I ask for someone to make a list > for us so we can consider it seriously. I would think that searching on Math standards at Google.com might produce some such lists. > When (in K-12) is the notion of area introduced, and when are area > formulas developed and for what kinds of regions? I've only taught at grade 9 and above, but I have observed that my own children did study area for at least certain shapes in elementary school. > What early versions or elements of similarity are taught, and at what > grade level? I seem to recall working with my daughter on some worksheets about similar triangles when she was in middle school. -- Sheila King http://www.thinkspot.net/sheila/ http://www.k12groups.org/ http://www.mathxy.com -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: Re: 8th grade >A first lesson on slope should emphasize (imo) the meaning of that >measurement. What does it MEAN for a line to have slope of 2? 1? 1/2? -1/2? >Students should be able to associate this value both with the graph and >with the equation of the line. A small interjection: The first lessons on slope should happen long before these abstractions. Using T-tables and Cartesian graphs to models scenarios such as total earnings from a job that pays $8 an hour, or the charge for ordering silk-screened shirts with a $25 setup fee and a rate of $12 per shirt, is both utilitarian and helpful for the beginner in his quest to grasp the notion of slope. I'd also have at least a discussion, or better a demonstration of how to use a framing square (pitch of a roof), and talking about how water drains from athletic fields that have been excavated with a 1 to 2 percent grade. I might even toss in some mention of monter - Fr. to climb or to mount, (apologies to Karen D. ;-) ) and certainly I'd mention that most of the rest of the classrooms around the world use the word gradient, rather than slope. -- charlie dick The right to be left alone -- the most comprehensive of rights, and the right most valued by a free people. - Justice Louis Brandeis, Olmstead v. U.S. (1928). -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: Re: 8th grade A first lesson on slope should emphasize (imo) the meaning of that >measurement. What does it MEAN for a line to have slope of 2? 1? 1/2? -1/2? >Students should be able to associate this value both with the graph and >with the equation of the line. A small interjection: The first lessons on slope should happen long before these abstractions. > Using T-tables and Cartesian graphs to models scenarios such as total > earnings from a job that pays $8 an hour, or the charge for ordering > silk-screened shirts with a $25 setup fee and a rate of $12 per shirt, is > both utilitarian and helpful for the beginner in his quest to grasp the > notion of slope. I'd also have at least a discussion, or better a > demonstration of how to use a framing square (pitch of a roof), and > talking about how water drains from athletic fields that have been > excavated with a 1 to 2 percent grade. I might even toss in some mention > of monter - Fr. to climb or to mount, (apologies to Karen D. ;-) ) and > certainly I'd mention that most of the rest of the classrooms around the > world use the word gradient, rather than slope. > -- > charlie dick Oh, come now, Charlie. You know that such discussions should best be saved for the Applications lesson that comes at the end of each chapter in the algebra text. ;) -- Sheila King http://www.thinkspot.net/sheila/ http://www.k12groups.org/ http://www.mathxy.com -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: Re: 8th grade > In terms of how students respond to things, I note that you keep > saying should. One can say should all one wants in this regard, > but then there's reality. Sure. the reality is, using seemingly strange things like x, y, f(x) and what not, can be just as if not more confusing to some, than seeing a Greek letter. the simple fact of the matter is, if a student is comfortable with the concepts aside from whatever notation is being used to convey them, then they, well, understand the concepts _aside_ from the notation being used to convey them. Steering clear of introducing a commom notation for a common concept not only in h.s. math but beyond (namely Delta x) for fear of some hindrance to understanding, is more suggestive of, well, a lack of understanding of the basic concept than an implication that the notation is getting in the way. Those that understand the concepts are not the ones who need steer clear of the Greek notation. > All I did was report on what is, on how some > students actually respond, and how I responded to what is. Some (as in > many) students actually do respond differently to using an alphabet > with which they are familiar vs. using one with which they are not. Then that settles it. Remove pi from the texts. Call it something else. Why should this be any different? > Some teachers are more sensitive to what they actually observe in some > students. This is a good thing. As I see it, that's all Ladnor was > doing (and by extension, what some other math teachers do) on using a > foreign language alphabet - being more sensitive to what is, and for > the sake of these students, responding accordingly, a good thing. Brushing it under a rug only makes it worse. One day, like it or not, on some standardized test or some (yes even some _high school_) course and/or text, they are going to be exposed to it. What you are suggesting is that you just blow the issue off until then. Hoipefuly it will be someone else (I guess is the logic) that introduces them to it, and must deal with all the I've never seen that before... > What's your actual argument here? Are you really that confused? My argument is clear. It's silly to suggest all Greek letters be removed from all k-12 (actually, I think the claim was k-14) mathematics. Even if pi is excluded, which BTW there was never any logic revealed why this should be an exception, there are other Greek letters that are used in h.s. mathematics. uppercase Sigma comes to mind, as do a few others (alpha, beta, gamma, theta...) That teachers who are more sensitive > to what they actually observe in some students should not be? I never argued that. Instead of putting words in my mouth, why don't you respond to what I actually am writing instead of what you think I am writing. of course they should be sensitive to such observations, but that does not come close to implying a complete removal of all Greek letters from the literature and chalkboard. you seem to be making the argument that, if one should be sensitive, then that implies one should avoid Greek letters. Yes, it > is a judgement call as to how far to go in this regard. But I don't > understand the ferocity in the response to what he said, which I think > all quite reasonable. Completely avoid Greek letters entirely in K-14? You find that reasonable? Yoiu are so deep into your defense of your comrad, that you don't even see the obvious harm that would come from that. I can see it now.....make sure we adapt only texts that never use any Greek, until then scratch out all occurances of Greek letters in rthe current texts, redo any exams, handouts, and other materials that conmtain them, etc. etc. all for naught since the very next class they take, they probably *will* see a Greek letter and oh no, now whatever fear they had is even worse, since you, the teacher, reinforced their fear from the year before instead of trying to show that there is nothing to be afraid _of_. Suggesting to do away with all Greek in k-14 mathematics, is akin suggesting to do away with all latin in pre-med. Its simply silly to suggest such a thing, as it would be silly for me to contiue after tonight even having this debate with those that are obviously so closed minded to even consider that I may have a point. and we wonder sometimes why we are so far behind. let's just say it's getting clearer to me by the day. Hint-- it's *not* because our students are less intelligent, or somehow less capable of learning the same things kids in other countries do. -- Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: Re: Why integrated math <130d30lq3p2fhkv2gthbifevsa47vuspqa@4ax.com>: > What's so great about integrated math. I haven't been able to figure > this out yet. If someone can please tell me a GOOD reason for it, > i'll listen. I am trying to get it kicked out of my district. I think it is important to distinguish between the notion of an integrated curriculum, vs. the available published curriculums that use integrated math. I think the concept of teaching geometry and algebra in parallel so that the ideas from one branch can be used in the other and thereby a connection and emphasis between the two branches can be established, is an excellent goal. However, the last time I looked (about 5 years ago...) I did not see any integrated math series from the usual textbook publishing companies that I would have felt worthwhile. -- Sheila King http://www.thinkspot.net/sheila/ http://www.k12groups.org/ http://www.mathxy.com -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: Re: Why integrated math > What's so great about integrated math. I haven't been able to figure > this out yet. If someone can please tell me a GOOD reason for it, > i'll listen. I am trying to get it kicked out of my district. > I know that the primary reason that integrated math was instituted in my district is this: - the state-mandated tests for my state are first given in 10th grade and include both algebra and geometry - a student who takes algebra in 9th grade (as is typical) but fails that year generally repeats algebra, and so has to take the state tests without ever having seen geometry; and thus is doomed on that test. - our poorer math students take integrated math in order to be exposed to both algebra and geometry concepts during both 9th and 10th grades, in the hope that they will retain SOME of each and have a better chance to attain the minimum passing requirements. Probably 20-25% of our students are in the integrated math track (oh, that's right, we don't call it tracking). Since we have a 93% pass rate on the first try (and 99% have passed by their fourth try), it actually seems to be achieving its goal pretty well. Prior to our integrated math courses, the pass rate was measureably lower. Just my two cents.... -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: Re: Can this be simplified? sinhc(a+b)+sinhc(a-b) > I have an expression which contain the term: > sinh(a+b)/(a+b) + sinh(a-b)/(a-b) > Although it looks like something that should reduce further, after > playing around with it for a while (expanding sinh(a+b) and sinh(a-b) > etc.) I wasn't able to find any simpler form. So I thought I would post > it here in case someone had some insights. I think it's arguable that what you gave in your title sinhc(a+b) + sinhc(a-b) _is_ itself the simplification. But in case you already had a nice implementation of sinc(z), it might be noted that your expression is equivalent to sinc(i(a+b)) + sinc(i(a-b)). David ==== Subject: Re: Can this be simplified? sinhc(a+b)+sinhc(a-b) Thanks to everyone for the responses. I think perhaps the originial expression is about a simple as it can get, but I appreciate the suggestions anyway. Thanks again. -Pat > I have an expression which contain the term: sinh(a+b)/(a+b) + sinh(a-b)/(a-b) Although it looks like something that should reduce further, after > playing around with it for a while (expanding sinh(a+b) and sinh(a-b) > etc.) I wasn't able to find any simpler form. So I thought I would post > it here in case someone had some insights. > I think it's arguable that what you gave in your title > sinhc(a+b) + sinhc(a-b) > _is_ itself the simplification. But in case you already had a nice > implementation of sinc(z), it might be noted that your expression is > equivalent to > sinc(i(a+b)) + sinc(i(a-b)). > David ==== Subject: Re: sinc(x+y) relations? Originator: kblomste@cc.hut.fi (Kasimir Blomstedt) >Thanks! - More food for thought. >BTW, what is the title of the text by Abramowitz & Stegun? >Pat Its the classical 'Handbook of Mathematical Functions', edited by Milton Abramowitz and Irene A. Stegun. regards, -Kasimir Blomstedt, kblomste@vipunen.hut.fi ==== Subject: Re: about fortran >> please i will like to know how fortran files can be printed and also >> give me an examp Well. There really is no such thing as fortran files. There are files which are somehow stored on a computer ( often on a hard drive ). These files have their info stored in some sort of format which can be translated and then sent to a printer for hardcopy output. The problem is... you have to know something about the computer/operating system you are on in order to have a file printed. You may also have to know something about how the file was created. This problem ( though... I'm not attempting to indicate difficulty here ) is that this holds true for whatever language you are using. In other words, it's not just Fortran specific. However, you might want to look up Fortran's WRITE statement to learn how you can code Fortran to write or print out various types of data. Last point: If you already have a file ( that may have been created by a Fortran program ) and all you really need to do is send the file to a printer, then, your problem is not really Fortran related. You merely need to know how to use the comp. system you are on to print out an existing file ( assuming it is in an understandable format ). Dan :-) ==== Subject: Re: about fortran Dan: >> please i will like to know how fortran files can be printed and also >> give me an examp > Well. There really is no such thing as fortran files. There are files which > are somehow stored on a computer ( often on a hard drive ). These files have > their info stored in some sort of format which can be translated and then sent > to a printer for hardcopy output. Hmmmm... I don't exactly understand the original poster's question, but in case just perhaps... here's a thought. It may be that by fortran files the original poster is referring to files [Say for example files he has found on a PC's hard drive] that simply have the file extension .for. For example he may see files in his directory or folders with names like foo.for, or main.for, etc... and just can't get them to open or print. If this is what the original poster means by a fortran file then it might just be that all he really needs is some kind of general or special text editor program [Notepad, Word, VI, EMACS, etc...] which he can set up to operate on, or import, files with the extension .for. Or perhaps he could acquire an integrated development environment [IDE] like MS Visual Studio, etc... directly on his computer monitor and then use the editor's or IDE's print facilities to print the file. If that's what the original poster was asking, perhaps the informtion above helps, if not then.... I dunno! -- Peter Consultant - Signal Processing and Analog Electronics Indialantic By-the-Sea, FL ==== Subject: Modes of vibration. I would like to find freeware to demonstrate/calculate vibrational modes in plates, cylinders spheres etc. What is easy to use and free Spam forces me to ignore emails to my demon address. -- ddwyer ==== Subject: Re: Simple question regarding frequency detection Hi Maurice, Thanks for the code for Goertzel algorithm. It's amazing !!!! But I could not make out why this algo should work .. if you have time can you please give me a brief explanation as to how this thing works ? Atri. > I am writing an application to detect a particular frequency(viz. 4.5 > Khz) in an input audio signal. I have written the code to capture the > sound using a microphone; but I have to properly design a digital filter > which will return TRUE as soon as it detects sound of this frequency in > the input signal. Also my project demands that I have to detect the > signal by looking at a very small number of samples e.g. 44. So I will > apply the digital filter on a window of 44 samples of the input signal > repeatedly till I get a high response indicating that I have got the > reqd. frequency. I know DFT/FFT is an option but are there any better algorithms I can > use for my project. Please suggest the best algorithm that will do my > work. I am writing the code in C++ so if anyone can point me to existing > code on the net that will be really helpful. > Atri. > Here is Matlab code for the Goertzel algm if you just need a > TRUE/FLASE indication. Set a threshold, and if y is greater than the > threshold, then the frequency is detected. > x = input vector > f = frequency desired > N = number of samples to test over > Fs = sample frequency > function y = goert(x,f,N,Fs) > k = fix(0.5 + N*f/Fs); > w = (2*pi/N)*k; > coeff = 2 * cos(w); > Q1 = 0; > Q2 = 0; > for j = 1:N > Q0 = coeff * Q1 - Q2 + x(j); > Q2 = Q1; > Q1 = Q0; > end > y = sqrt(Q1^2 + Q2^2 - Q1 * Q2 * coeff); > Here is code to test the alghm. Plot F aganist y to see the detector > output as a function of frequency. > fdet is the frequency desired > N = number of samples to test over > Fs = sample frequency > function [F,y] = testgoert(fdet,N,Fs) > t = 0:1/Fs:((1/Fs)*N - (1/Fs)); > k = 1; > for f = fix(fdet/2:(fdet/2)/15:fdet*2) > x = sin(2*pi*f*t); > y(k) = goert(x,fdet,N,Fs); > F(k) = f; > k = k + 1; > end > y = y(:); > F = F(:); > Maurice Givens ==== Subject: Re: Simple question regarding frequency detection To detect is to decide whether what you have is the desired signal, rather than the other stuff - noise processes - you would expect to see. The decision will depend on any consequences of wrong decisions of either type, and on any prior knowledge of liklihood. It will also depend importantly on the null hypothesis - what patterns you expect in the absence of signal. Testing for a known frequency sine wave in stationary white noise is prety simple - just correlate to estimate the amplitude and use the known noise level. You can do a Bays decision using the gaussian model or use some stats cook book confidence rule. If the noise is more variable you could still model it as gaussian in a local time-frequency region. You could correlate as before to get the signal power and filter the residue signal in a time-frequency window to give the local noise power - the distortion of the pure signal you expect. There are lots of approaches - I find it best to stick to a simple bays rule and be honest and careful about the implicit assumptions of the statistical model. The problem depends on the noise as well as the signal. A tone in speech, a tone in a little or a lot of white noise, a tone in music, one specific tone amother other tones, a tone with a narrow range of possible frequencies,... they all demand different tests. PS Shouldn't this be in comp.dsp? ==== Subject: Re: Simple question regarding frequency detection > y = y(:); > F = F(:); Maurice. What do the above two lines do? Bob -- Things should be described as simply as possible, but no simpler. A. Einstein ==== Subject: Re: How to approach Dif eq problem with Mathcad. > I have a hydraulic system I want to model. I have it running in an excel > spread sheet now but it is very messy and very slow. I wish to convert > the model to Mathcad but I need to solve a system of linear and non-linear > differential equations AND have limits. For instance the pressures can go > below 0 and the position can't go beyond the end of the cylinders. I > have written this in C++ using Runge Kutta but I get bogged down in the > graphics as I am not a windows programmer. I could roll my own own Runge Kutta algorithm with limits but this would > not be as easy a doing it in C and buying a graphic library. Any hints as to the best tools and approach? Assumptions: 1. You have a clear understanding of the physical system and you can express it as one or more differential equations. 2. The differential equations are either amenable to analytical solution or can be handled numerically. 3. You need graphics to show a physical model, or the results of the computation, or both. 4. You have some programming exerience. So write it in Java. Java has the required graphic abilities, is cross-platform, and is relatively easy to learn (its syntax is similar to C and C++, but its libraries are much more comprehensive). There are also many texts in bookstores and tutorial pages on the Web. Creating an animation in Java is relatively easy, and animations are included in many Java tutorials and textbooks. ... doing it in C and buying a graphic library ... Java is free, and so are its libraries. Even entire Java development environments are free (e.g. NetBeans, free for downloading at http://www.netbeans.org/downloads/ide). Good luck! -- Paul Lutus http://www.arachnoid.com ==== Subject: Maple files Dear newgroup: I have a lot of files of a decade ago or more regarding my research. Most of them are saved on file.m on Maple2. I would appreciate if someone tell me how could I find out about the list of contents of the saved files written on files.m (i.e. access them). I still have my Maple 2 available somewhere on my computer, but I do not know the contents of my file.m. Is there a way to transfer them to Maple7? with my Maple7. Is it sufficient to transfer to Latex and have the requirements of the most of the Journals? other exports of the Maple? Shall we transfer the files to files.doc or others? Thanks Sincerely Dr.Mehran Basti ==== Subject: Re: Journals and my papers Dear newgroup: I have noted the recent remarks. I have full confidence in the new science (since the last two decades) and the behavior of the editors with its all aspects of power struggle within the academia in broad sense, will not diminish the new science. The only message they give me is that they are struggling to justify their highly abstract works, which has mainly lost its values. I have always my choice of writing my lecture notes and disseminate it myself. So, if editors behave, they can have this new science for the mathematicians of the world, otherwise it just take longer to reach into that stage. I am a discoverer of the new universe in mathematics, they like it or not, it will not change its nature. This is the mathematics for the centuries, I am sure about that, and I do not need lectures of others. So hopefully they will allow science develop through its natural course. Thanks Sincerely Dr.Mehran Basti ==== Subject: Re: Journals and my papers - Reality's A Bitch, Isn't It? Looks like you're getting a dose of cold reality, Basti, the rejections just keep rolling in... I feel so sorry for your students under your 'learned' tutelage. Do you tell them you're the discoverer of a new universe in mathematics with every lecture? If I heard that nonsense from a professor I'd tape record it, take it to the dean, and get his delusion filled head fired pronto. Caesar Garcia > Dear newgroup: I have noted the recent remarks. I have full confidence in the new > science (since the last two decades) and the behavior of the editors > with its all aspects of power struggle within the academia in broad > sense, will not diminish the new science. The only message they give me is that they are struggling to justify > their highly abstract works, which has mainly lost its values. I have always my choice of writing my lecture notes and disseminate it > myself. So, if editors behave, they can have this new science for the > mathematicians of the world, otherwise it just take longer to reach > into that stage. I am a discoverer of the new universe in mathematics, they like it or > not, it will not change its nature. This is the mathematics for the centuries, I am sure about that, and I > do not need lectures of others. So hopefully they will allow science develop through its natural > course. Thanks Sincerely Dr.Mehran Basti ==== Subject: Re: Journals and my papers Dear newgroup: The paper On Associated Legendre was initially posted here. http://mathforum.org/epigone/sci.math.symbolic/kulbresmai/ BA06F975.588%25Bas ti@worldnet.att.net In the paper I have fully explained the theory behind it relative to two other of my papers on New methods of Riccati differential equations. All the future classical equations in the textbooks can be transferred accordingly. This has advantages that current software will not permit. I had shown one of my examples in the paper such as The Riccat differential equation: Maple code: diff(x(t),t)+(x(t))^2=(k*t^2+(6-2*k)*t+k)/(t^2*(-1+t)^2); k is any constant. Maple solution has complex integrals and mine does not have, no integration, logarithem, trigonometric and exponential. This is the difference. scientific computing (look at its editorial policy) and over 40 days they were searching for an appropriate editor, they could not find it! I am sure they are possibly no true lovers of science; I do not know why they are there? Sincerely Dr.Mehran Basti ==== Subject: Re: Journals and my papers Dear newgroup: looks like the actual posting did not go through Google). Particularly the paper on associated Legendre was matching all the descriptions of the Journal. will forcefully influence the algebra and analysis of the 21st century. The nature of the papers is very computational, elementary and not at all abstract. Looks like to me that the current leaders of Mathematics particularly sciences and about 23 years ago this was one of my concerns in the status of mathematics in the world, i.e. much abstract results. Sincerely Dr.Mehran Basti ==== Subject: Re: Journals and my papers I asked to review your material, but you have not let me do so. In numerous prior postings you have made errors which I have detected and corrected. You made claims about thin tubes of solutions of DEs outside the range of the General Solution, and those proved to be in error as well. Any editor who has seen any such refutation of your work and claims would indeed be entitled to be skeptical of your papers, and require a well-reasoned, detailed, and CORRECT derivation and verification. The mere claim that, say, MAPLE, can't simplify an expression to 0 directly, is not sufficient; I worked much harder to establish that 2 distinct forms were the same. When repeated editors find that your papers are not suitable, despite the descriptions matching the journal, you should consider the quality of the material presented. Apply the methods I used to your work to make sure it is valid. Or let me review a paper to see if you are on track at all. If I find the same errors repeated in the papers as were present in the newsgroup postings, you won't be getting much published. > Dear newgroup: > looks like the actual posting did not go through Google). > Particularly the paper on associated Legendre was matching all the > descriptions of the Journal. > will forcefully influence the algebra and analysis of the 21st > century. > The nature of the papers is very computational, elementary and not at > all abstract. > Looks like to me that the current leaders of Mathematics particularly > sciences and about 23 years ago this was one of my concerns in the > status of mathematics in the world, i.e. much abstract results. > Sincerely > Dr.Mehran Basti ==== Subject: Re: Journals and my papers by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i1LLaNx23836; Dear newgroup: I have already answered several times the concerns of Mr. Leo Harten. Facts are there, he can publish what he believes. Similarly for Mr.David Wilkinson. Sincerely Dr.Mehran Basti ==== Subject: Re: Journals and my papers Dr Basti Have you thought to read between the lines? The Editor of a Journal may not want to get into potentially protracted arguments with authors they reject who may, like yourself, think their papers are the best thing since sliced bread. Not suitable for their publication may be a euphemism for almost any collection of defects they see in the paper that they are too busy to discuss. Diverting you to other Journals softens the blow, leaves you with hope and turns your attention elsewhere. You are doing the right thing in seeking publication in peer-reviewed Journals but repeated rejection, for whatever stated reason has its own message. If you look back on the reactions of contributors to this NG they have been universally opposed to your claims. Why would you think reviewers would think differently? > Dear newgroup: > looks like the actual posting did not go through Google). > Particularly the paper on associated Legendre was matching all the > descriptions of the Journal. > will forcefully influence the algebra and analysis of the 21st > century. > The nature of the papers is very computational, elementary and not at > all abstract. > Looks like to me that the current leaders of Mathematics particularly > sciences and about 23 years ago this was one of my concerns in the > status of mathematics in the world, i.e. much abstract results. > Sincerely > Dr.Mehran Basti ==== Subject: Re: Geometry later in education The comments so far imply that mostly Geometry as seen in high school & community colleges is important mostly for education; that people who will teach will have some or a bit of emphasis on this. Most maths major students will not have this kind of emphasis in their selection of courses. It was important in the development of Mathematics, but not so important in applied work; not so important in university work, with the exception of people who expect to teach in high schools and community colleges. At community colleges, this Euclidean Geometry is often viewed as remedial. The nonremedial stuff starts at the first semester of Calculsu+Analytic Geometry. G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: The Schur Multiplier I have only just begun the Group Cohomology course, and my only background is a Group Theory course so be gentle. The Schur multiplier (M(G)) is defined as M(G)=A intersection X` , where X->G is a projective central extension with kernel A (X and G are groups, X->G is an epimorphism, and its kernel is a subgroup of Z(X), such that for every other Y->H with the aforementioned properties, and for every homomorphism G->H there exists a homomorphism X->Y such that the square is commutative). A very basic property of M(G) is that it is well-defined. Meaning it doesn`t depend on the Y->H and G->H picked. I have to mention that X->G is a projective central extension if and only if X and G are groups, X->G is an epimorphism, and its kernel is a subgroup of Z(X), such that for every other Y->G with the aforementioned properties there exists a homomorphism X->Y such that the triangle is commutative. Somehow, using this property, they prove that M(G) is well-defined. I`m afraid I can`t seem to prove it on my own... Can you help me? Thanks ahead, HH. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: Re: The Schur Multiplier Don't know a thing about the subject, myself, but I thought I'd point out that you might get more replies in alt.math.undergrad Of course, I expect there's probably two or three people in this group who know what you're talking about as well :-) > I have only just begun the Group Cohomology course, and my only background > is a Group Theory course so be gentle. The Schur multiplier (M(G)) is defined as M(G)=A intersection X` , where > X->G is a projective central extension with kernel A (X and G are groups, > X->G is an epimorphism, and its kernel is a subgroup of Z(X), such that > for every other Y->H with the aforementioned properties, and for every > homomorphism G->H there exists a homomorphism X->Y such that the square is > commutative). > A very basic property of M(G) is that it is well-defined. Meaning it > doesn`t depend on the Y->H and G->H picked. > I have to mention that X->G is a projective central extension if and only > if X and G are groups, X->G is an epimorphism, and its kernel is a > subgroup of Z(X), such that for every other Y->G with the aforementioned > properties there exists a homomorphism X->Y such that the triangle is > commutative. > Somehow, using this property, they prove that M(G) is well-defined. I`m > afraid I can`t seem to prove it on my own... Can you help me? Thanks ahead, > HH. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html ==== Subject: Sequence For arbitary real # c, I know there exists sequence (x_n) which consists of rational # and converges to c & there exists sequence (y_n) which consists of irrational # and converges to c. Then, For arbitary real # c, Can we say there is sequence (z_n) WHICH consists of rational # and irrational # AND converges to c ? And, When we can calculate lim f(x_n) = f (lim (x_n)) ? If Someone can help me, please post reply... Thank you. ==== Subject: Re: Sequence > I know there exists sequence (x_n) which consists of rational # and > converges to c > & there exists sequence (y_n) which consists of irrational # and > converges to c. > For arbitary real # c, > Can we say there is sequence (z_n) WHICH consists of rational # and > irrational # AND converges to c ? x1,y1,x2,y2,x3,y3,... for one example > When we can calculate lim f(x_n) = f (lim (x_n)) ? What do you mean? When can we have lim f(xj) = f(lim xj) ? When f is continuous, that's when. ==== Subject: Re: Banach spaces > If X is a Banach space and Y a closed subspace of X, then prove that > the quotient space X/Y is a Banach space. What i need is not the usual proof that can be found in almost every > functional analysis handbook, but a proof based exclusevely on the > following criterion: X is a Banach space if and only if SUM_{n=1}^{infinity}||x_{n}|| > converges, implies that SUM_{n=1}^{infinity} x_{n} converges too, > where || || is the norm on X. Sketch: Suppose x_n + Y is Cauchy in X/Y. It suffices to show that a subsequence of this converges in X/Y. WLOG, we can assume that ||[x_(n+1) - x_n] + Y|| < 1/2^n (because this is true of some subsequence). Choose y_n in Y such that ||[x_(n+1) - x_n] + y_n|| < 1/2^n. Because X is a Banach space, x_1 + ([x_2 - x_1] + y_1) + .... converges in X to some z. Perhaps this z can be of some help ... ==== Subject: Re: Algebra question If N is a normal subgroup of a group G, > Then Can we say G/N is a subgroup of G ? No. For G/N to be a subgroup, the members of G/N would have to be members of G, but they are not. By the common view, as you give below, the members of G/N are subsets of G, rather than members. I read definition of Quotient group from book, > When N is a normal subgroup of a group G, > The quotient group G/N is defined as G/N={gN | g in G}.... etc ==== Subject: Re: application of definite intregral > The problem: > Find the volume of the solid rotated around the y-axis. The solid is a > donut with the center of the donut at 0,0. The center of one side of > the donut is at 4,0 (x=4, y=o) with a radius of 1 (center of other > side at -4,0). It will be bound by x=3, and x=5. Does this make sense? > Can you picture the solid? Thanks - any help with setting up the > formula would be much appreciated! > Look up the second theorem of Pappus, re volumes of revolution. ==== Subject: calculus of variation How do I find out if an extremum in a problem of calculus of variations is a minimum or a maximum? I previuos used a kind of non-rigorous method based on pertubating the functional by a test function and then split the new pertubated functional into three parts; P(y+w)=P(y)+first variation+P(w). Because of the vanishing of the 1st variation the difference P(y+w)-P(y)=P(w) decides if its an min/max. Is this a formally correct solution? ==== Subject: General algorithm for vector cross-product Hey all, Alas, there doesn't seem to be a good newsgroup for mathematical algorithms, so I'm posting here. I am using the cross-product to find a normal that us perpendicular to two vectors. All of the examples and code snippets that I have ween deal with the 3D case. Correct me if I am wrong, but we can find the cross-product of other dimensions (either lower or higher), can we not? To handle higher dimensions, we could recursively find the determinent of the vectors, but if we have n-dimensional vectors, do we need n-1 vectors to fill the n x n matrix? Also, how would we lower dimensions? I imagine that the cross of one-dimensional vectors (i.e. numbers) is just their arithmetic product. What about R^2? So is there some general algorithm for handling all cases? Dave ==== Subject: Re: General algorithm for vector cross-product > .... > I am using the cross-product to find a normal that us perpendicular to two > vectors. All of the examples and code snippets that I have ween deal with > the 3D case. Correct me if I am wrong, but we can find the cross-product of > other dimensions (either lower or higher), can we not? To handle higher dimensions, we could recursively find the determinent of > the vectors, but if we have n-dimensional vectors, do we need n-1 vectors to > fill the n x n matrix? If I understand you aright, the answer is yes. Suppose you have the components of n - 1 vectors relative to an orthonormal basis e_1. e_2, ... e_n of R_n. You can get a vector perpendicular to all of them by calculating the formal determinant |row of components of the 1st vector| |row of components of the 2nd vector| | ......... | |row of components of the (n-1)th vector| | e_1 e_2 e_n |. (It's not an ordinary determinant because the entries in the last row aren't scalars, but you probably know what I mean.) This gives a _binary_ operation (combining just two vectors) when n - 1 = 2, i.e. in space of dimension n = 3 only. > Also, how would we lower dimensions? I imagine that the cross of > one-dimensional vectors (i.e. numbers) is just their arithmetic product. > What about R^2? .... I don't follow that. But the above determinant with n = 2 does give you a vector perpendicular to the one vector you start with in R_2. Ken Pledger. ==== Subject: Re: General algorithm for vector cross-product Adjunct Assistant Professor at the University of Montana. >Hey all, >Alas, there doesn't seem to be a good newsgroup for mathematical algorithms, >so I'm posting here. >I am using the cross-product to find a normal that us perpendicular to two >vectors. All of the examples and code snippets that I have ween deal with >the 3D case. Correct me if I am wrong, but we can find the cross-product of >other dimensions (either lower or higher), can we not? No. How would you define the cross product of vectors in 2 dimensions? What would it mean? While there are many things one could define, they do not, in general, define good analogues to the cross product for dimensions other than 3. The cross product is a creature of 3-space. -- ==== ====================================================== ==== It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) ==== ====================================================== ==== Arturo Magidin magidin@math.berkeley.edu ==== Subject: Re: General algorithm for vector cross-product Hey all, Alas, there doesn't seem to be a good newsgroup for mathematical algorithms, >so I'm posting here. I am using the cross-product to find a normal that us perpendicular to two >vectors. All of the examples and code snippets that I have ween deal with >the 3D case. Correct me if I am wrong, but we can find the cross-product of >other dimensions (either lower or higher), can we not? No. How would you define the cross product of vectors in 2 > dimensions? What would it mean? While there are many things one could define, they do not, in general, > define good analogues to the cross product for dimensions other than > 3. The cross product is a creature of 3-space. Nevertheless, there is a vector product in dimensions 1, 3 and 7 (and no others). -- G.C. ==== Subject: solution by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i29LQdP12513; t1= time for up journey = distance travelled/speed = 200/55 t2 = time for down journey = 200/40 Average speed = total disstance travelled/total time taken=400/(t1+t2) ==== Subject: Re: solution > t1= time for up journey = distance travelled/speed = 200/55 > t2 = time for down journey = 200/40 > Average speed = total disstance travelled/total time taken=400/(t1+t2) nice. What was the question? -- P.A.C. Smith The vast majority of Iraqis want to live in a peaceful, free world. And we will find these people and we will bring them to justice. ==== Subject: ==== Subject: Sequence Original Message: ==== Subject: Sequence For arbitary real # c, I know there exists sequence (x_n) which consists of rational # and converges to c & there exists sequence (y_n) which consists of irrational # and converges to c. Can we say there is sequence (z_n) WHICH consists of rational # and irrational # AND converges to c ? Suggestion: How about z_n=y_n for odd n and z_n=x_n for even n? Then, For arbitary real # c, When we can calculate lim f(x_n) = f (lim (x_n)) ? The above equation holds if f is continuous at lim (x_n) Hope this helps. Rob George