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Re: if using Mathematica to solve an algebraic problem
Factoring integers or factoring polynomials? In any case, if you wanted to teach factoring methods why would you use Factor or FactorInteger? You would use more primitive routines that did various steps in the factoring process and students would practice with these. If they did enough of that they might get to know the techniques. Why would you deliberately use a routine that hides all the steps? You are always throwing up instructional methods that are certain not to work and ignoring approaches that could work. If people want to do mathematics with Mathematica it is because they see some advantage in it. The problem is that they don't know Mathematica well enough (because it really does take time and practice to get good at it) and Mathematica doesn't provide all the routines that might be necessary or useful for some particular subject (which means they have to be provided by the professor or the student himself) and it isn't totally tuned up for this kind of study (but it keeps getting closer). David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Richard Fateman [mailto:fateman at cs.berkeley.edu] Bill Rowe wrote: <snip> If one becomes very skilled at using Mathematica to > solve problems correctly wouldn't there have to be some > corresponding gain in understanding of how the same problems > would be solved without Mathematica? Not necessarily. If you use programs like Factor, regardless of how many times you use them, why would you have the slightest idea of how you would factor polynomials without Mathematica? > It seems becoming highly > skilled at getting correct results from Mathematica requires > mastery of these details to a large degree. And it also seems > understanding those details are exactly what is required to > solve the problem without Mathematica. Not necessarily. This newsgroup is filled with messages that look like -- I want to solve problem X; I know how to solve it by hand; how do I get Mathematica to do it?