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Re: if using Mathematica to solve an algebraic problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109031] Re: if using Mathematica to solve an algebraic problem
  • From: "David Park" <djmpark at comcast.net>
  • Date: Sun, 11 Apr 2010 04:30:42 -0400 (EDT)

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?


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