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Re: if using Mathematica to solve an algebraic problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109021] Re: if using Mathematica to solve an algebraic problem
  • From: Richard Fateman <fateman at cs.berkeley.edu>
  • Date: Sat, 10 Apr 2010 06:55:34 -0400 (EDT)
  • References: <hpmlcd$9v0$1@smc.vnet.net>

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?
> 
> The point I am trying to get at is areas Mathematica fails or
> shows limitations invariably require understanding of details of
> the problem and computer arithmetic.

Not necessarily. Often when Mathematica fails, the only thing that is
revealed is that Mathematica fails. The reason may only pertains to
Mathematica and is not inherent in the problem or the computer.

> 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?
> 
> I wonder if it is really possible to become highly skilled at
> getting good results from Mathematica without also learning the subject.

It may work for you, since you have a certain level of curiosity about
the subject and about Mathematica.  For students who have no curiosity
about either, they will learn as little as possible. Perhaps in college
you encountered subjects for which you wanted to get a passing grade,
but you did not have any interest in learning. Now imagine that subject
is calculus.

RJF
> 
> 


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