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Re: if using Mathematica to solve an algebraic problem

An instructive example when one is teaching techniques of integration:

   Integrate[ Exp[-x^2],x ]

Why this is instructive is left as an exercise to the reader.

On 4/9/2010 3:34 AM, Bill Rowe wrote:
> On 4/8/10 at 8:03 AM, dave at (David Bailey) wrote:
>> I also think that if Mathematica had been available to me back then,
>> I would have felt it was a bit like an addictive substance - very
>> interesting in small doses, but also terribly dangerous. There would
>> have always been the possibility of becoming skilled in answering
>> questions through Mathematica, rather than actually learning the
>> subject!
> While I think I understand the concern you express here, I still
> wonder. 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?
> 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. 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.

Murray Eisenberg                     murray at
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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