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MathGroup Archive 1999

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Re: Re: Mathematica can't win against Tiger Woods

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19833] Re: [mg19765] Re: [mg19677] Mathematica can't win against Tiger Woods
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Sun, 19 Sep 1999 01:20:21 -0400
  • Organization: University of Western Australia
  • References: <7rshoi$3hi@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Leszek:

> Think about the education which is precisely about solving again and
> again old problems. How you are going to justify the usefulness of
> Mathematica in education, if it can't easily replicate known results?

I understand what you are saying -- but to me you've identified one
of the major problems with "traditional" education!  If education only
involves solving again and again old problems -- which, by construction,
usually have "nice" closed-form solutions or can be solved by tricks or
heuristic methods -- then students come away thinking that all problems
are of this type.

The original example that started this thread was to solve for the motion
of a particle with air resistance. Because no closed-form solution was
expected for the full problem (but there is one!) the problem was "simplified"
by linearizing the air-friction -- in an attempt to develop more insight.
It is this "simplification" that actually muddies the water!

As another example, instead of getting students to solve the Schrodinger
equation for hydrogen using the "classical" approach (and I admit I do get my
students to work through this problem using Mathematica) get them to
compute the ground state energy for helium using a variational method.
This is described in all the classical text books -- but is never set as a
problem because it is thought to be too (computationally) demanding
for undergraduates.  But is actually rather easy to do using Mathematica.

And, to me, this is an example of the correct application of a tool like
Mathematica in education (and research).

Cheers,
    Paul

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA  6907                     mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________




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