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Re: Mathematica and Education

• To: mathgroup at smc.vnet.net
• Subject: [mg65002] Re: Mathematica and Education
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Sat, 11 Mar 2006 05:15:38 -0500 (EST)
• Organization: The University of Western Australia
• References: <durk95$lou$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <durk95$lou$1 at smc.vnet.net>,
 "King, Peter R" <peter.king at imperial.ac.uk> wrote:

> I should like to say that as an educator of science students in a
> (predominantly) non-mathematical branch of science (earth sciences) I am
> very concerned about this approach. 

However, is it reasonable to expect your students to gain the level of 
mathematical expertise that you have (unless they are going to become 
professional researchers also)? If not, what should they be taught?

> Sure Mathematica is a wonderful
> tool. As a professional researcher I use it all the time for doing
> tedious calculations to save time, or to check claculations where I may
> have got things wrong and so on and so on. If I didn't think Mathematica
> was useful I wouldn't have it and wouldn't subscribe to this list.
> 
> But it is still a tool. IT can't know what calculations to do, what
> approximations to make and sometimes when there are mathematical choices
> to be made. For example there are times when Mathematica's choice of
> branch cut doesn't correspond to the one I want to make. Not a problem I
> can tell it what I really want. There are times when its choice of
> simplification doesn't suite my purpose. Again not a problem I can tell
> it what to do or simply carry on by hand if that's easier. But how do I
> know when the defaults don't suite my purpose, because I have spent many
> years doing things by hand and gaining that experience to know what I
> want. 

A question remains though: how much of your accumulated expertise _can_ 
be automated. In some fields, e.g., summation, computer algebra can 
automate nearly all operations of interest (see the books 
generatingfunctionology <http://www.math.upenn.edu/~wilf/DownldGF.html>
and "A=B" <http://www.cis.upenn.edu/~wilf/AeqB.html>).

> that I am not convinced that if I had done all my mathematics within
> Mathematica I would have gained the same experience. But I am open to
> discussion on this if anyone wants to put the counter case. However, I
> would need very strong convincing that it is good for students never to
> have to do old fashioned calculations on paper. In the same way I think
> it is important for children to learn multiplication rather than rely on
> a calculator or to learn to write rather than use a word processor.

Agreed. As I've previously posted on this newsgroup, I think that Bruno 
Buchberger has got it right. See 

  http://www.risc.uni-linz.ac.at/people/buchberg/white_box.html 

However, I think that the potential for discovery using computer 
mathematics is underestimated -- and is only taught in very few 
University courses.

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
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