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Re: decoding inbuilt function

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  • Subject: [mg121054] Re: decoding inbuilt function
  • From: "David Park" <djmpark at>
  • Date: Thu, 25 Aug 2011 07:05:41 -0400 (EDT)
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  • References: <> <4592974.8304.1314168104259.JavaMail.root@m06>

Mathematica is not directly a tool for teaching mathematics, nor so much a
tool for doing mathematics. It more a meta-tool for constructing the tools
you need for doing these things. Almost any field such as pedagogy or
application to specific areas of engineering, mathematics or science will
require that someone construct the needed tools.

WRI provides basic, and powerful, algorithms to do many things and auxiliary
tools such as the notebook interface with sectional grouping and Text cells,
which provides the ability to write literate documents. It is not reasonable
to expect WRI to flesh out all the possible applications. There are just too
many and they wouldn't even be the best people to do it.

Mathematica is poor at teaching basic mathematical ideas. Rather, it has
extensive and maybe "messy" algorithms to do various things such as limits
and integrals. If you want to teach these things you have to bypass the
Mathematica routines and provide routines or rules, probably in the form of
axioms, that can be directly applied to expressions to carry out
calculations and derivations. I have an example of this for limits in one of
the essays in the Presentations application. Somewhere in the Mathematica
Book there is an example of writing rules for evaluating a limited kind of
integral. Again Presentations has a StudentsIntegral section for
manipulating single variable integrals by various basic techniques before
evaluation from a table, or handing them over to Mathematica.

No one knows how to use Mathematica (including me)! It is too new a medium
with such new powerful capabilities. One can't just mechanize old
approaches. There is A LOT of work and development to be done, and not just
by WRI.

How can you get more students to actually do mathematics on their own? To
take off and fly solo? One thing that I feel fairly certain of is that
humans understand actions better than static diagrams or lists of equations.
Just seeing a notebook evaluated step by step (even if it is rather minimal)
is better than looking at a pre-evaluated notebook. And moving sliders or
pushing buttons might illustrate a point but it is a long way from DOING
mathematics. That's why I question the utility of CDF and use of single
Manipulates. It's a diversion from better solutions. (And besides, the
development of CDF seems to be corrupting regular Mathematica in use of
system functions such as saving notebooks.)

Just get regular Mathematica - early - and start learning how to use it.

David Park
djmpark at  

From: Ralph Dratman [mailto:ralph.dratman at] 

If a student comes to your office saying she cannot seem to understand this
"limit" thingy, I wonder if you would wish to say, "Don't feel too bad, Ms
Liddell. No one in our department understands limits much better than you
do! Anyway, not enough to program a computer to do them. Only Wolfram has
the algorithm for that."

This seems unconscionable to me. But then, I didn't realize taking limits
was so difficult. In order to differentiate something, obviously you have to
take a limit. Yet I never heard of anything one couldn't manage to
differentiate. And then having the derivative of a function would surely
help in taking other limits involving that function. What's the big


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