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From: wfh58@leah.albany.edu (William F. Hammond)
Newsgroups: sci.math,comp.edu
Subject: Re: Fortran for Math Majors
Keywords: Maple, Rexx, Euclidean rings
Message-ID: <1991Feb16.204512.28591@sarah.albany.edu>
Date: 16 Feb 91 20:45:12 GMT
References: <1991Feb12.151552.17331@pdn.paradyne.com> <1991Feb13.131044.19020@sarah.albany.edu>
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In article <1991Feb13.131044.19020@sarah.albany.edu> hb136@leah.albany.edu
(Herb Brown) writes:
>In article <1991Feb12.151552.17331@pdn.paradyne.com> reggie@paradyne.com
>(George W. Leach) writes:
>> ...                This person intends on majoring in Math and perhaps
>>minoring in CS.  The question pertains to how much is Fortran used in a
>>typical Mathematics Department for undergraduate coursework?   ...
>>
>>      Is any other language used in Math Departments other than Fortran?
>
>At the University at Albany no mathematics course (undergraduate or graduate)
>uses Fortran (or any other cs language).
                            ^^^^^^^^^^^
                       Almost but not quite.

>                                          However, we offer several courses
>ranging from elementary courses for non-science/math majors to junior/senior
>mathematics courses in a specially designed Computer Classroom using MAPLE
>software on Amiga Computers. We are into the second semester of this venture
>and so far our colleagues are quite pleased with the results.
>

The junior level algebra course based on the book "A Concrete Introduction
to Higher Algebra" by Lindsay Childs (Springer Verlag) that I taught last
fall in our computerized classroom used the general purpose interpreted
computer language REXX, implemented on the Amiga as "ARexx".

(One of the nice things about REXX, among general purpose languages, for
mathematicians is its ability to accept a function *definition*, like
(x**2)*exp(x)  at run time as *data* without a programming kludge.)

Symbolic manipulation packages such as "Maple" are more commonly used by
mathematicians than are general purpose programming languages.  In fact,
the better symbolic manipulation packages, "Maple" included, have their
own "scripting" facilities, and in that sense can be regarded as offering
a "language".

Part of the point is that mathematicians, generally, are interested in
mathematical questions, and any interest in computer programming is
ancillary for most.

  The junior level course in algebra that I mentioned above could have
been done with a symbolic manipulation package.  I rejected that approach
because the students would not have been forced deeply enough into an
understanding of the algorithms that underlie the content of the course.
(It's a course about Euclidean rings.)  Too much is built into "Maple";
my philosophy is that the ability to write a script to do something
with polynomials, given with coefficients modulo a prime, shows evidence
of understanding of the subject that would not be shown by the ability
to use canned functions effectively.  For the level beyond this course,
however, I am using "Maple", and for a still higher level beyond that
I would use "Macaulay".

----------------------------------------------------------------------
William F. Hammond                   Dept. of Mathematics & Statistics
518-442-4625                         SUNYA, Albany, NY 12222
hammond@leah.albany.edu              wfh58@albnyvms.bitnet
----------------------------------------------------------------------