I am happy to see that others besides myself have tried to use GAP as
a pedagogical aid in teaching abstract algebra. I am currently teaching
an undergraduate course, using Gallian's book, which I find to be an
excellent text. My students are primarily computer programming majors,
who take abstract algebra because they have to. Thus, one would think
that my class is an ideal laboratory for introducing GAP to students.
However, I can only report limited success. Perhaps some of you in the
forum can give me some suggestions.
I am reluctant to make assignments involving GAP, because I am fairly
new to it myself. I would not know how to evaluate the results. Hence,
the projects I suggest in class are "extra credit". I find the students'
intellectual curiousity is insufficient to cause them to play with GAP
on their own. A manual should include a section telling us mathematicians
how to evaluate computer homework.
I think the GAP manual is pretty intimidating to undergraduates. My students
are struggling with concepts like "isomorphism" and "coset". Even at this
level, they could benefit from some of GAP's capabilities, if they just
ignore all the stuff about character tables, representation theory, etc.
There is a much more user-friendly and simple program called "An Introduction
to Groups / A Computer Illustrated Text" (comes with a disc) by D. Asche,
available from IOP Publihsing for about $40. It does calculations in S_4,
mainly. Even with this, you have to wait until Chapter 5 (in Gallian's text)
before the students can use it. In my class, this is more than halfway through
the first semester. I might consider doing Chapter 5 sooner just so I can
use this software. Still, it seems that programmers ought to be more
interested in GAP. There is a saying, "You can lead a student to a computer,
but you can't make him think." Can we? At the undergraduate level? And with
non-math majors? After I tackle this, I will work on making them like it!
I'd appreciate any suggestions. Thanks.
University of Wisconsin-Stout