Increasing Accessibilty of Examples in Abstract Algebra Using Computer-based Projects
Abstract:
Abstract Algebra is a proof-oriented course commonly taken by math majors in their junior or senior year. As the name might indicate, this course explores a variety of algebraic structures some of which can be viewed as abstractions of structures already familiar to a student (for example, the integers under addition and multiplication). Other structures are completely unknown and abstract to the typical student. In fact, because of the level of abstraction involved, abstract algebra is often considered to be the most difficult course in the math major.
We propose to work collaboratively to develop computer-based labs for abstract algebra with the goal of making concrete examples more accessible to students. Such examples are often easy to define, yet complicated to analyze without the aid of technology. Programs such as GAP (Groups, Algorithms, and Programming) are designed to handle large algebraic computations -- computations which were impossible to approach a decade ago. In our collaborative efforts, we plan to use both Maple and GAP. We will use Maple for those labs which are visual in nature, and GAP for those which are computational. The labs will be used on both campuses starting in the fall of 1999 at Kenyon and in the spring of 2000 at Denison.