The PascGalois Project: Visualization Projects for Abstract Algebra

Michael J. Bardzell
Kathleen M. Shannon
Cynthia J. Woodburn

With support from the National Science Foundation (award #DUE-0087644) we have developed and are testing visualization projects for use in the first course in Abstract Algebra. In this paper we will describe the projects and report on the results of field testing at several institutions in Fall 2002. Abstract algebra has traditionally been one of the most difficult and least visual subjects in the undergraduate mathematics curriculum. Often it is the least popular course in the minds of many mathematics majors by the time they finish their degree. Many attempts are underway to address this issue. We are using a different approach; our PascGalois Project provides an interesting class of objects and computer generated representations that allow students to "see" numerous algebraic concepts including subgroup lattices, quotient groups and automorphisms. These structures, generalized versions of Pascal's Triangle and other cellular automata, have not previously been used to explore abstract algebra.