The PascGalois Project is developing materials that use computing technology to enhance the teaching of abstract algebra which has traditionally been one of the most difficult and least visual subjects in the undergraduate mathematics curriculum. These materials provide an interesting class of objects and computer generated representations that allow students to "see" numerous algebraic concepts. This project has its origin in a simple exercise with Pascal's triangle. The interest in this construction lies in the fact that Pascal's triangle mod n is the group multiplication for the cyclic group Z . This construction is being generalized using other finite groups. Like Pascal's triangle mod n, PascGalois triangles can have self-similar properties. Many of these properties can be described using subgroups, quotients, and automorphisms of the group G. The project is developing software to create these images and higher dimensional generalizations (e.g. automata, similar to Conway's Game of Life) on demand so that students can investigate these patterns and their relationships to group structure.
The primary objectives of the project are: to develop laboratory exercises that provide a visual component for the junior/senior level Abstract Algebra courses; to develop students' visual and intuitive understanding of difficult concepts; to model effective use of technology for prospective mathematics teachers and thus better prepare them to implement the National Council of Teachers of Mathematics standards; to stimulate interest in abstract algebra and encourage graduate study in mathematics, and to increase participation in undergraduate research in mathematics by providing a source of interesting and accessible research projects.
