This project is enhancing the usability of the free and open computer algebra system GAP for use in undergraduate abstract algebra and number theory courses as well as for undergraduate research projects. In recent years, computer algebra systems have been used in the undergraduate curriculum as both an illustrative and experimental tool. One obstacle to the effective use of such systems, however, is a lack of functionality and documentation aimed at the undergraduate teaching environment, as well as an installation process and user interface that is too complicated for many potential users. This project is providing new functionality and simplifying installation and use. This new material is being tested by a group of interested faculty at their institutions. Results of the project are being made available on the Internet.
Intellectual Merit: The project is developing new methods to perform concrete calculations in algebraic structures in the context of an undergraduate course. It provides a new resource for teachers who want to use a computer algebra system in the undergraduate abstract algebra curriculum or for undergraduate research/investigation projects. These new and enhanced components aid students majoring in mathematics (including mathematical education), computer science and engineering in the understanding of concepts from abstract algebra by providing the means to study examples that would not be feasible with pencil and paper.
Broader Impact: Improvements to installation and user interface benefit any user of the system GAP, including undergraduate and graduate students and the large research community. Analogous to the now established use of computation and calculators in calculus courses, the availability of a system for algebraic calculations with a user-friendly interface enables teachers of abstract algebra courses to show examples that cannot simply be done by hand calculation. As the system is already in use for teaching algebra at many institutions, this enhancement has a substantial group of users and will ultimately enhance the teaching of abstract algebra to a substantial part of the student population who take the course.
