Using the Magma Computer Algebra System in Abstract Algebra Courses

Students meeting their first serious course in abstract algebra commonly experience difficulty understanding many of the basic concepts. This makes it very hard for them to interpret and generate proofs. The first step in reaching an understanding of such concepts is often best achieved by constructing and manipulating instances in particular algebraic structures. Computer algebra systems open up the possibility of students being able to experiment rapidly and conveniently with such concepts in a variety of structures having non-trivial size and complexity. The new Magma computer algebra system has a syntax and semantics based directly on fundamental algebraic notions, and consequently should provide an appropriate learning environment for those branches of mathematics that are heavily algebraic in nature. This paper describes the development of Magma-based exercises and a course methodology that utilizes Magma as a key learning tool in a Pass-level Rings and Fields course given at the University of Sydney.