The basic mission of the Computational Algebra Group is the development of computer techniques for solving symbolic problems in mathematics, with particular emphasis on the areas of algebra, number theory and geometry. The activities extend from the design of algorithms through to the construction of computer algebra packages and languages. The group concentrates on what might be called discrete algebraic and combinatorial structures: groups, rings, fields, modules, algebras, designs and geometries. A particular strength of the group is its expertise in computational methods across several major branches of mathematics.

The Computational Algebra Group provides a unique environment in that it brings together mathematicians, computer scientists and software engineers. The development of good algorithms requires the involvement of leading researchers from the relevant areas of mathematics. The efficient implementation and embedding of these algorithms in large integrated software systems requires sophisticated techniques from computer science. The design and implementation of algebraic programming languages requires the involvement of both mathematicians and computer scientists.

The group holds a regular Computational Algebra Seminar, and hosts approximately twenty visitors each year. The Computational Algebra Group also distributes the computer algebra system Magma, which has been cited in approximately 4000 research publications.