The contents of the lectures will include:
Introduction: symmetry plays a central role in mathematics as well as in nature, art and science. The language of symmetry is group theory. The module will develop and study the axiomatic theory of groups; including such issues as group actions, subgroups, generators, cosets, homomorphisms, conjugacy, commutativity, quotient and product constructions. Examples of groups to be considered are cyclic groups, dihedral groups, symmetric groups and orthogonal groups.
Subgroups: the concept of a subgroup will be introduced and special subgroups such as normal subgroups and the centre of a group, as well as the concept of a generator and the role of Lagrange's theorem, will be presented.
Quotient and product constructions: direct products and quotient groups will be introduced, as well as the role of cosets.
Morphisms: the concepts of isomorphism, homomorphism and automorphism will be introduced and applied to the study of groups.
Groups: examples of groups to be studied are the dihedral groups, reflection groups, cyclic groups, permutation groups and orthogonal groups.