Students will cover the basics of ordinary representation theory. Two approaches are presented: representations as group homomorphisms into matrix groups, and as modules over group algebras. The correspondence between the two will be discussed.
The second part is an introduction to the ordinary character theory of finite groups, intrinsic to representation theory. Students will learn the concepts of R-module and of group representations, the main results pertaining to group representations, and will handle basic applications in the study of finite groups.
They will also learn to perform computations with representations and morphisms in a selection of finite groups