Representation theory of finite groups

Core topics covered include: Structure of the group algebra over the complex numbers, Schur's Lemma, orthogonality relations, number of irreducible representations, techniques for computing character tables, operations of multilinear algebra on representations and their characters (tensor, symmetric and exterior products), induced characters, and an illustration of some applications of character theory to group theory. Additional topics may include a selection from: Integrality of characters, Frobenius groups, M-groups, Artin/Brauer theorems on induced characters, Burnside's p^aq^b theorem.