*Instructor:* Dr. Péter Pál Pálfy

*Text: *I. Martin Isaacs, Character Theory of Finite Groups

*Prerequisite: *A course in abstract algebra including basic group theory,
ring theory and Galois theory, plus linear algebra.

*Course description: * Representation theory studies how groups appear as
groups of linear transformations (or groups of matrices). This course will
be restricted to the classical case, the study of representations of
finite groups over the complex field. The basic tool is the character of a
representation, a complex valued function defined on the group. The
beautiful theory of characters is applied to prove important results in
group theory such as the solvability of groups of order divisible by only
two distinct primes.

*Topics:*
Algebras, modules, and representations

Group representations and characters

Characters and algebraic integers

Products of characters

Induced characters

Characters of normal subgroups

Trivial intersection sets and exceptional characters

Brauer's characterization of characters

Projective representations

Results on linear groups