MATM46 Representation Theory, 7.5 credits, is an elective course for a Master of Science degree in mathematics. The course can be taken as an stand-alone course. The course is given at half-study pace during the spring semester. The language of instruction is English.

Course Content
The course gives an introduction to representations of finite groups over the complex numbers and to character theory.

The course treats

Group representations: linear representations, equivalent representations, regular representation, induced and restricted representations, irreducible representations, Maschke’s Theorem, dual representations and tensor product of representations
Character theory: characters of representations, induced characters, irreducible characters, orthogonality relations, integrality, character tables, the Mackey formula, Frobenius reciprocity
Applications to groups: Burnside’s Theorem, Frobenius’ Theorem, Frobenius divisibility

Teaching
The teaching consists of lectures and seminars.

Assessment
The assessment consists of a written examination followed by an oral examination at the end of the course. The oral examination may only be taken by those students who passed the written examination.

Course Literature

Advanced calculus of several variables by C.H. Edwards, Jr; New York : Academic Press, 1973.

Official Course Description

Course Evaluation
Link to course evaluations on the department's website:

Course Evaluations, Mathematics at Faculty of Science