Mathematics 333rt - Topics in Abstract Algebra-Representation Theory

Representation theory is used everywhere, from number theory, combinatorics, and topology, to chemistry, physics, coding theory, and computer graphics. The core question of representation theory is: what are the fundamentally different ways to describe symmetries as groups of matrices acting on an underlying vector space? This course explains each part of that question and key approaches to answering it. Discussions may include irreducible representations, Schur’s Lemma, Maschke’s Theorem, character tables, orthogonality of characters, and representations of specific finite groups. MTH 233 is recommended but not required. Prerequisite: MTH 211.