MTH5143 · Representation theory

Overview

Representation theory combines the notions of symmetry and linearity, both of which are ubiquitous in mathematics. Initially, it utilised and unified ideas from group theory and linear algebra; however, it has progressed far beyond these humble beginnings. Representation theory is now known to have deep connections to other areas of mathematics and profound applications to the sciences and engineering. The unit starts by developing the theory of representations of finite groups over the complex numbers, with an emphasis on characters and symmetric groups. This theory forms the basis for the study of more advanced topics, such as the following examples: applications to abstract group theory; representation-theoretic algorithms; random walks on groups; representations of Lie algebras; Schur-Weyl duality.

Areas of study: Master of Mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Formulate complex problems using appropriate terminology in algebra;
2. Demonstrate a deep understanding of abstract concepts in representation theory;
3. Appreciate the nature of algebraic proofs and be able to use a variety of proof techniques arising in representation theory;
4. Use the knowledge and ideas developed in applications to other areas of mathematics and the sciences.

Workload

• Two 1.5-hour seminars; • One 1-hour applied class and • 8 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.