MATH5735 Modules and Representation Theory

MATH5735 is a Honours and Postgraduate Coursework Mathematics course. It is a core course for all Pure Mathematics Honours students. See the course overview below.

Units of credit: 6

Prerequisites: A good grounding in the basic theories of groups and rings.

Cycle of offering: Course not offered every year.

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information: This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus. 

The Online Handbook entry contains information about the course. (The timetable is only up-to-date if the course is being offered this year.)

If you are currently enrolled in MATH5735, you can log into UNSW Moodle for this course.

Course Overview

Performing linear algebra over a ring of scalars instead of a field leads to the notion of a module. The theory of modules is surprisingly subtle and has many applications, not only to other parts of mathematics like the linear representation theory of groups, but also to mathematical physics. 

The course starts with a study of the linear representation theory of finite groups - how groups act as linear transformations on vector spaces. In particular, we will find numerical invariants attached to group elements through these linear representations, and then use these invariants to derive group-theoretic information (for example, the existence of normal subgroups). 

Linear representations of groups correspond to modules over the group algebra, so our investigations lead naturally to the study of modules and the Artin-Wedderburn theory of semisimple rings.