MATH5735 is an honours and postgraduate coursework mathematics course. It is a core course for all pure mathematics honours students.

Units of credit: 6

Prerequisites:  MATH3711 or MATH5706.  Note, a good grounding in the basic theories of groups and rings is recommended.

Cycle of offering: Term 1 2023

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

More information: The course handout (PDF) contains information about course objectives, assessment, course materials and the syllabus. This will be made avaiable closer to the commencent of tem being offered.

Important additional information as of 2023

UNSW Plagiarism Policy

The University requires all students to be aware of its policy on plagiarism.

For courses convened by the School of Mathematics and Statistics no assistance using generative AI software is allowed unless specifically referred to in the individual assessment tasks.

If its use is detected in the no assistance case, it will be regarded as serious academic misconduct and subject to the standard penalties, which may include 00FL, suspension and exclusion.

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.