MTH4143 - Representation theory

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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.

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Dr Norm Do

Unit Coordinator(s)

Dr Norm Do

Notes

This unit is offered in alternate years commencing Semester 1, 2022

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5143 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4143. The assignments and exam in this unit will use some common items from the MTH4143 assessment tasks, in combination with several higher level questions and tasks.

Learning outcomes

On successful completion of this unit, you should be able to:

Formulate complex problems using appropriate terminology in algebra;

Demonstrate a deep understanding of abstract concepts in representation theory;

Appreciate the nature of algebraic proofs and be able to use a variety of proof techniques arising in representation theory;

Use the knowledge and ideas developed in applications to other areas of mathematics and the sciences.

Assessment summary

Continuous assessment: 40% (Hurdle)
Examination (3 hours and 10 minutes): 60% (Hurdle)

Hurdle requirement: If you would otherwise have passed the unit but you do not achieve at least 45% of the marks available for both the end-of-semester examination and the continuous assessment you will receive a Hurdle Fail (NH) grade and a mark of 45 on your transcript.

Workload requirements

Workload