This is an archived handbook for a previous year. The current undergraduate and postgraduate handbooks can be viewed using the links above.
Undergraduate Handbook 2025-2026 (archived)
Module MATH4241: REPRESENTATION THEORY IV
Department: Mathematical Sciences
MATH4241: REPRESENTATION THEORY IV
| Type | Level | Credits | Availability | Module Cap | Location |
|---|---|---|---|---|---|
| Open | 4 | 20 | Available in 2025/2026 | Durham |
Pre-requisites
- Mathematics modules to the value of 100 credits in Years 2 and 3, with at least 40 credits at Level 3 and including Algebra II (MATH2581).
Corequisites
- None.
Excluded Combinations
- None.
Aims
- To develop and illustrate representation theory for finite groups and Lie groups.
Content
- Representations of finite groups.
- Character theory.
- Induced representations.
- Lie groups and Lie algebras and their representations.
- Representations of SL(2,C), SU(2), SO(3).
Learning Outcomes
Subject-specific Knowledge
- By the end of the module students will: be able to solve novel and/or complex problems in Representation Theory.
- have a systematic and coherent understanding of theoretical mathematics in the field of Representation Theory.
- have acquired a coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas:
- Representations of finite groups.
- Character tables.
- Induced representations, Frobenius reciprocity.
- Representations of abelian groups.
- Lie groups and algebras, exponential map.
- Examples of representations of Lie groups and algebras.
Subject-specific Skills
- In addition students will have highly specialised and advanced mathematical skills in the following areas: Abstract Reasoning.
Key Skills
Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module
- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
- Assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
- The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.
Teaching Methods and Learning Hours
| Activity | Number | Frequency | Duration | Total Hours | Attendance Monitored |
|---|---|---|---|---|---|
| Lectures | 42 | 2 in Michaelmas and Epiphany; 2 in Easter. | 1 Hour | 42 | |
| Problems Classes | 8 | Fortnightly in Michaelmas and Epiphany. | 1 Hour | 8 | |
| Preparation and Reading | 150 | ||||
| Total | 200 | ||||
Summative Assessment
| Component | Component Weighting | Element | Length/Duration | Element Weighting | Resit Opportunity |
|---|---|---|---|---|---|
| Examination | 100% | three-hour examination | 100% |
Formative Assessment
Eight assignments to be submitted.
Students who do not attend monitored activities shown under Teaching Methods
and Learning Hours, or who fail to complete the summative or formative
assessment(s) specified above, may be subject to the Academic Progress
procedures defined in the University's General Regulation V, and may be
required to leave the University.