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MATH4241: REPRESENTATION THEORY IV

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Type	Open
Level	4
Credits	20
Availability	Available in 2024/2025
Module Cap
Location	Durham
Department	Mathematical Sciences

Prerequisites

Mathematics modules to the value of 100 credits in Years 2and 3, with at least 40 credits at Level 3 and including Algebra II(MATH2581).

Corequisites

None.

Excluded Combinations of Modules

None.

Aims

To develop and illustrate representation theory for finite groupsand Lie groups.

Content

Representations of finite groups.
Character theory.
Induced representations.
Lie groups and Lie algebras and theirrepresentations.
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 solvenovel and/or complex problems in Representation Theory.
have a systematic and coherent understanding of theoreticalmathematics in the field of Representation Theory.
have acquired a coherent body of knowledge of these subjectsdemonstrated 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 andalgebras.

Subject-specific Skills:

In addition students will have highly specialised andadvanced mathematical skills in the following areas: AbstractReasoning.

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 theapplication 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 theapplication 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 unpredictableproblems.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total
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: Examination		Component Weighting: 100%
Element	Length / Duration	Element Weighting	Resit Opportunity
three-hour examination		100

Formative Assessment

Eight assignments to be submitted.

More information

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