# Unit information: Representation Theory in 2015/16

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Unit name Representation Theory MATHM4600 20 M/7 Teaching Block 2 (weeks 13 - 24) Professor. Tim Dokchitser Not open MATH 21100 Linear Algebra 2; MATH 33300 Group Theory (may be taken concurrently). None School of Mathematics Faculty of Science

## Description including Unit Aims

Unit aims

To develop the basic theory of linear representations of groups, especially of finite groups over the complex numbers. To develop techniques for constructing characters and character tables. To explore applications of the theory.

General Description of the Unit

After setting up the basics of the general theory of representations of groups, this unit will concentrate on representations of finite groups over the complex numbers. The theoretical properties of the character table of a group will be studied in detail, together with practical methods of calculating the character tables of particular groups, and several applications of the theory will be given.

Relation to Other Units

This is one of three Level 7 units which develop abstract algebra in various directions. The others are Galois Theory and Algebraic Topology.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

## Intended Learning Outcomes

Learning Objectives

After taking this unit, students should:

• know the standard general properties of the character table of a finite group, and have an understanding of why these properties hold.
• be able to apply a variety of methods for constructing characters.
• be able to deduce properties of a group from its character table.

Transferable Skills

The application of abstract ideas to concrete calculations. The ability to tackle problems by making a sensible choice from among a variety of available techniques.

## Teaching Information

Lectures, exercises to be done by the students. (If there is not sufficient demand this unit may be given as a directed reading course, or not at all).

## Assessment Information

100% Examination.

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.