| Unit name | Representation Theory |
|---|---|
| Unit code | MATHM4600 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Professor. Tim Dokchitser |
| Open unit status | Not open |
| Units you must take before you take this one (pre-requisite units) | |
| Units you must take alongside this one (co-requisite units) |
None |
| Units you may not take alongside this one |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
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.
Unit Description
Representation theory studies the linear actions of a group G on a vector space V defined over a field. By fixing a basis for V, such an action yields a map from G to a group of invertible matrices, so we can "represent" the elements of G in a very concrete form. Moreover, this viewpoint allows us to apply techniques and tools from linear algebra to study groups, and this turns out to be a very powerful idea.
In this course, we will develop the basic theory of linear representations of groups, with a particular focus on finite groups and representations defined over the complex numbers. We will also introduce the theory of characters as a tool for studying representations and we will develop techniques for constructing characters and character tables. We will also describe some important applications of the theory, including Burnside's famous theorem on the solubility of finite groups of order p^aq^b.
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.
Learning Objectives
After taking this unit, students should:
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.
The unit will be taught through a combination of
90% Examination 10% Coursework
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.
If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.
If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.
If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATHM4600).
How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours
of study to complete. Your total learning time is made up of contact time, directed learning tasks,
independent learning and assessment activity.
See the University Workload statement relating to this unit for more information.
Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit.
The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.
