Undergraduate Programme and Module Handbook 2018-2019 (archived)
Module MATH4241: REPRESENTATION THEORY IV
Department: Mathematical Sciences
MATH4241:
REPRESENTATION THEORY IV
Type |
Open |
Level |
4 |
Credits |
20 |
Availability |
Not available in 2018/19 |
Module Cap |
|
Location |
Durham
|
Prerequisites
- 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
Excluded Combination of Modules
- Representation Theory III (MATH3371).
Aims
- To develop and illustrate representation theory for finite groups
and Lie groups.
Content
- Representations of finite groups.
- Character theory.
- Modules over group algebra.
- Lie groups and Lie algebras and their
representations.
- Representations of SL(2,C), SU(2), SO(3).
- Reading material on a topic related to: Representations of
the symmetric group, representations over finite fields.
Learning Outcomes
- 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.
- In addition students will have highly specialised and
advanced mathematical skills in the following areas: Abstract
Reasoning.
- Students will have an advanced understanding in one of the
following areas: Representations of the symmetric group,
representations over finite fields.
- Students will have developed independent learning of an
advanced topic.
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.
- Subject material assigned for independent study develops the
ability to acquire knowledge and understanding without dependence on
lectures.
- Assignments for self-study develop problem-solving skills and
enable students to test and develop their knowledge and
understanding.
- Formatively assessed 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 |
|
Lectures |
42 |
2 per week for 20 weeks and 2 in term 3. |
1 Hour |
42 |
|
Problems Classes |
8 |
Four in each of terms 1 and 2 |
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% |
|
Eight written assignments to be assessed and
returned. Other assignments are set for self-study and complete solutions
are made available to students.
■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University