This is an archived handbook for a previous year. The current undergraduate and postgraduate handbooks can be viewed using the links above.
Undergraduate Handbook 2010-2011 (archived)
Module MATH3191: REPRESENTATION THEORY & MODULES III
Department: Mathematical Sciences
MATH3191: REPRESENTATION THEORY & MODULES III
| Type | Level | Credits | Availability | Module Cap | Location |
|---|---|---|---|---|---|
| Open | 3 | 20 | Not available in 2010/2011 | None. | Durham |
Pre-requisites
- Linear Algebra II (MATH2021), Algebra & Number Theory II (MATH2061).
Corequisites
- None.
Excluded Combinations
- Representation Theory and Modules IV (MATH4101).
Aims
- To develop and illustrate the theory of modules and that of complex characters of finite groups.
Content
- Rings and ideals.
- Modules and submodules.
- Modules over principal ideal domains.
- Similarity of matrices over a field.
- (Finite dimensional) semisimple algebras.
- Representations of Groups over C.
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 and Modules.
- have a systematic and coherent understanding of theoretical mathematics in the field of Representation Theory and Modules.
- have acquired a coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas: Representations of groups.
- Character tables.
- Frobenius reciprocity.
- Modules and submodules including structure of modules over a PID.
- Jordan normal form and rational canonical form.
- Simple and semi-simple rings.
Subject-specific Skills
- In addition students will have specialised mathematical skills in the following areas which can be used with minimal guidance: 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.
- 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 | Attendance Monitored |
|---|---|---|---|---|---|
| Lectures | 40 | 2 per week | 1 Hour | 40 | |
| Preparation and Reading | 160 | ||||
| Total | 200 |
Summative Assessment
| Component | Component Weighting | Element | Length/Duration | Element Weighting | Resit Opportunity |
|---|---|---|---|---|---|
| Examination | 100% | three hour written examination | 100% |
Formative Assessment
Four written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.
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.