Durham University
Programme and Module Handbook

Undergraduate Programme and Module Handbook 2007-2008 (archived)

Module MATH3191: REPRESENTATION THEORY & MODULES III

Department: Mathematical Sciences

MATH3191: REPRESENTATION THEORY & MODULES III

Type Open Level 3 Credits 20 Availability Available in 2007/08 and alternate years thereafter Module Cap None. Location Durham

Prerequisites

  • Linear Algebra II (MATH2021), Algebra & Number Theory II (MATH2061).

Corequisites

  • None.

Excluded Combination of Modules

  • 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
    Lectures 40 2 per week 1 Hour 40
    Preparation and Reading 160
    Total 200

    Summative Assessment

    Component: Examination Component Weighting: 100%
    Element Length / duration Element Weighting Resit Opportunity
    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.

    ■ 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