Module code: MAT3032

## Module Overview

This module extends the abstract algebra introduced in Year 2, providing a deeper insight into the structure of groups and introducing some additional algebraic structures.

### Module provider

Mathematics

FISHER David (Maths)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 117

Lecture Hours: 33

Semester 1

## Prerequisites / Co-requisites

MAT2048 Groups and Rings

## Module content

Indicative content includes:

• Further group theory.  Simple groups.

• Finite abelian groups.

• Group actions, conjugacy.

• Burnside’s formula and application to colouring problems.

• The Sylow theorems and their applications

• Further ring theory.   Division rings.  The quaternions.

• Idempotents and ring decompositions.

• Group algebras.

## Assessment pattern

Assessment type Unit of assessment Weighting
Examination EXAMINATION 80
School-timetabled exam/test IN-SEMESTER TEST (50 MINS) 20

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate their ability to

·         construct and interpret mathematical arguments in the context of this module;

·         display subject knowledge by recalling key definitions and results;

·         apply the techniques learnt to both routine and unfamiliar problems.

Thus, the summative assessment for this module consists of:

·         One two-hour examination at the end of Semester 2, worth 80% of the module mark.

·         One or more in-semester tests, together worth 20% of the module mark.

Formative assessment and feedback

Students receive written comments on their marked coursework assignments.  Maple TA may be used in assignments to provide instant grading and immediate feedback.  Verbal feedback is provided in lectures and office hours.

## Module aims

• extend students' knowledge of abstract algebra and their appreciation of the inter-connectedness of the different areas of the subject.
• provide familiarity with some classical theorems in algebraic structure theory.
• establish a basis for further algebraic study, e.g. in Representation Theory or Lie Algebras.

## Learning outcomes

 Attributes Developed 1 Demonstrate an enhanced knowledge of groups and rings. K 2 Understand the concept of a group action and identify some of its applications. KC 3 Analyse the structure of finite groups by methods including the Sylow thoerems. KC 4 Know the definition of an algebra and appreciate its relation to other structures. KC 5 Construct simple proofs similar to those encountered in the module. KCT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• An enhanced awareness of the theory and applications of abstract algebra.

• Experience of the methods used to interpret, understand and solve problems in the topics covered.

The learning and teaching methods include:

• Three 50-minute lectures per week for eleven weeks, some being used as tutorials, problem classes and in-semester tests.

• Online notes supplemented by additional examples in lectures.

• Two unassessed coursework assignments, marked and returned.

• Personal assistance given to individuals and small groups in office hours.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.