2008/09 Undergraduate Module Catalogue

MATH3071 Groups and Symmetry

15 creditsClass Size: 100

Module manager: Dr A Parker
Email: parker@maths.leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

Pre-requisites

MATH1022

Introductory Group Theory

This module is approved as an Elective

Module summary

Informal description: The theory of groups is the mathematical theory of symmetry - not only of geometric figures but also symmetries of sets - that is permutations. The ultimate aim of the theory is to describe (the structure) of all groups. Applications of group theory range throughout mathematics.

Objectives

To obtain some of the more important subgroup and structure theorems in the theory of groups.

On completion of this module, students should be able to:
a) calculate the full symmetry groups of simple geometric figures;
b) represent such a group by permutations groups;
c) Make use of direct products and Sylow's Theorems in determining the structure of special groups. Including simple groups - and, possibly abelian and nilpotent groups;
d) Prove (and be able to use) the homomorphism theorems and the Jordan-Hvlder theorem.

Syllabus

Preliminaries. Symmetries of plane and solid figures; Permutation groups. Groups acting as sets; Factor groups; Homomorphism theorems. Direct products. Sylow's theorems and applications plus topics from : Structure of finitely generated abelian groups; Structure of finite nilpotent groups (via Sylow subgroups). Free groups, generators and relations. Groups acting on graphs. Mathieu groups.

Teaching methods

Delivery type	Number	Length hours	Student hours
Example Class	7	1.00	7.00
Lecture	26	1.00	26.00
Private study hours			117.00
Total Contact hours			33.00
Total hours (100hr per 10 credits)			150.00

Methods of assessment

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	3 hr	100.00
Total percentage (Assessment Exams)		100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 19/07/2010

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