2016/17 Undergraduate Module Catalogue

MATH3071 Groups and Symmetry

15 creditsClass Size: 50

Module manager: Dr Joao Faria Martins
Email: j.fariamartins@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2016/17

Pre-requisite qualifications

MATH2020 or MATH2022 or equivalent

This module is approved as a discovery module

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, chemistry and physics

Objectives

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;
c) make use of direct products and Sylow's Theorems in determining the structure of special groups, including determinine when groups are simple;
d) prove (and be able to use) the homomorphism theorems;
e) find composition series of small groups.

Syllabus

- Preliminaries.
- Symmetries of plane and solid figures; Permutation groups.
- Groups acting on sets; Factor groups; Homomorphism theorems.
- Direct products.
- Sylow's theorems and applications.
- Simple groups and composition series.
- Orbit-Stabiliser theorem.

Teaching methods

Delivery type	Number	Length hours	Student hours
Lecture	33	1.00	33.00
Private study hours			117.00
Total Contact hours			33.00
Total hours (100hr per 10 credits)			150.00

Private study

Studying and revising of course material.
Completing of assignments and assessments.

Opportunities for Formative Feedback

Regular problem solving assignments

Methods of assessment

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 30 mins	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: 20/07/2016

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