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MAT-30013 - Module Specification
School of Computing and Mathematics
Faculty of Natural Sciences

For academic year: 2020/21 Last Updated: 25 February 2021

MAT-30013 - Group Theory
Coordinator: Raymond N Turner Room: MAC2.27 Tel: +44 1782 7 33739
Lecture Time: See Timetable...
Level: Level 6
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2020/21

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

MAT-20025: Abstract Algebra

Barred Combinations

None

Description for 2020/21

This module builds on the Group Theory introduced in MAT-20025 to develop some of the mathematics underlying the classification of finite groups. This culminates in a proof of Sylow's First Theorem which offers a partial converse to Lagrange's Theorem proved in MAT-20025. The module also develops some applications of Group Theory, the natural setting for which is that of group actions. Several examples of applying group theoretic ideas to counting combinatorial configurations are presented.

Aims
The aim of this module is to develop some of the mathematics underlying the classification of finite groups and to develop some applications of Group Theory.

Intended Learning Outcomes

demonstrate knowledge of basic concepts such as abelian groups, normal subgroups, quotient groups and group actions: 1,2
derive Burnside¿s Lemma and use it in counting configurations: 1,2
demonstrate knowledge of group homomorphisms and the role of homomorphism as a unifying principle in Group Theory: 2
derive and apply the First Isomorphism Theorem: 2
demonstrate knowledge of conjugates, centralisers, the Class Equation and Sylow¿s theorems: 2
derive and apply Sylow¿s First Theorem: 2

Study hours

Learning/teaching comprises 30 hours video lectures, 5 hours flipped examples classes, and 2 hours final exam.
Independent study comprises 30 hours examples class preparation, 10 hours for completion of assignment, 20 hours preparation for examination, and 53 hours consolidation of lecture material.

School Rules

None

Description of Module Assessment

1: Assignment weighted 20%
Online, take-home assignment
One take-home, written assignments to be completed on-line. The assignment consists of a set of questions with pre-allocated space for written solutions which will be uploaded to the KLE. Students should expect to spend 10 hours on the assessment.

2: Open Book Examination weighted 80%
2 HOUR OPEN BOOK EXAM
The examination paper will consist of no less than five and not more than eight questions all of which are compulsory. The examination will be online and open book.

This document is the definitive current source of information about this module and supersedes any other information.

Last Updated: 25 February 2021