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

For academic year: 2024/25 Last Updated: 24 April 2024

MAT-30013 - Group Theory
Coordinator:
Lecture Time: See Timetable...
Level: Level 6
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2024/25

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

MAT-20025: Abstract Algebra

Barred Combinations

None

Description for 2024/25

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: 1,3
derive Burnside¿s Lemma and use it in counting configurations: 1,3
demonstrate knowledge of group homomorphisms and the role of homomorphism as a unifying principle in Group Theory: 2,3
derive and apply the First Isomorphism Theorem: 2,3
demonstrate knowledge of conjugates, centralisers, the Class Equation and Sylow¿s theorems: 3
derive and apply Sylow¿s First Theorem: 3

Study hours

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

School Rules

None

Description of Module Assessment

1: Assignment weighted 15%
Take-home assignment
Written assignment. The assignment consists of a set of questions with pre-allocated space for written solutions. Students should expect to spend 5 hours on the assessment.

2: Coursework weighted 15%
Take-home Coursework
Written coursework. This consists of a set of questions with pre-allocated space for written solutions. Students should expect to spend 5 hours on the assessment.

3: Exam weighted 70%
2 HOUR CLOSED 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 closed book.

Please note that for the 2022/23 Academic Year programmes may be adapted to operate in accordance with a flexible, digital approach. This means that there may be some changes made to how modules are delivered and assessed. The latest information will be provided to you by your School in module handbooks. We endeavour to give you as much notice as possible of any changes and details about the circumstance in which changes are made to programmes can be found in the Student Agreement, available at: https://www.keele.ac.uk/student-terms-and-conditions/

Last Updated: 24 April 2024