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MAT-20025 - Module Specification
School of Computer Science and Mathematics
Faculty of Natural Sciences

For academic year: 2025/26 Last Updated: 04 December 2025

MAT-20025 - Abstract Algebra
Coordinator: Paul Truman Room: MAC2.16 Tel: +44 1782 7 33246
Lecture Time: See Timetable...
Level: Level 5
Credits: 15
Study Hours: 150
School Office: 01782 733075

Programme/Approved Electives for 2025/26

None

Available as a Free Standing Elective

No

Co-requisites

None

Prerequisites

MAT-10047 Algebra

Barred Combinations

None

Description for 2025/26

Abstraction is a powerful idea in Mathematics: by focusing on the underlying properties of Mathematical systems we can identify connections and similarities that are not visible on the surface. In this module you will explore these techniques and styles of thinking. The central concept is that of a group. You will study some of the fundamental abstract results concerning groups, and discuss applications in combinatorics, geometry, and number theory.
You will encounter new topics via guided investigations, develop the theory via lectures, and consolidate your knowledge via practice sessions.

Aims
This module will illustrate the power of abstraction via a formal treatment group theory as an axiomatic system, as well as exploring applications to combinatorics, geometry and number theory. Each topic will be encountered via guided investigations and developed more formally via lectures. In this way you will gain develop intuition and insight alongside subject knowledge.

Intended Learning Outcomes

define and identify abstract algebraic concepts and structures including binary operations, permutations, groups, subgroups, and homomorphisms: 1,2
state, prove, and apply fundamental theorems in group theory: 1,2
select and apply appropriate group theoretic concepts to solve problems arising in combinatorics, geometry, or number theory: 2
make judgements and evaluate different approaches to problem solving: 1,2

Study hours

Active Learning Hours:
Exploration sessions: 12 hours
Lectures: 24 Hours
Practice sessions: 12 hours
Independent Study Hours:
Preparation for and completion of assignments: 12 hours
Consolidation of lecture material: 64 hours
Examination preparation: 24 hours
Final examination: 2 hours.

School Rules

None

Description of Module Assessment

1: Assignment weighted 30%
Assignment on Foundations of Group Theory
An assignment comprising approximately 5 questions design to examine students' progress towards the ILOs concerning the foundations group theory. Solutions will be uploaded to the KLE. Students should expect to spend 12 hours on the assessment.

2: Exam weighted 70%
Closed book 2 hour examination
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.

The University undertakes a continuous review of its teaching and research provision to ensure programmes are of a high quality and changes may be made to modules where it is necessary and reasonable to do so. Please be aware that minor changes to modules, such as a change to an individual assessment, can occur up until enrolment, although we endeavour to give you as much notice as possible of any changes. 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/legalgovernancecompliance/governance/actcharterstatutesordinancesandregulations/studenttermsconditions/

Last Updated: 04 December 2025