2024/25 Undergraduate Module Catalogue

MATH1120 Introduction to Group Theory

10 creditsClass Size: 275

Module manager: Bethany Marsh
Email: B.R.Marsh@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2024/25

Pre-requisite qualifications

Grade B in A-level Mathematics or equivalent.

This module is not approved as a discovery module

Module summary

Group theory is a fundamental branch of mathematics, central also in theoretical physics. The concept of a group may be regarded as an abstract way to describe symmetry and structure. In this module, we will introduce group theory, with motivation from, and application to, specific examples of familiar mathematical structures such as permutations of lists and symmetries of shapes.

Objectives

This module will introduce students to first steps in abstract algebra, by introducing group theory. Students will learn key definitions and axioms, and be exposed to the practice of proving results rigorously from those axioms.

Learning outcomes
On successful completion of the module students will have demonstrated the following learning outcomes relevant to the subject:
1. Recall and explain the main concepts of group theory
2. Determine elementary properties of a given group, and its elements
3. Determine whether a given subset of a group is a subgroup.
4. Determine whether a given relation is an equivalence relation
5. Write proofs within an axiomatic framework

Skills Learning Outcomes
SLO1. Communicate through written work technical information and reasoning.
SLO2. Apply analytical thinking and technical knowledge to solve problems.
SLO3. Write in a clear, concise, and focused way.
SLO4. Manage workloads, deadlines, and workplace pressure through prioritisation and productivity skills.

Syllabus

The following topics will be covered:
1. Permutations
2. Symmetries of shapes
3. The axioms of a group
4. Subgroups and product groups
5. The order of a group element
6. Group actions
7. Equivalence relations
8. Modular arithmetic
9. Lagrange’s theorem

Additional topics that build on these may be covered as time allows. Such topics may be drawn from the following, or similar:
10. The orbit-stabiliser theorem
11. The orbit-counting theorem
12. Colouring problems

Methods of Assessment

We are currently refreshing our modules to make sure students have the best possible experience. Full assessment details for this module are not available before the start of the academic year, at which time details of the assessment(s) will be provided.

Assessment for this module will consist of;

1 x Portfolio of assessed questions
1 x In-person exam

Teaching methods

Delivery type	Number	Length hours	Student hours
Lecture	22	1.00	22.00
Seminar	5	1.00	5.00
Independent online learning hours			24.00
Private study hours			49.00
Total Contact hours			27.00
Total hours (100hr per 10 credits)			100.00

Opportunities for Formative Feedback

Regular example sheets.

Reading list

The reading list is available from the Library website

Last updated: 30/09/2024

Disclaimer

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