Module manager: Bethany Marsh
Email: B.R.Marsh@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2024/25
Grade B in A-level Mathematics or equivalent.
This module is not approved as a discovery module
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.
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.
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.
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
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 22 | 1 | 22 |
| Seminar | 5 | 1 | 5 |
| Independent online learning hours | 24 | ||
| Private study hours | 49 | ||
| Total Contact hours | 27 | ||
| Total hours (100hr per 10 credits) | 100 | ||
Regular example sheets.
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| Portfolio | Portfolio of assessed questions | |
| Total percentage (Assessment Coursework) | 0 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Unseen exam | 2.0 Hrs Mins | |
| Total percentage (Assessment Exams) | 0 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 9/30/2024
Errors, omissions, failed links etc should be notified to the Catalogue Team