Overview

Groups in geometry, linear algebra, and number theory; cyclic and abelian groups; permutation groups; subgroups, cosets and normal subgroups and quotient groups; homomorphisms, isomorphisms and isomorphism theorem; group actions; Sylow theorems, group presentations.

Offerings

S1-01-CLAYTON-ON-CAMPUS

Contacts

Chief Examiner(s)

Professor Heiko Dietrich

Unit Coordinator(s)

Professor Heiko Dietrich

Notes

This unit shares lectures with MTH3141 but has separate assessments.

Learning outcomes

On successful completion of this unit, you should be able to:
1.

Communicate the beauty and the power of pure mathematics;

2.

Capture the mathematical notion of symmetry via group theory;

3.

Apply the fundamental concepts of abstract algebra;

4.

Explain the notion of proof in mathematics and be able to carry out basic proofs;

5.

Describe the power of the generality of the concepts in group theory;

6.

Pursue further studies in abstract algebra and pure mathematics more generally.

Teaching approach

Problem-based learning
Peer assisted learning
Active learning

Assessment

1 - Continuous assessment
2 - Final assessment - Exam (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions
Seminars

Workload requirements

Workload

Availability in areas of study

Applied mathematics
Mathematical statistics
Mathematics
Pure mathematics