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
Requisites
Prerequisite
Prohibition
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
Mathematical statistics
Mathematics
Pure mathematics