MTH3141 - Algebra 1: Group theory

Overview

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

Offerings

S1-01-CLAYTON-ON-CAMPUS

Requisites

Prohibition

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Professor Heiko Dietrich

Unit Coordinator(s)

Professor Heiko Dietrich

Notes

This unit shares lectures with MTH2141 but has a separate assessment. In this unit, the assessment tasks will require greater insight and mathematical maturity compared to MTH2141.

Learning outcomes

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

Communicate the beauty and the power of pure mathematics;

Capture the mathematical notion of symmetry via group theory;

Apply the fundamental concepts of abstract algebra;

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

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

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

Teaching approach

Active learning

Primary content is delivered through traditional lectures (which will be recorded, and available for review via the Moodle page). Applied classes will be active learning. Small groups of students will work together around a whiteboard to solve problems. A key aspect is that this component involves writing your solutions on the board and critiquing the solutions of others, meaning that both written and spoken communication of mathematical ideas are developed (with input from your tutor). You also develop strategies for solving the questions together, meaning this is peer-assisted learning. Assignments will be problem-based learning. The questions will involve techniques from recent lectures and applied classes, but sometimes in settings or formats that are not immediately familiar. Thus, part of the challenge is adapting what you previously knew or have just learnt to a new setting.

Peer assisted learning

Problem-based 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