MTH5141 - Computational group theory

There is a more recent version of this academic item available.

Overview

Groups are abstract mathematical objects capturing the concept of symmetry, and therefore are ubiquitous in many mathematical disciplines and other fields of science, such as physics, chemistry, and computer science. This unit is an introductory course on group theory and computational methods, using the computer algebra system GAP (www.gap-system.org). This unit will cover a selection of topics from the following list. Abstract Groups: knowing the basic definitions and standard results; Group Actions: orbits, stabilisers, and the orbit-stabiliser theorem; Group Presentations: free groups, abelian invariants, Todd-Coxeter algorithm; Permutation Groups: stabiliser chains, bases and strong generating sets, membership test; Nilpotency and Solvability: knowing the basic definitions and properties. Polycyclic Groups: polycyclic series and generating sets, polycyclic presentations; GAP: learn how to use the computer algebra system GAP to compute with groups. Some of the material will be self-taught through guided reading.

Offerings

S1-01-CLAYTON-ON-CAMPUS

Requisites

Prerequisite

Prohibition

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Associate Professor Heiko Dietrich

Unit Coordinator(s)

Associate Professor Heiko Dietrich

Learning outcomes

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

Formulate complex problems using appropriate terminology in algebra

Demonstrate a profound understanding of abstract concepts in group theory

Appreciate the nature of algebraic proofs, be able to use a variety of proof-techniques unique to working with groups;

Apply a variety of expert algorithms for different algebraic objects, in particular, groups

Use the computer algebra system GAP to compute with groups and related structures.

Teaching approach

Active learning

This is an established way to teach high-level abstract mathematics effectively. In this model, students are expected to revise the theory explained in the lectures at home. This active learning process will assist students in fully understanding the new concepts. There will be three assignments on theoretical questions and programming questions. In the final unit mark, the final exam counts for 60%, the continuous assessment count for 40%

Assessment summary

Assessment

1 - Continuous assessment

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. If you are enrolled in MTH5141 you will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4141. The assignments and exam in this unit will use some common items from the MTH4141 assessment tasks, in combination with several higher level questions and tasks.

Value %:40

Hurdle type:Threshold

Hurdle description:

If you would otherwise have passed the unit but you do not achieve at least 45% of the marks available for the continuous assessment you will receive a Hurdle Fail (NH) grade and a mark of 45 on your transcript.

2 - Examination (3 hours and 10 minutes)

Value %:60

Hurdle type:Threshold

Hurdle description:

If you would otherwise have passed the unit but you do not achieve at least 45% of the marks available for the end of semester examination you will receive a Hurdle Fail (NH) grade and a mark of 45 on your transcript.

Scheduled and non-scheduled teaching activities

Applied sessions

Lectures

Workload requirements

Workload

Learning resources

Technology resources

Other unit costs

Costs are indicative and subject to change.
Miscellaneous items required (Printing, Stationery)- $100.

Availability in areas of study

Master of Mathematics