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.

Requisites

Prohibition

Prerequisite

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Associate Professor Heiko Dietrich

Unit Coordinator(s)

Associate Professor Heiko Dietrich

Notes

This unit is offered in alternate years commencing S1, 2019

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.

Assessment summary

Examination (3 hours and 10 minutes): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit you must achieve at least 50% overall and at least 40% for the end-of-semester exam.

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.

Other unit costs

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

Availability in areas of study

Master of Mathematics