MTH5141 · Computational group theory

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 advanced course on group theory and computational methods, using the computer algebra system GAP. This unit will cover a selection of topics from the following list. Abstract groups: solvable groups, nilpotent groups, groups of prime power order, group extensions and cohomology; Permutation groups: orbit stabiliser algorithm, bases and strong generating sets, membership tests; Group presentations: abelian invariants, Todd-Coxeter algorithm, quotient algorithms; Polycyclic Groups: polycyclic series and generating sets, polycyclic presentations, computing group cohomology; GAP: learn how to use the computer algebra system GAP to compute with groups.

Areas of study: Master of Mathematics

Offerings

The Handbook publishes no offerings for this unit.

Assessment

The Handbook lists an examination for this unit.

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.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Formulate complex problems using appropriate terminology in algebra
2. Demonstrate a profound understanding of abstract concepts in group theory
3. Illustrate the nature of algebraic proofs, be able to use a variety of proof-techniques unique to working with groups;
4. Apply a variety of expert algorithms for different algebraic objects, in particular, groups
5. Use the computer algebra system GAP to compute with groups and related structures.

Workload

• 3 hours of seminars; • 1 hour of applied sessions (weeks 2-12) and • 8 hours independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.