MTH5141 Computational group theory
Faculty of Science
MTH5141 Computational group theory is a level 5, 6-credit-point, postgraduate unit from the Faculty of Science, offered in 2027 in Semester 1 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2027
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 1 other task
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Requisites
Before MTH5141
No prerequisites or corequisites besides the enrolment rules below.
After MTH5141
No unit lists MTH5141 as a prerequisite in the 2027 handbook.
Enrolment rules
PROHIBITION: MTH4141
COREQUISITE: Enrolment in the Master of Mathematics
PREREQUISITE: You must have passed one of MTH2121, MTH3121, MTH2141 or MTH3141
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.
Offerings in 2027
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hour 10 minutes)Examination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
Learning outcomes
When you finish this unit, you should be able to:
- 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 and teaching
- Seminars36 hours
- Applied sessions11 hours
- Teaching approachActive learning
- 3 hours of seminars;
- 1 hour of applied sessions (weeks 2-12) and
- 8 hours independent study per week.
The teaching approach for this unit is a blend of lectures and applied classes, involving active learning. The content of the unit will be delivered in three hours of lectures; this is an established way to teach high-level abstract mathematics effectively. In this model, you are expected to revise the theory explained in the lectures at home. This active learning process will assist you in fully understanding the new concepts. The written assignments (solving selected problems in computational group theory) have the same effect: you are required to study the lectures in order to derive solutions to the exercises. The theory will be exemplified in the applied classes: this is the place where the theoretical concepts of the lectures are discussed interactively with explicit examples. These classes will also involve group work where you have to work on problems in teams. The computational aspects of the unit will be illustrated with the computer algebra system GAP.
Learning resources
Technology resources
You must download and install the computer algebra system GAP, which can be obtained freely from http://www.gap-system.org <http://www.gap-system.org>.
Contacts
- Unit Coordinators
- Professor Heiko Dietrich
- Chief Examiners
- Professor Heiko Dietrich
Common questions
What are the prerequisites for MTH5141?
MTH5141 has no prerequisites, but enrolment rules apply.
When is MTH5141 offered?
In 2027, MTH5141 runs in Semester 1 at Clayton.
Does MTH5141 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.