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 2021 in Semester 1 at Clayton. It needs MTH3121 or MTH2121.
- Credit points
- 6
- Offered in 2021
- Semester 1
- Clayton
- Assessment
- Exam 60%
- and 1 other task
This is the 2021 handbook entry. See the 2027 entry.
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Requisites
Before MTH5141
Prohibitions
You can't enrol if you have passed any of these.
Prerequisites
Pass these before you enrol.
After MTH5141
No unit lists MTH5141 as a prerequisite in the 2021 handbook.
Enrolment rules
PREREQUISITE: Enrolment in the Master of Mathematics
Equivalent units
The same content under another code. Only one of them counts.
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 in 2021
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentOtherThreshold hurdle40%
- Examination (3 hours and 10 minutes)ExamThreshold hurdle60%
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
Appreciate 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
- Applied sessions11 hours
- Lectures36 hours
- Teaching approachActive learning
3 hours of lectures, 1 hour applied session and 8 hours of independent study per week.
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%
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
- Associate Professor Heiko Dietrich
- Chief Examiners
- Associate Professor Heiko Dietrich