MTH4141 Computational group theory
Faculty of Science
MTH4141 Computational group theory is a level 4, 6-credit-point, postgraduate unit from the Faculty of Science. It isn't offered in 2020. It has no prerequisites.
- Credit points
- 6
- Offered in 2020
- Not offered
This is the 2020 handbook entry. See the 2026 entry.
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Requisites
Before MTH4141
No prerequisites or corequisites besides the enrolment rules below.
After MTH4141
No unit lists MTH4141 as a prerequisite in the 2020 handbook.
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. 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.
Offerings in 2020
The 2020 handbook lists no offerings for MTH4141.
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
- 3 hours of lectures and 1 hour tutorial per week.
- 8 hours independent study per week.
Contacts
- Chief Examiners
- Associate Professor Heiko Dietrich
- Unit Coordinators
- Associate Professor Heiko Dietrich
Common questions
What are the prerequisites for MTH4141?
MTH4141 has no prerequisites, but enrolment rules apply.
When is MTH4141 offered?
MTH4141 has no offerings listed in the 2020 handbook.