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 2022. It has no prerequisites.
- Credit points
- 6
- Offered in 2022
- Not offered
- Assessment
- Exam 60%
- and 2 other tasks
This is the 2022 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 2022 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 2022
The 2022 handbook lists no offerings for MTH4141.
Assessment
- AssignmentsAssignment30%
- Mid-semester testIn class test10%
- 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 of applied sessions 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 3 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 students in fully understanding the new concepts. The written assignments (solving selected problems in computational group theory) have the same effect: students 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
- Associate Professor Heiko Dietrich
- Chief Examiners
- 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 2022 handbook.
Does MTH4141 have an exam?
Yes. The exam is worth 60% of the final mark, alongside 2 other tasks.