Groups and Symmetries - MA5503

Location Term Level Credits (ECTS) Current Convenor 2017-18 2018-19
Canterbury Autumn
View Timetable
5 15 (7.5) DR CD Bowman-Scargill







The concept of symmetry is one of the most fruitful ideas through which mankind has tried to understand order and beauty in nature and art. This module first develops the concept of symmetry in geometry. It subsequently discusses links with the fundamental notion of a group in algebra. Outline syllabus includes: Groups from geometry; Permutations; Basic group theory; Action of groups and applications to (i) isometries of regular polyhedra; (ii) counting colouring problems; Matrix groups.


This module appears in:

Contact hours


Method of assessment

80% Examination, 20% Coursework

Preliminary reading

M. Armstrong: Groups and Symmetry. Undergraduate Texts in Mathematics, Springer, 1988.
Peter J. Cameron, Introduction to Algebra, Second edition, Oxford University Press, 2007.

See the library reading list for this module (Canterbury)

See the library reading list for this module (Medway)

Learning outcomes

The intended subject specific learning outcomes.
On successfully completing the module students will be able to:
1 demonstrate knowledge and critical understanding of the well-established principles within basic group theory and symmetries;
2 demonstrate the capability to use a range of established techniques and a reasonable level of skill in calculation and manipulation of the material to solve problems in the following areas: isometries of the plane, groups, action of groups, matrix groups, symmetric groups, cyclic groups and dihedral groups;
3 apply the concepts and principles in group theory in well-defined contexts beyond those in which they were first studied, showing the ability to evaluate critically the appropriateness of different tools and techniques.

The intended generic learning outcomes.
On successfully completing the module students will be able to:
Demonstrate an increased ability to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make use of information technology skills such as online resources (Moodle), internet communication;
7 communicate technical material competently;
8 demonstrate an increased level of skill in numeracy and computation.

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