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.
Total contact hours: 40
Private study hours: 110
Total study hours: 150
Method of assessment
Assessment 1 Exercises, requiring on average between 10 and 15 hours to complete 20%
Assessment 2 Exercises, requiring on average between 10 and 15 hours to complete 20%
Examination 2 hours 60%
The coursework mark alone will not be sufficient to demonstrate the student's level of achievement on the module.
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)
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.
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Credit level 5. Intermediate level module usually taken in Stage 2 of an undergraduate degree.
- ECTS credits are recognised throughout the EU and allow you to transfer credit easily from one university to another.
- The named convenor is the convenor for the current academic session.
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