Groups, Knots and Fields - MA6521

Location Term Level Credits (ECTS) Current Convenor 2019-20
Canterbury Spring
View Timetable
6 15 (7.5)


MAST5003 (Groups and Symmetries); MAST5014 (Rings and Fields)





• Groups: revision, presentations of groups, Sylow's theorems and applications (e.g. classification of groups)
• Finitely generated abelian groups: finite abelian groups, Smith normal form, classification, applications (e.g. systems of linear Diophantine equations)
• Knots: introduction, Reidemeister moves, knot invariants, the Abelian knot group
• Fields: revision, soluble groups, Galois Theorem, applications (e.g. impossibility of solving the quintic)


This module appears in:

Contact hours


Method of assessment

80% examination, 20% coursework

Indicative reading

Group theory:
M. Aschbacher: Finite Group Theory (Cambridge Studies in Advanced Mathematics), Cambridge University Press, 2000
B. Baumslag and B. Chandler: Schaum's Outline of Group Theory, McGraw Hill Professional, 1968
A. Kerber, Applied Finite Group Actions, Springer, 1999
Knot theory:
C. Livingston, Knot theory, Mathematical Association of America, 1993
V. Manturov, Knot Theory, Chapman & Hall, 2004

Field theory:
John M. Howie, Fields and Galois Theory, Springer, 2006

See the library reading list for this module (Canterbury)

Learning outcomes

The intended subject specific learning outcomes. On successfully completing the level 6 module students will be able to:
1 demonstrate systematic understanding of key aspects of Groups, Knots and Fields;
2 demonstrate the capability to deploy established approaches accurately to analyse and solve problems using a reasonable level of skill in calculation and manipulation of the material in the following areas: groups, Sylow's Theorems, finitely generated abelian groups, Smith normal form, knots and their invariants, Galois extensions;
3 apply key aspects of Groups, Knots and Fields theory in well-defined contexts, showing judgement in the selection and application of tools and techniques.

The intended generic learning outcomes. On successfully completing the level 6 module students will be able 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 competent use of information technology skills such online resources (Moodle), internet communication;
7 communicate technical material competently;
8 demonstrate an increased level of skill in numeracy and computation;
9 demonstrate the acquisition of the study skills needed for continuing professional development.

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