This module is not currently running in 2024 to 2025.
• 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)
Total contact hours: 42
Private study hours: 108
Total study hours: 150
80% examination, 20% coursework
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)
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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