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This web page is intended purely as a repository for the electronic versions of lecture notes, revision notes and essays that I produced while studying Maths at Cambridge University. If you have any comments or corrections to these notes, however small, please email me.

Lecture notes

These lecture notes are intended to provide a fairly complete representation of the courses from which they are derived. If you are a student at Cambridge University, please note, hovever, that the content of courses changes from year to year — the notes are not intended to be a substitute for attending lectures. In addition, there will undoubtedly be errors and omissions — I would very much appreciate being told of any that you may find.

Revision notes

These revision notes were produced for my own personal use and in no sense do they attempt to cover the entirety of their related courses. I have usually omitted proofs, examples and detailed explanations. In some cases, whole topics or sections of the course are not represented here, because I felt that they were not essential, because I already understood them very well or didn't understand them at all, or simply because I ran out of time. Finally, the presentation of the material is very much in my own style and often completely different to that of the lecturers.

Having said this, I hope that they may prove useful at the start of term as an outline of the material likely to be covered in the courses, or when revising as a summary of some of the material that was covered.


This is the essay that I wrote for Part III, under the supervision of Dr Jan Saxl. I hope that it would be fairly comprehensible to anyone with a graduate-level knowledge of Group Theory, or, by skipping over a few of the more technical sections, to an undergraduate having studied some Group Theory.