# Maths

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.

- IIA/B Groups, Rings and Fields – dvi pdf

- IIB Combinatorics – dvi pdf
- IIB Representation Theory – dvi pdf
- IIB Algebraic Topology – dvi pdf
- IIB Number Fields – dvi pdf

## Essays

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.

- Sporadic Simple Groups – dvi pdf