planet gareth : maths


Part IA


Numbers & Sets

Analysis I

Vectors & Matrices

Vector Calculus

Part IB

Linear Algebra

Groups, Rings & Modules

Metric & Topological Spaces

Complex Methods

Parts II & III

I don't supervise Parts II and III. However:

Tripos Papers

Past Tripos Papers for recent years can be found on the university maths website.

They are sorted by year there, but are sorted by course here.

Some older past papers can be found on my old things page. (Requires Raven login.)

Example Sheets

Example sheets can be found on the DPMMS or DAMTP pages.

Below are the most recent sheets for the courses I supervise. (Sheets in brackets are from last year.)

Groups one two three four
Numbers & Sets one two three four
Analysis I one two (three) (four)
Vector Calculus one two three four
Linear Algebra one two three four
Groups Rings & Modules (one) (two) (three) (four)
Complex Methods (one) (two) (three)

Some older example sheets can be found on my old things page. (Requires Raven login.)

Other Things

"The Zeta Function of sl2 and Resolution of Singularities", a paper by Marcus du Sautoy and me.
(My only actual paper, but it got me an Erdős number of 4, so that's okay.)

Solitaire Army

Simon and I came up with a fun extension to Solitaire Army. Simon has produced a page with pretty animations of our result.


Ben Millwood wrote me a poem about the Heine-Borel Theorem.
Patrick Stevens wrote poems which prove Sylow's theorems.

A juggling theorem

"Given a collection of positive integers with integer average, there is some permutation of them which is a valid siteswap."

Here is a proof. And here is an implementation of the algorithm, written in Python by Simon.