As part of the Master of Mathematics / Master of Advanced Study, candidates may choose to offer an essay. This will count for 3 units, or about a sixth of the course. There is no prescribed length for an essay, but the general opinion seems to be that 6,000 to 10,000 words is a natural length. The essay does not have to be original in content.
Each year members of the Faculty propose suitable topics; links to those for the most recent submissions are provided below (subsequent years are expected to be broadly similar, although not identical). Students are also free to propose their own topic (subject to confirmation by the Faculty Board of Mathematics). Note that if an essay is written on a particular topic in a given year then that exact topic can not be set in the next year.
A list of extra topics is generally offered during Lent Term, on the same basis and terms as the any on the initial list (listed as "Additional Essay Topics").
The primary requirement on the presentation of Part III essays is that they are legible. Hand-written essays are acceptable (if legible), but you may prefer to use the text formatting software which is available on the University PWF network.