### Exam timetable

The provisional 2020 examination timetable is available here. Please express any concerns by email to the Undergraduate Office (undergrad-office@maths.cam.ac.uk) by Saturday 1 February 2020.

### Exam rubrics

Exam rubrics will be uploaded in May, in advance of the examinations. For past years' rubrics, see the cover pages of the past papers below.

### Past exam papers

*All papers are copyright by the University of Cambridge and may not be reproduced without permission.*

*The papers are stored as PDF files. The PDF files can be viewed and printed using the Adobe Acrobat viewer. This program is available free of charge from the Adobe web site.*

*Papers are available for past years from 2001. Click on the links below to select the year you wish to view:*

### Essay

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 5,000 to 8,000 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 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.

### Essay descriptors

The Part III Committee believes that the essay is a key component of Part III. It also believes that it is entirely reasonable and possible that candidates may obtain higher marks for essays than in their examination, both because of the typical amount of effort devoted to the essay, and also the different skill set which is tested compared to a time-limited written examination. In light of these beliefs, as well as the comments of both the internal examiners and the external examiners, the Part III Committee believes that it is appropriate to suggest the following descriptors for the various possible broad grade ranges for an essay. The committee trusts that these guidelines prove useful in guiding the judgement of the inevitably large numbers of assessors marking essays, and that these guidelines strengthen the mechanisms by which all essays are assessed uniformly. They are not meant to be either prescriptive or comprehensive, but rather general guidance consistent with long-standing practice within the faculty.

**An Essay of Distinction Standard**

Typical characteristics expected of a distinction standard essay include:

- Demonstration of clear mastery of all the underlying mathematical content of the essay.
- Demonstration of deep understanding and synthesis of advanced mathematical concepts.
- A well-structured and well-written essay of appropriate length (5000-8000 words) with:
- very few grammatical or presentational issues;
- a clear introduction demonstrating an appreciation of the context of the central topic of the essay;
- a coherent presentation of that central topic;
- a final section which draws the entire essay to a clear and comprehensible end, summarising well the key points while suggesting possible future work.

An essay of distinction standard would be consistent with the quality expected of an introductory chapter of a PhD thesis from a leading mathematics department. A more elegant presentation and synthesis than that presented in the underlying papers, perhaps in the form of a shorter or more efficient proof of some mathematical result would be one possible characteristic of an essay of distinction standard. Furthermore, it would be expected that an essay containing publishable results would be of a high distinction standard, but, for the avoidance of doubt, publishable results are **not necessary** for an essay to be of high distinction standard. An exceptionally high mark (a+) should be justified by a specific extra statement from the assessor highlighting precisely which section of the essay was of particularly distinguished quality.

**An Essay of Merit Standard**

Typical characteristics expected of a merit standard essay include:

- Demonstration of good mastery of most of the underlying mathematical content of the essay.
- Demonstration of understanding and synthesis of mathematical concepts typical of the content of a Part III course.
- A largely well-structured essay of appropriate length (5000-8000 words) with:
- some, but essentially minor, grammatical or presentational issues;
- an introduction demonstrating an appreciation of at least some context of the central topic of the essay;
- a reasonable presentation of that central topic;
- a final section which draws the entire essay to a comprehensible end, summarising the key points.

An essay of merit standard would be consistent with the quality expected of a first class standard final year project from a leading mathematics department. Such essays would not typically exhibit extensive reading beyond the suggested material in the essay description, or original content.

**An Essay of Pass Standard**

Typical characteristics expected of a pass standard essay include:

- Demonstration of understanding of some of the underlying mathematical content of the essay.
- An essay exhibiting some non-trivial flaws in presentation through, for example:
- an inappropriate length;
- repetition or lack of clarity;
- lack of a coherent structure;
- the absence of either an introduction or conclusion.

An essay of pass standard would be consistent with the quality expected of an upper second class standard final year project from a leading mathematics department. For the avoidance of doubt, an excessively long essay (i.e. of the order of twice the suggested maximum length or more) would be likely to be of (at best) pass standard. A key aspect of the essay is that the important mathematical content is presented clearly in (at least close to) the suggested length.