# Mathematics

The Cambridge Mathematics course has always enjoyed a very high reputation, and a Cambridge Mathematics degree is highly regarded world-wide. It provides a good qualification for entry into a very wide range of careers, and also for post-graduate academic work in a variety of technical subjects. All undergraduates, regardless of college, receive the same lectures and sit the same exams, which are given by the University's Faculty of Mathematics. The best way to find out detailed and up-to-date information about the course is to look at the Faculty's undergraduate page .

## Number of students per year |
10-12 |

## Essential subjects |
A-level or similar qualification in Mathematics and Further Mathematics. |

## Typical offer |
A*A*A or 7,7,6 (42+ overall) in the IB or the equivalent in other educational systems, and a 1 & 1 in STEP ll & lll. For Scottish Highers and Advanced Highers, offers usually require AAA at Advanced Higher Grade; bands may be specified. |

## Written assessment |
There is currently no pre-interview assessment for mathematics applicants. |

**Applying for Mathematics at Clare**

#### Fellows in Mathematics

- Professor Maciej Dunajski Director of Studies in Mathematics, University Professor of Mathematical Physics

My research interest is mathematical physics, in particular the interplay between differential geometry, integrable systems, and general relativity. While it acknowledged that physicists need mathematics, it also appears that theorems in pure mathematics can be proven using ideas from research on black holes! Einstein's theory of gravitation was recently used to establish the Poincare conjecture: If S is a three--dimensional space which is finite in size, consists of one piece, has no boundary and has an additional property that all closed loops in this space can be continuously deformed to a point, then S can be continuously deformed into a three--dimensional sphere.

- Professor Gordon Ogilvie Professor of Mathematical Astrophysics.

I use mathematical methods to study astrophysical fluid flows such as the discs of magnetized plasma swirling around black holes, the dusty gas discs around young stars where planets form, and the tides raised in planets and stars by their orbital companions. Astronomical observations provide some clues to what is happening in these systems, and my theoretical work aims to reveal their dynamics through mathematical analysis and physical interpretation of the governing equations, aided by numerical computations.

- Professor Andrew Thomason Professor of Combinatorial Mathematics.

My research deals with finite discrete structures (as opposed to the continuous structures more common in classical mathematics). These kinds of structures occur frequently in modern application of mathematics. Quite often I work with graphs, which are sets of points, some pairs of which are associated in some way, which can be represented by an edge joining them. Suppose, at a party, each pair of people present are either friends or enemies. It is possible to have a party of 5 people without either three mutual friends or three mutual enemies, but it is impossible to avoid one of these occurring in a party of 6 (try it). It is possible to have a party of 17 without four mutual friends/enemies, but not 18. It is known that if the party is big enough you will get five mutual friends/enemies, but how large must it be? No-one knows. Surprisingly, this little puzzle has profound applications.

- Dr Julia Wolf University Lecturer in Pure Mathematics.

Much of my research is motivated by simple questions about whole numbers which have remained unsolved for several decades or more. An example of such an open problem is due to Goldbach, who speculated in 1742 that every even number greater than 2 can be written as the sum of two primes. One technique employed to attack problems of this type is Fourier analysis, which is widely used across science and engineering to decompose a signal into oscillatory components. In the number-theoretic context, it allows us to decompose the set of primes, for example, into a structured and a random-looking part. Such a decomposition can in turn be used to identify patterns within the set of primes, and I am particularly interested in understanding how classical Fourier analysis can be (and when it must be) generalised to detect certain classes of patterns.

#### Honorary Fellows

#### Student Profiles

#### Alumni Profiles

#### Reading Lists

Click here for a list of recommended books.