Mathematics

The Cambridge Mathematics course is one of the most demanding and most rewarding mathematics courses in the world. It offers a wide range of subjects in pure and applied mathematics, theoretical physics and statistics.

Students are expected to study all the courses on offer in the first year (Part IA), and hence obtain a thorough background in all these areas. In the second year there is more flexibility, and there is no single course that all students must take. Some students choose to begin specialising in one area of mathematics, be it pure, applied or applicable (the latter referring to probability and statistics). It is, however, still possible to study most of the courses to cover greater breadth of material. Students then specialise in the third year (Part II) by choosing somewhere between 8 and 12 courses out of the 35 on offer. The courses in Part II cover as diverse areas as logic, black holes, financial mathematics and many more. In the second and third years there is also an optional Computational Projects course for which students investigate mathematical problems using numerical techniques.

After three years of studies about two thirds of students graduate with a BA, whereas the rest continue studying for a fourth year of the course known as Part III which leads to an MMath degree. For most people, Part III is the stepping stone to research. Many of the most famous mathematicians and physicists of the world today took this course.

There is also a `Mathematics with Physics' option. Students taking this option replace 25% of the first year of Mathematics with lectures and practicals offered by the Physics Department within Natural Sciences. At the end of the first year students taking this option can choose either to change to Natural Sciences to study Physics or to continue studying mathematics as part of the Mathematics course.

Mathematics at Peterhouse

We currently take around 8 students per year making Mathematics one of the bigger subjects in Peterhouse. We have 5 Fellows covering a wide range of research interests. They provide the College-based teaching (supervisions) for our undergraduates. We also have 7 PhD students some of whom contribute to undergraduate teaching. The size of Mathematics in Peterhouse means that we can cover most of our teaching need for the first two years of the course. In the third year colleges form groups and divide the task of arranging supervisions within the group. In the case of Peterhouse it is Trinity College that arranges supervisions for our students. It is still the case that in some subjects the supervisor will be a Peterhouse Fellow. For a student's perspective on life as a Mathematician at Peterhouse, have a look at the JCR's alternative prospectus.

Famous Petreans in Mathematics include Lord Kelvin (of temperature fame), Charles Babbage (programmable computer), Klaus Roth (winner of the Fields Medal in 1958, Honorary Fellow of Peterhouse) and Charles Burkill (former Master of the college, his textbooks on analysis are to this day on the Mathematics reading lists). Current Fellows and their research interests in Mathematics are:

Dr Anders Hansen (Fellow and Director of Studies): applied functional analysis, spectral theory, compressed sensing, mathematical signal processing, sampling theory, computational harmonic analysis, inverse problems, complexity theory, geometric integration, numerical analysis, C*-algebras.

Dr Clarice Poon (Research Fellow): compressed sensing, mathematical signal processing, sampling theory.

Dr David Tourigny (Research Fellow): the structure and applications of topological string/field theories; topics associated with mathematical biology; geometrical problems with applications to the natural sciences.

Dr András Zsák (Fellow, Director of Studies and Admissions Tutor): Banach space theory, problems with a combinatorial and set-theoretic flavour.

Course requirements

All applicants for Mathematics will be expected to be taking Mathematics and Further Mathematics to A level, or to be following an equivalent course of mathematical study. Students studying the International Baccalaureate must be studying both Mathematics and Physics to Higher Level. In the first year only, there are two options: Pure and Applied Mathematics; and Mathematics with Physics. Candidates who intend to take the latter option are expected to indicate this when they apply, but a final decision does not have to be made at that stage. For more information see the Faculty course guide. Physics to A level or equivalent is essential for applicants to Mathematics with Physics and is considered advantageous for all applicants to Mathematics.

The application process

Candidates are given two interviews, both of which aim to test their ability to think about unfamiliar mathematical problems. The material required to solve these problems does not go beyond what candidates would have already covered in school and no special preparation is necessary. You can also expect a pre-interview maths test of between 30 to 45 minutes. You will discuss your answers to this test during one of your interviews. Candidates wishing to study Mathematics with Physics will have an additional Physics interview.

Typical conditional offers

Our typical conditional offer for Mathematics is A*A*A at A level, plus a STEP offer tailored to the individual student, usually 1, 1 in STEP II and III. IB offers are usually for a minimum of 40-42 points, to include 776 or 777 at Higher level in relevant subjects, plus similar STEP grades.

Offers are designed to be realistic, taking into account individual circumstances, and to reflect potential and likely levels of achievement. Although most applicants are understandably nervous about interviews and STEP Mathematics, we have found them to be a better indicator of mathematical potential than A level results alone.

STEP

We make extensive use of STEP for the following reasons:

(i) We can see the exact marks and even the scripts;

(ii) It compares, reasonably fairly, candidates with different backgrounds, providing a common exam for all candidates who may be taking A levels from different examining boards or, indeed, other kinds of sixth-form examination;

(iii) Most importantly, we believe that it tests the mathematical ingenuity and potential of a candidate better than the rather standard A level questions. However, the papers contain a wide range of questions so that candidates who have taken different A level syllabuses should be able to find sufficient questions on material which they have covered.

(More information can be found in the Faculty's Guide to Admissions in Mathematics pdf).

The papers are designed to be substantially more challenging than A levels. Candidates are advised to obtain past papers for practice, and it is hoped they will be able to obtain assistance from their teachers. We do not expect candidates to receive extensive additional teaching for STEP. The Faculty offers a range of resources to help students prepare for STEP, including a STEP Easter school, a new Correspondence Course for Year 12 students thinking of applying for courses and universites which use the STEP, with support continuing through Year 13.