Mathematics

Director of Studies:
Dr Robert Hunt

Other Fellows in Mathematics:
Mr Julian Holstein
Professor Frank Kelly
Professor Peter Landshoff
Professor Simon Tavaré

Number of students admitted each year: 10–12

University Website: http://maths.cam.ac.uk

A Day in the Life of a Christ's Mathematician

Introduction

Since the foundation of Christ's College, people of all backgrounds have been coming to the College to study and appreciate the beauty of mathematics. Our current Fellows continue that great tradition and combine world-class research with outstanding teaching. Professor Frank Kelly is a Fellow of the Royal Society and is famous for his work on mathematical systems, including the invention of an algorithm for answering large numbers of incoming telephone calls. This algorithm, still in use today, is known as Dynamic Alternative Routing and improved on previous algorithms by more than 20%. The Director of Studies in Mathematics at Christ's, Dr Robert Hunt, was also the Deputy Director of the renowned Isaac Newton Institute for Mathematical Sciences, and is now the Senior Tutor of the College. He holds a prestigious Pilkington Prize from the University of Cambridge for excellence in teaching.

The University Course

The Faculty of Mathematics at Cambridge has for many years offered one of the most highly regarded Mathematics degree courses in the world. The course is constantly updated and modernised, and caters both for students who wish to follow a career in Mathematics and for those who leave to pursue wider interests after graduation. Study of the Cambridge Mathematical Tripos (as the course is traditionally known) can extend over three or four years. The Honours B.A. degree is awarded after three years of study; students can then decide whether they wish to continue for a fourth year leading either to the Certificate of Advanced Study in Mathematics (also known as Part III Mathematics) or to the M.Phil. in Mathematical Statistics.

All Mathematics students take the same basic courses during their first two years at Cambridge, referred to as the Part IA and Part IB years respectively. These courses introduce a wide range of topics in Pure Mathematics, Statistics, Applied Mathematics and Theoretical Physics which are regarded as core knowledge. There is flexibility as to when many of the courses can be studied; thus well prepared students who have studied mathematics beyond the syllabus at school are able to take some courses early and still find the Tripos challenging. In addition, there is a small number of optional courses available in the second year.

The third year (known as the Part II year) contains courses of two different styles. Firstly, there are courses intended to be enjoyable and rewarding for those students whose third year will be their last year of formal mathematical studies before they graduate and take employment. The emphasis is on either combining previous work into one of the high points of Mathematics, or on introducing practical applications that are relevant to careers in technology, the business world, commerce and industry. These courses also appeal to students who wish to gain a wide overview of modern mathematics without being held up by an extended amount of technical detail.

Secondly, there are Part II courses which cater for those who wish to continue studying rigorous, detailed mathematics at a higher level, and in particular for those who intend taking the fourth year or who wish to undertake mathematical research elsewhere. Those taking these courses will normally have taken some optional courses in their second year.

It is entirely possible (and indeed expected) for students taking Part II to mix and match courses of these two different styles freely, as their own interests and ambitions dictate. The available courses at this level cover an exceptionally wide range of mathematics, from Logic, Algebra, Analysis, Topology, Probability, Statistics and Financial Modelling through to Fluid Dynamics, Numerical Analysis, Special & General Relativity, Quantum Mechanics and Cosmology: there are around 35 courses in total, from which a student might choose up to about 8 for examination.

The fourth-year Part III course is an outstanding preparation for research in cutting-edge mathematics, statistics or theoretical physics as recognised by the influx of students from other universities, both in the UK and abroad, who come to Cambridge to take Part III as a separate one-year course. For students already at Cambridge, it is not necessary to make the decision as to whether or not to continue to Part III until they have completed their Part II year. (The option of a fourth year of study in Mathematics has been available for over 60 years in Cambridge, and for most non-overseas Cambridge undergraduates the associated LEA award for Part III will be automatic.)

In each year, there is a University Tripos examination: Parts IA, IB, II and III are examined at the end of the year in which they are taken. Students start each year with a clean sheet, i.e., the results of earlier years do not affect their classification in subsequent examinations. Cambridge does not operate a modular system, so all examination papers cover many different courses at once. In both the second and third years, there is also an option to study computer projects and to submit coursework based around these projects; this option, known as CATAM, teaches programming, investigative and presentational skills. In Part III, there is an optional mathematical essay paper, which takes the form of a review of current research topics, or even an original research project.

Cambridge also offers first-year students the option of taking a course in Mathematics with Physics. In this option students drop one quarter of the first-year Mathematics courses in favour of lectures in physics . At the end of Part IA they then decide whether to continue with Mathematics full-time, or to switch to studying Physics full-time at no disadvantage. Students whose long-term interests lie in Theoretical Physics can study for this subject equally well either through the Physics options in the Natural Sciences Tripos, or by taking three years of the Mathematical Tripos (specialising in the Theoretical Physics options at Part II). Taking Part IA Mathematics with Physics is therefore a good way of finding out which route appeals most, without limiting options at an early stage. The Mathematical Tripos is also regarded as good preparation for a number of other subjects, e.g., Economics, Management Studies or Astronomy.

Mathematics at Christ's

Every student at Cambridge must be a member of one or other of the 29 Colleges for undergraduates of the University. The course content, lectures and examinations are the responsibility of the University Faculty, and are the same for every student reading Mathematics at Cambridge regardless of their College. In the first and second years, lectures are given in University lecture rooms near the centre of the city, about 5 minutes walk from Christ's College. In the third year, lectures take place at the new purpose-built Centre for Mathematical Sciences, about 15 minutes walk from the College.

Colleges are responsible for the selection and admission of undergraduates, the provision of social facilities such as accommodation, and ongoing personal and academic support. Every College has at least one Director of Studies in Mathematics, part of whose job is to advise students in their choice of options and to arrange supervisions for them. Supervisions are tutorial teaching sessions in small groups: students in Mathematics will typically have two supervisions per week in groups of two. Any difficulties with the lectures or their associated examples and problem sheets are tackled during these sessions. Supervisions are one of the major advantages of a Cambridge education, providing individually tailored help and tuition. They offer a more directed and relevant approach to a students own work than is possible at most other universities, where similar material can only be covered in example classes involving much larger numbers of students. Each College makes its own arrangements for supervisions.

Currently, Christ's College has five Fellows in Mathematics: Dr R.E. Hunt (Director of Studies), Mr Julian Holstein (Junior Research Fellow), Prof F.P. Kelly FRS, Prof P.V. Landshoff and Prof S. Tavaré, whose teaching and research interests between them span a wide range of areas of Pure and Applied Mathematics, Statistics and Theoretical Physics. In Parts IA and IB, teaching is organised entirely within the College, and much of the supervision is given personally by these Fellows. At Part II, in order to cover the many options available, Christ's joins forces with other Colleges to ensure that supervisions are given by specialists in the appropriate subject. For many years, Mathematics has been one of the subjects in which Christ's College has been particularly strong and this has been reflected not least in the excellent results achieved in recent years by our Mathematics undergraduates. Dr Hunt is one of only four lecturers currently in the Cambridge Mathematics Faculty to have been awarded the Pilkington Prize, the University-wide annual prize for excellence in teaching.

The Mathematical Tripos includes the CATAM option described above which shows students how to use computers to solve mathematical problems that may be analytically intractable. Dr Hunt has particular expertise in this option. The computer projects are completed over the course of a year outside the written examination, but count towards examination results. The College has its own computer facility, available 24 hours a day, consisting of a network of machines all linked to the University network. Moreover, all College rooms have been wired with computer points to enable every student to have a full Ethernet connection to the Internet and to the University network. Similar facilities are available in the Centre for Mathematical Sciences and in the  University Computer Laboratory. On arrival, all students are given a University email account.

Students with interests beyond mathematics may also attend almost any other lecture in the University; many members of the University take advantage of this in order to learn or improve a foreign language. In some cases it may be possible to use this study to gain a formal qualification (Certificate or Diploma) in a foreign language in addition to a students degree in Mathematics. In addition there are many academic societies in Cambridge which arrange talks that may be of interest to students of Mathematics, e.g., the Archimedeans (University Mathematical Society) and the Astronomical Society.

Mathematics is one of the most (maybe the most) versatile and marketable of degree subjects, and graduates from the Cambridge Mathematical Tripos are highly sought by employers.

College Facilities

Christ's is distinctive amongst the Cambridge Colleges. It offers strong tutorial support to its students as they pursue their academic work, and is able to offer accommodation for three years to all of its undergraduates. The College also provides a modern library, a theatre, sporting facilities, playing fields, social activities and clubs and societies open to all.

How to Apply

In addition to nominating Cambridge as one of your selected universities on the UCAS application form, it is also desirable to choose a College of preference (the alternative is to submit an Open Application and allow a College preference to be chosen for you by computer). This can appear to add to the complexity of applying to Cambridge, but in reality the option of stating your particular College preference increases the control which you have over your own application. Many criteria can be used for choosing a College of preference, including such factors as location, architecture and accommodation, and academic, musical or sporting reputation. If you are able to visit Cambridge (preferably on a College Open Day) you may get a better idea of the location, atmosphere and facilities of various Colleges.

Christ's College does not have fixed quotas of places for different subjects and the exact numbers admitted in any one year will depend upon the strengths of the fields of applicants in various subjects. However, Christ's aim is to admit around a dozen students each year in Mathematics. Applicants are usually interviewed in November or December: normally applicants will have one short general tutorial interview (of about 10-15 minutes) and two Mathematics interviews (about 25 minutes each). Candidates for the courses in Mathematics with Computer Science or Physics may have an additional interview in Computer Science or Physics, possibly replacing one of the Mathematics interviews. During the subject interviews, we may ask questions on topics with which you are not already familiar: the aim here is to assess your innate mathematical ability when working through unprepared questions and your ability to absorb quickly new ideas. This approach minimises the effects of a candidates background and teaching and creates a level playing field. We will not try to catch you out but rather will help you work through unseen problems. We sometimes ask candidates to think out loud as they tackle interview problems as a means of helping us to understand their individual approach to Mathematics. We are not simply trying to test knowledge or memory of theorems, etc., as these will be tested in due course by A-level or other examinations.

Entry requirements are likely to be A*AA or AAA at A-level, or comparable grades in other qualifications. Everyone can have a bad day, a bad interview, or a bad examination so we try to avoid allowing the prospect of a place at Cambridge to rest on a single observation. Therefore, all offer-holders for Mathematics places at Christ's are usually asked to obtain top grades in both A-levels (or equivalent) and in STEP. The advantage of STEP (Sixth Term Entrance Papers) is that we can see the exact marks achieved by a candidate, and can also look at a candidates scripts where appropriate in order to judge the quality of the answers. In general we prefer candidates to take two STEP Papers rather than one, in order to build a small amount of redundancy into the system: there can be few candidates who have never performed at less than their best on the odd occasion. The use of STEP allows us to make more conditional offers than if we relied on A-levels alone, and in Mathematics we make about five offers for every four places. Our offers depend upon the subjects studied at A-level (or equivalent). As a very rough guideline:

Candidates who are taking Double-subject Mathematics A-level (or equivalent) will normally be asked to take both Paper II and Paper III of the Mathematics STEP.

Candidates who are taking Single-subject Mathematics A-level (or equivalent) will probably be asked to obtain a grade 1 in the STEP Paper I devised especially for them; under certain circumstances they might also be asked to take STEP Paper II.

However, a flexible attitude is taken to these requirements, and we are always ready to review them on a personal basis in the light of special circumstances. We are sympathetic to the problems that some schools have in providing special teaching, and we always pay particular attention to the assessment of candidates by their own teachers.

A final point worth making is that we only make offers to candidates that we believe they have a realistic chance of achieving. Our aim is to admit the best students regardless of their background.

Some candidates may wish to take a gap year. Because of the danger particular to Mathematics of going "off the boil" and losing the knack of algebraic manipulation, we would expect you to explain what relevant activities you would undertake during your gap year and how you would ensure that your mathematical skills are kept honed.

Information about deadlines and further details can be found here.

Application statistics for Mathematics: approximately 10-12 places per annum; applicant to acceptance ratio around 3.5:1.

Further Information

If you are able to come to a College Open Day, we will be glad to tell you more about the College and the Mathematics course in person. Some candidates may also be interested in finding out more about the many ways in which Mathematics can be combined with other subjects within the Cambridge Tripos system. If you are not able to come to an Open Day, we will be happy to answer any queries you may have that are not covered by the normal literature. Please address any such enquiries to the Admissions Tutor, Christ's College, Cambridge, CB2 3BU, or by e-mail to admissions@christs.cam.ac.uk.