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St John’s College has a long tradition of excellence in Mathematics, dating back at least to Brook Taylor (after whom Taylor’s Theorem is named) in the early 18th century, and including such giants as James J Sylvester in the 19th century, and Paul Dirac in the 20th. We currently have five Teaching Fellows in Mathematics, a number of Research Fellows and four Professors.

St John’s College awards the prestigious Pythagoras Prize to a selected first year undergraduate student coming to read Mathematics at the College.

We take about 15 undergraduates a year to read Mathematics, and they are normally taught (for an average of about two hours a week) by the Fellows, or by research students of the College, in addition to attending the University lecture courses. The College has excellent library facilities for those reading Mathematics, and there is a well-equipped computer room as well as the possibility of connecting your own computer to the University network from your own room.  The Adams Society, the College’s mathematical society, is one of the oldest undergraduate societies in the University, and meets regularly to hear speakers on mathematical topics, some serious and some less so; it also organises social events.

Courses in Mathematics

The Cambridge Mathematical Tripos is probably one of the best and most wide-ranging undergraduate mathematics courses at any university in the world. Although it is certainly a demanding course, enthusiasm and determination to meet the challenge of understanding new mathematical concepts count for far more than the amount of material you have covered at school.

The structure of the Tripos is designed to accommodate a fairly wide range of different backgrounds. The basic idea is that, in the exams at the end of the first two years, all candidates take the same papers (with the exception of those doing Maths with Physics or Maths with Computer Science — for which see below), covering the basic material in pure mathematics, applied mathematics, theoretical physics, probability and statistics which all educated mathematicians need to know. However, many of the individual lecture courses in these two years may be taken either earlier or later, depending on the readiness of individual students to move on to new material in different areas. Thus a student can tailor the structure of the course to suit his or her own abilities and background.

The third-year course, Part II of the Tripos, consists both of courses of a more general nature and of specialised courses. The courses of a general nature are intended for those who see a B.A. degree in Mathematics as the culmination of their study of the subject. There are some 10–15 courses giving a broad overall perspective on mathematics and its applications in the modern world. The specialised courses are deeper and more challenging; they are aimed at those who intend to go on to postgraduate work in some area of mathematics. Students are allowed to choose freely among both types of courses, depending on their own needs and abilities.

In the first year, in addition to the standard Mathematics course, there is one option called ‘Mathematics with Physics’. This is taken, in a typical year, by about 10% of our intake; in each of them, students take three-quarters of the standard first-year Mathematics courses, and the remaining quarter is replaced either by the Physics lectures from Part IA of the Natural Sciences Tripos. The intention of these options is to accommodate students who wish to defer a decision on their final degree subject until they have experienced both subjects taught at university level. Our experience is that, of those who take them, about half choose to continue with Mathematics in subsequent years, and the other half transfer to Natural Sciences.

There are many other subjects to which students can and do transfer after either one or two years of Mathematics in Cambridge. They include Astrophysics, Economics, Education, Engineering, Management Studies and Philosophy.

The ability of logically analysing and understanding abstract models and unknown environments is one of the main reasons why Mathematicians are successful in very different careers. Many of our recent Mathematics students entered PhD programmes in Mathematics, Physics, Computer Science or Finance at Cambridge or at other top UK or US Universities. Others joined management consultancies, investment banks or insurance companies for exciting careers in financial mathematics or actuarial mathematics. Several of our Mathematicians have also entered PGCE programmes or took up teaching positions at leading UK schools.

UCAS Code: G100

Entry Requirements

At least A*A*A at A Level. Mathematics and Further Mathematics (or Mathematics and Physics) essential; STEP (at least Grades 1 in STEP II and STEP III)

Application to St John’s

The traditional dichotomy between Single and Double Mathematics A-level has been rendered increasingly obsolete in recent years by the growing popularity of modular A-level syllabuses: these days our applicants may be taking the equivalent of 1, 1½, 2, 2½ or even 3 A-levels in Mathematics, but the majority of them take at least two Mathematics A-levels, and we certainly recommend this as the best possible preparation for the Mathematical Tripos. Nevertheless, we are keen to encourage applications from candidates who have not, because of the particular circumstances in their schools, been able to study the full double-subject A-level syllabus; and our experience is that such candidates often go on to highly successful careers in mathematics, if they have the determination to succeed. For those of you following other educational systems, please click here for a list of alternative offer levels.


Those invited for interview normally have three interviews, each of 20–25 minutes duration: one with the Tutor for Mathematicians, who will be concerned to find out what you can contribute to the College in addition to your academic skills, and two subject interviews, one with the Director of Studies in Applied Mathematics and one with the Director of Studies in Pure Mathematics. In the subject interview, our aim is to probe your mathematical ability as well as your motivation for studying the subject; we shall probably ask you to tackle some unseen mathematical problems, but no special preparation for these is necessary or even desirable.

Further information


For Pre-A-level applicants taking two or more Mathematics A-levels, our normal conditional offer involves at least A*A*A grades at A2 (two in Mathematics and one in another subject), plus at least Grades 1 in Mathematics II and Mathematics III at STEP. However, we are always willing to consider variations in these conditions in the light of individual circumstances.

For candidates not offering two Mathematics A-levels, our conditions are always decided in the light of individual circumstances, but would be likely to include A*A*A grades at A2 (in Mathematics, Physics and one other subject), plus a Grade 1 in Mathematics I and/or Mathematics II at STEP.

The STEP syllabus is based on the subject cores for A-level syllabuses (and thus requires no additional knowledge), the questions are of a searching kind designed to test qualities like insight, originality, grasp of broader issues and the ability to use standard techniques in unusual ways and situations. The papers are intended to supplement and amplify the information provided by A-level results.

St John’s is extremely concerned to ensure that no potential candidate is put off from applying here on account of these extra conditions of STEP level for Mathematics. Please bear in mind that there are advantages in including STEP in our offers, both for the applicants and for us.

Application to sit STEP papers should be made through your school or college, and the papers must be taken at a recognised centre. If you have any difficulties over this contact: OCR, 1 HILLS ROAD, CAMBRIDGE, CB1 2PT, Tel: 01223 553311. If you would like copies of past papers or of the Regulations and Syllabuses booklet contact: OCR Publications, Mill Wharf, Mill Street, Birmingham, B6 4BU (www.ocr.org.uk). Enquiries should be made by mid-January if possible

Admissions to Part III Mathematics

Admission into Part III leading to the M.Math, degree normally requires a First Class result at Part II but the Faculty of Mathematics will consider requests for Part III from students within the top third of the II.1s (in terms of merit marks) in Part II Mathematics and who demonstrate evidence of First Class potential.

Further Information

Please contact The Mathematics Faculty Office, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WA, or visit their website at http://www.maths.cam.ac.uk/

Mathematics Course Video, courtesy of the University of Cambridge