### Mathematics Overview

St John's has a large and diverse Mathematics community, with about 15 undergraduates in each year group, drawn from across the UK and overseas. A significant number continue to Part III (the optional fourth year), where they are joined by some of the top students from other institutions around the world. We encourage applications from bright students of all backgrounds, and award an annual Pythagoras Prize of £10,000 to a first year home undergraduate in Mathematics, based on academic excellence and financial need.

Students attend lectures organised by the Faculty of Mathematics, alongside their peers from other Colleges. These are complemented by supervisions, arranged separately by the College, where students are taught in small groups (usually pairs) by a Fellow or research student. The discussion is typically based around problem sheets which students attempt in advance, and forms a crucial part of the Cambridge teaching system. Each student has a Director of Studies (in fact, two! - one in Pure and one in Applied; an unusual feature of St John's) who follows their progress in the course and provides guidance on academic matters. They also have a personal tutor, who provides pastoral support.

In the first year students can expect twelve hours of lectures per week, plus two hours of supervisions. The load in later years is similar but students have a great deal of flexibility to choose a programme that suits their interests and goals. Another unusual feature of St John's is that all of the first year students come together, once per week in each of Pure and Applied Mathematics, for additional Examples Classes to complement the lectures and supervisions. These classes continue, at a reduced rate, into the second year, to reinforce the important ideas that form the foundation for further study.

The College has an active mathematical society, the Adams Society, which organises regular talks and social events. The society is named after John Couch Adams, a Mathematics graduate of the College from the 19th Century, who correctly predicted the existence of Neptune. He is just one of many distinguished alumni, alongside Brook Taylor, of Taylor's Theorem, and pioneers of quantum mechanics Paul Dirac and Abdus Salam.

### Subject Video

##### Subject Video

### Course

##### 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.

### Entry Details

**UCAS Code**: G100

##### Typical Entry Requirements

__A Level:__ A*A*A

__International Baccalaureate:__ 42 points, with 776 at Higher Level

__STEP (Sixth Term Examination Paper):__ At least Grades 1 in STEP II and STEP III

__Essential Subjects:__ A Level Mathematics and Further Mathematics. IB Higher Level Mathematics: analysis and approaches or Mathematics: Applications and Interpretation.

*N.B. The IB Higher Level Mathematics: the Mathematics Analysis and Approaches or the Applications and Interpretation syllabi will be accepted at higher level, but Analysis and Approaches is preferred.*

__Desirable Subjects:__ None

__Submitted Work:__ None

__Pre/At-interview Assessment:__ None

##### 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.

##### Admissions Interviews

Those invited for interview normally have two subject interviews with Maths Teaching Fellows, each of around 25 minutes duration. At least one of these interviews will be with a Director of Studies in Mathematics. Please find the list of Pure Mathematics Interviewers for 2021 here.

Almost all of the interview time will be spent talking through maths problems. The problems will cover a range of topics but are designed to test how you think, rather than what you know. We are more interested in how you approach unfamiliar concepts, and in how you make or follow suggestions, than in whether you simply know the right answer. You don’t need any special knowledge and it is not a memory test, so there is no need to try to prepare lots of answers or memorise many things. What is most important is that you describe your thoughts to the interviewers. There are no trick questions or puzzles.

Interviews in December 2021 will be conducted remotely via Zoom. You will not need a writing tablet or similar; indeed, you will not be allowed to use one. The interviewers will act as scribes, so you are free to focus on the mathematics and to talk through your thoughts. You are welcome to have a pen and paper to hand if this helps you.

##### STEP

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.

### People

**Directors of Studies**

Dr Matthias Dörrzapf - Mathematics

Dr Jack Smith - Pure Mathematics

**Tutor**

Canon Mark Oakley

**Subject Fellows**

Dr Sue Colwell

Dr D J H (Ben) Garling

Professor Peter Johnstone

Dr Alan Macfarlane

Professor Nicholas Manton

Dr Dhruv Ranganathan

Professor Richard Samworth

Dr Jack Smith

Professor David Stuart

Professor Yuri Suhov

Professor John Taylor

Professor Andrew Woods

### Student Views

What makes maths at John’s really special is the community we have here.

The upside of being a relatively large maths cohort is that you are likely to find other mathematicians who are on a similar wavelength. We all support each other a tremendous amount and, because of the collegiate system, you can seek advice from people in older years; there’s a real sense of mentorship, which is so invaluable. Supervisions are another unique aspect of Cambridge, they’re an opportunity to really consolidate your learning, often with prominent academics in that field.

I have found that having teaching in such small groups has given me the confidence to ask any questions I want, and clarify parts of the course without feeling shy or nervous.

** - Anusha**

St John's has a very welcoming maths community. There’s plenty of individualised support from college, so you can make the most of what is a challenging and rewarding course. I really like the sense of belonging you get from being in a large group of mathematicians; it’s always nice to spot a fellow mathematician walking around in college!

One particular highlight is a student run mathematics society. They regularly organise mathematical talks – one of my favourites is about the distributions of primes, which linked in nicely with the 1A Probability course we had just finished in Lent term. There’s social events as well, from board games to formal dinners, and it’s a great opportunity to unwind.

** - Sae**

In my (unbiased) opinion, St John’s is the best college for maths. We have expert teaching staff, who are also very friendly. We get extra support in the form of example classes in first and second year – which I found really helpful. And we are ideally situated between the centre of town and the CMS. John’s is the best college for student life too!

Excellent facilities. Kind and skilled staff. Beautiful buildings. Vibrant clubs and societies. Lovely people. I have been able to get involved with Ultimate Frisbee, Jazz, Ballroom Dancing, a choir, Fives, and even Comic Opera!

** - Lennie**

I've absolutely loved my first two years doing maths at St John's. I feel the maths community here is a lot more relaxed and family-like than at other colleges, with fellows and students alike happy to socialise when we get a break from example sheets! I think we have just the right number of mathematicians at John's too - enough so you can make friends easily, but it is still a very personal experience.

Away from maths, I'm captain of the college hockey team, which is an excellent distraction from working. John's is also very generous - they paid for me to go on a trip to Marrakesh at the end of my first year, and I should be heading out soon to Nagoya, in Japan, for the return leg of a cultural exchange!

** - Connor**

### Further Information

##### 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/