Mathematics

Equally demanding and fulfilling, Cambridge's renowned Mathematics Tripos offers unparalleled opportunities to develop your mathematical intuition and reasoning across a diverse array of topics, from abstract logic to black holes.

Overview

Ucas code

G100

Campus code

X

Typical offers made per year

23

Typical Undergraduate cohort

51

Minimum offer level

A Levels: A*A*A, with A* in Mathematics and Further Mathematics

IB: 42 points, with 776 at Higher Level.

Other qualifications: check what other international qualifications are accepted at Cambridge

STEP (SIXTH TERM EXAMINATION PAPER)

At least Grades 1 and 1 in STEP II and STEP III

COURSE DURATION

BA (Hons) 3 years full-time, or MMath 4 years full-time

Essential subjects

A-level Mathematics and Further Mathematics

Desirable subjects

None

ADMISSIONS ASSESSMENT

Admissions Assessment: Normally successful applicants have to take the Sixth-Term Examination Paper (STEP) alongside A-levels (or equivalent) as part of a conditional offer. Further information is available here.

Submitted Work: None

Why Choose St John's for Mathematics?

A photograph of the Penrose tiling outside the College Library

Since our foundation, St John’s has attracted brilliant mathematicians. Henry Billingsley made the first English translation of Euclid’s Geometry; Brook Taylor laid the foundations of differential calculus; Sir John Herschel discovered Uranus; John Couch Adams predicted the existence of Neptune (his handwritten calculations are held in our Library); Max Newman revolutionised topology; and Sir Roger Penrose’s contributions to mathematical physics culminated in a Nobel Prize in 2020.

Backed by strong representation in our Fellowship, our strong and lively Mathematics community includes over 50 undergraduates and a large number of graduate students. We believe it’s the ideal size: small enough to build up a close relationship between the students and the teaching Fellows, and sufficiently large to stimulate vibrant mathematical discussions.

St John’s teaching Fellows cover the full breadth of the Mathematics course. In addition to supervisions, we provide examples classes to our students in the fundamental topics, to develop their mathematical presentation and interaction skills.

Our 100-year-old, student-led Mathematics society, the Adams Society, is active in organising talks, socials and a very popular annual dinner.

Watch this video to find out more about studying Mathematics at St John's College.

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Our academics

Director of Studies

Sub-Director of Studies

Dr Susan Colwell

Fellow

Director of Studies

Sub-Director of Studies

Dr Matthias Dörrzapf

Fellow

Director of Studies

Sub-Director of Studies

Dr DJH (Ben) Garling

Fellow

Director of Studies

Sub-Director of Studies

Dr Peter Goddard

Fellow

Director of Studies

Sub-Director of Studies

Dr Joshua Jackson

Fellow

Director of Studies

Sub-Director of Studies

Professor Peter Johnstone

Fellow

Director of Studies

Sub-Director of Studies

Dr Jef Laga

Fellow

Director of Studies

Sub-Director of Studies

Professor Po-Ling Loh

Fellow

Director of Studies

Sub-Director of Studies

Dr Alan J Macfarlane

Fellow

Director of Studies

Sub-Director of Studies

Professor Dhruv Ranganathan

Fellow

Director of Studies

Sub-Director of Studies

Dr George Reid

Fellow

Director of Studies

Sub-Director of Studies

Professor Richard J Samworth

Fellow

Director of Studies

Sub-Director of Studies

Professor Benjamin Simons

Fellow

Director of Studies

Sub-Director of Studies

Professor David Stuart

Fellow

Director of Studies

Sub-Director of Studies

Professor Yuri Suhov

Fellow

Director of Studies

Sub-Director of Studies

Professor John R Taylor

Fellow

Director of Studies

Sub-Director of Studies

Professor Andrew W Woods

Fellow

Course structure and information

After set courses in the first year to lay the foundations, you’ll then have more choice each year to specialise in your areas of interest, whether they are pure, applied or applicable.

Find out more about the course structure and what to expect when studying at St John's College.

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Supporting your studies

Academic skills support

All St John's students have access to academic skills support throughout their studies. Academic skills workshops are offered throughout the academic year, and focus on a variety of topics including general study tips, essay-writing skills and revision strategies.

Some subjects hold compulsory academic skills workshops during the Michaelmas term. If you require individual support you can contact one of our Academic Skills Advisers, who each have a range of specialities, including essay writing tips, numeracy, presentation skills, prioritisation and revision skills. We have specialists in Arts and Humanities and in STEM, and in particular in Engineering.

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Summer Bursaries

Our generous Summer Bursary scheme enables St John's undergraduates to pursue their academic or educational interests or career-development opportunities for a period of up to eight weeks during the Long Vacation.

Any activity which would clearly add value to your career and personal development can be considered, and students have used their Summer Bursaries to fund a wide range of activities including research projects, summer courses at other institutions, intermediate and advanced language courses, unpaid work experience and volunteering work in the UK and overseas.

Exchange Programmes

St John's is proud to collaborate with a number of great institutions to provide exciting cultural and academic exchanges. Our current exchange partners include Caltech Scholars exchange, Collegio Ghislieri di Pavia University Exchange, Heidelberg University Exchange, Nagoya University Exchange Scheme and NUS Research Exchange Programme.

Discover student life

meet our students

The mathematical heritage of St John’s is deeply inspiring, the academics who teach us in College challenge our thinking and encourage us to be creative

Michelle, Mathematics, undergraduate

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The mathematical heritage of St John’s is deeply inspiring, the academics who teach us in College challenge our thinking and encourage us to be creative

Michelle, Mathematics, undergraduate

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I’ve always loved maths and when a Fellow from St John’s came to give a talk at my school in Liverpool, he encouraged me to visit the College and apply to Cambridge. Even though I don’t consider myself to be a very sociable person, I still wanted to be at a large College so I was part of a sizable group of students to talk about maths with and support one another.

The Adams Society is very active at St John’s and I go to every event because it is an excellent chance to learn about the latest research directly from the people doing it. We are lucky because we have something called example classes for all first and second-year Maths students at St John’s, when our Fellows revisit a lecture to explain the concepts again, and we can ask questions – it’s invaluable.

Applying

Mathematics at Cambridge is one of the most challenging and exciting undergraduate courses in the world. It’s for students who are relentlessly curious about and excited by mathematics, are doing very well in it at school, and who are ambitious to see how far they can go.

Doing exceptionally well in your school examinations is essential, and the STEP examination is very important. Start practising STEP papers long before you even make an application – don't wait until after your interview.

We are looking for evidence in your application that you have pursued Mathematics beyond your school syllabus, thinking more deeply about it and being keen to understand mathematical structures. Explore your interest in Mathematics through wider reading, project work, your independent thinking, and Maths competitions if you have access to them.

Interact mathematically with others, perhaps in Maths clubs online or in person, and find opportunities to present your ideas and be challenged on your mathematical thoughts and understanding. Mathematics is very active – exchanging ideas is central to studying here.

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If you are invited to interview, you will be asked to complete a pre-interview test. On the day, you will normally have two interviews with Fellows in Mathematics, each about 25 minutes long.

Almost all of the interview time will be spent talking through Maths problems. These 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, there are no trick questions and it is not a memory test. We are looking for those who can develop insight into new Mathematics with our guidance and are able to engage in a mathematical conversation about problems they have not thought about before. What is most important is that you describe your thoughts to the interviewers.

STEP (Sixth Term Examination Paper)

St John’s provides tailored STEP support to our offerholders at state schools who have no or little access to STEP preparation. STEP requires no special knowledge or training, beyond A-level Maths and Further Maths. It is a very good indicator of suitability to study Mathematics at Cambridge. Working through STEP questions is an excellent way to see whether you enjoy the style of mathematical thinking you will encounter here, and to prepare for Cambridge maths interviews. We strongly encourage applicants to start preparing early for STEP, ideally over the summer between Years 12 and 13. The questions are designed to be challenging for all applicants, so do not worry if they seem difficult: you will improve significantly with practice. There is more information here, with links to free online resources.

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Life after St John's

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Our societies

Adams Society

The mathematical society of St John’s College is called the Adams Society. Founded in 1923, we are one of the oldest undergraduate societies in Cambridge.

We are named after St John’s mathematician John Couch Adams, who is famous for predicting the existence of the planet Neptune using nothing but its gravitational effects on the orbit of Uranus.

Our members are Mathematics undergraduate and postgraduate students and Fellows at St John’s. We hold academic talks by well-known mathematicians and our social events include an annual dinner and garden party.

Find out more Visit society's website

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Notable alumni

Professor Paul Dirac

1923

Mathematician

Nobel Laureate

Royal Medal winner

Academy Award winner

Pulitzer Prize winner

Olympic Medal winner

Poet Laureate

Credited with founding quantum electrodynamics, Dirac arrived at St John's for his PhD in 1923 and a decade later (having joined the Fellowship) he won the Nobel Prize (jointly with Schrödinger) for the discovery of new productive forms of atomic theory. He predicted the existence of anti-matter and formulated the relativistic equation for the electron. A room in College is named after him and his gown still hangs in the Master's Lodge.

Sir Roger Penrose

1952

Mathematician

Nobel Laureate

Royal Medal winner

Academy Award winner

Pulitzer Prize winner

Olympic Medal winner

Poet Laureate

Penrose was Rouse Ball Professor of Mathematics at Oxford. He researched the mathematical physics of general relativity and cosmology, proving that black holes can arise from the gravitational collapse of dying stars. He was awarded a Nobel Prize in Physics in 2020. He also invented twistor theory, popularised the Penrose Triangle, and discovered aperiodic Penrose tilings, which exhibit fivefold rotational symmetry. In College, an example of Penrose tiling can be seen outside the Library and a bi-annual Penrose Lecture is held.

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