Cambridge has a world-leading reputation for Mathematics that spans the centuries, from Isaac Newton to Stephen Hawking. The undergraduate course, or Mathematical Tripos, is unsurpassed in its breadth and depth, making it challenging but extremely rewarding. It is an ideal preparation for those who might ultimately embark on research in Mathematics or related areas, but it is also an excellent foundation for a range of other careers, whether in industry, management, computing, finance, or teaching.
The first year (Part IA) follows on from material that will be familiar from school, helping students to make the transition to university. Courses include Numbers & Sets (foundational material), Vectors & Matrices, Groups (introducing axiomatic abstract algebra), Differential Equations, Analysis (rigorous treatment of limits, continuity, differentiation and integration), Probability, Vector Calculus (differentiation and integration in many dimensions), and Dynamics & Relativity. There is also a short introduction to mathematical problem solving using computers, in preparation for project work in the second and third years. And there are non-examinable courses for those who have not had the opportunity to do much Mechanics at school, and for those who are interested in getting a broader perspective on Theoretical Physics.
Students pursuing the Mathematics with Physics option (only applicable to the first year) take Part IA Physics in the Natural Sciences Tripos in place of two of the eight Mathematics courses. This allows the possibility of changing to Natural Sciences (Physics) in the second year, or continuing with Mathematics.
The second year of Mathematics (Part IB) offers a certain amount of flexibility in the choice of courses, while the third year (Part II) offers a very wide choice of subjects, with areas as diverse as Number Theory, Topology, Probability, Quantum Mechanics and Mathematical Biology.
For students who have done well, there is the option to continue to a fourth year (Part III)—essentially a taught Masters course—leading to an MMath degree.
Mathematics at Caius
Students at all Colleges attend lectures organised by the Faculty of Mathematics as a whole, but they attend supervisions (small classes of one or two students) arranged within their own College. At Caius, we are fortunate to have a very strong teaching team in Mathematics, which means that students in their first two years will usually be taught by Fellows of the College. We aim to admit about ten undergraduates in Maths each year, and the friendly and informal atmosphere in supervisions helps students to get to know each other and their supervisors, reinforcing the sense of a supportive mathematical community. Caius also runs a short preliminary course in Mathematics to help new students adjust to study at Cambridge; this has proved to be both popular and successful.
We encourage candidates sitting A-levels to take double Mathematics at school if possible.[*] Candidates in other exam systems are welcomed, and should study as much advanced Mathematics as their systems allow. Some general guidelines on entrance requirements are provided at the University's web pages.
Applicants to Caius usually have two Mathematics interviews (one a general mathematics interview, and the other on a selection of chapters from a book we would ask you to look at in advance). Both interviews last about 30 minutes and involve the discussion of mathematical problems—our aim is to find out how you think about Mathematics.
Like most Colleges, we ask candidates to take STEP, the special papers for Cambridge entrance. A typical offer from Caius might be A*A*A at A-level and 1,1 in STEP papers (the STEP grades are S,1,2,3).
[*] For A-level students planning to apply in October 2018 (for October 2019 entry), A-level Further Mathematics will be a requirement.
Preparing for STEP
We recommend very strongly that anyone applying for Mathematics looks closely at the STEP papers, since these form an important part of our admissions process. STEP is administered by Cambridge Assessment. Detailed information, including paper specifications, past papers with answers, and examiners’ reports are available from the Cambridge Assessment webpages on STEP.
The Faculty of Mathematics also has its own helpful pages about STEP. The booklet by Stephen Siklos is particularly useful. You might also benefit from looking at some of the other resources on his website, including the past papers and a link to the NRich website. The Further Mathematics Support Programme can also offer support for both AEA and STEP preparation.