Cambridge is one of the leading international centres for research and teaching in Mathematics, with a reputation dating back to Sir Issac Newton (Lucasian Professor 1669–1696). The Cambridge Mathematics course provides an excellent basis for a huge range of careers (financial management, teaching, accountancy, computing, actuarial, civil service, industry), as well as for research in Mathematics and related areas.
The first year’s work follows on from material that will be familiar from A–level, helping students to make the transition to university–level Mathematics. The courses are Algebra & Geometry (which includes topics such as vectors, matrices, groups), Differential Equations, Numbers and Sets, Analysis (sequences and limits, functions, continuity, differentiation and integration), Vector Calculus, Probability and Dynamics. There is also a short introduction to computing in preparation for project work in the next two years. For those who feel that they have not done enough Physics at school, there is a non–examinable course on the basics of this subject.
There is a certain amount of flexibility in the second year as far as timing and choice of courses is concerned, while in the third year you will be able to choose from a very wide selection of subjects, ranging from Groups and Number Theory to Quantum Mechanics or Mathematical Biology. If you do well, there is the possibility of taking the fourth year "Certificate of Advanced Study in Mathematics". Further information about the Mathematical Tripos is available here.
Mathematics at at Caius
Students at all colleges attend lectures organised collectively by the Faculty of Mathematics, but they attend supervisions (small classes of one or two students) which are arranged within their own college. At Caius, we are fortunate to have a very strong teaching team in Mathematics and students in their first two years will usually be taught by Fellows of the College. We admit about ten undergraduates in Mathematics each year, and the friendly and informal atmosphere in supervisions helps students get to know each other and their supervisors. Caius is also one of the few colleges to run a short preliminary summer course in Mathematics to support students in their first term at Cambridge, which has proved to be very popular.
Over the last decade Gonville & Caius has been very successful in Mathematics: in the unofficial tables of Tripos examination results, we do very well and are consistently one of the top Colleges.
The College has eight Fellows in Mathematics:
Professor S.W. Hawking, C.H., C.B.E., Ph.D., Hon Sc.D., F.R.S, Fellow. Lucasian Professor of Mathematics, Department of Applied Mathematics and Theoretical Physics (DAMTP). Research on cosmology, black holes and quantum gravity. His books, A Brief History of Time and The Universe in a Nutshell, are best–sellers. His contribution to the theory of general relativity has made a huge impact on both mathematics and physics.
Professor T.J. Pedley, Sc.D., F.R.S. Fellow. G.I. Taylor Professor of Fluid Mechanics and Head of Department of Applied Mathematics and Theoretical Physics. Research on fluid mechanics applied to biology and medicine.
Professor J. Saxl, Fellow, Director of Studies in Pure Mathematics. University Professor in Algebra. Works in Abstract Algebra, with particular interest in groups acting on algebraic, geometric and combinatorial objects.
Dr J.M. Evans, Fellow, Tutor, Director of Studies in Applied Mathematics. Research interests include quantum field theory and string theory.
Dr R.J. Gibbens, Fellow in Mathematics and Computer Science. Research interests in mathematical modelling of telecommunication networks, computer-based modelling techniques.
Professor F. Quevedo, Fellow in Applied Mathematics. Research interests include string theory and supersymmetry.
Dr I. Smith, Fellow, Reader in Pure Mathematics. Research interests in Geometry.
Dr Ed Brambley, Research Fellow, Assistant Director of Studies. Research interests in waves, especially mathematical models used to model acoustic linings in aircraft engine intakes.
Apart from the Fellows mentioned above we have a Visiting Fellow in Mathematics every year. In the last few years, the Visiting Fellows have been Professor J. H. Conway, FRS, perhaps the best-known of our former Mathematics students, famous for his work on knots, games, numbers, logic and groups, Professor Benoit Mandelbrot, well known for his fundamental work on the theory of fractals, Professor G. Margolis, a Fields Medallist with interests in a broad range of Pure Mathematics, and Professor M. Rabin, famous for his pioneering work in theoretical Computer Science and Cryptography.
Admissions
Most of our candidates apply in the year before taking their A–levels, and all are interviewed. We encourage candidates to take double maths at school if at all possible and we usually ask candidates to take STEP, the special papers for Cambridge entrance (most colleges ask for STEP — one advantage is that it allows us some flexibility in cases where candidates do not quite meet the conditions of their offer, because we have access to their scripts). A typical offer might be A*AA at A–level and a 1 and a 2 in STEP papers (the STEP grades are S, 1, 2, 3). Details on preparing for STEP are available below.
Candidates 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 involve the discussion of mathematical problems and our aim is to find out how you think about Mathematics.
Most Mathematics students in Cambridge have done two Mathematics A–levels, and this is clearly an advantage during the course. Nevertheless, candidates with a single A–level in Mathematics are welcome to apply to Cambridge. Ideally, such a candidate would do a standard Pure Mathematics A–level (preferably not with Statistics) and would also take Physics and one other subject.
We look forward to hearing from anyone who is thinking of applying to Cambridge. Our Open Days are normally held in May and July. Visits can also be arranged independently of these. If you would like further information please contact the Admissions Tutor.
Preparing for STEP
We recommend very strongly that anyone who has applied for Maths, or is considering applying for Maths, looks into the STEP papers which form an important part of our admissions selection. STEP is now administered by Cambridge Assessment and you can find Examiners’ reports for last year and the specification for the papers here.
If you have any difficulty in obtaining past papers, then you should contact Cambridge Assessment direct on:
stepinfo@cambridgeassessment.org.uk
The Maths faculty has its own very helpful pages about STEP that can be found here.
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. There is also a link there to the NRich website which also has excellent resources. The Further Maths network (see http://www.fmnetwork.org.uk/online.php) can also offer support for both AEA and STEP preparation.
