In 2020, the admissions process is not operating as set out in the text below. The interviews in 2020 will be conducted remotely, and as a result the structure of the interviews and some of the assessments will be changing for this year. All applicants in the 2020-21 round should instead consult the ‘Pre-interview and interview notes’ document for 2020, which they will have been sent separately.
The Mathematical Tripos was historically the first Tripos to be established at Cambridge and the study of Mathematics has always been seen as one of the University’s main strengths. The course provides a solid foundation for progression to advanced mathematics, develops the student’s mathematical understanding to a very high level, and allows a very wide choice of topics in which to specialise. There is also a fourth year course, leading to a M.Math degree, intended mainly, but not exclusively, for those who wish to go on to research. This course covers a wide range of advanced mathematics, and also many areas of theoretical physics, and about 50% of Trinity undergraduates stay on to take it.
In the first year of the Tripos mathematics students follow a common, core course. The aim of the core course is to provide an introduction to both pure and applied mathematics. The second year has more flexibility and it is possible to begin specialising in one area of mathematics, be it pure, applied, or applicable (where, in Cambridge terminology, ‘applicable’ means probability and statistics). In the second and third years there are also separately assessed computer projects. Although not compulsory, students are encouraged to do these, at least in the second year.
The Cambridge Mathematics course also provides a very good basis for studying a variety of other subjects. Although the numbers in any year are not large, students who have decided to change from Mathematics at the end of their first or second year have had an excellent record of subsequent achievement in Computer Science, Natural Sciences, Engineering, Economics and a range of other subjects.
Trinity has a strong reputation in Mathematics and many of our undergraduates achieve outstanding results in Tripos examinations. But the College does not take a narrowly academic view of the subject. Trinity is a large college and the success of our students owes as much to the breadth and depth of our teaching resources as it does to the students’ natural abilities. The 40 or so students we admit each year go on to pursue a wide range of careers. Many go on to higher degree courses, others find attractive positions in many fields, particularly in the financial sector and in computing.
There is a separate option Mathematics with Physics in which 25% of the first year lectures are replaced by some from Natural Sciences. The threshold for admissions, in particular in terms of mathematical background, is no different from Mathematics, and is not an easier option.
There are currently ten teaching Fellows in Mathematics (listed below with their wide range of research interests), who take the main responsibility for undergraduate supervision, as well as many research Fellows and graduate students, who also undertake some College teaching. Trinity has the capacity not only to stretch the brightest students but also to provide individual assistance for any who find difficulty with parts of the course.
The large number of undergraduate mathematicians at Trinity results in a strong sense of ésprit de corps among our students who learn a lot by interacting with each other. This is manifested in a thriving Mathematical Society which runs an extensive programme of talks and social events.
Applicants for places at Trinity will be taking two Mathematics A-levels. In most years, there are also applicants taking Pre-U examinations in Maths and Further Maths, and the International Baccalaureate with Higher Level Maths and Further Maths.
The College is always keen to attract women mathematicians. We are also willing to consider applications from those seeking to defer entry for a year, although it is felt that deferred entry is not generally beneficial for those wishing to study mathematics.
The interview is about 40-45 minutes with two members of the Mathematics teaching staff. It is preceded by a one-hour written test and the candidate’s attempts at the problems in the test form the basis of much of the discussion in the interview itself. Some specimen questions are available here:
A slightly different test is set for Mathematics with Physics, but candidates for this option need to be aware that they will be judged primarily on their mathematical ability and how they have done in the preceding test.
A typical offer is a conditional offer, which typically asks for A*A*A at A-level plus good grades (usually grades 1,1) in STEP Mathematics papers II and III; comparable conditions are set for those taking the IB and other school-leaving examinations. It is extremely rare for a candidate to achieve good grades on the STEP papers and not to achieve the A-level grades. If anyone has already achieved our usual requirements in any of the relevant STEP examinations or A-levels, they are not required to repeat these exams.
Although the level of our offers may seem high, we often admit a small number of candidates who narrowly fail to meet the conditions they were set.
Teaching Staff in Mathematics
- Tom Fisher (number theory)
- Eric Lauga (fluid dynamics)
- Imre Leader (combinatorics)
- John Lister (fluid dynamics)
- Jason Miller (probability and geometry)
- Harvey Reall (general relativity)
- David Skinner (quantum field theory)
- Michael Tehranchi (financial mathematics)
- David Tong (string theory)
- Henry Wilton (topology and groups)
If you want further information about the Tripos, the Faculty of Mathematics has a website.
The website above includes a link to a specimen STEP paper. Infomation about STEP is also contained in the Cambridge Admissions Prospectus.