Mathematics

Pembroke has a rich tradition in Mathematics having had mathematicians as eminent as William Hodge and George Stokes as Fellows. Recent years have seen the flourishing of a vibrant mathematics community within the College along with the development of close academic and social interaction between students of the various year groups and Fellows.

Although Pembroke is a relatively small college, the number of mathematicians, at all levels, is comparable with those in much larger colleges. All the supervising in the first year, and almost all in the second, is undertaken by Fellows of the College. In the third year, because of the broad range of options available to students, like every other college we join with a group of ten colleges in the organisation of supervisions.

Mathematics at Cambridge has a particularly high reputation world-wide. At Pembroke we seek to admit around eight mathematicians each year from a very wide range of school backgrounds, from both the UK and abroad. Moreover we also admit students from other non A-level backgrounds and have had successful applicants from several countries across the world.

Pembroke College is also very well situated in Cambridge for those who wish to study mathematics. All lectures for the first two years are held in lecture theatres close to the College, and the University bus service, that links the Centre of Mathematical Sciences (www.maths.cam.ac.uk) with the city, has a stop directly outside the College.

Almost all successful candidates will have, or be predicted to achieve, A* or A grades in A-level Mathematics, Physics and Further Mathematics (or equivalent). A separate sheet of information for non A-level candidates interested in the Mathematics Tripos is available from the Admissions office.

We shall ask you to take two of the Cambridge Sixth Term Examination Papers (STEP).

What are STEP?

The STEP are administered by the Cambridge Assessment on behalf of the Cambridge Colleges. There are three papers in Mathematics: offers require candidates to take Papers II and III. These papers are intended to be of A-level standard, but not based on A-level syllabus. Hence they have a large number, currently 14, of questions from which you are asked to select just six. You can find out more about past STEP papers from the Faculty of Mathematics’ website. From these you will be able to see which are the questions you are likely to be able to answer on the basis of your particular syllabus. You will also be able to get a feeling for the style of question favoured by the STEP examiners, which in general will be somewhat different from what you are used to.

A word of warning: you will also find, particularly in the earlier years, that the questions are a good deal harder than you would expect. Don’t be misled by this. They are hard for everybody and that simply means that a grade’1′, for example, would be awarded for the equivalent of two or three correct answers, rather than the four or five which you might expect from your A-level experience. There is an excellent booklet available containing solutions to 42 STEP-type questions, complete with a general discussion ahead of each proof and comments during it on the less obvious points. This will give you a good idea of how to approach STEP questions and what is expected from you. It is available from the Faculty of Mathematics’ website.

So why do I have to take the STEP?

There are two main reasons why we like you to do the STEP if you can. We are trying to reach a fair and accurate assessment of your ability and aptitude for the Cambridge Mathematical Tripos. This is much easier if all of the candidates have taken at least one common paper, even if we do still have to make allowances for the different backgrounds from which they approach it. It is also the case that in Mathematics an A* or A grade can cover a wide range of abilities. A great advantage of the STEP, and the major reason for their introduction, is that we have access to your scripts which is denied to us in the case of the public examinations. This is particularly important if you do not quite get the grades required.

The Faculty offers a number of free online resources to help potential Mathematics applicants prepare for sitting STEP. These include online resources for individual additional study, starting in Y12 (first year of A-level), and a new online discussion forum. Further details are given below. All the resources can be accessed via a new portal at http://maths.org/step. The free online resources include:

  • a series of linked modules developed by our NRICH project. Each module focuses on a specific mathematical topic or technique, and the programme is designed to provide an accessible and supportive introduction to advanced problem-solving
  • a new pilot project funded by the DfE, the STEP Correspondence Course, launched in January and run by Dr Stephen Siklos, providing structured fortnightly assignments through which to work. Each assignment starts with preparatory work, and leads to a STEP question. Feedback is published on each assignment after the closing date to help users learn and assess progress
  • NRICH has just launched a new discussion board to support Y12 and Y13 students preparing for STEP: users can ask for help and hints if stuck, share what they’ve tried so far, and get guidance from Cambridge students who have taken STEP themselves (http://maths.org/step/forum).

How important are the interviews?

For most candidates they will be very important. However no special preparation is either necessary or advisable except to ensure that you are well rested and mentally alert for them. During them we shall be trying to discover a number of things about you and your background, starting from your teachers’ references and other information on your application form.

In the mathematical interviews we try to assess not how much you know, but how easily you can grasp new ideas. For this you will be given a few problems to look at for half an hour before one of the interviews for further discussion during the interview itself. The interviews are conducted as mini-‘supervisions’ as this is very much how you will be studying throughout your years at Cambridge: the lecturer will give a fairly rapid exposition of a subject which it will then be up to you to understand with the help of a supervisor, discussing problems explicitly designed to test your understanding and point out any gaps.

If you are from a non-A-Level background, you may find this additional information helpful.

Useful addresses and websites

OCR Publications, Annesly, Nottingham NG15 0DL; Email publications@ocr.org.uk

University website http://www.maths.cam.ac.uk/

See also page about Mathematics on the University website.