Applying for Mathematics at Cambridge University

Cambridge University is renowned for the excellence of its Mathematics course. Equally challenging and rewarding, it offers the opportunity to study a wide range of subjects: everything from abstract logic to black holes.

Two aspects of the Mathematics course that Cambridge students greatly appreciate are its flexibility and the breadth of subjects offered. The amount of choice increases each year and after Year 1 students may choose the number of options to study. Some students take as many options as they can; others take fewer and study them very thoroughly.

This structure allows students to keep their options open, giving them the opportunity to discover their strengths, extend their knowledge and develop their interests before specialising.

Academic Requirements
- A-levels: A*AA to include Mathematics and Physics. The A* must be in Mathematics, Physics, or Further Mathematics
- Advanced Highers: AA/AAB
- IB: 39 (including core points) with 766 at HL (the 7 should be in either Physics or Mathematics)

How did you decide between Oxford and Cambridge?

Cambridge supposedly has a better reputation for the sciences. Having had a look around the place, and fallen in love with it, the decision was easy. (Profile 505)

Cambridge seemed more scientific. (Profile 168)

Differences between the courses on offer, and just heard that Cambridge had a better reputation for maths. (Profile 521)

Do you have any advice for future applicants in terms of preparation?

Practise the bread-and-butter maths that's likely to come up. Graph sketching, calculus, the easier mechanics. If you're going to mention a longish book in your personal statement, refer to a specific part of it, so that you can be fairly sure what the questions will consist of. (Profile 505)

Make sure that the work that you have done at A-Level is comparable to what other students are likely to have done. I thought that I had had a similar level of mathematical input as anyone else, but it turned out that students from other schools/VI Forms had been taught far more than I. (Profile 168)

The practice interviews really are useful, but only if you prepare for them as if they are the real thing. It doesn't matter how good your interview skills are if you can't remember the formulae for circular motion or whatever the question is on. Revise all your AS work because this is probably what the interview questions will be based on- they don't know how much of the A level course you will have studied. I think I made the mistake a couple of times in my interview of trying to do things the hard way when all the questions required was basic C1/C2 knowledge. Most interview questions involve applying old knowledge in new ways so maths challenge/BMO questions are quite useful preparation for this. Trying out STEP questions can also be a good thing and Oxford admissions tests are good because they are the right standard and questions aren't too long. But the best preparation is definitely practice so badger your school/teachers/family friends/anyone you know who is already at oxbridge to give your a sort of mock interview. Even if you just try to solve a problem in front of a few friends this can be useful as it gets you over the barrier of being embarrassed to say what you're thinking (not sure if boys have this problem but most girls seem to). (Profile 735)

Revise all your basic rules. Also, have a go at some of the questions from "Advanced Problems in Mathematics" by Dr Siklos. (Profile 511)

How was/were the interview(s), in general?

The personal interview was just about me: plans for the future, interests, hobbies, activities I would persue in the college. The applied maths interview began with a couple of curves to sketch. With a little prodding in the right direction I managed to draw something resembling the actual graphs. Then there was a mechanics question. A bead on a wire: simple constant acceleration stuff with a bit of trig to complicate things. The pure interview was mainly about calculus. Differentiate this, integrate that. I completely forgot the easy was to integrate tan x, but I managed to do it very long-windedly with a substitution. Also a question about binomial coefficients and Pascal's triangle (prove that every number in the triangle is the sum of the two above it). (Profile 505)

I had three interviews. In the first we worked through some Applied Maths (Mechanics) examples, talking about what I had done in the past. Next was pure maths, a similar style. Finally there was a social interview with the Senior Tutor, I was able to talk about my own experiences. (Profile 168)

First Interview (with two maths fellows: one who spoke, one who wrote):

At the time, felt fine about it. Actually after waiting for 3 hours in the Marshall room (JCR), I quite enjoyed it just because it was something to do. The interview went really quickly and I was worried about how few questions I answered and also some of the stupid things I'd said/done, including twice missing a incredibly obvious answer and doing things a much harder way. However, was reassured that I could see the notes one of them was writing and although I only dared take brief glances, I saw he first word was "excellent". So all in all, went to bed feeling quite happy.

Second interview (with Dr Siklos, director of studies or some other important title):

Was quitely confident after the first interview had gone OK, and even more so after I'd seen the problem we were left to do beforehand and found I could actually do all of it, which I hadn't been expecting. But when I got in, Dr Siklos gave me quite a hard time, questioning everything I said. I couldn't tell if this was because he was trying to push me or because I was getting everything wrong, but it did stress me out more than I would have anticipated and I spent a particularly panicked 2 minutes trying to explain why a straight line crossed the graph y=sin x only in the twice in the range 0-pi/2 when all that was in my head was "because that's what sin x looks like". The only thing I could say was "because it bulges up a bit" which he repeated back to me in a slightly sarcastic way and then let me sweat for a few minutes before saying "I think the word you were looking for is convex". He also asked me one question about Music of the Primes, which I'd put on my personal statement, because apparently everyone does. Annoyingly, I've read the book several times and still didn't answer the question very well. Overall, didn't enjoy that interview as much as the first. (Profile 735)

The first question on the test was very easy, I think it was just to put you at ease. I didn't quite finish the second one.Then I went through the questions with the maths tutor who helped me with ideas etc. to finish the other question, then went through another one with me. Supposedly like the supervisions for students.

The second interview was with the admissions tutor, who talked more about my other subjects and related maths to them. Was very interested in critical thinking. (Profile 521)

What questions were you asked during your interview(s)?

The interview was almost entirely done on paper: the questions were simply mathematical fragments to work through. (A-Level standard) (Profile 168)

All maths questions apart from one personal statement question in the second interview. Most questions on either properties of prime numbers, intergration of graph sketching, often involving a combination of the last two.

Was told several times not to reveal this sort of info, but here is a question I was asked in a practice interview which I found useful in my interview (interview question involved the same idea about divisibility by three):

Show that if x is a prime number greater than 3, x^2-1 is divisible by 24 (Profile 735)

The test questions are the same every year I think... The other interview I was asked about how maths fitted in with my other subjects, and talked about how 'pure' I considered maths. (Profile 521)

Oh, so what you're doing this [gap] year? have you been to Cambridge before? You are done with all A-levels? you still remember Maths? :) here we go... 1) Sketch the curve (y^2-2)^2+(x^2-2)^2=2. I told them i thought there were 2 'rings'? and they pressed on me until actually 4 rings were found...phew... 2) 3 girls and 4 boys were standing in a circle. What is the probability that two girls are together but one is not with them. After flawed reasoning i told them answer..."yes, but..." was response, it got bit blank and intolerable, until they made me draw all possible arrangements...but worse was about to come 3) Guessed algorithm right...but had to show why it was a solution to x^4+....i fiddled with graphs showing them how it converged...They set me straight again, but I had no frigging clue to what their hints were leading to...messed binomial theorem up...Oxford history repeats itself! 4) Is there such number N that 7 divided N^2-3? Tried contradiction, nowhere...Then I asked them another expression for N, which turned out to be N=7r+s....Then i blurted out "oh no the question just repeat itself!" until they they led me to see that s had only values between 1 and 6. hence... Oh dear... 5) prove 1+1/2+1/3+...+1/1000<10. I said "hey, that's 10=e^ln10 and then Taylor series!" "Oh no" the prof winced and it was quickly seen that geometric series was needed....then fiasco again with simple mental arithmetics, could hear them he-he-he...whilst i desperately tried to find the product... Ok..Who is helping you with preparations for STEPs? Any questions? (Profile 496)

Graph sketching, relationships between primes and other number, integrating things like 1/(1-lnx) (Profile 511)