Example science interview
Shortlisted applicants are asked to come to Oxford for interviews (there are separate arrangements for some overseas candidates). These occur in December. The precise format of the interviews varies from college to college. Candidates will generally have one or two interviews in their first choice college, and at least one other interview at another college. All of the interviews will occur over a 3 day period - you won't be called back for interviews at a later date.
Our interviews last for about 25 minutes, and are largely mathematical in nature. We may ask you to tell us about an area of mathematics you have studied; we may look in detail at a point of technique, or curve sketching; we may ask you puzzle-type questions; we may give you a mathematical definition and ask you to work out some of its consequences. We are trying to see how you think when you do Mathematics, and we may ask you to work at the board and to talk us through your thought processes.
How to prepare
Although we are good mathematicians, we are not mind-readers - if you don't say anything, we can't tell what you're thinking! To this end, it may be helpful for you to arrange a practice interview with a teacher - perhaps they can ask you to work out a past MAT question in front of them. Alternatively, try explaining concepts from your Maths A-level to your less mathematically-minded friends and family. This not only gets you used to explaining your thoughts out loud, but also helps to consolidate your knowledge of the subject.
We very much don't want applicants to feel they need special training for our admissions. The main thing is that you do mathematics, lots of it, and that you find it interesting. We advise you to do lots of problems, on and near your syllabus, so that you really understand the mathematics you are learning. This doesn't mean you shouldn't also read any of the excellent and interesting books about famous mathematical subjects such as Fermat's Last Theorem, but although these books are fascinating and inspirational, the maths they cover is pretty difficult. After all, even in Oxford only a handful of people properly understand Andrew Wiles's proof!
Curve sketching question
After the interviews
After all the interviews, the individual colleges prepare a list of the applicants they think are worth a place. Then, all the colleges acting together draw up a list of offers to be made, and these offers are sent out by college Admissions Offices. There is a very efficient and effective system for transferring applications between colleges so that if your first choice college is oversubscribed but you definitely should have a place, one can be found at another college.