Please note: this is not official advice endorsed by any institution, rather it is an article based on my own experiences and the experiences of students I've worked with, offering our informal advice about university applications.

So you've decided you want to study Mathematics at a prestigious university, you've sent off your application, and you're waiting to hear back from them. A great use of your time now would be to prepare yourself in case you are invited to an interview!

Why do some universities interview candidates?
Not every university invites applicants to an interview, but some universities who receive a great many highly qualified applicants want to meet students for themselves to see whether they are well suited to that university's degree programme.

What is my chosen university looking for?
Mathematics courses at different universities will be looking for slightly different things, but there are a few general pieces of advice that will apply to virtually all courses. Those in charge of university admissions are looking for:

• Students who want to study Mathematics
• Students who are capable of meeting the demands of the course

What should I do to convince the interviewer that I am a good candidate?
Be prepared to talk about what it is that attracts you to mathematics as an academic discipline. It's not enough just to say that maths is your best subject, or you liked it since you were seven, but you need to be able to demonstrate a genuine interest in mathematics.

Have you ever thought about which areas of mathematics interest you the most? Do you have a favourite topic in mathematics? Perhaps you could spend some time researching areas of higher mathematics that you might be interested in pursuing some day. It might also be worthwhile for you to spend some time reading some popular mathematics books. There is a selection of recommended books here. And of course Plus is full of exciting mathematical articles for you to browse. Of course, you must never claim to have read something that you haven't; the interviewer will not be trying to catch you out but will expect you to be able to talk intelligently about what you have read.

What will the interviewer want to know about my maths skills?
Your application will give the interviewer a good overview of your academic progress so far. Some institutions give students maths problems to do as part of the interview process; this helps the interviewer to see how you respond to a piece of new maths. It is not a test of your previous knowledge, but is a chance for you to show off your mathematical thinking skills! There may be a short maths test beforehand or you might be given a problem in the interview. The interviewer may be interested in your thought processes and how you respond to hints, to see whether you respond well to learning new mathematics, so don't be afraid to voice your thoughts out loud, even if you think your approach might lead to a dead end.

A good preparation for this aspect of an interview is to practise solving mathematical problems. You may find it useful if you haven't already done so to work through some of our STEP Prep Problem Solving module. Alternatively, have a go at some UKMT Maths Challenge questions, or Olympiad questions, or browse the NRICH website for something that interests you. This will also give you something to talk about if the interviewer asks you about some maths that you have enjoyed recently. Problem solving will also stand you in good stead for being an undergraduate - if you don't enjoy mathematical problem solving, then is a three-year maths degree really for you?

What about all my other achievements?
Mathematics at University is unlike school mathematics in that you will be expected to take more responsibility than ever before for your own learning. If you can demonstrate to the interviewer (through your application form or through what you say in the interview) that you are busy with activities other than Mathematics, this will stand you in good stead, as it shows that you can manage to balance an academic workload with the other demands of life. A maths interviewer probably won't mind too much whether your other achievements are musical, sporting, having a part-time job, or writing fifteen novels by the age of twelve, and so you shouldn't worry that all the other candidates might have more interesting extra-curricular activities than you! The main thing the interviewer wants to know is that you're really interested in maths, and you will be able to live up to the demands of the course. Of course, university is a great place to get involved in new activites or continue with old ones, but first and foremost, you attend university to work towards a degree, so don't expect the interviewer to be impressed if you say you want to come to their institution because it has a good hockey team.

I didn't get in! What did I do wrong?
Following the advice above will not guarantee you a place at your first choice of university, for the simple reason that many top universities have a great deal more applications than places! So it's not necessarily something that you did wrong, but rather that there were many many candidates as good as or slightly better than you. But it's not the end of the world, there are lots of people who were turned down by their first choice of university and went on to have a great time and achieve an excellent degree elsewhere. And if you have practised problem solving and read around the subject to find your favourite areas of maths, you've put yourself in an excellent position to succeed wherever you end up.

Good luck!