The Oxford math interviews can be hard, but the good thing is, it's all about preparation! The more you practice, the more you'll know what to expect and the smoother the process will be. Here are my top 8 tips to prepare and ace the Oxford math interviews.
1. Practice, practice and practice
The Oxford math interviews are technical interviews. You will be asked to solve mathematical problems, from sketching graphs to computing complex integrals. Your interviewers will assess you along many dimensions, but most importantly, they will want to see that you understand the maths and can come up with a solution. And there is no secret to getting this right... practice, practice and practice.
Practice solving as many mathematical problems as you can. There is only a finite number of topics your interviewers can test you on and if you've worked through enough questions, you will be familiar with all of them. In my case, I trained on hundreds of past interview questions, and apart from 2 to 3 niche questions, I was familiar with most of the ones I was asked.
There are many good websites out there with real math interview questions (including mine hopefully). Just search around the web and solve what you can find, you'll see that, with practice, you will get better at it.
2. Practice out loud
The math interviews are not just about solving every problem your interviewers give you. It's also about being able to clearly explain your thought process and how you plan on getting to the solution.
In the end, math is about prooving theorems, and proofs are meant to be shared and read by others. A good proof is not one that gets to the solution in the least amount of lines, it is a proof that is elegant and easy to understand. Comunication in maths is a crucial skill and that's something your interviewers will look out for.
In the interviews, you will be asked to explain verbally how you are approaching the problem. It is therefore a good idea to practice that beforehand, even by yourself!
3. Set up a mock interview with your math teacher
A great way to prepare for the interviews is to put yourself in the most realistic environment. For example, if you are close to your math teacher, ask them to give you a mock interview. This is probably the closest thing you can get to the real interviews, and will help you familiarise with the process of explaining your solutions to another mathematician. This will also add a layer of stress, which you most likely don't have at home!
4. Work through the Further Math syllabus
The Oxford math interviews are meant to be challenging. Your interviewers will want to see how you approach questions or topics you've never seen before. The Further Math syllabus offers your interviewers a wide range of choice, since you're not meant to have covered everything by the time you take the interviews.
Proof by induction, complex numbers, polar coordinates, infite series and hyperbolic functions are all must-know if you want to ace the Oxford math interviews... and that's all covered in the Further Math syllabus!
5. Focus on your weaknesses
The Oxford math interviews are long. They will feel short, because of the adrenaline, but the truth is you'll spend about an hour and a half working through mathematical problems in front of multiple Oxford tutors. During that time, your interviewers will have the chance to ask you many questions and it's important to prepare for all eventuality. In my case, I went through 3 interviews of 30 minutes each and had to solve questions related to topics including number theory, integration, complex numbers, probability and graph sketching.
Don't assume there is a 50/50 chance that you won't have any probability questions. You most likely will, so prepare for it. Take a week or two to focus on the maths you find the hardest and work diligently through as many questions as you can. With time and practice, you will improve and feel more comfortable.
6. Take your time
Don't rush your interviews, take your time. Oxford tutors don't expect you to solve their questions from the get-go. It's ok to take 5 minutes at the start to think, suggest some ideas and get some feedback from your interviewers. It's a much better strategy than to rush the maths and solve random equations that won't bring you anywhere.
Sometimes, you'll be heading in the wrong direction and they won't warn you. If that happens, don't worry, it's totally normal. It's part of the process of solving mathematical problems and your interviewers will want to see how you react to it. So again, take your time, understand why your approach does not work and brainstorm other ideas.
7. Listen to hints
If you happen to be struggling, your interviewers might jump in and and give you a hint. For example, they might suggest you to consider a particular function, to plot its graph etc.. If that happens, pause your train of thought and listen to them. By giving you hints, interviewers are trying to help you. Make use of it! Don't ignore them and go down your own path, you could accidently appear arrogant.
8. Be smiley and friendly
Finally, don't forget to be smiley and friendly to your interviewers. If you pass the interviews, you'll be working with them multiple hours a week for 3 to 4 years. Oxford tutors want to hire friendly people who will foster a healthy learning environment. So leave a good impression: smile, show that you are passionate about the subject and that you are a pleasant person to work with.
That's all! I hope that you enjoyed this article and that you are now in a better position to ace your interviews! Don't forget to also check out the 10 math questions I put together, along with detailed solutions, to prepare the Oxford math interivews.