Dr Ana Khukhro answers questions from prospective students about studying maths at Cambridge.
I'm the Director of Studies in mathematics at Murray Edwards College. I work in geometric group theory, which lies at the intersection of many areas of mathematics. Groups are mathematical objects that describe symmetries – the larger the group of symmetries of an object, the more symmetric it is. Groups can interact in an extremely interesting way with geometry, analysis, and algebra – such "bridges" between different fields is something I find truly beautiful in mathematics!
Q: What's special about maths at Cambridge?
A: There are many universities with fantastic maths degrees to choose from. One advantage of the Cambridge course is the flexibility and choice that it is able to offer. Students start by taking a mix of pure and applied courses in the first year to form a basis for future study. They can then follow the direction which interests them the most in the second year, with just under 40 courses to choose from in the third year, and over 70 courses in the fourth year!
Another advantage of Cambridge is the supervision system: students attend lectures given by the maths department, and then have feedback sessions (known as supervisions) on their work with a member of academic staff. Supervisions usually take place with just a pair of students at a time, allowing for very personalised feedback and giving students the opportunity to discuss their solutions to the often challenging exercises with an expert in the subject.
Q: How will my choice of College affect my studies?
A: The College is there to support you pastorally and academically throughout your degree, as well as organising accommodation, extra-curricular activities, and in-College dining. In a large university such as Cambridge, being part of a College can give you the feeling of being part of a smaller community and can make the experience of starting university less daunting. In College, you will have a Director of Studies who is there to advise you on your course choices, to arrange your supervisions, and generally make sure you are getting the most out of things, mathematically.
Q: How does Murray Edwards College support its maths students?
A: At Murray Edwards, we pride ourselves on the support we provide for our students. We do our best to foster an environment in which students feel comfortable asking questions and discussing ideas. We ensure supervisions are helpful and that they give our students the confidence to express themselves mathematically. We have a very warm and welcoming community of maths students and academics that we truly feel is unparalleled at Cambridge. Relaxed weekly social meetings and study groups mean strong bonds both within each year group, as well as between different year groups.
Q: What's different at a women-only College?
A: Having a close-knit community of people with the shared experience of being a female mathematician at Cambridge has proved to be a great source of support and strength for our students. Women are still underrepresented in maths at Cambridge, and being part of the Murray Edwards maths community provides a good support network of like-minded, friendly fellow mathematicians who understand the challenges that come with being a minority in one of the most demanding mathematics degrees in the world.
Q: What are you looking for at interview?
A: We are looking for mathematical skills, and the ability to understand and use mathematical ideas. As such, in the interview, we will be looking to see how you solve maths problems, and how you react to hints and new ideas. When you are solving one of our tricky interview problems, we want you to explain your thinking out loud so that we can follow your thought process, and maybe nudge you in the right direction.
We will rarely ask you about your personal statement – we want to fit as much actual maths into the interview as possible!
Q: What is STEP and how do I prepare?
A: STEP is an additional maths exam, taken at the end of Year 13, which usually forms part of a conditional offer to do maths at Cambridge.
Although demanding, STEP preparation gives you a chance to flex your mathematical wings and engage with interesting mathematics. Although STEP is based on A Level Mathematics and Further Mathematics material, the questions may seem a lot more challenging than A Level questions at first. However, just as with A Level questions, one can learn how to solve questions of this style with practice – STEP is not detecting "mathematical genius", it is an exam like any other in which experience and feedback will help you improve. There are many resources available online to get you started on solving STEP questions; in particular, the book "Advanced Problems in Mathematics" by Stephen Siklos (available to download for free) is a great place to begin.
Q: How does the degree compare to STEP?
A: STEP is a good stepping stone to university-level mathematics because it aims to develop and stretch your mathematical reasoning, independence and confidence. STEP is based on material that will be familiar from A Levels, but is designed to be more challenging. The degree at Cambridge is also designed to provide a sufficient depth of difficulty for even the brightest, most hard-working students. Just as STEP can help you get a better understanding of concepts covered at school, the exercises in each course will help you master the many new definitions, proofs and ideas that you will meet during your maths degree.
Q: What do you mean there are lectures on a Saturday??