It’s quite a different style of teaching to school: an hour’s lecture will give you lots of new concepts (methods for solving differential equations, proofs of set theory results) which you then spend time absorbing after the lecture. (I learnt that I didn’t expect to understand the finer points – or sometimes the main points – of every proof while sitting in the lecture hall.) Instead you become more familiar with the material by working through ‘problem sheets’ – exercises using concepts and methods from the lectures. This is where lots of problem solving comes in, because usually the questions require you to apply the lecture material in unfamiliar situations. Since this was one of the aspects of maths I really loved at NLCS, I was pleased that there was lots of opportunity to continue solving interesting problems while at university!
Now I am moving on to the big scary world outside of academia, I have more of a sense of how maths is used more widely. At the moment data analysis and machine learning seem to be everywhere, as well as more traditional opportunities around finance, for example. I think the other thing I have learnt is that you don’t necessarily need to know where you are going when you start – either in terms of what you specialise in at university or where you want to head afterwards. Instead you just need to enjoy doing maths. The Cambridge course allows you to experience many different types of maths in the first year or two, and then you can specialise lots in the third year. I chose mostly pure maths, which I didn’t necessarily see myself doing at the start.
Overall I’d say that doing maths at university has been hard work, but lots of fun. Every course will be different, but if you enjoy doing maths, are interested in exploring the huge amount of maths out there, and solving interesting problems along the way, then I highly recommend it!