Science at Cambridge: Mathematics

University

My name is Naomi Arnold and a few weeks ago I finished my second term at Murray Edwards College studying Mathematics. Amazingly I now have just the ‘exam term’ to go to complete my first year of study.

I first developed an enthusiasm for maths when I was studying it at GCSE level. Our class frequently went to the ‘Maths Inspiration’ events where mathematicians would give fun, engaging talks about aspects of maths that interested them or about the maths involved in their field of work. Until then I had always been very good at maths but I’d always just seen it as necessary and functional – I hadn’t realised the breadth of its applications, and it had certainly never occurred to me how fun and rewarding maths could be.

Going from studying Maths at A level to degree level has been quite a big transition but one that was made a lot smoother with the help of the supervisions system and having a really supportive community at Murray Edwards. It took a while adjusting to how much time I had to spend just thinking about how best to tackle questions – often, especially in Pure Mathematics topics, there can be multiple ways of looking at a question, all of which are valid, but not all of which lead you in the right direction. Sometimes just choosing the right method; figuring out what you actually need to prove, breaking a hefty problem into more palatable steps and choosing the order in which to carry them out can be the most difficult part of the problem. Whilst adjusting has been very challenging, it’s also been incredibly rewarding – the feeling you get when you crack a problem you’ve been working on for ages is truly refreshing.

One of the topics I’ve enjoyed this year is ‘Analysis’. It could be described as a course that proves and makes more rigorous the maths that you cover at A level, as well as some other interesting theorems of course! For example, we define differentiation properly and starting from that basic definition we go on to prove the common results covered at A level like the Chain Rule, Product Rule and that integration is, under certain conditions, the reverse of differentiation etc. On the surface it can sometimes seem tedious – why do we need to bother proving things we already know to be true? Why is it necessary to understand the proofs when we can just use the results? I think firstly some of the techniques that mathematicians have used in the past are quite universal and are useful to add to your problem-solving toolkit. Secondly it can offer insight into why certain mathematical processes work in the way that they do and can help when it comes to actually applying relevant results.

What I would say to anyone who’s interested in studying maths is simply to be really inquisitive about the maths that you’re currently doing. In this respect, I found the Nrich website a great resource, with plenty of problems to try.  And if the harder the problems get the more you find yourself engrossed, you are well on the road to enjoying maths at degree level.

Naomi Arnold
Undergraduate student

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