Pure mathematics personal statement example

Why do you want to study this course or subject?

What draws me to pure mathematics is that a proof settles something for good. In my first term of Further Maths I met proof by induction and spent a wet weekend convincing myself that the argument really did cover every case rather than merely a great many of them. That shift, from checking examples to knowing why no counterexample can exist, is the reason I want to spend three or four years on the subject rather than treating it as a tool for something else. I like the parts of my A level that hint at bigger structures: modular arithmetic, which behaves like ordinary arithmetic until suddenly it does not; complex numbers, where rotations and multiplication turn out to be the same operation in different clothing. Reading around, I have been working slowly through a general introduction to proof and set theory borrowed from my college library, and Cantor's diagonal argument was the first piece of mathematics that made me put the book down and walk about the room. I am comfortable with the idea that undergraduate work will be harder and slower than school problems, and that some weeks I will not finish a sheet. Analysis appeals to me most at present, because the definitions of limit and continuity seem designed to close loopholes I had not noticed were open, but I expect abstract algebra and topology to change my mind. I want a degree where the questions are open, the reasoning is my responsibility, and the answer is either justified or it is not.

How have your qualifications and studies helped you to prepare?

My A levels in Mathematics, Further Mathematics and Physics have taught me different habits. Physics rewards estimation and a willingness to accept an approximation; Further Maths rewards patience with algebra and precision in setting out an argument. Matrices, series, differential equations and polar coordinates have been the most useful topics so far, partly because they keep reappearing in Physics mechanics in disguised form, which has made me think about why certain structures are so widely applicable. For my Extended Project I studied plane tilings, starting from the question of which regular polygons tile the plane and why only three of them do. Working through the angle conditions myself, then reading about the classification of the seventeen wallpaper groups, gave me a first real sense of what symmetry means as a mathematical object rather than a description of a pattern. I could not follow every group-theoretic detail, so I concentrated on presenting the parts I genuinely understood and stating clearly where my account stopped. My tutor's main criticism was that I had asserted a result without proof in one section, and rewriting that page properly took longer than the rest of the draft. Alongside this I have kept a notebook of problems from a university outreach problem sheet and from past olympiad-style papers, which has trained me to spend twenty minutes on a question before deciding I am stuck, and then to write down exactly which step fails.

What else have you done to prepare outside of education, and why are these experiences useful?

I help run my college's maths club, which mainly involves working with Year 11 pupils who visit on Thursday afternoons. My job is to set up puzzles and then resist solving them for people. Explaining why the sum of the first n odd numbers is a square, using dots arranged in an L-shape, showed me how much clearer my own understanding became when I had to justify each step to someone who was quite willing to say they did not believe me. Last spring I put together a short session on the pigeonhole principle; two pupils found a neater argument than mine for one of the examples, which I now use. On Saturdays and in the holidays I work at a garden centre, on the tills and restocking. It is ordinary work, but it has made me calmer under pressure: a queue of a dozen customers, a card machine that has frozen and someone wanting to know whether a plant will survive clay soil all have to be handled without losing patience. I was asked to train two new seasonal staff on the till system in the spring, which meant breaking a familiar routine into steps someone else could follow. Badminton in a local league takes up my Tuesday evenings and is the main reason I have any balance in my week; playing doubles has taught me more about communication than most group tasks at college. Between them, these commitments have taught me to plan my time around fixed obligations, which I expect to matter when problem sheets arrive weekly.

This example has 4,377 characters across the three answers. Use it for ideas and structure. Your own UCAS answers must fit within 4,000 characters in total, including spaces.