Applied Mathematics MMath (Hons) personal statement example

Why do you want to study this course or subject?

The hardware shop where I work sells chain by the metre, and a length of it hangs in a loop beside the till. Last year a customer asked whether the curve was a parabola, and I said yes, then went home and found I was wrong. A hanging chain forms a catenary, described by the hyperbolic cosine. What caught me was not the correction but the reasoning behind it. The shape follows from balancing tension along the chain against its weight, and the equation drops out of that balance. Applied mathematics appeals to me because it works like this. A physical situation is translated into equations, the equations are solved or approximated, and the answer is checked against what actually happens. I enjoy each of those stages, especially the first, where you must decide what to ignore. I want to study the subject at a depth that lets me model problems like this one properly, rather than finding the answer in a textbook.

How have your qualifications and studies helped you to prepare?

Further Maths has given me the tools I was missing when I first met the catenary. Solving second-order differential equations, and then using them for damped and forced oscillations in the mechanics modules, showed me how one equation can describe a spring, a circuit and a swinging door. In Physics I carried out the required practical on damped oscillations, timing a mass on a spring in air and then in water. Our measured decay was close to exponential, and comparing it with the model from Further Maths was the first time two of my subjects answered the same question. For my independent project I photographed chains of different lengths hung against squared paper, recorded coordinates from the images and fitted both a parabola and a catenary by least squares in a spreadsheet. For shallow loops the two curves were almost indistinguishable, but for deep loops the catenary fitted clearly better, which matches the Taylor expansion of cosh. Reading Steven Strogatz's Infinite Powers helped me see calculus historically, as a method developed to handle continuous change, and Timothy Gowers's Mathematics: A Very Short Introduction made me think about what it means to choose an abstract model at all. I have also taken part in the UKMT Senior Mathematical Challenge, which I enjoy because its problems reward patience more than speed.

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

I have worked Saturdays at the hardware shop for two years. Most of the job is ordinary: restocking screws, cutting keys and explaining to customers which wall plug suits plasterboard. I have become reliable at estimating quantities, such as how much paint covers a room once doors and windows are subtracted, and the manager now asks me to check the weekly stock order before it is sent. Working with the public has made me better at explaining technical things plainly, a skill I want to keep as the mathematics becomes harder. Outside work, I play bassoon in a county youth wind band. Rehearsals have taught me to practise a difficult passage slowly and repeatedly until it holds together, which is also how I approach long proofs. Through the band I became curious about why a bassoon's conical bore produces its particular tone, and I read enough to realise that the acoustics of wind instruments involves the same wave equations I have started to meet in Physics. I do not yet understand the details, but it is a question I would like to return to. On weekday evenings I walk a neighbour's elderly spaniel, an arrangement that began when she broke her wrist and continued because we both enjoy it. It is an hour away from screens, and I often think through a problem from that day while we walk. These commitments have taught me to organise my time, and they have shown me that mathematical questions turn up in unexpected places.