Applied and Computational Mathematics postgraduate personal statement example

Personal statement example

At the bakery where I work on weekends, the dough for our sourdough rests overnight in a proving cabinet, and the first thing I do at six in the morning is check its core temperature with a probe. For a long time I simply wrote the number down. Then, during my final year, I started wondering how quickly heat actually moves from the cabinet air into the centre of a loaf-sized mass, and realised I could write down the problem I was solving in my project. That small overlap between a routine task and my coursework is a fair picture of why I want to study applied and computational mathematics: I enjoy the moment when an ordinary process becomes an equation, and then the less glamorous work of getting a computer to solve it reliably.

My undergraduate degree in mathematics gave me a solid grounding in analysis, linear algebra and differential equations, but the modules I enjoyed most were numerical analysis and partial differential equations. For my final-year project I wrote a Python solver for the one-dimensional heat equation using finite differences. I implemented an explicit scheme and the Crank–Nicolson method, then compared them against an exact series solution. The most satisfying part was watching the explicit scheme behave exactly as the stability analysis predicted: once the ratio of time step to the square of the spatial step passed one half, the solution developed oscillations that grew until they swamped everything. Crank–Nicolson stayed stable at much larger steps, although I found it could still produce small spurious oscillations near a sharp initial temperature jump. Explaining that in my write-up meant reading more carefully about the difference between stability and accuracy, and it was the first time I felt I understood a method rather than just using it. I also had to learn to solve tridiagonal systems efficiently instead of calling a general solver, which made a clear difference to run times on finer grids.

Outside the project I have read parts of Trefethen and Bau's Numerical Linear Algebra, mainly the chapters on QR factorisation and conditioning, because I wanted to understand why some of my test matrices gave less accurate answers than others. I would like to build on this with more rigorous study of numerical methods for PDEs, optimisation and scientific computing, and I am also curious about stochastic modelling, which I met only briefly as an undergraduate.

My job has taught me things a degree does not. As a shift lead on Saturdays I organise three other staff, decide the baking order so the ovens are used without gaps, and handle the morning when a delivery is late or a mixer fails. None of it is complicated, but it has made me calm under time pressure and practical about planning. I also tutor two GCSE students in maths each week. Explaining simultaneous equations to a fifteen-year-old who has decided she is bad at algebra forces me to find several routes to the same idea, and I have found this helps my own clarity when I write up technical work.

In my spare time I do orienteering with a local club. It is not mathematical in any formal sense, but choosing a route under uncertainty, weighing a longer path on clear ground against a direct line through thick woodland, has the same flavour as many of the trade-offs I enjoy in modelling.

I am applying for postgraduate study because I want the depth that my degree only began to provide: stronger theory behind numerical methods, more experience writing careful scientific code, and the chance to work on larger, less tidy problems than a single heat equation. I am a steady, persistent worker who likes checking results against something independent, and I would bring that habit, along with good programming foundations and practical experience of working in a team, to an applied and computational mathematics course.