Master in Computational and Applied Mathematics postgraduate personal statement example

Personal statement example

Twice each shift at the leisure centre where I work, I take a water sample from the main pool and record chlorine and pH in a log. Over a year the log has become a dense record of how the pool behaves. Chlorine drops sharply after the Saturday swimming lessons, recovers slowly overnight, and responds to the dosing pump with a delay that varies with temperature. I once sketched a simple decay-and-dosing model on the back of a rota to see whether the delay made sense. It did not quite fit, and working out why kept me occupied for several lunch breaks. That habit of turning a messy, real system into equations and then testing them is what I want to develop properly through a master's in computational and applied mathematics.

My undergraduate degree was in mathematics, and the modules I enjoyed most were the ones where analysis met computation: numerical analysis, ordinary and partial differential equations, and a second-year course in mathematical biology. My final-year project combined all three. I wrote a solver in Python for the Fisher-KPP equation, which describes a population that spreads by diffusion and grows logistically. I began with an explicit finite-difference scheme and confirmed in practice what I had derived on paper: the solution became unstable once the ratio of the time step to the square of the spatial step, scaled by the diffusion coefficient, went above one half. I then implemented a Crank-Nicolson scheme, which removed that restriction. However, it produced small oscillations near the steep front when I started from a step-function initial condition, so I compared results with smoother initial data and with finer grids. The most satisfying part was checking that the numerical travelling wave settled towards the theoretical minimum speed of two times the square root of the diffusion coefficient multiplied by the growth rate. Measuring that speed accurately from discrete output was harder than I expected and taught me to treat post-processing as part of the method, not an afterthought.

The project also showed me the limits of what I currently know. Each Crank-Nicolson step needs a linear system solved, and I relied on a library routine for tridiagonal matrices without fully understanding the alternatives. Since graduating I have been working through parts of Trefethen and Bau's Numerical Linear Algebra in the evenings, particularly the chapters on conditioning and stability. I have reached the material on iterative methods and would like to study it with proper guidance, along with optimisation and the numerical treatment of problems in more than one spatial dimension.

My job has given me skills that a degree alone did not. As a duty assistant I build the weekly lifeguard rota, balancing qualifications, minimum staffing for each pool session and people's availability. I moved it from a handwritten grid to a spreadsheet that flags any session left uncovered. It is not sophisticated, but colleagues use it and I have learned to design something for people who did not ask for mathematics. The job has also made me calm and methodical when something goes wrong mid-shift.

Outside work I drive my younger brother to his college three mornings a week, which has made me disciplined about organising my own study time. At weekends I swim at a local lake with a small group. Over two summers I have built up from short loops to a continuous two kilometres.

I am looking for a programme that will deepen my grounding in numerical methods and modelling while giving me more experience of writing reliable scientific code. In the longer term I would like to work on applied problems in industry or research where modelling decisions have practical consequences. I am ready for the step up in independence and rigour that postgraduate study requires.