Computational Applied Mathematics MSc postgraduate personal statement example

Personal statement example

At the bakery where I work early shifts, the sourdough proving schedule is written on a whiteboard by the walk-in fridge. Over the last year I have adjusted those times by hand when the kitchen runs warm, and I started noting the room temperature beside each batch to see whether my adjustments held up. They mostly did, but only within a narrow range. Beyond it, small temperature differences changed the dough far more than I expected. That gap between a rule of thumb and the behaviour of the system is the kind of question I want to study properly, and it is why I am applying for postgraduate study in computational applied mathematics.

My undergraduate degree was in physics. The modules I enjoyed most were classical mechanics, mathematical methods and a second-year computing course in Python, where we wrote simple solvers for ordinary differential equations. For my final-year project I compared the fourth-order Runge–Kutta method with the Störmer–Verlet scheme for integrating a two-body orbit, and then a restricted three-body problem, over very long times. RK4 was more accurate over short runs at the same step size. Over thousands of orbits, though, its energy drifted steadily, while Verlet's energy error stayed bounded and oscillated. Reading about why led me to the idea of symplectic integrators preserving the geometric structure of Hamiltonian systems, and to backward error analysis. I could only follow parts of the theory, but I reproduced the behaviour carefully. I varied step sizes, plotted error against time on log scales and checked my code against known circular orbits. My supervisor's main comment was that my results were well tested but my explanation of the theory was thin. That is fair, and it is a large part of what I want from a masters.

Since graduating I have been reading to fill the gaps a physics degree left. I worked through the early lectures of Trefethen and Bau's Numerical Linear Algebra, writing my own QR factorisation by Householder reflections and comparing its stability with classical Gram–Schmidt on badly conditioned matrices. I have also started learning about finite element methods through online lecture notes, solving Poisson's equation on a square in one and two dimensions. My analysis is weaker than that of a mathematics graduate, particularly in functional analysis, and I am working through an introductory text on real analysis in the evenings to prepare.

My job has given me useful habits even though it is not mathematical. I start at five, and the oven schedule for the morning depends on getting three products through two ovens in the right order. I now plan that schedule each week for the head baker, which has taught me to keep a system working when one part goes wrong, such as an oven running cold or a delivery arriving late. Outside work I coordinate the watering rota for the community allotment near my flat, which mostly means a shared spreadsheet and patient messages in dry spells. I also play fiddle in a ceilidh band. It has nothing to do with numerical methods, but it is where I learnt to rehearse slowly until something is reliable rather than impressive.

I want to develop a firmer grounding in numerical analysis for differential equations, both ordinary and partial, and to learn how to judge when a method can be trusted rather than only observing that it works. I am especially interested in structure-preserving methods and in problems from physical modelling where long-time behaviour matters. My physics background means I am used to asking what a model actually represents, and my project showed I can build, test and question code independently. A masters would give me the mathematical depth to explain what I find, and I would like to keep open the option of further research or work in scientific computing afterwards.