Mathematical modelling postgraduate personal statement example

Personal statement example

Most mornings at the bus depot where I work as a duty scheduler, I check whether yesterday's driver changeovers happened on time. A changeover at the hospital stop is planned to take two minutes, but on weekdays it rarely does: a late bus arrives, the relief driver is waiting, and the delay passes to every stop that follows. Last spring I collected eight weeks of arrival times from our ticket machine logs and fitted a simple queueing description to them in a spreadsheet. It showed that the problem was less the changeover itself than the variability of arrivals before it, and that moving the changeover two stops earlier, to a quieter layby, would absorb more of that variation. My manager trialled the change on one route. Punctuality there improved, though I could not separate the effect cleanly from a road reopening the same month. That uncertainty is a large part of why I want to study mathematical modelling properly: I can build something useful, but I do not yet have the tools to judge how far to trust it.

My degree in physics gave me a solid grounding in differential equations, linear algebra and numerical methods. My final-year project modelled heat loss through the walls of a Victorian terraced house, using a one-dimensional finite difference scheme for the heat equation with boundary conditions taken from a temperature logger I fixed inside and outside my shared student house over a winter fortnight. The most instructive part was not the scheme but the mismatch. My model underestimated night-time cooling until I accounted for a draughty sash window, which I represented crudely as an extra convective term. I learned to treat disagreement between model and data as information rather than failure, and to state my assumptions plainly in the write-up. I also learned the limits of my approach: I chose parameters by trial and adjustment, and I would now like to understand parameter estimation and sensitivity analysis in a more principled way.

Since graduating I have kept reading. Steven Strogatz's Nonlinear Dynamics and Chaos helped me see how qualitative analysis of fixed points and stability can explain behaviour before any numbers are computed, and I worked through its chapters on bifurcations with Python. Bus bunching, where buses on a frequent route drift into clusters, turned out to be a good example of an unstable equilibrium, and recognising that link was satisfying. I have also taught myself enough basic probability and statistics to read operational reports critically, though I am aware this is an area I need to strengthen formally.

My job has shaped how I think about communication. Schedules are used by drivers, controllers and union representatives, and none of them want equations. I have become practised at explaining why a timetable change is proposed in terms of a single clear chart and a sentence about what it will and will not fix. I expect this to matter in postgraduate study, where models are often built for people with other expertise.

Outside work I coach a junior table tennis session at a community centre on Thursday evenings. It is not mathematical in any obvious sense, but planning drills for twelve children of different abilities in ninety minutes has taught me patience and the value of preparation that adapts once things begin. I also bake sourdough at weekends, which has made me unreasonably interested in how temperature affects fermentation times.

I am applying for postgraduate study in mathematical modelling because I want to move from improvised models to well-founded ones: to learn how to formulate problems from messy situations, choose appropriate methods, quantify uncertainty and test conclusions honestly. I bring a sound mathematical background, experience of working with real operational data, and the habit of explaining results to people who will act on them. I would like to develop these into the skills to tackle transport, energy or environmental problems with more rigour than a spreadsheet allows.