Mathematical modelling postgraduate personal statement example

Personal statement example

My interest in mathematical modelling settled during a second-year module on differential equations, when we compared the logistic growth model with real population data for a fish stock. The fit was reasonable until harvesting was introduced, and the discussion that followed – about which assumptions to relax first, and how much complexity a decision actually needs – was more interesting to me than the solution methods themselves. Since then I have looked for opportunities to work on problems where the modelling choices are the substance of the task.

My final-year project gave me that. I studied waiting times at my university's health centre using data the service published on appointment numbers and opening hours, supplemented by my own timed observations in the waiting room over three weeks. I began with a straightforward M/M/c queue, which predicted much shorter waits than I was seeing. Working through the discrepancy taught me more than the original model did: arrivals were far from uniform across the day, walk-ins and booked appointments behaved differently, and consultation lengths had a long right tail. I moved to a discrete-event simulation in Python, fitting service times to a lognormal distribution and splitting arrivals into hourly rates. The simulation reproduced the observed midday peak reasonably well, and I used it to test the effect of staggering appointment slots. I was careful in my write-up to state what the model could not tell me – I had no data on why patients arrived when they did, so any prediction about behavioural change was speculation. My supervisor's main criticism was that I had validated against the same period I fitted to, which is a fair point and something I would handle differently now.

The programming side has become a habit rather than a requirement. I have written a small agent-based model of pedestrian flow through a bottleneck, mostly to understand how simple local rules produce jamming, and I have worked through parts of a textbook treatment of compartmental epidemic models, implementing SIR variants and experimenting with how sensitive the peak timing is to the initial infectious fraction. These are exercises rather than research, but they have made me comfortable moving between the analytic and computational sides of a problem and have shown me where my numerical methods knowledge is thinnest, particularly stiff systems and parameter estimation.

I collaborated on one piece of group work that I found genuinely useful: a coursework task in which four of us modelled traffic light phasing at a junction. I took responsibility for the sensitivity analysis. It was a manageable share, and it required me to keep asking the others which parameters they had guessed at rather than measured, which sharpened the final report considerably.

Alongside my degree and since graduating I have tutored numeracy part-time at a further education college, working mainly with adults returning to study. Explaining why a percentage change is not reversible, or what an average conceals, has made me much clearer about my own assumptions. I also keep the scoresheets and league table for a local netball club, which is administratively dull but has taught me something about the gap between data that exists and data that is recorded accurately.

I am applying for a master's because I want formal training in the areas my undergraduate degree only introduced: stochastic modelling, inverse problems and the practicalities of fitting models to imperfect data. In the longer term I would like to work as an analyst in transport or healthcare planning, where the questions are concrete and the modelling assumptions have to be defensible to people who are not mathematicians.