Applied mathematics postgraduate personal statement example

Personal statement example

When our brass band finishes rehearsal on a Thursday night, forty people leave a small car park through a single gate onto a busy road. Sitting in that queue during my final year, I realised I was watching the thing my dissertation was trying to describe: a dense block of cars thinning out from the front while a slow wave of stopping and starting travelled backwards through it. I want to study applied mathematics at postgraduate level because I enjoy exactly this movement between an everyday situation and the equations that capture its essential behaviour.

I graduated with a 2:1 in Mathematics and Physics. My strongest modules were in differential equations, vector calculus and numerical methods, and I particularly valued a course on fluid dynamics, where the derivation of conservation laws from a control volume argument made sense to me in a way rote formulae never had. Physics gave me the habit of checking whether an answer has the right units and the right limiting behaviour before trusting it.

My final-year project used the Lighthill-Whitham-Richards model, which treats traffic density as a continuous quantity obeying a conservation law, with flux determined by a chosen speed-density relation. I worked through the method of characteristics by hand for a simple traffic-light problem, showing where characteristics cross and a shock forms, and found the shock speed from the Rankine-Hugoniot condition. I then wrote a Python program using a Godunov-type finite volume scheme to simulate the same scenario numerically. The most satisfying part was comparing the two: the simulated shock sat where the analysis predicted, though smeared over several cells. Investigating why led me to read about numerical diffusion and to test how refining the grid sharpened the front. My supervisor encouraged me to discuss the model's limitations honestly, so I included a section on why a single-lane continuum model cannot explain phenomena such as lane changing.

Since graduating I have worked as a dispensing assistant in a community pharmacy. The job is not mathematical in an obvious sense, but it demands accuracy, careful checking and calm communication with people who are often worried or unwell. I have also become the person who reorganised our repeat-prescription tracking sheet so that collection dates are flagged automatically, which reduced the number of last-minute requests on Fridays. Outside work I volunteer with a canal restoration group, clearing vegetation and helping rebuild a section of towpath wall. Watching how water levels change through a lock flight as boats pass has given me a new set of questions about flow that I would like to be able to answer properly.

To keep my skills current, I have been working through the early chapters of Strogatz's Nonlinear Dynamics and Chaos, sketching phase portraits for the examples and checking them numerically. I have also been revisiting partial differential equations, particularly separation of variables and Fourier series, because I know my undergraduate grounding there was functional rather than deep. Playing cornet in the band for ten years has taught me patience with slow, repeated practice, which I find has much in common with getting comfortable with a difficult technique.

At postgraduate level I hope to strengthen my analytical methods, especially asymptotic and perturbation techniques, and to learn more rigorous numerical analysis so that I understand not just whether a scheme works but why. I am interested in continuum modelling broadly, from fluids to biological and transport systems, and I would like a dissertation that combines analytical approximation with computation, as my undergraduate project did on a smaller scale. I am realistic that the step up will be demanding, but I have shown that I can teach myself new material, write working code and explain results clearly, and I am ready to build on that foundation.