Mathematical physics personal statement example

Why do you want to study this course or subject?

In Further Maths last autumn my teacher spent five minutes showing that e^(iθ) traces out the unit circle. A fortnight later in Physics we were analysing alternating current, and I realised that the phase shift between voltage and current in a capacitor could be written as multiplication by i. A question I had been working through with awkward trigonometric identities became two lines of algebra. I am drawn to mathematical physics by this kind of moment, when a piece of pure mathematics turns out to be the natural language for a physical system. I enjoy physics most when I can see why an equation takes the form it does, and mathematics most when it describes something I can measure. I have since noticed the same pattern elsewhere. One second-order differential equation describes a mass on a spring, a pendulum at small angles and, as I found when reading ahead, an LC circuit. I want a degree where these connections are central rather than an occasional bonus, and where I can learn the tools that make them precise.

How have your qualifications and studies helped you to prepare?

My A levels are Maths, Further Maths, Physics and Computer Science. Further Maths has given me the most new ideas, particularly matrices as transformations and the solution of differential equations, which I now use to check Physics answers. For my Extended Project I am writing Python simulations of a planet orbiting a star. I began with the simple Euler method and found that the orbit slowly spiralled outwards, so the computed energy grew with each loop. Working out why led me to leapfrog integration, which advances position and velocity in staggered half-steps. Over long runs its energy error stays bounded rather than drifting. I plotted energy against time for both methods and different step sizes, and explaining that difference is now the core of my write-up. Alongside school I have been reading The Theoretical Minimum by Leonard Susskind and George Hrabovsky. Its chapters on the principle of least action were difficult at first. Rederiving the equation of motion for a pendulum from its Lagrangian, and getting the same result as from Newton's laws, helped me see why the approach is useful. I worked through these chapters slowly with a notebook, and I now have a list of questions I hope a degree will answer. The energy plot was a better test of the method than the apparent smoothness of the orbit.

What else have you done to prepare outside of education, and why are these experiences useful?

On weekday afternoons I collect my nine-year-old sister from school and look after her until my mum finishes her shift at a care home. That means cooking tea, getting homework done and keeping to bedtime. It has made me organised, because my own study has to fit around those hours, so I plan my Further Maths problem sets in advance and use the time after she is asleep. Helping her with fractions has also taught me something about explanation. When she was stuck on dividing by a half, the rule meant nothing to her until we asked how many halves fit into three pizzas. I try to apply the same principle to my own learning and look for a picture behind each method. On Saturdays I work at a local garden centre, unloading deliveries, restocking shelves and working the till during busy spells. It is not related to physics, but I am trusted to open up with a supervisor and train new weekend staff on the till. I also play five-a-side football every Thursday with friends from school, which gives me an hour away from screens and equations. These commitments have shown me that I can manage steady responsibility alongside demanding study, and I am ready for the independence of university work.