Mathematical and Theoretical Physics postgraduate personal statement example

Personal statement example

The plot that convinced me my final-year project was working showed two humps on a line. The taller one caught the shorter one, the two merged briefly, and then they separated with their shapes unchanged. What I had not expected was that the taller wave came out slightly ahead of where it would have been if it had travelled alone, and the shorter one slightly behind. My supervisor pointed me to the exact two-soliton solution of the Korteweg–de Vries equation. When I compared my measured shifts with the formula, they agreed to within the error I had estimated from the grid spacing. That afternoon was the clearest moment so far of what I want from postgraduate study: watching a calculation on paper and a computation on screen describe the same thing.

My degree is in mathematics rather than physics. I chose physics-facing options wherever I could: classical mechanics, quantum theory, electromagnetism and fluid dynamics, alongside core analysis, linear algebra and partial differential equations. The project grew from the fluids course. I wrote a split-step Fourier code in Python, treating the linear dispersive term exactly in Fourier space and the nonlinear term with a small time step. A good part of the work was unglamorous. The code conserved mass well but drifted in energy until I reduced the step and filtered the highest modes. Reading about why KdV has infinitely many conserved quantities, and how the Lax pair formulation explains this, was the point at which the project stopped being numerical and started to feel like physics. I now want the training to understand integrability properly, and to see where it fails.

Outside my courses I have been working through David Tong's freely available lecture notes on quantum field theory, mostly on train journeys. I can follow canonical quantisation of the free scalar field and have worked the exercises on Noether currents. I am still slow with interacting theories, and I would rather admit that than pretend otherwise. A structured postgraduate course would give me the group theory, differential geometry and field theory that my mathematics degree touched only in passing.

I have paid for my studies partly by invigilating exams at a local college and working Saturdays on a cheese and bread stall at the town market. Invigilating is quiet, careful work: checking seating plans, timing papers exactly, handling access arrangements without fuss. The market stall is the opposite. It involves quick mental arithmetic and remembering what regular customers ordered last week, and I have become steadily more comfortable talking to strangers. Both jobs taught me to manage my time, which mattered in my final year when deadlines clustered.

I also interpret for my father at medical and council appointments, as his English is functional but not technical. Translating precisely, without adding my own interpretation, is harder than it sounds and has made me more careful about the words I use in written mathematics.

On Sunday mornings I ring bells at a village church. Change ringing is really a walk through permutations of the bells, and learning methods by their structure rather than by rote was my first experience of group theory before I met it formally. It is also a team activity in which one lapse of concentration is heard by the whole village, which keeps me honest.

I am applying for an advanced taught course in mathematical and theoretical physics because I want a rigorous foundation before deciding whether to pursue research, possibly in integrable systems or mathematical aspects of field theory. I bring solid analytical training, working computational skills and the habit of checking results two ways. I want to learn to ask better questions.