Applied mathematics personal statement example

Why do you want to study this course or subject?

What draws me to applied mathematics is the moment a messy situation becomes a set of equations that can actually be solved. Last winter I got interested in the pedestrian crossing outside my college, where a long queue builds up at the end of lunch. Using the stopwatch on my phone I recorded the green and red phases over several days, then wrote a short Python script to simulate people arriving at random and waiting. I had read about the Poisson distribution in a library copy of an introductory probability text, and it was satisfying to see that assuming random arrivals gave queue lengths close to the ones I had counted by eye, at least outside the lunchtime rush, when arrivals are clearly not independent. The model was crude and I could not test any changes in real life, but it taught me something my textbook exercises had not: choosing the assumptions is most of the work, and knowing which ones you have broken matters as much as the answer. I want to study applied mathematics because I would like to do that properly, with the analysis and numerical methods behind it rather than a script I patched together. I am particularly keen to learn differential equations and modelling in more depth, and to understand where approximations come from instead of accepting them. I also like that applied mathematics does not belong to one industry; the same techniques appear in fluid flow, epidemiology and scheduling, and I would rather keep those options open than narrow down now.

How have your qualifications and studies helped you to prepare?

I am studying Mathematics, Further Mathematics and Physics at A level. Further Mathematics has been the most useful preparation: the mechanics content showed me how a physical situation is stripped down into a model, and the further pure work on complex numbers and matrices gave me tools that keep reappearing. Learning to diagonalise a matrix felt abstract until I used the same idea to work out the long-run behaviour of a simple two-state random process in my own reading, which made eigenvalues feel like a practical instrument rather than a procedure to memorise. Physics has trained me to keep track of units and to sanity-check a result before trusting it, a habit that saved me several times when my traffic script produced negative waiting times. In Mathematics I enjoy calculus most, especially integration by substitution, where the difficulty is spotting a structure rather than following steps. For my EPQ I wrote about numerical methods for solving equations that cannot be solved exactly, comparing the bisection method and Newton's method on the same functions and discussing why Newton's method can fail badly if the starting guess is poor. Researching it meant reading well beyond the syllabus and asking my teacher questions she pointed me to books for, which was the first time I had to work out what I did not understand on my own. Outside lessons I have worked through problems from past STEP and admissions test papers with two friends. We meet in a free classroom on Thursdays and take turns explaining solutions on the whiteboard, which has improved my written reasoning considerably; explaining a step out loud exposes the places where I have guessed.

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

I work most Saturdays and two evenings a week at a garden centre, on the tills and restocking. It is not mathematical work, but it has given me a lot of practice at staying accurate and polite when the queue is long, and at counting stock quickly without a calculator. During the spring rush the manager asked me to keep a tally of how many customers came through in each hour so she could plan staffing, and I ended up making her a simple spreadsheet chart of the pattern across the week. She now uses it when writing the rota, which pleased me more than I expected. At home I look after my two younger brothers after school on weekdays, cooking and going through their maths homework with them. Teaching a ten-year-old why you cannot add fractions by adding the tops and the bottoms has forced me to understand things I had stopped thinking about, and it is partly why I like explaining problems to my friends. I play badminton in a local club league on Sunday mornings, which is a useful break from sitting at a desk, and I have been learning Python steadily from free online material, mostly through small projects: a script that plots my brothers' spelling test scores, and a rough simulation of a dice game we argued about. None of these are sophisticated, but they have made me comfortable with reading error messages, breaking a problem into functions and checking results against something I can calculate by hand. Between shifts, family and coursework I have had to be organised about my time, and I expect that habit to help me with the pace of a mathematics degree.

This example has 4,747 characters across the three answers. Use it for ideas and structure. Your own UCAS answers must fit within 4,000 characters in total, including spaces.

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