Applied mathematics personal statement example

Why do you want to study this course or subject?

A two-litre lemonade bottle with a hole punched near the base has spent most of this year on our kitchen windowsill. I first filled it after a physics lesson mentioned Torricelli's law, which says the speed of water leaving a small hole depends on the square root of the height of water above it. If that holds, the level should fall quickly at first and then slow down, and the emptying time should be predictable from the starting height. I marked the straight-sided part of the bottle every centimetre with tape, filmed it draining on my phone and read off the times frame by frame. The shape of my data matched the prediction, but the bottle always took longer to empty than the simple model said. Working out why taught me more than the agreement did. The jet narrows just after leaving the hole, so the effective area is smaller than the hole itself, and allowing for this with one correction factor brought my predictions within a few seconds. Applied mathematics appeals to me because of this movement between a clean equation and a messy situation: deciding which assumptions matter and testing them against something real. I want to study differential equations and numerical methods properly, so I can tackle problems with no neat answer.

How have your qualifications and studies helped you to prepare?

I study A levels in Mathematics, Physics and Economics. My school does not offer Further Mathematics, so since Year 12 I have worked through further pure topics on my own using free online materials and a second-hand textbook, meeting a maths teacher once a fortnight at lunchtime to check my work. Complex numbers and first-order differential equations have been the most useful; solving dh/dt = -k√h by separating variables was the first time I had derived a model myself rather than being handed one. In Physics, the simple harmonic motion practical showed me how much careful uncertainty analysis changes what a result means, and I now plot residuals rather than only a line of best fit. Economics offers a different kind of model, where supply and demand curves are simplifications whose usefulness depends on what is held constant. Silvanus Thompson's Calculus Made Easy helped me build intuition about small changes before I met formal limits, and Ian Stewart's In Pursuit of the Unknown showed how equations such as the wave equation and the Navier-Stokes equations grew out of physical questions. I am learning Python through free tutorials and have used it to solve my bottle equation with Euler's method, comparing step sizes against the exact solution.

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

For two years I have worked Saturdays and two evenings a week at a launderette near our flat. The job is mostly practical: emptying lint filters, helping customers with the card machines and keeping the place clean. Out of curiosity I kept a tally of how many machines were in use each half hour for six weeks. The pattern was clear: Saturday mornings were overloaded while Sunday afternoons were nearly empty. I showed the owner a simple chart and she now advertises a cheaper service wash on quieter afternoons. It was a small change, but it showed me that careful counting can be useful to someone. At home I collect my younger brother from primary school three days a week and help with his homework, which has made me better at explaining ideas, especially fractions, without just giving him the answer. On Thursday nights I play five-a-side football with friends and handle the pitch booking and payments for the group. Fitting these around study has taught me to plan my time, and I have kept my project going in the gaps. I am ready for a demanding course and keen to learn the mathematics behind models I have so far only approached on my own.