## Mathematics

### Applied in: Winter 2013

### University Offers: Cambridge, Imperial College, Warwick, Durham, Bristol

Nothing is more satisfying than working through a conceptually-challenging problem and solving it successfully. My favourite problems in Mathematics are those which have no apparent method in the first instance, such that only with patience and creativity can a breakthrough be achieved. The thought of being able to encounter such challenges for the rest of my life is exhilarating, leaving no other subject I would rather study.

Inspired by a brief overview of a topic during a problem-solving class, I read a book entitled 'Number Theory Through Inquiry' by David C. Marshall. I was drawn into deriving proofs of various theorems using techniques I had gathered throughout the book, which grew in complexity the further I read. New concepts were left to the reader to formulate and prove, guided by exercises. I particularly enjoyed the several proofs of there being infinitely many prime numbers. However, my favourite was Euclid's proof since although not initially obvious, its simplicity meant that even a pupil with no knowledge of complex theorems in number theory could understand the proof.

At times, a proof could take me hours, but in persisting I was able to get through with the added reward of a beautifully constructed proof. This experience of tackling a problem in which the methods are not immediately obvious has given me some sense of what an undergraduate Mathematics student might experience.

An aspect of the AS Further Mathematics syllabus I found especially fascinating was the application of complex numbers. The fact that such numbers go against natural instinct, yet have practical relevance in our world astounds me. Whilst studying Euler's Identity, I found it extraordinary that values such as e, a number known for its uses in compound interest; i, an imaginary number whose square is -1; and pi, the ratio between a circle's diameter and circumference, are related in such a way. Similarly, the proof that the relationship between the length of the diagonal and side length of a regular pentagon was the golden ratio, using the Argand diagram, presented me with a link between two areas of Mathematics I originally thought were completely unrelated.

Before coming to Westminster School, I attended Buxton School where I had the honour of being assigned the role of Head Boy during my final year, organising a team of prefects to help run aspects of the school. Moreover, I won many awards including the Outstanding Award in Mathematics for achieving the top mark in my school for every module in GCSE Mathematics and Statistics; and a Jack Petchey Award for attaining the highest mark my school had ever seen in Additional Mathematics. I was awarded an HSBC scholarship that enabled me to join the sixth form at Westminster School.

Amongst other opportunities, I have been able to attend problem-solving classes to develop my understanding and knowledge of Mathematics outside the A Level syllabus. It was at these classes where I first realised the emphasis of a thorough yet concise proof. In addition to this, I taught at an elementary school in the Philippines and volunteered at a local state school, teaching Mathematics to young children. I managed to introduce them to new concepts in such a way that they understood the subject. For example, rather than just telling them angles in a triangle add up to 180 degrees, I showed them why this is so using parallel lines which they hadn't previously realised. This made me question how I approached Mathematics as a subject. I felt the need to discover the derivations of such concepts and examine why they actually work, in an analytical rather than experimental way, before I used them.

Whilst I hope my future work in Mathematics might have practical applications in engineering or economics, I am predominantly motivated by intellectual curiosity to dig even deeper into a subject which has no bounds.