Mathematics and Philosophy/Computer Science
What first drew me to Mathematics was the challenge of problem-solving. Simply starting with a few elementary axioms and being able to derive a single solution through various different procedures has always held a real fascination for me. However, I feel as though the true reason why I enjoy Mathematics so dearly is due to my character and individuality. My need for precision captivates neat workings, my vision allows the acceptance of advanced ideas and my positive mind-set gives rise to my success. All problems have a solution; the challenge and gratification are in the construction of reaching them. During a lecture on Mathematics in Music, I was struck by the vast influence of ratios and patterns in some of the most beautifully poignant pieces of music. Mozart's subtle use of the Fibonacci sequence and Schumann's use of musical cryptograms has unequivocally widened my view on how mathematics effects such enormous disciplines. In pursuit of similar talents, I recently began attending piano lessons studying classical music. This was further brought to light as I read Alex Bellos' "Alex Through the Looking Glass". By its conclusion, I also gained an interest on his thoughts on mathematical proof. He explored famous theorems such as the Banach-Tarski paradox and Euclid's proof of the infinitude of primes. I was captivated at how simple proofs can have such resonance in mathematics. I reinforced my investigations by completing an online course on mathematical thinking. It enabled me to prove by induction, approach challenging integration problems, and also gave an insight into number theory. As Bellos mentions Aristotle being one of the first to study the nature of proof, I discovered that his concern was in fact philosophy, yet his ideas had a profound influence in mathematics. Philosophy has since piqued my interest; I have been listening to podcasts that discuss similar topics to Hume's argument concerning induction and Locke's take on personal identity. I have also excelled in an online course on philosophy which highlighted my appeal towards epistemology and relativism. I have also exploited a mathematical link to computer science during my volunteering work at a local library where I lead a Coding Club for children. I planned and gave lessons on basic programming techniques orientated on several different mathematical problems. The experience allowed me to hone my organisational skills and also taught me to value listening and working within a team. Satisfying as it was working with children, an added benefit was that my foundational knowledge was being constantly reinforced which supported me in grasping A level content. Since this, I've progressed in my knowledge of programming from writing basic procedural code to more problematical object-oriented programming code. I found that to become comfortable with the paradigm, it was vital to understand the concept of its functionality before delving into the code. I did this by taking on projects such as a Complex Number calculator and a Critical Path Analysis software. While attending a summer school at the University of Cambridge for Computer Science, I spent a week investigating fresh, approachable undergraduate topics such as dynamic programming and recursive algorithms. This gave me the opportunity to explore areas of computer science I would not otherwise have encountered, along with a small but insightful taste into university life. The highlight of the week was partaking in an overview session with a PhD student; witnessing how an academic decomposes, abstracts and analyses such problems has highly improved my assiduity in computational thinking by further reinforcing my problem-solving abilities. It was a thought-provoking experience which reinforced my love for mathematics in conjunction with computer science. As for my future, I hope to undertake it with optimism and positivity, to face new opportunities and to embark on an amazing part of life that is University.