Recommended Reading for Personal Statement

Your engagement with super-curricular material is far more important that the specific book or resource chosen. However, some books are overused and cliché so should be avoided if possible. For example, interviewers and admissions tutors will likely read about Fermat’s Last Theorem by Simon Singh in every other personal statement they pick up!

These are some recommendations from the Vantage team:

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George Polya, How to Solve It (1990)

Recommended for: Mathematics, Computer Science

This is a great book that covers general problem-solving ideas rather than abstract technical mathematics. It’s a very welcome antidote to the rote learning emphasised by many school syllabuses and introduces the way of thinking seen at university, so it’s good for admissions tutors to see it in a personal statement! It also provides useful training for admissions tests and interviews.

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Richard Courant and Herbert Robbins, What is Mathematics? (1996)

Recommended for: Mathematics

This is a classic book: it gives a whistle stop tour of lots of areas of undergraduate mathematics, from analysis to topology. The authors don’t assume knowledge beyond A level/IB but doesn’t refrain from teaching some technical detail. This book is especially good because it covers lots of topic, allowing you to find a particularly interesting topic to pursue further.

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Ernest Nagel and James R Newman, Gödel’s Proof (1958)

Recommended for: Mathematics, Computer Science

This book is rather heavy reading but provides a thorough walkthrough of one of the most profound proofs in mathematics. It demonstrates that a formal system cannot be both complete and consistent, i.e., there are either true things it can’t prove or false things it can prove. The book doesn’t assume any technical knowledge and there are plenty of interesting points to consider.

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H Davenport, The Higher Arithmetic (2008)

Recommended for: Mathematics

This book is fairly technical to read but provides a good introduction to first year undergraduate number theory. The proofs are particularly interesting and plenty of opportunity to make an interesting commentary. It might be advisable to work on small sections on this book rather than reading cover to cover, as it goes through sophisticated material fairly quickly.

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Anany Levitin and Maria Levitin, Algorithmic Puzzles (2011)

Recommended for: Mathematics, Computer Science

This book provides an excellent range of fun, computer science-style problems with fantastic explanations that thoroughly explain the thought process behind them. The vast range of problems included means that most students will find a problem of particular interest that they can talk about at length. It may also be useful preparation for admissions tests and interviews, especially Computer Science interviews and Q5 of the MAT.

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Roger Penrose, The Emperor’s New Mind (2016)

Recommended for: Mathematics, Computer Science

This text introduces a controversial thesis about the relationship between quantum mechanics and conscious minds, which required Penrose to provide a really clear, detailed overview of the mathematical theory of computation, including a fun dive into topics such as countable and uncountable infinities.

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Jeremy Kubica, Computational Fairy Tales (2012)

Recommended for: Computer Science

Like What is Mathematics?, this book provides a gentle introduction to a wide range of topics, from recursion to basic programming. It is broad enough that you are likely to find a topic you would like to explore in greater detail.

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Avinash Dixit and Barry Nalebuff, The Art of Strategy (2016)

Recommended for: Economics

This is an excellent book for economists, especially those applying for the more mathematically focused economics courses like the Cambridge course. Dixit and Nalebuff provide some discussion of game theoretic ideas in an abstract sense and provide real life case studies which are especially helpful for economics. Counter examples are given to the various principles discussed, illustrating the messiness of real world situations, which is thought provoking and provides good ground for discussion.

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