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Numbers: A Very Short Introduction

Peter M. Higgins
OXFORD UNIVERSITY PRESS 2011, 230 PAGES PRICE (PAPERBACK) £7.99 ISBN 978-0-19-958405-5

This beautiful 230 page paperback is one of a series of 260 Very Short Introductions to a variety of topics, from Aristocracy, through Quantum Theory to Architecture. The aim of the book is stated in the preface: to explain, in language that will be familiar to everyone, what are the various kinds of numbers that arise, and how they behave. Nowhere is the target audience of the book stated. For myself, I found the chapters dealing with factorisation, prime numbers and the like, interesting and generally well explained; I was already acquainted with the material. Perhaps the only part that was not familiar to me was the discussion of how factorisation of large numbers forms the basis of modern cryptography. I must admit that I still do not understand exactly how ciphers work.

I have one small criticism: the book contains very few proofs. One of the very few is Euclid’s proof that there is an infinity of prime numbers; I would have welcomed more proofs. To offset this, the chapter ‘To Infinity and Beyond’ introduces the reader to Cantor’s theory of sets, Russell’s paradox, Fibonacci numbers, continued fractions, and many more such important and intriguing topics, always with a light and sensitive touch. I heartily recommend this Very Short Introduction.

Graham Gladwell FIMA
University of Waterloo, Ontario, Canada
Mathematics Today December 2011

Numbers: A Very Short Introduction can be purchased at Amazon.co.uk