Two other books in the OUP VSI series that complement and expand on the current one are Mathematics by the Field’s medallist Timothy Gowers and Cryptography by Fred Piper and Sean Murphy. Probability and statistics,elds that were neglected here in Numbers, are the subject of the VSI Statistics by David J. Hand.

An insight into the nature of numbers can be read in David Flannery’s book, The Square Root of 2:A Dialogue Concerning a Number and a Sequence(Copernicus Books,2006). This leisurely account is in the Socratic mode of a conversation between a teacher and pupil. One to Nine:The Inner Life of Numbers by Andrew Hodges(Short Books,2007)analyses the signicance of therst nine digits in order. Actually it uses each number as an umbrella for examining certain fundamental aspects of the world and introduces the reader to all manner of deep ideas. This contrasts with Tony Crilly’s 50 Mathematical Ideas You Really Need To Know(Quercus Publishing,2007), which does as it says,digesting each of 50 notions into a four-page description in as straightforward a manner as possible. The explanations are mainly through example with a modest amount of algebraic manipulations involved, rounded off with historical details and timelines surrounding the commentary. A particularly nice account on matters concerned with binomial coefcients is the paperback of Martin Griffiths, TheBackbone of Pascal’s Triangle(UK Mathematics Trust,2007), in which you will read proofs of Bertrand’s Postulate and Chebyshev’s Theorem, givingbounds for the number of primes less than n.

Apopular account of the Riemann Zeta Function is the bookby Marcus du Sautoy, TheMusic of the Primes, Why an Unsolved Problem in Mathematics Matters(HarperCollins,2004), while Carl Sabbagh’s, Dr Riemann’s Zeros(Atlantic Books,2003)treats essentially the same topic.

There are two accounts of the solution to Fermat’s Last Theorem,those being Fermat’sLast Theorem:Unlocking the Secret of an Ancient MathematicalProblem by Amir D. Aczel(Penguin,1996)and Fermat’s Last Theorem by Simon Singh(Fourth Estate,1999).cipher is also an effort of Simon Singh:The Code Book(Fourth Estate,2000). The unsolvability of the quintic(fifth-degree polynomial equations)was not explained in our text here but is the subject ofan historical account:Abel's Proof:An Essay on the Sources andMeaningofMathematical Unsolvability(MIT Press,2003)by Peter Pesic.

Websites

Avery high-quality web page that allows you to dip into any mathematical topic, and is especially rich in number matters, is Eric Wolfram's Math World:mathworld.wolfram.com. For mathematical history topics, try The MacTutor History of Mathematics archive at St Andrews University, Scotland:www-history.mcs.st-andrews.ac.uk/history.index.html. Web pages accessed 8 October 2010. Wikipedia's treatment ofmathematics by topic is generally serious and ofgood quality, although the degree of difficulty of the treatments is a little variable. For example, Wikipedia gives a good quick overview ofimportant topics such as matrices and linear algebra.