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Mathematics Reading List

The following is a list of books that you might find useful to buy or borrow from a library (some may be out of print). Be selective, but try to find ones that challenge your mathematical thinking. The list is in the following sections:

Study Skills
Mathematics Revision
Popular Texts
More Challenging Mathematical Texts

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Study Skills
Cottrell. S. (1999) The Study Skills Handbook, Macmillan Press Ltd, Basingstoke & London. A general guide to study skills with useful checklists

Kahn. P. (2001) Studying Mathematics and its Applications, Palgrave, Wokingham. Advice on how to study and apply complex mathematical ideas with exercises and extension material..

Northedge. A., Thomas. J., Peasgood. A. (1997) The Sciences Good Study Guide, The Open University, Milton Keynes. A study guide for students of science, technology and engineering with a basic (sub A–level) mathematics help section.


Mathematics revision
Abbott, P. (1996) Teach Yourself Algebra, Teach Yourself, London
Abbott, P. Neill, Hugh (1997) Teach Yourself Calculus, Teach Yourself, London
Abbott, P. Neill, Hugh (Ed) (1998) Teach Yourself Trigonometry, Teach Yourself, London
Graham, Alan (1999) Teach Yourself Statistics, Teach Yourself, London

Graham. L., Sargent.D., (1981) Countdown to Mathematics Vol 1 and Vol 2, Addison–Wesley Publishers Ltd in association with Open University Press, Wokingham. Vol 1 arithmetic, simple algebra, graphs, representing data; Vol 2 algebra, trigonometry.

There are plenty of other mathematics textbooks around; look in bookshops and libraries until you find one that suits your needs (maybe lots of practice exercises at your level and beyond, perhaps offering straightforward or multiple explanations). Some revision guides can be succinct yet informative enough to refresh your understanding


Wider mathematical reading
Popular texts
Acheson, D (2002),1089 and all that, Oxford University Press, Oxford. A little book of  mathematical puzzles and other delights.

Barrow, John D. (1993) Pi in the Sky: Counting, Thinking and Being, Penguin, London. The author discusses rival views of where maths comes from and how it is done.

Blastland, M (2007) The Tiger that Isn't, Profile Books, London. Illustrates how to understand numbers in the media with many everyday examples.

Doxiadis, Apostolos (2000) Uncle Petros and Goldbach’s Conjecture Faber & Faber, London. Though this is a work of fiction, it is a story of the search for a solution to a famous problem and of the possible pitfalls in a research project that is too restricted in its outlook. There is a mix of humour, pathos and mathematics.

Eastaway, Rob & Wyndham, Jeremy (1998) Why Do Buses Come in Threes?, Robson Books, London. Practical uses for probability theory, Fibonacci series, matrices, Venn Diagrams, prime numbers and more.

Eastaway, Rob & Wyndham, Jeremy (2002) How long is a piece of string?, Robson Books, London. More on the hidden mathematics of everyday life.

Flannery, Sarah (2000) In Code: A Mathematical Journey, Profile Books, London. This is a book about growing up in a mathematical household written when Sarah was a teenager. It includes some problems with solutions and explanations.

Guillen, Michael (1995) Five Equations that Changed the World, Abacus, London. Tells the stories of five of the most important mathematicians and scientists in history and gives the background to their discoveries of ‘world changing’ equations.

Guedji, Dennis (1998) Numbers the Universal Language, Thames & Hudson, London. Small book with good illustrations and extracts from historic documents.

Hoffman, Paul (1998) The Man Who Loved Only Numbers, Fourth Estate, London. The story of Paul Erdös and the search for mathematical truth

Huntley, H.E. (1970) The Divine Proportion A Study in Mathematical Beauty, Dover, New York. Topics more or less directly connected with the ‘Golden Section’ or ratio.

Ifrah, Georges (1998) The Universal History of Numbers, The Harvill Press, London. About the history of numbers and counting from pre–history to the age of computers.
Paulus, John Allen (1990) Innumeracy Mathematical Illiteracy and its Consequences, Penguin, London.
Real–world examples of innumeracy – stock scams, medical claims, risk perception, election statistics and more.

Peterson, Ivars (2001) The Mathematical Tourist: New and Updated Snapshots of Modern Mathematics, Palgrave, Basingstoke.

Pólya.G (1990) How to Solve It, Penguin, London. The classic text on mathematical problem solving with helpful forward by Ian Stewart.

Salsburg, D (2001) The Lady Tasting Tea, Henry Holt and Co., New York. The story of twentieth century statistics

Singh, Simon (2000) The Code Book Fourth Estate, London. A history of codes and ciphers and their modern applications in internet security.
Singh, Simon (1998) Fermat’s Last Theorem Fourth Estate, London. An account of Andrew Wiles’ proof of Fermat’s Last Theorem, but it touches on many of the problems that have interested mathematicians over the centuries.

Stewart, Ian (1996) From Here to Infinity, Oxford University Press, Oxford. An introduction to how mathematics is developing today, it shows how many ideas, old and new, can be important in answering questions in today’s world.
Stewart, Ian (1997) Does God Play Dice? Penguin, London. An introduction to the field of chaos, it gives an insight into the mathematics behind fractals as well as many other situations where you can find chaotic behaviour.
Stewart, Ian (1998) The Magical Maze: seeing the world through mathematical eyes, Orion Paperback , London.
Stewart, Ian (1998) Nature’s Numbers: discovering order and pattern in the universe, Orion Paperback, London.

Wilson, Robin (2002) Four Colours: How the Map Problem was Solved, Allen lane Science. An account of proving the four–colour conjecture that has at last been achieved with the aid of a computer.


More challenging mathematical texts
Courant R. and Robbins, H. (revised by Ian Stewart) (1996) What is Mathematics? Oxford University Press, Oxford. This is a classic book, covering a broad spectrum of fundamental mathematical ideas. It has been updated to describe mathematical developments such as the proof of the Four Colour Theorem and Fermat’s Last Theorem.

Fauvel, John & Gray, Jeremy (1987) The History of Mathematics: A Reader, Macmillan Education with The Open University, Basingstoke. Readings from a wide variety of sources to show the nature and development of mathematics from the earliest time to the twentieth century.

Hogben, Lancelot (1968) Mathematics for the Millions, The Merlin Press, London. From pre–history arithmetic to calculus with exercises and problems.

Gardner, Martin (2001) The Colossal Book of Mathematics, Norton, New York & London. Number theory, algebra, geometry, probability, topology, game theory, infinity, and other topics of recreational mathematics.

Kuhn, Harold W (Ed) (2002) The Essential John Nash, Princeton University Press. This book explains Nash’s work and reprints his most famous papers.

Simmons, George F. (1991) Calculus Gems: Brief Lives and Memorable Mathematics McGraw–Hill, Berkshire. This book includes brief lives of 33 important mathematicians. They are followed by 26 notes on significant moments in maths, from Pythagoras’ theorem to rocket propulsion.

Mathematics reference
There are several mathematical dictionaries available. Some are more technical, giving definitions in symbols and words, whereas others give explanations in words and include short biographies of mathematicians. Choose one that suits you.