Ten books accessible to as and Higher students



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Ten books accessible to AS and Higher students

1089 and all that: A Journey into Mathematics

David Acheson

Oxford University Press, 2002, ISBN 0198516231, £13.50

A mathematician’s account of the maths that’s intrigued and interested him, it is written in a highly accessible and entertaining style, with plenty of puzzles and illustrations. It communicates the buzz the author gets from maths as well as introducing many mathematical ideas. Something to curl up and read or just dip into.



Fermat’s Last Theorem

Simon Singh

Fourth Estate, 2002, ISBN 1841157910, £8.99

Simon Singh’s very readable bestseller focuses on Andrew Wiles’ proof of Fermat’s Last Theorem, and also manages to touch on most of the puzzles that have occupied mathematicians over the centuries. The Daily Mail likened it to a chronicle of an obsessive love affair.



also by Simon Singh

The Code Book: The Secret History of Codes and Code-breaking

Fourth Estate, 2000, ISBN 1857028899, £9.99


Flatland: A Romance Of Many Dimensions

Edwin Abbott

Kessinger, 2004, ISBN 0760755876, £10.95

This fresh and original mind-expanding book, easily accessible to layman and mathematician alike, was first published in 1884. An enduring classic, in story form, it explores how it might be to live in worlds of other dimensions. The worlds are inhabited by characterful geometric forms whose activities paint a satirical picture of Victorian Society and, at the same time, illuminate and deepen our understanding of dimensions. The book has the virtues of being short, entertaining and illuminating, a combination not always found in Maths books!


How to Take a Penalty

Rob Eastaway and John Haigh

Robson Books, 2005, ISBN 1861058365, £12.99

This book shows how mathematics can help improve performance in athletics, darts, football, snooker and tennis, among other sports. It does this, as well as giving much more information about the mathematics of sport, in a lively and accessible fashion.



by Rob Eastaway and Jeremy Wyndham

How Long is a Piece of String?

Robson Books, 2003, ISBN 1861056257, £6.99



Why do Buses Come in Threes?

Robson Books, 2006, ISBN 1861058624, £6.99



In Code: A Mathematical Adventure

Sarah Flannery and David Flannery

Profile Books, 2001, ISBN 1861972717, £8.99

Sarah was a teenage mathematician who wrote, with her father’s help, about her childhood with daily puzzles set by her father, which led to a love of problem solving and also to knowledge of cryptology that won her international recognition. It includes problems to solve (with solutions) and an easy-to-follow explanation of her work.


It Must be Beautiful

Graham Farmelo (editor)

Granta Books, 2003, ISBN 1862075557, £9.99

The essays in this book cover a wide range of the scientific research of the twentieth century. The main content is in the field of mathematical physics but chemistry, environmental science and human behaviour are also included. The book is very readable and can be enjoyed by students with little mathematical or scientific expertise. The essays are seasoned with anecdotes and short biographies of some of the major scientific personalities of the last hundred years.


Polyominoes

Solomon Golomb

Princeton University Press, 1996, ISBN 0691024448, £15.95

Polyominoes are shapes made by joining squares edge to edge. You'll have seen tetrominoes if you've played the game Tetris. This book looks at the mathematics behind these shapes. You'll be introduced to proofs by colouring, which will convince you that you'll never be able to tile a 5 by 4 rectangle with the 5 tetrominoes, and how to create fault-free tilings using dominoes. There's a jigsaw using the 1285 enneominoes (nine squares) but what if, instead of squares, you used equilateral triangles? Or cubes? ...



The Magical Maze

Ian Stewart

Phoenix Press, 1998, ISBN 0753805146, £7.99

Very readable collection of diverse mathematical topics such as the Monty Hall problem, optimisation and chaos. This book places maths in a real life context. Some of the mathematics will be familiar to AS students but most will find something new and stimulating in this book.



also by Ian Stewart (see also overleaf)

From Here to Infinity

Oxford Paperbacks, 1996, ISBN 0192832026, £9.99


The Penguin Dictionary of Curious and Interesting Numbers

David Wells

Penguin, 1997, ISBN 0140261494, £8.99

This book takes the form of a numerical dictionary starting with -1 and i and ending with Graham's number. The entries give mathematical properties and historical facts. Many concepts, such as Fermat and Catalan numbers, are explained. Tables of common sequences are included. This book is ideal for dipping into, by GCSE as well as AS students. Find out why 13 is lucky, why 28 is perfect and about the first uninteresting number.


Uncle Petros and Goldbach’s Conjecture

Apostolos Doxiadis

Faber & Faber, 2000, ISBN 0571202039, £9.99

This novel is a delightful 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 wonderful mix of humour, pathos and maths.




Ten more advanced works

The Book of Numbers

John Conway and Richard Guy

Springer, 2006, ISBN 038797993X, £20.50

This book presents a highly idiosyncratic but immensely stimulating choice of properties of numbers – not just integers, though there are plenty of those, but fractions, real numbers, complex numbers, infinite numbers, and Conway's own most important contribution to mathematics: surreal numbers. He approaches the topic in his inimitable manner, stripping away much of the detail to reveal the structure of his argument with unusual clarity. You will see, among other things, how geometric visualization can help with number properties, why Fibonacci numbers occur in nature, and how to do arithmetic with infinite numbers. Many of the book's gems are easy to pick up and admire with bare hands; others demand perseverance and more mathematical sophistication, but with correspondingly rich rewards.


Does God Play Dice?

Ian Stewart

Penguin, 1997, ISBN 0140256024, £9.99

A very accessible introduction to the exciting field of chaos, it gives an insight into the mathematics behind fractals as well as many other situations in which you can find chaotic behaviour.


e: The Story of a Number

Eli Maor


Princeton University Press, 1998, ISBN 0691058547, £12.95

A chronological tale of the development of e. Starting with Napier and progressing to Newton, Leibniz and the Bernouillis, it discusses logarithms, series, areas and curves. Applications in mechanics, geometry and music are included.



Four Colours Suffice

Robin Wilson

Penguin, 2003, ISBN 014100908X, £8.99

If your experience of proof in mathematics is always algebraic or geometric, it is difficult to imagine how you could prove that any map needs at most four colours so that no adjoining regions have the same colour. This book explains the ideas clearly and gives a fascinating account of this problem, posed in 1852 and solved in 1976. Even if the four colour proof is complicated, the proof that five colours suffice is beautiful.



The Man Who Knew Infinity: A Life of the Genius Ramanujan

Robert Kanigel

Abacus, 1992, ISBN 0349104522, £10.99

Srinivasa Ramanujan, born in India in 1887, was from an early age fascinated with mathematics. Largely self-taught, a letter to G. H. Hardy at Cambridge University led to him spending most of the rest of his short life working there. This is the story of his life, giving the reader an insight into his extraordinary mathematical vision and how his ideas continue to fascinate the mathematical world.


The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, & Personalities

William Dunham

John Wiley & Sons, 1990, ISBN 0471176613, £14.95


This book offers incisive profiles of the great theorems, conundrums, disputes, and unsolved mysteries that have shaped mathematics. Dunham doesn’t just state the theorems, he gives the original proofs in ways accessible to A level students. Insights include how Euler used the binomial theorem in his work on partitions and how Archimedes calculated the surface area of a sphere.

also by William Dunham

Euler, the Master of us all

MAA, 1999, ISBN 0883853280, £22.99



Mathematics: A Very Short Introduction

Timothy Gowers

Oxford Paperbacks, 2002, ISBN 0192853619, £6.99

The author captures the essence of maths and gives a feel for how maths is approached beyond school level. Many advanced ideas are introduced in a clear and accessible style which relates theoretical concepts to practical applications.



Maths for the Mystified

Michael J de Smith

Troupador, 2006, ISBN 1905237812, £14.99

From irrational numbers to fractional dimensions, from image processing to credit card security, this book is a treasury of the most exciting maths and its application to today’s sophisticated world. Accurate yet accessible to the lay reader, the book’s content ranges from delightful anecdotes to serious insights and applications. The author does not side-step the mathematical reasoning but instead lucidly explores and explains it.


The Millennium Problems

Keith Devlin

Granta Books, 2005, ISBN 1862077355, £9.99

In May 2000 the Clay Foundation in the United States offered $1 000 000 for the solution of the seven most difficult mathematical problems today, known as the Millennium Problems. Keith Devlin offers a very clear description of the background to these problems and describes in simple terms exactly what they are. This is a very readable book that gives a good insight into the frontiers of mathematics.


The Music of the Primes

Marcus du Sautoy

Harper Perennial, 2004, ISBN 1841155802, £8.99

Great mathematics and a great read, as the author describes the quest for the truth about the Riemann Hypothesis, one of the most famous unsolved questions in maths, and describes many interesting episodes en route. This book’s high reputation is well deserved.


This booklist was compiled by
the Post-16 Subcommittee of
the Teaching Committee of
The Mathematical Association
(www.m-a.org.uk) and
published in April 2007.






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