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Read any good (maths) books lately?
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Read any good (maths) books lately?
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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