A list of recommended books
for school pupils and their teachers
Latymer pupils will find many of these texts available to
borrow
from PDM's office. Others should encourage their libraries or
maths departments to get
them in stock.
Books for younger pupils
Enzensberger, H. M., The Number Devil.
Granta, 2006.
For younger children, up to year 7 or so. Nice ideas, though
the terminology is non-standard.
Popular Mathematics.
None are too heavy going in terms of the maths required,
although they do contain some.
Eastaway, R. and Wyndham, J., Why
Do Buses Come in Threes? and How Long Is A Piece of String?
Robson Books, 1998 and 2002.
Gleick, James, Chaos:
Making a New Science. Vintage, 1997.
A good overview of the ideas behind chaos. Pretty pictures,
too.
Stewart, Ian, Does God
Play Dice? The New Mathematics Of Chaos.
Penguin, 1990.
Another book on chaos. Plenty of maths to get one's teeth
into.
Hoffman, Paul, The Man
Who Loved Only Numbers. Fourth Estate, 1998.
A biography of the mathematician Paul Erdos, with details of some of
the problems he addressed.
Wilson, Robin, Four
Colours Suffice: How The Map Problem Was Solved.
Penguin, 2003.
An overview of the famous four colour theorem.
Livio, Mario, The
Golden Ratio: The Story of Phi, The Extraordinary Number Of Nature, Art
and Beauty. Headline Review, 2002.
The golden ratio and its use in mathematics and appearance in nature
and art.
du Sautoy, Marcus, The
Music of the Primes: Why an Unsolved Problem in Mathematics Matters.
Harper Perennial, 2004.
An historical overview of the Riemann hypothesis. Not much
maths, but a good read.
Derbyshire, John, Prime
Obsession: Bernhard Riemann and the Greatest Unsolved Problem in
Mathematics. Plume Books, 2004.
Same subject matter as du Sautoy's book, but more meaty in terms of the
maths involved.
Singh, Simon, The Code
Book: The Secret History of Codes and Code-Breaking.
Fourth Estate, 2000.
A history of cryptography, with plenty of examples and explanations.
Also by Singh is his account of the history and proof of
Fermat's
Last Theorem.
Piper, F. and Murphy, S., Cryptography:
A Very Short Introduction. Oxford, 2002.
Overview of secret codes.
Stewar, Ian, Letters to
a Young Mathematician. Basic Books, 2006.
Blastland, L. and Dilnot, A., The
Tiger that Isn't: Seeing Through a World of Numbers.
Profile, 2007.
A readable account of the regular mis-interpretation of numbers in the
media.
More mathematical books for good sixth-form
mathematicians and their teachers.
Davis, Donald, The
Nature and Power of Mathematics. Dover, 2004.
A superb book, covering interesting ideas from the world of
mathematics. Not much except basic algebra is required, but topics are
treated in a rigorous fashion. Highly recommended for sixth formers
interested in mathematics.
Wells, David, You are a
Mathematician. Penguin, 1995.
Lots of examples and problems to solve.
Acheson, David, 1089
and All That - A Journey into Mathematics.
Oxford, 2002.
A brief introduction to some advanced topics and what the study of
mathematics is all about.
Gowers, Timothy, Mathematics:
A Very Short Introduction. Oxford, 2002.
An overview of mathematics at higher level. Not too technical.
Dunham, William, Journey
Through Genius: The Great Theorems of Mathematics.
Wiley, 1990.
An excellent book. Takes major theorems from the history of
mathematics and gives details of their proofs.
Ball, Keith, Strange
Curves, Counting Rabbits and other Mathematical Explorations.
Princeton, 2003.
Investigations of various mathematical topics beyond the A level
syllabus, each with explanations, exercises and suggestions for further
reading.
Korner, T. W., The
Pleasures of counting. Cambridge, 1996.
Expensive, but excellent. Lots of examples of mathematics
applied
to real-life situations. Gives a good insight into what mathematics at
a higher level is like, without being too technical.
Nelsen, Roger, Proofs
without Words: Exercises in Visual Thinking, 2 volumes.
MAA, 1997 and 2000.
Exactly what the title suggests: often beautiful visual proofs of
theorems from various mathematical disciplines.
Cuoco, Al, Mathematical
Connections: A Companion for Teachers and Others.
MAA, 2005.
Advanced ideas for use in the classroom.
Dunham, William, Euler:
The Master of Us All. MAA, 1999.
Chapters on various aspects of Euler's work. Each topic is
explored in detail, with plenty of mathematics to get one's teeth into.
Books on problem solving techniques, useful for those doing maths
competitions
Niven, Ivan, Maxima and
Minima Without Calculus. MAA, 2006.
The first chapter gives an excellent primer on inequalities; other
chapters cover geometrical and other optimisation problems.
Benjamin, A. T. and Quinn, J. J., Proofs
that Really Count: The Art of Combinatorial Proof. MAA,
2003.
Counting problems and methods of proof.
Zeitz, Paul, The Art
and Craft of Problem Solving. Wiley, 2006.
Books recommended for those wishing to study maths at university
Stewart, I. and Tall, D. The
Foundations of Mathematics. Oxford, 1977.
An excellent intoduction to the way maths is taught at university.
Read this and be ready for your first analysis course.
Courant, R. and Robbins, H., What
is Mathematics? An Elementary Approach to Ideas and Methods.
Oxford, 1996.
A brilliant book, containing an awful lot of material on higher level
mathematics. Great stuff.
