Cambridge reading list
Mathematics
For sixth formers and maths enthusiasts
The Cambridge Faculty of Mathematics’ own reading list for sixth formers thinking of a maths degree, and for anyone who loves maths: biographies and histories, puzzles, popular mathematics and physics, and a few textbooks to bridge the gap to university.
Source: Mathematical Reading List, Faculty of Mathematics, University of Cambridge (September 2022). Read the original ↗
67 books and sites, in Cambridge’s sections. Cambridge’s own notes on each are in the original; the labels and notes under each book, and the books added first, are ours.
For a personal statement, which book matters less than what you did with it: a problem you worked through, an idea you followed further, something you disagreed with. Only mention books you’d happily talk about at interview.
In each section, the books that stand out in a personal statement come first, then the most recommended, then those easy to dip into, then the rest.
Our additions
Not on Cambridge’s list
Three older books we’d add. Loney and Hall & Knight were written for school mathematics, and their problem sets are superb practice for olympiad-style questions.
Plane Trigonometry
S. L. Loney · Cambridge University Press, 1893
Stands out in a personal statement
Written for school-level trigonometry, with hundreds of graded problems, many as hard as olympiad questions. Rarely named, and you can talk about problems you solved.
Higher Algebra
H. S. Hall and S. R. Knight · Macmillan, 1887
Stands out in a personal statement
School algebra taken a long way: inequalities, series, combinatorics and probability, with very good problem sets for olympiad-style practice.
Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work
G. H. Hardy · Cambridge University Press, 1940; AMS Chelsea reprint, 1999
Stands out in a personal statement
Hardy on the mathematics he and Ramanujan shared, in his own words. Harder going, out of print, and a rare choice: a strong follow-on to The Man Who Knew Infinity.
Doing mathematics
How to solve problems, and how to study maths at university.
How to Think Like a Mathematician
Kevin Houston · CUP, 2009
Stands out in a personal statement
Nearly everyone names Pólya; saying what you learnt from Houston’s exercises shows real work.
How to Solve It
George Pólya · Penguin, 1990
Most recommended
Cambridge calls it highly recommended: the problem-solving classic. Very often named, so be specific about it.
How to Study for a Mathematics Degree
Lara Alcock · OUP, 2013
Easy to dip into
Practical advice: read a chapter at a time, as you need it.
Historical and general
Where the ideas came from, and the people who had them.
Closing the Gap: The Quest to Understand Prime Numbers
Vicky Neale · OUP, 2017
Stands out in a personal statement
Recent, with real number theory you can discuss in detail, and problems to try.
Euler’s Pioneering Equation
Robin Wilson · OUP, 2018
Stands out in a personal statement
Short and properly mathematical, and less often named than the classics.
A Russian Childhood
Sofya Kovalevskaya, translated by Beatrice Stillman · Springer, 1978
Stands out in a personal statement
An unusual choice. Little mathematics in it, so pair it with a book that has more. You could say it made you want to learn more about the Russian tradition of rigour in mathematics.
A Mathematician’s Apology
G. H. Hardy · CUP, 1992
Most recommended
Named very often, and for a reason, but if you use it, say something specific.
The Man Who Knew Infinity
Robert Kanigel · Abacus, 1992
Most recommended
Ramanujan’s life, and a vivid picture of how mathematics gets done.
Fermat’s Last Theorem
Simon Singh · Fourth Estate, 2002
Most recommended
A gripping story with real mathematics. Named very often, so say something specific.
Mathematicians: An Outer View of the Inner World
Mariana Cook · Princeton University Press, 2009
Easy to dip into
One portrait at a time.
The Simpsons and Their Mathematical Secrets
Simon Singh · Bloomsbury, 2013
Easy to dip into
Light and fun: dip in for the episodes you know.
Mathematics: Queen and Servant of Science
E. T. Bell · Spectrum, 1996
Alan Turing: The Enigma
Andrew Hodges · Vintage, 2014
In Code: A Mathematical Journey
Sarah Flannery and David Flannery · Workman Publishing, 2001
Surely You’re Joking, Mr Feynman!
Richard P. Feynman · Arrow Books, 1992
Named very often, and more about Feynman than mathematics.
The Music of the Primes
Marcus du Sautoy · HarperCollins, 2003
Named very often in personal statements: if you use it, say something specific.
Finding Moonshine: A Mathematician’s Journey Through Symmetry
Marcus du Sautoy · Fourth Estate, 2008
Symmetry and the Beautiful Universe
Leon M. Lederman and Christopher T. Hill · Prometheus, 2004
Readable mathematics
Real mathematics written to be read for pleasure, from pocket introductions to problem books.
Calculus for the Ambitious
T. W. Körner · CUP, 2014
Stands out in a personal statement
Takes sixth-form calculus further: good to discuss at interview.
Logical Labyrinths
Raymond M. Smullyan · CRC Press, 2008
Stands out in a personal statement
Puzzles that lead into real logic.
Insights into Game Theory: An Alternative Mathematical Experience
Ein-Ya Gura and Michael B. Maschler · CUP, 2008
Stands out in a personal statement
Rigorous proofs with little notation, and exercises to try.
Curves for the Mathematically Curious
Julian Havil · Princeton University Press, 2019
Stands out in a personal statement
Recent, and rarely named.
Chaos and Fractals: An Elementary Introduction
David P. Feldman · OUP, 2012
Stands out in a personal statement
Goes further than Gleick, with exercises.
Mathematics: A Very Short Introduction
Timothy Gowers · OUP, 2002
Most recommended
By a Fields medallist, and it fits in your pocket.
The Pleasures of Counting
T. W. Körner · CUP, 1996
Most recommended
Something for everyone, from cholera maps to Enigma.
What Is Mathematics?
Richard Courant and Herbert Robbins, revised by Ian Stewart · OUP, 1996
Most recommended
A demanding classic, revised by Ian Stewart.
The Math Book
Clifford A. Pickover · Sterling, 2009
Easy to dip into
One milestone a page.
What’s Happening in the Mathematical Sciences
Dana Mackenzie and Barry Cipra · AMS, a series since 1993
Easy to dip into
Short, illustrated articles on recent discoveries.
The Penguin Dictionary of Curious and Interesting Numbers
David Wells · Penguin, 1997
Easy to dip into
Look up a number and read on.
The Mathematical Experience
Philip J. Davis and Reuben Hersh · Penguin, 1990
Solving Mathematical Problems
Terence Tao · OUP, 2006
Archimedes’ Revenge
Paul Hoffman · Penguin, 1991
Luck, Logic, and White Lies: The Mathematics of Games
Jörg Bewersdorff · A K Peters, 2004
Beyond Numeracy
John Allen Paulos · Penguin, 1991
From Here to Infinity
Ian Stewart · OUP, 1996
50 Visions of Mathematics
Sam Parc (editor) · OUP, 2014
Reaching for Infinity
Stan Gibilisco · Tab/McGraw-Hill, 1990
The Computational Beauty of Nature
Gary William Flake · MIT Press, 2000
Chaos
James Gleick · Minerva, 1997
Cambridge notes that nine in ten candidates once named it: pick something less common, or go further with Feldman.
Algorithms Unlocked
Thomas H. Cormen · MIT Press, 2013
Readable theoretical physics
Physics for the mathematically minded, from the very small to the very large.
Black Hole Blues
Janna Levin · Vintage, 2016
Stands out in a personal statement
Recent: the story of the gravitational waves you’d meet in a maths degree’s third year.
The New Quantum Universe
Tony Hey and Patrick Walters · CUP, 2003
Stands out in a personal statement
Particle physics all the way to the Higgs.
The Strangest Man: The Hidden Life of Paul Dirac
Graham Farmelo · Faber and Faber, 2009
Most recommended
Dirac’s life, and the mathematics of quantum theory behind it.
A Short History of Nearly Everything
Bill Bryson · Black Swan, 2004
Easy to dip into
Chapter by chapter, in any order.
A Brief History of Time
Stephen Hawking · Bantam, 1988
One of the most-named books of all: fine to love, hard to stand out with.
Readable textbooks
A first taste of university mathematics, many with exercises and solutions.
A Concise Introduction to Pure Mathematics
Martin Liebeck · Chapman & Hall/CRC, 2010
Stands out in a personal statement
Working through a real first-year text and its exercises is what tutors most like to hear about.
Groups: A Path to Geometry
R. P. Burn · CUP, 1987
Stands out in a personal statement
A real university topic, worked through.
Yet Another Introduction to Analysis
Victor Bryant · CUP, 1990
Stands out in a personal statement
Analysis from first principles, with solutions to check yourself.
Advanced Problems in Mathematics: Preparing for University
Stephen Siklos · Open Book Publishers, 2016 (free to download)
Most recommended
Free, and the best preparation for STEP.
Towards Higher Mathematics: A Companion
Richard Earl · CUP, 2017
Most recommended
Bridges school and university maths, with over 1,500 graded exercises.
Mathematical Methods for Physics and Engineering
K. F. Riley, M. P. Hobson and S. J. Bence · CUP, 1998
Easy to dip into
A reference to look things up in, not to read cover to cover.
The Art of Statistics: Learning from Data
David Spiegelhalter · Pelican, 2019
What Is Mathematical Analysis?
John Baylis · Macmillan, 1991 (out of print)
A First Course in Mechanics
Mary Lunn · OUP, 1991
Understanding Probability
Henk Tijms · CUP, 2012
Mathematical adventures and recreations
Puzzles to keep you thinking, and lively tours of real mathematics.
Problem Solving Through Recreational Mathematics
Bonnie Averbach and Orin Chein · Dover, 2000
Stands out in a personal statement
Hints and solutions, so you can show how you got there.
A Mathematical Mosaic
Ravi Vakil · Brendan Kelly, 2008
Stands out in a personal statement
Problems you can say you actually solved.
The Colossal Book of Mathematics
Martin Gardner · Norton, 2004
Most recommended
Martin Gardner at his best, over 700 pages of it.
Cut the Knot
Alexander Bogomolny · Website, since 1996
Easy to dip into
A website to wander through for hours.
Game, Set and Math
Ian Stewart · Penguin, 1997
Easy to dip into
Separate essays, in any order.
Cakes, Custard and Category Theory
Eugenia Cheng · Profile Books, 2015
Easy to dip into
Light, and a chapter at a time.
To Infinity and Beyond
Eli Maor · Princeton, 1991
Source: Mathematical Reading List, Faculty of Mathematics, University of Cambridge (September 2022). Read the original ↗