Mathematics Reading List

Alex Bellos

The Puzzle Ninja (2017) & Can You Solve My Problems? (2017)

Stephen Siklos

Advanced Problems in Mathematics (2016, download from StepMaths)

An excellent selection of graded problems, including hints, solutions and discussions for each. A good preparation for STEP.

George Pólya

How To Solve It (1945)

The classic work on mathematical problem solving for students and teachers

The Stanford Maths Problem Book (1974)

Similar to “Advanced Problems” above, this is an excellent collection of problems with hints and solutions. The problems are designed to test aptitude rather than achievement and will reward creativity and insight.

Thomas Povey

Professor Povey’s Puzzling Problems (2015)

A collection of interesting physics problems, with discussions of each. This is particularly useful for students considering courses in physics or engineering, where these types of questions may come up in interviews.

Raymond Smullyan

What Is The Name Of This Book? (1981)

Smullyan’s style is engaging and entertaining. These are mainly riddles, for example the lying and truth-telling Cretans of whom you can only ask one question.

Frederick Mosteller

Fifty Challenging Problems in Probability (Dover, 2000)

More than any other area of mathematics, the solutions to probability problems can seem counter intuitive and contrary to our expectations. These puzzles cover many classic and interesting situations and encourage critical thinking about chance and risk.

Anany and Maria Levitin

Algorithmic Puzzles (2011)

A collection of interesting problems that require you to find an algorithm to solve a problem, or generalise to solve a whole class of problems. Finding an algorithm is part of the exercise, proving it works in all cases may be harder! These problems would appeal to students studying the discrete/decision modules in further maths, or students studying maths with computer science.