Mathematics reading recommendations

Supplemental textbooks

Book	Author	ISBN and purchase links	Why we're recommending it
Introduction to Algebra	Richard Rusczyk	ISBN 978-1-934124-14-7, paperback	This is a first year high school algebra textbook published by Art of Problem Solving that teaches elements of mathematical thinking and problem solving, as opposed to rote drill. The series has been reviewed very favorably, for example, on Quora.
Introduction to Geometry	Richard Rusczyk	ISBN 978-1-934124-08-6, paperback	This is a high school geometry textbook published by Art of Problem Solving that teaches elements of mathematical thinking and problem solving, as opposed to rote drill. The series has been reviewed very favorably, for example, on Quora.
Measurement	Paul Lockhart	ISBN 978-0674057555, Amazon paperback	Paul Lockhart is a professional mathematician who spent years teaching high school developing innovative curriculum. This offers a mathematical sophisticate's accessible take on geometry and calculus. The portion on geometry can be learned concurrently with geometry, and the portion on calculus can be learned concurrently with calculus.
Intermediate Algebra	Richard Rusczyk and Matthew Crawford	ISBN 978-1-934124-04-8, paperback	This is a second year high school algebra textbook published by Art of Problem Solving, that teaches elements of mathematical thinking and problem solving, as opposed to rote drill. The series has been reviewed very favorably, for example, on Quora.
Precalculus	Richard Rusczyk	ISBN 978-1-934124-16-1, paperback	This is a precalculus textbook published by Art of Problem Solving, that teaches elements of mathematical thinking and problem solving, as opposed to rote drill. The series has been reviewed very favorably, for example, on Quora.

|- | | Precalculus || Richard Rusczyk || ISBN 978-1-934124-16-1, paperback || This is a precalculus textbook published by Art of Problem Solving, that teaches elements of mathematical thinking and problem solving, as opposed to rote drill. The series has been reviewed very favorably, for example, on Quora.

Mathematical history

Book	Author	ISBN and purchase links	Why we're recommending it
The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics	Marcus du Sautoy	ISBN 978-0062064011, Amazon paperback	This book is one of the best books for a general audience on the history 19th and 20th century mathematical research. It focuses on the Riemann Hypothesis, which is one of the most famous unsolved mathematical problems, but manages to tie together many threads, which offers the reader a sense of perspective. Art of Problem Solving founder Richard Rusczyk named it one of his favorite math popularization books. The book requires no mathematical background.
The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography	Simon Singh	ISBN 978-0385495325, Amazon paperback	This book gives a history of the mathematical field of cryptography, which has affected society on many levels. Students who have learned first year high school algebra are probably able to understand the book.
Journey through Genius: The Great Theorems of Mathematics	William Dunham	ISBN 978-0140147391, Amazon paperback	This book presents highlights from the history of mathematics. In doing so, it gives a sense for mathematics as a human intellectual accomplishment. A number of mathematicians remember it as their favorite math book from their high school days. It's accessible to students who have learned most of high school geometry and second year algebra.
Euler: The Master of Us All	William Dunham	ISBN 978-0883853283, Amazon paperback	This book is a fascinating survey of some of the most significant work of one of the greatest mathematicians who ever lived. It's accessible to students who have learned calculus.

Higher math

Book	Author	ISBN and purchase links	Why we're recommending it
The Shape of Space	Jeffrey Weeks	ISBN 978-0824707095, Amazon paperback	This book introduces the reader to hyperbolic geometry in two and three dimensions, giving the reader a glimpse of modern geometry. It's accessible to readers who have learned high school geometry
The Shape of Space	Jeffrey Weeks	ISBN 978-0824707095, Amazon paperback	This book introduces the reader to hyperbolic geometry in two and three dimensions, giving the reader a glimpse of modern geometry. It's accessible to readers who have learned high school geometry
Integers, Polynomials, and Rings: A Course in Algebra	Ronald S. Irving	ISBN 978-0387201726, Amazon paperback	This is a very gentle introduction to the mathematical field called abstract algebra. It's accessible to a high schooler who has learned second year high school algebra, and has some very pretty material.
Excursions in Calculus: An Interplay of the Continuous and the Discrete	Robert M. Young	ISBN 978-0883853177, Amazon paperback	This book has some very nice applications of calculus. It's accessible to students who have completed a calculus course.