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AoPS Online Books

Much of AoPS's curriculum, specifically designed for high-performing math students in grades 5-12, is now available online!

Our online books offer the same content as our print books. The online books work directly in your web browser: there is no additional software to download. (Students must be signed onto the AoPS website to access an online book.) Students will have immediate access to the online book upon purchase: no waiting for a print book to be shipped.

Schools: Please contact us at sales@artofproblemsolving.com for institutional licensing.

View a sample:

Prealgebra Chapter 5, Section 3: Solving Linear Equations II

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Introductory Curriculum

Our Introduction series serves as a complete curriculum for students in grades 6-10. The series covers the standard Prealgebra-Algebra-Geometry sequence, but at a more advanced level and with more challenging problems than a typical curriculum. The series also covers important discrete math topics in Counting & Probability and Number Theory that are usually underrepresented in typical middle-school and high-school curricula.
Prealgebra Online Book
Richard Rusczyk, David Patrick, Ravi Boppana
Online Book
Prealgebra prepares students for the rigors of algebra and also teaches students problem-solving techniques to prepare them for prestigious middle school math contests such as MATHCOUNTS, MOEMS, and the AMC 8. The text is written to challenge students at a much deeper level than a traditional middle school prealgebra course.
Related courses: Prealgebra 1 and Prealgebra 2
Introduction to Algebra Online Book
Richard Rusczyk
Online Book (2nd edition)
A thorough introduction for students in grades 6-9 to algebra topics such as linear equations, ratios, quadratic equations, special factorizations, complex numbers, graphing linear and quadratic equations, linear and quadratic inequalities, functions, polynomials, exponents and logarithms, absolute value, sequences and series, and more!
Related courses: Introduction to Algebra A and Introduction to Algebra B
Introduction to Counting & Probability Online Book
David Patrick
Online Book (2nd edition)
A thorough introduction for students in grades 7-10 to counting and probability topics such as permutations, combinations, Pascal's triangle, geometric probability, basic combinatorial identities, the Binomial Theorem, and more.
Related course: Introduction to Counting and Probability
Introduction to Geometry Online Book
Richard Rusczyk
Online Book (2nd edition)
A full course in challenging geometry for students in grades 7-10, including topics such as similar triangles, congruent triangles, quadrilaterals, polygons, circles, funky areas, power of a point, three-dimensional geometry, transformations, introductory trigonometry, and more.
Related course: Introduction to Geometry
Introduction to Number Theory Online Book
Mathew Crawford
Online Book
A thorough introduction for students in grades 7-10 to topics in number theory such as primes & composites, multiples & divisors, prime factorization and its uses, base numbers, modular arithmetic, divisibility rules, linear congruences, how to develop number sense, and more.
Related course: Introduction to Number Theory

Intermediate Curriculum

Our Intermediate series serves as a complete curriculum for advanced high-school students. The books in this series are more challenging and rigorous than most standard textbooks and contain many topics not normally covered in the typical high-school curriculum. These books lay a foundation for further study at the university level in higher mathematics, physics, engineering, or computer science.
Intermediate Algebra Online Book
Richard Rusczyk and Mathew Crawford
Online Book

A comprehensive textbook covering Algebra 2 and topics in Precalculus. This book is the follow-up to the acclaimed Introduction to Algebra textbook. In addition to offering standard Algebra 2 and Precalculus curriculum, the text includes advanced topics such as those problem solving strategies required for success on the AMC and AIME competitions.
Related course: Intermediate Algebra

Intermediate Counting & Probability Online Book
David Patrick
Online Book
An intermediate textbook in counting and probability for students in grades 9-12, containing topics such as inclusion-exclusion, recursion, conditional probability, generating functions, graph theory, and more.
Related course: Intermediate Counting and Probability
Precalculus Online Book
Richard Rusczyk
Online Book (2nd edition)

A comprehensive textbook covering precalculus topics. Specific topics covered include trigonometry, complex numbers, vectors, and matrices. Includes many problems from the AIME and USAMO competitions.
Related course: Precalculus

   $ 59.00
Calculus Online Book
David Patrick
Online Book (2nd edition)

A comprehensive textbook covering single-variable calculus. Specific topics covered include limits, continuity, derivatives, integrals, power series, plane curves, and differential equations.
Related course: Calculus

Contest Prep Math

Our classic Art of Problem Solving texts have been used for over 20 years by students preparing for prestigious math contests such as MATHCOUNTS and the American Mathematics Competitions (AMC). These texts are not just a collection of "tricks": the emphasis is on learning and understanding methods for problem-solving, which enables students to solve a large variety of challenging problems.
   $ 47.00
the Art of Problem Solving, Volume 1: the Basics Online Book
Sandor Lehoczky and Richard Rusczyk
Online Book (7th edition)
A classic problem solving textbook for students in grades 7-10 who are preparing for contests like MATHCOUNTS and the AMC 8/10/12.
Related courses: MATHCOUNTS/AMC 8 Advanced and AMC 10 Problem Series
   $ 49.00
the Art of Problem Solving, Volume 2: and Beyond Online Book
Richard Rusczyk and Sandor Lehoczky
Online Book (7th edition)
A classic problem solving textbook for students in grades 9-12 who are preparing for advanced high school contests like the AMC 12, AIME, and the Harvard-MIT Mathematics Tournament.
Related courses: AMC 12 Problem Series, AIME Problem Series A, and AIME Problem Series B

Schools: Please contact us at sales@artofproblemsolving.com for institutional licensing.