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AoPS Curriculum

Our curriculum is specifically designed for high-performing math students in grades 5-12. We present a much broader and deeper exploration of challenging mathematics than a typical math curriculum and show students how to apply their knowledge and problem-solving skills to difficult problems. We help students learn the critical problem-solving skills necessary for success at mathematics competitions (such as MATHCOUNTS and the AMC), top universities, and competitive careers.
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
Richard Rusczyk, David Patrick, Ravi Boppana
Paperback
Text: 608 pages. Solutions: 224 pages.
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
Richard Rusczyk
Paperback (2nd edition)
Text: 656 pages. Solutions: 312 pages.
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
David Patrick
Paperback (2nd edition)
Text: 256 pages. Solutions: 120 pages.
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
Richard Rusczyk
Paperback (2nd edition)
Text: 557 pages. Solutions: 226 pages.
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
Mathew Crawford
Paperback
Text: 336 pages. Solutions: 144 pages.
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
Richard Rusczyk and Mathew Crawford
Paperback
Text: 720 pages. Solutions: 336 pages.

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
David Patrick
Paperback
Text: 400 pages. Solutions: 208 pages.
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
Richard Rusczyk
Paperback (2nd edition)
Text: 528 pages. Solutions: 272 pages.

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

Calculus
David Patrick
Paperback (2nd edition)
Text: 336 pages. Solutions: 128 pages.

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.
Text and Solutions   $ 47.00
Volume 1
Sandor Lehoczky and Richard Rusczyk
Paperback (7th edition)
Text: 288 pages. Solutions: 144 pages.
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
Text and Solutions   $ 49.00
Volume 2
Richard Rusczyk and Sandor Lehoczky
Paperback (7th edition)
Text: 320 pages. Solutions: 184 pages.
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
Competition Math for Middle School
Jason Batterson
Paperback
390 pages.
Contains over 700 examples and problems in the areas of Algebra, Counting, Probability, Number Theory, and Geometry. Examples and full solutions present clear concepts and provide helpful tips and tricks.
Related course: MATHCOUNTS/AMC 8 Basics