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# AoPS Curriculum

What would you like to study?
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.
Text and Solutions   \$ 59.00
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
Text and Solutions   \$ 67.00
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
Text and Solutions   \$ 49.00
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
Text and Solutions   \$ 65.00
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
Text and Solutions   \$ 55.00
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.
Text and Solutions   \$ 74.00
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

Text and Solutions   \$ 56.00
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
Text and Solutions   \$ 62.00
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

Text and Solutions   \$ 59.00
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
\$ 29.50
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

What would you like to study?
Beast Academy is our curriculum for students ages 6–13. Each level consists of four units (A through D). Each unit includes both Guide and Practice materials.
• Guide materials are written in an engaging, comic-book style which provides comprehensive, rigorous instruction.
• Practice materials provide hundreds of exercises, problems, puzzles, and games to reinforce the lessons from the Guide.

In Level 1, each unit (A through D) contains both Guide and Practice materials in a single book. In Levels 2-5, the Guide and Practice materials are separated into two books per unit.

Beast Academy covers the core fundamentals and then goes well beyond these basics to present material at a deeper and more challenging level than a typical elementary-school math curriculum.

Jason Batterson. Illustrated by Erich Owen and Sarah Leuver.
Paperback
216 pages.

Beast Academy 1A is the first part in a four-part series for students ages 6–8. Level 1A includes chapters on counting, shapes, and comparing.

Jason Batterson. Illustrated by Erich Owen and Sarah Leuver.
Paperback
240 pages.

Beast Academy 1B is the second part in a four-part series for students ages 6–8. Level 1B includes chapters on addition, subtraction, and categories.

Jason Batterson. Illustrated by Erich Owen and Sarah Leuver.
Paperback
248 pages.

Beast Academy 1C is the third part in a four-part series for students ages 6–8. Level 1C includes chapters on addition & subtraction, comparison, and patterns.

Jason Batterson. Illustrated by Erich Owen and Sarah Leuver.
Paperback
240 pages.

Beast Academy 1D is the fourth part in a four-part series for students ages 6–8. Level 1D includes chapters on big numbers, measurement, and problem solving.

Chris Page, Jason Batterson, and Anderson Wang. Book design by Doğa Arı.
Paperback
224 Pages.
Beast Academy Puzzles 1 contains over 500 puzzles in 12 different styles that will delight puzzle solvers ages 7 and up. It can be used by itself or as a supplement to the full Beast Academy level 1 curriculum.
Guide and Practice   \$ 30.00
Jason Batterson, Kyle Guillet, Chris Page. Illustrated by Erich Owen.
Paperback
Guide: 96 pages. Practice: 136 pages.

Beast Academy Guide 2A and its companion Practice 2A are the first part in a four-part series for students ages 7–9. Level 2A includes chapters on place value, comparing numbers, and addition.

Guide and Practice   \$ 30.00
Jason Batterson, Kyle Guillet, Chris Page. Illustrated by Erich Owen.
Paperback
Guide: 104 pages. Practice: 160 pages.

Beast Academy Guide 2B and its companion Practice 2B are the second part in a four-part series for students ages 7–9. Level 2B includes chapters on subtraction, expressions, and problem solving.

Guide and Practice   \$ 30.00
Jason Batterson, Kyle Guillet, Chris Page. Illustrated by Erich Owen.
Paperback
Guide: 104 pages. Practice: 152 pages.

Beast Academy Guide 2C and its companion Practice 2C are the third part in a four-part series for students ages 7–9. Level 2C includes chapters on measurement, addition and subtraction strategies, and odds & evens.

Guide and Practice   \$ 30.00
Jason Batterson, Kyle Guillet, Chris Page. Illustrated by Erich Owen.
Paperback
Guide: 112 pages. Practice: 160 pages.

Beast Academy Guide 2D and its companion Practice 2D are the fourth part in a four-part series for students ages 7–9. Level 2D includes chapters on big numbers, algorithms, and problem solving.

Chris Page, Palmer Mebane, and Jason Batterson. Book design by Doğa Arı.
Paperback
200 pages.
Beast Academy Puzzles 2 contains over 400 puzzles in 12 different styles that will delight puzzle solvers ages 7 and up. It can be used by itself or as a supplement to the full Beast Academy level 2 curriculum.
Guide and Practice   \$ 30.00
Jason Batterson, Shannon Rogers. Illustrated by Erich Owen.
Paperback
Guide: 104 pages. Practice: 128 pages.

Beast Academy Guide 3A and its companion Practice 3A are the first part in a four-part series for students ages 8–10. Level 3A includes chapters on shape classification, skip-counting, and perimeter and area.

Guide and Practice   \$ 30.00
Jason Batterson, Shannon Rogers. Illustrated by Erich Owen.
Paperback
Guide: 104 pages. Practice: 128 pages.

Beast Academy Guide 3B and its companion Practice 3B are the second part in a four-part series for students ages 8–10. Level 3B includes chapters on multiplication, perfect squares, and the distributive property.

Guide and Practice   \$ 30.00
Jason Batterson, Shannon Rogers. Illustrated by Erich Owen.
Paperback
Guide: 112 pages. Practice: 144 pages.

Beast Academy Guide 3C and its companion Practice 3C are the third part in a four-part series for students ages 8–10. Level 3C includes chapters on variables, division, and units and measure.

Guide and Practice   \$ 30.00
Jason Batterson, Shannon Rogers. Illustrated by Erich Owen.
Paperback
Guide: 112 pages. Practice: 160 pages.

Beast Academy Guide 3D and its companion Practice 3D are the fourth part in a four-part series for students ages 8–10. Level 3D includes chapters on fractions, estimation, and area.

Chris Page, Mark Richard, Palmer Mebane, and Jason Batterson. Book design by Doğa Arı.
Paperback
216 pages.
Beast Academy Puzzles 3 contains nearly 500 puzzles in 12 different styles that will delight puzzle solvers ages 9 and up. It can be used by itself or as a supplement to the full Beast Academy level 3 curriculum.
Jason Batterson and Stephanie Sadrian. Book design by Doğa Arı. Comic illustrations by Erich Owen and Sarah Leuver.
Paperback
352 Pages.
Beast Academy Science 3A is the first part in a two-part series for students 8-10. Level 3A includes chapters on motion, weather, and survival.
Jason Batterson and Stephanie Sadrian. Book design by Doğa Arı. Comic illustrations by Erich Owen and Sarah Leuver.
Paperback
368 Pages.
Beast Academy Science 3B is the second part in a two-part series for students 8-10. Level 3B includes chapters on forces, the atmosphere, and traits.
Guide and Practice   \$ 30.00
Jason Batterson, Shannon Rogers. Illustrated by Erich Owen.
Paperback
Guide: 112 pages. Practice: 176 pages.

Beast Academy Guide 4A and its companion Practice 4A are the first part in a four-part series for students ages 9–12. Level 4A includes chapters on shapes, multiplication, and exponents.

Guide and Practice   \$ 30.00
Jason Batterson, Shannon Rogers. Illustrated by Erich Owen.
Paperback
Guide: 112 pages. Practice: 152 pages.

Beast Academy Guide 4B and its companion Practice 4B are the second part in a four-part series for students ages 9–12. Level 4B includes chapters on counting, division, and logic.

Guide and Practice   \$ 30.00
Jason Batterson, Shannon Rogers. Illustrated by Erich Owen.
Paperback
Guide: 112 pages. Practice: 168 pages.

Beast Academy Guide 4C and its companion Practice 4C are the third part in a four-part series for students ages 9–12. Level 4C includes chapters on factors, fractions, and integers.

Guide and Practice   \$ 30.00
Jason Batterson, Shannon Rogers. Illustrated by Erich Owen.
Paperback
Guide: 112 pages. Practice: 152 pages.
Beast Academy Guide 4D and its companion Practice 4D are the fourth part in a four-part series for students ages 9–12. Level 4D includes chapters on fractions, decimals, and probability.
Chris Page, Anderson Wang, Palmer Mebane, and Jason Batterson. Book design by Doğa Arı.
Paperback
224 pages.
Beast Academy Puzzles 4 contains over 500 puzzles in 12 different styles that will delight puzzle solvers ages 10 and up. It can be used by itself or as a supplement to the full Beast Academy level 4 curriculum.
Guide and Practice   \$ 30.00
Jason Batterson, Shannon Rogers, Kyle Guillet. Illustrated by Erich Owen.
Paperback
Guide: 112 pages. Practice: 160 pages.

Beast Academy Guide 5A and its companion Practice 5A are the first part in a four-part series for students ages 10–13. Level 5A includes chapters on 3D solids, integers, and expressions & equations.

Guide and Practice   \$ 30.00
Jason Batterson, Shannon Rogers, Kyle Guillet. Illustrated by Erich Owen.
Paperback
Guide: 112 pages. Practice: 160 pages.

Beast Academy Guide 5B and its companion Practice 5B are the second part in a four-part series for students ages 10–13. Level 5B includes chapters on statistics, factors & multiples, and fractions.

Guide and Practice   \$ 30.00
Jason Batterson. Illustrated by Erich Owen.
Paperback
Guide: 104 pages. Practice: 160 pages.

Beast Academy Guide 5C and its companion Practice 5C are the third part in a four-part series for students ages 10–13. Level 5C includes chapters on sequences, ratios & rates, and decimals.

Guide and Practice   \$ 30.00
Jason Batterson, Shannon Rogers, Kyle Guillet, and Chris Page. Illustrated by Erich Owen.
Paperback
Guide: 112 pages. Practice: 144 pages.

Beast Academy Guide 5D and its companion Practice 5D are the fourth part in a four-part series for students ages 10–13. Level 5D includes chapters on percents, square roots, and exponents.

# Other Books & Gear

What would you like to study?
In addition to our own AoPS books, we also offer various AoPS paraphernalia and a selection of books from other publishers.
Shirts
\$ 15.00
Art of Problem Solving T-shirt
Show your AoPS pride with our new AoPS T-Shirt! 100% cotton. All sizes are adult unisex sizes.
\$ 49.99
Art of Problem Solving Hoodie
Show your AoPS pride in this cozy navy hoodie! All sizes are adult unisex sizes.
\$ 15.00
Do math in style with the whole Beast Academy crew! 100% Ringspun cotton T-shirt. We have unisex youth and adult sizes.
Kitchen Table Math
The Kitchen Table Math books, by Dr. Chris Wright, are written for parents of children ages 2-8. The books are step-by-step guides to how you can help your child develop strong math skills. They include activities and games that you can use at home with your child, so that you and your child can have fun while developing crucial mathematical skills.
\$ 21.95
Kitchen Table Math Book 2
Chris Wright
Paperback
280 pages.
This book covers arithmetic at the elementary school level. In addition to the arithmetic, this book plays with numbers with chapters on number sense, number theory, number bases, and the history of numbers.
\$ 21.95
Kitchen Table Math Book 3
Chris Wright
Paperback
254 pages.
This book covers the non-arithmetic aspects of elementary school mathematics. It starts with chapters on solving equations and then uses that skill to solve many kinds of word problems. This is followed by chapters on reasoning, probability and counting, statistics and graphing, geometry, measurements, and money.
MOEMS
Math Olympiads for Elementary and Middle Schools, founded in 1977, are problem-solving contests for students in grades 4-8. MOEMS publishes the books shown below to help students and teachers prepare for their contests.
\$ 37.95
MOEMS Contest Problems: Volume 2
Richard Kalman, Ed.
Paperback
309 pages.
A collection of 425 problems of the Math Olympiads for Elementary and Middle Schools contests, with hints, complete solutions, and problem solving lessons. Ideal for beginners grades 4-8.
\$ 39.95
MOEMS Contest Problems: Volume 3
Richard Kalman & Nicholas J. Restivo, Eds.
Paperback
294 pages.
A collection of 400 problems of the Math Olympiads for Elementary and Middle Schools contests from 2005-2013, with hints, complete solutions, and problem solving lessons. Ideal for beginners grades 4-8.
MATHCOUNTS
MATHCOUNTS is the premier mathematics contest for U.S. students in grades 6-8, with over 100,000 students participating annually. AoPS is proud to be a MATHCOUNTS National Sponsor, and we offer two collections of MATHCOUNTS practice competitions, by 2-time National Champion coach Josh Frost.
\$ 35.00
Practice Competitions for MATHCOUNTS
Josh Frost
Paperback
128 pages.
A collection of 4 complete practice competitions (including Sprint, Target, and Team rounds) for MATHCOUNTS. Includes full solutions to every problem.
\$ 35.00
Practice Competitions for MATHCOUNTS Volume 2
Josh Frost
Paperback
144 pages.
A collection of 4 complete practice competitions (including Sprint, Target, and Team rounds) for MATHCOUNTS. Includes full solutions to every problem.
American Mathematics Competitions
For more than 60 years, students across the country have taken up the challenge of America's longest-running and most prestigious math contests, the American Mathematics Competitions (AMC). Over 300,000 students each year participate in the AMC 8, AMC 10, or AMC 12 contests, with many students continuing on to the invitational AIME and USA(J)MO contests. The Mathematical Association of America administers the contests and publishes a series of books to help students prepare.
\$ 35.00
Contest Problem Book VI
Leo J. Schneider
Paperback
212 pages.
Past problems with complete solutions from the American High School Mathematics Exam (now called the AMC 12), which is the first test in the series of contests that determines the United States International Math Olympiad team. This book includes tests from 1989-1994.
\$ 51.00
Contest Problem Book VII
Harold Reiter
Paperback
183 pages.
Past problems with complete solutions from the American Mathematics Contests (AMC 10 and AMC 12), which is the first test in the series of contests that determines the United States International Math Olympiad team. This book includes tests from 1995-2000, including the 50th Anniversary AHSME issued in 1999.
\$ 51.00
Contest Problem Book IX
David Wells and J. Douglas Faires
Paperback
230 pages.
Past problems with complete solutions from the American Mathematics Competitions 12 (AMC 12), which is one of the first tests in the series of contests that determines the United States International Math Olympiad team. This book includes all AMC 12 tests from 2001-2007.
Mandelbrot
The Mandelbrot Competition is a year-long high-school-level math contest run by Greater Testing Concepts. The competition was co-founded in 1990 by AoPS founder Richard Rusczyk. Greater Testing Concepts publishes books of past years' contests, written by co-founder and current director Sam Vandervelde.
\$ 25.00
Mandelbrot Morsels
Sam Vandervelde
Paperback
180 pages.
Past problems with complete solutions from The Mandelbrot Competition 2002-09. Contains problems that are excellent practice for the American Mathematics Competitions as well as excellent problems for students first learning how to tackle challenging proof problems.
\$ 23.00
The Mandelbrot Problem Book
Sam Vandervelde
Paperback
148 pages.
Past problems with complete solutions from years 1995-2002 of The Mandelbrot Competition. Contains problems that are excellent practice for the American Mathematics Competitions as well as excellent problems for students first learning how to tackle challenging proof problems.
\$ 20.00
The First Five Years
Sam Vandervelde
Spiralbound
112 pages.
Past problems with complete solutions from the first five years (1990-95) of The Mandelbrot Competition. Contains problems that are excellent practice for the American Mathematics Competitions as well as excellent problems for students first learning how to tackle challenging proof problems.