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AoPS Curriculum

Our curriculum is specifically designed for high-performing math students in grades 6-12. 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.
Introduction to Algebra
Richard Rusczyk
Paperback
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!
Introduction to Counting and Probability
David Patrick
Paperback
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.
Introduction to Geometry
Richard Rusczyk
Paperback
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.
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.

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.

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.
Precalculus
Richard Rusczyk
Paperback
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.

Calculus
David Patrick
Paperback
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.

Problem Solving Series

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   $ 42.00
Volume 1
Sandor Lehoczky and Richard Rusczyk
Paperback
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.
Text and Solutions   $ 45.00
Volume 2
Richard Rusczyk and Sandor Lehoczky
Paperback
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.
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.

Beast Academy

Beast Academy is our curriculum for students in grades 2-5. Beast Academy is currently under production, with grade 3 and most of grade 4 currently available. Each grade consists of four pairs of books (A through D), and each pair consists of:
  • A Guide book: a fully-illustrated textbook written in an engaging, comic-book style, which provides comprehensive, rigorous instruction; and
  • A Practice book: a workbook providing hundreds of exercises, problems, puzzles, and games to reinforce the lessons from the Guide.
Beast Academy materials cover the core fundamentals of a standard math curriculum or the Common Core State Standards and go well beyond these basics to present material at a deeper and more challenging level than a typical elementary-school math curriculum.

Grade 3

Beast Academy 3A
Jason Batterson. 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 3rd grade mathematics. Level 3A includes chapters on shape classification, skip-counting, and perimeter and area.

Beast Academy 3B
Jason Batterson. 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 3rd grade mathematics. Level 3B includes chapters on multiplication, perfect squares, and the distributive property.

Beast Academy 3C
Jason Batterson. 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 3rd grade mathematics. Level 3C includes chapters on variables, division, and units and measure.

Beast Academy 3D
Jason Batterson. 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 3rd grade mathematics. Level 3D includes chapters on fractions, estimation, and area.

Grade 4

Beast Academy 4A
Jason Batterson. 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 the planned four-part series for 4th grade mathematics. Level 4A includes chapters on shapes, multiplication, and exponents.

Beast Academy 4B
Jason Batterson. 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 the planned four-part series for 4th grade mathematics. Level 4B includes chapters on counting, division, and logic.

Beast Academy 4C
Jason Batterson. 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 the planned four-part series for 4th grade mathematics. Level 4C includes chapters on factors, fractions, and integers.

Other Books & Gear

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% preshrunk cotton. All sizes are adult sizes.
   $ 30.00
Art of Problem Solving Hoodie
Show your AoPS pride in this cozy charcoal hoodie! 55% cotton/45% polyester. All sizes are adult sizes.
   $ 15.00
Art of Problem Solving Algebra T-Shirt
100% preshrunk cotton T-shirt with white print featuring a variety of Algebra formulas and notes! All sizes are 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 1
Chris Wright
Paperback
282 pages.
For parents of children ages 2-8. A step-by-step guide to how you can help your child develop good math skills and do well in school. It also includes activities and games so that you and your child can have fun while exploring these early stages of your child's mathematical journey.
   $ 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.
   $ 37.99
Creative Problem Solving in School Mathematics
Dr. George Lenchner
Paperback
284 pages.
A collection of lessons and challenging problems for beginning problem solvers in grades 4-8. Written by the creator of the popular Math Olympiads for Elementary and Middle Schools program.
   $ 35.95
MOEMS Contest Problems for Elementary and Middle Schools
Dr. George Lenchner
Paperback
280 pages.
A collection of sixteen years (400 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.
   $ 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.
   $ 34.00
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.
   $ 49.95
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.
   $ 49.95
Contest Problem Book VIII
J. Douglas Faires and David Wells
Paperback
212 pages.
Past problems with complete solutions from the American Mathematics Competitions 10 (AMC 10), 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 10 tests from 2000-2007.
   $ 49.95
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.
   $ 53.95
First Steps for Math Olympians
J. Douglas Faires
Hardcover
307 pages.
Lessons, examples, and exercises on topics useful for the AMC 10 and AMC 12. Ideal for self study for the AMC exams, and as a teaching resource for instructors developing lessons on various topics.

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.

Other Books

The United Kingdom Mathematics Trust organizes national mathematics competitions and other math enrichment activities for students aged 11-18 in the UK. We are pleased to offer a selection of their publications here in the US. We also offer a pair of books by Titu Andreescu.
   $ 24.95
UKMT The Backbone of Pascal's Triangle
Martin Griffiths
Paperback
180 pages.
Everything in this book is connected to the sequence of numbers: 2, 6, 20, 70, 252, 924, 3432, .... Students and teachers alike may be astounded at the variety and depth of mathematical ideas it can lead to. Includes exercises and answers.
   $ 24.95
UKMT Crossing the Bridge
Gerry Leversha
Paperback
200 pages.
Crossing the Bridge provides a course on geometry for use in the classroom. It re-emphasises some traditional features of geometrical education and the bulk of the text is devoted to carefully constructed exercises, either for classroom discussion or individual study.
   $ 24.95
UKMT Introduction to Inequalities
C. J. Bradley
Paperback
210 pages.
This text on inequalities covers material useful for high school national and international olympiads. The text includes materials used for training the United Kingdom Olympiad team.
   $ 24.95
UKMT Introduction to Number Theory
C. J. Bradley
Paperback
200 pages.
This text on number theory covers material useful for high school national and international olympiads. The text includes materials used for training the United Kingdom Olympiad team.
   $ 24.95
UKMT New Problems in Euclidean Geometry
David Monk
Paperback
128 pages.
This book should appeal to anyone who enjoys solving the kind of challenging and attractive geometry problems that have virtually vanished from the school curriculum, but which still play a central role in national and international mathematics competitions.
   $ 24.95
UKMT Plane Euclidean Geometry: Theory and Problems
A D Gardiner and C J Bradley
Paperback
264 pages.
This geometry text offers beginning and advanced geometric problem solving tactics, as well as numerous practice problems. The book is most appropriate for experienced geometers who are learning how to take on more challenging geometry problems, such as those offered at the high school olympiad level.
   $ 24.95
UKMT A Mathematical Olympiad Primer
Geoff Smith
Paperback
251 pages.
New second edition! A Mathematical Olympiad Primer is an excellent guide for young mathematicians preparing for competitions, such as the British Mathematical Olympiad. The book contains theory including algebra, combinatorics and geometry, and BMO1 Problems and Solutions from 1996 onwards. This is the revised and expanded 2nd Edition.
   $ 24.95
UKMT Ten Years of Mathematical Challenges: 1997 to 2006
UK Mathematics Trust
Paperback
188 pages.
This 188-page book contains problems and solutions for 10 Junior Challenges (1997-2006), 10 Intermediate Challenges (1997-2006) and 9 Senior Challenges (1997-2005) in the United Kingdom. These tests correspond roughly to the AMC 8, AMC 10, and AMC 12, respectively.
   $ 69.95
Problems from the Book
Titu Andreescu and Gabriel Dospinescu
Hardcover
554 pages.
A series of articles paired with collections of problems, designed for students preparing for high-level high school contests such as national olympiads.
   $ 69.95
Mathematical Reflections: the first two years
Titu Andreescu (Editor)
Hardcover
632 pages.
A compilation and revision of the 2006 and 2007 volumes from the online journal Mathematical Reflections.
ACS WASC
ACCREDITED
SCHOOL

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