Art of Problem Solving
AoPS Online AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy Beast Academy
Engaging math books and online learning
for students ages 6-13.
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Books for Ages 6-13 Beast Academy Online
AoPS Academy AoPS Academy
Small live classes for advanced math
and language arts learners in grades 1-12.
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Find a Physical Campus Visit the Virtual Campus

Have a great winter break! Please note that AoPS Online will not have classes Dec 21, 2024 through Jan 3, 2025.
How Classes Work
Course Catalog
Class Schedule
Introductory Math
Prealgebra 1Prealgebra 2Intro to Algebra AIntro to Counting & ProbabilityIntro to Number TheoryIntro to Algebra BIntro to GeometryParadoxes Seminar
Intermediate Math
Intermediate AlgebraIntermediate Counting & ProbabilityIntermediate Number TheoryPrecalculus
Advanced Math
Olympiad GeometryCalculusGroup Theory
Contest Preparation
USACO BronzeMATHCOUNTS/AMC 8 BasicsMATHCOUNTS/AMC 8 Adv.Special AMC 8 Seminar ASpecial AMC 8 Seminar BAMC 10 Problem SeriesAMC 10 Final FivesSpecial AMC 10 Seminar ASpecial AMC 10 Seminar BAMC 12 Problem SeriesAMC 12 Final FivesSpecial AMC 12 Seminar ASpecial AMC 12 Seminar BAIME Problem Series AAIME Problem Series BSpecial AIME Seminar ASpecial AIME Seminar BF=ma Problem Series
WOOT Programs
About WOOTMathWOOTCodeWOOTPhysicsWOOTChemWOOT
CS/Programming
Introduction to PythonIntermediate PythonUSACO BronzeCodeWOOT
Physics
Intro to PhysicsPhysics 1: MechanicsF=ma Problem SeriesRelativityPhysicsWOOT
Special Seminars
Paradoxes SeminarRelativitySpecial AMC 8 Seminar ASpecial AMC 8 Seminar BSpecial AMC 10 Seminar ASpecial AMC 10 Seminar BSpecial AMC 12 Seminar ASpecial AMC 12 Seminar BSpecial AIME Seminar ASpecial AIME Seminar B
Prospective Students & Parents
Math Jams
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Recommendations

What would you like to study?
Subject Courses
Before Prealgebra
Ready for Prealgebra
After Prealgebra
Some Algebra 1
After Algebra 1
After Geometry
After Algebra 2
After Precalculus
Beyond Calculus
Contest Preparation
MATHCOUNTS/AMC 8
AMC 10
AMC 12
AIME
USAMO
Computer Programming
Little or No Experience
Some Experience
Extensive Experience
Physics Courses
Little or No Experience
Some Experience
Extensive Experience

Course Map

For recommendations in computer science, click here. For information about our science courses, click here.

Below is the "map" of all of our math courses. Click on any course to learn more about it.

Core Subject Courses Other Subject Courses Contest Prep Courses
6
Elementary (Grades 1-5)
Introductory (Grades 5-10)
Intermediate (Grades 8-12)
Advanced (Grades 9-12)
AoPS Academy Virtual Campus Prealgebra 1 Prealgebra 2 Intro Algebra A Intro Counting & Probability Intro Algebra B Intro Geometry Intermediate Algebra Precalculus Calculus
Intro Number Theory Intermediate Count & Prob Olympiad Geometry Group Theory
Intermediate Number Theory
MC/AMC 8 Basics MC/AMC 8 Advanced AMC 12
AMC 10 AIME A/B MathWOOT 1 MathWOOT 2
7

The top row of the map consists of our core curriculum, which parallels the standard prealgebra-to-calculus school curriculum, but in much greater depth both in mathematical content and in problem-solving skills. For this reason, we often recommend that a new AoPS student who has already taken a course at their local school "retake" the same-named course in our online school. Students should then proceed through our core curriculum in left-to-right order, and should take other non-core courses as desired.

Our math courses fall into two categories:

  • Our subject courses (in green on the map) each offer a thorough exploration of a particular subject. Each course follows an AoPS textbook (except where noted). Students receive personalized written feedback to weekly homework assignments. At the Introductory level, these courses are linked to Alcumus, our online adaptive learning system.
  • Our contest preparation courses (in blue on the map) are designed for students preparing for specific math contests. These courses cover more topics, but offer less depth, than our subject courses. These courses do not use textbooks, and students do not receive personalized feedback, although there are weekly practice problems.

Still unsure? Please contact us for a specific recommendation.

Subject Course Recommendations

To determine where a student should start within our subject course curriculum, please view the appropriate section below and refer to the diagnostic tests for each individual course.

Before Prealgebra

For students in grades 1-6 who need to master the fundamentals of arithmetic, fractions, decimals, and integers before beginning prealgebra.

Students who are not yet ready for Prealgebra 1 should prepare by using our AoPS Beast Academy curriculum. Learn all about our books and online program for younger students at BeastAcademy.com.

Ready for Prealgebra

For students who have completed an elementary (through grades 5/6) math curriculum but not yet started prealgebra

Begin with Prealgebra 1, provided that the student passes the “Are you ready?” diagnostic test. (Students that do not pass this test are not yet ready for AoPS, and should instead consider using our Beast Academy materials.) A student with some exposure to Prealgebra topics might be able to start at Prealgebra 2 or Introduction to Algebra A.

Prealgebra 1

Prealgebra 1 includes a thorough exploration of the fundamentals of arithmetic, including fractions, exponents, and decimals. We introduce beginning topics in number theory and algebra, including common divisors and multiples, primes and prime factorizations, basic equations and inequalities, and ratios.
Required text: Prealgebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

Prealgebra 2

Prealgebra 2 includes percent, square roots, a thorough exploration of geometric tools and strategies, an introduction to topics in discrete mathematics and statistics, and a discussion of general problem-solving strategies.
Required text: Prealgebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

Introduction to Algebra A

(Formerly called Algebra 1) Fundamental concepts of algebra, including exponents and radicals, linear equations and inequalities, ratio and proportion, systems of linear equations, factoring quadratics, complex numbers, completing the square, and the quadratic formula.
Required text: Introduction to Algebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

After Prealgebra

For students in grades 6-9 who have completed prealgebra (or equivalent middle-school math curriculum)

Begin with Introduction to Algebra A, provided that the student passes the “Are you ready?” diagnostic test. A student who does not pass this test should expand their arithmetic and problem-solving skills by starting in Prealgebra 1 or Prealgebra 2.

Prealgebra 1

Prealgebra 1 includes a thorough exploration of the fundamentals of arithmetic, including fractions, exponents, and decimals. We introduce beginning topics in number theory and algebra, including common divisors and multiples, primes and prime factorizations, basic equations and inequalities, and ratios.
Required text: Prealgebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

Prealgebra 2

Prealgebra 2 includes percent, square roots, a thorough exploration of geometric tools and strategies, an introduction to topics in discrete mathematics and statistics, and a discussion of general problem-solving strategies.
Required text: Prealgebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

Introduction to Algebra A

(Formerly called Algebra 1) Fundamental concepts of algebra, including exponents and radicals, linear equations and inequalities, ratio and proportion, systems of linear equations, factoring quadratics, complex numbers, completing the square, and the quadratic formula.
Required text: Introduction to Algebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

Some Algebra 1

For students in grades 6-9 who have completed a non-honors algebra 1 course or some of an honors algebra course

Begin with either Introduction to Algebra A or Introduction to Counting & Probability, depending on how well the student performs on the Introduction to Algebra A “Do you need this?” diagnostic test. Such students should also consider Introduction to Number Theory.

Introduction to Algebra A

(Formerly called Algebra 1) Fundamental concepts of algebra, including exponents and radicals, linear equations and inequalities, ratio and proportion, systems of linear equations, factoring quadratics, complex numbers, completing the square, and the quadratic formula.
Required text: Introduction to Algebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.
Required text: Introduction to Counting & Probability: Text and Solutions
12 weeks
Are you ready?Do you need this?

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.
Required text: Introduction to Number Theory: Text and Solutions
12 weeks
Are you ready?Do you need this?

After Algebra 1

For students in grades 6-10 who have completed an honors algebra 1 course

Begin with Introduction to Counting & Probability or Introduction to Algebra B -- these courses can be taken in either order. Such students could also begin by taking Introduction to Number Theory.

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.
Required text: Introduction to Counting & Probability: Text and Solutions
12 weeks
Are you ready?Do you need this?

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.
Required text: Introduction to Number Theory: Text and Solutions
12 weeks
Are you ready?Do you need this?

Introduction to Algebra B

(Formerly called Algebra 2) Fundamental concepts of algebra, including quadratics, systems of equations, clever factorizations, complex numbers, functions, graphing, sequences and series, special functions, exponents and logarithms, and more.
Required text: Introduction to Algebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

After Geometry

For students in grades 8-10 who have completed geometry

The student should take the “Do you need this?” diagnostic tests for both Introduction to Algebra B and Introduction to Geometry. It is essential that students master the material in our Introduction to Algebra B course before proceeding to Introduction to Geometry, and similarly that they master Introduction to Geometry before proceeding to our intermediate-level courses. Students who do not pass one of the diagnostic tests should begin in that course. Students who pass both diagnostic tests should begin with Intermediate Algebra.

We also encourage all new students to “go back” and take Introduction to Counting & Probability or Introduction to Number Theory if desired.

Introduction to Algebra B

(Formerly called Algebra 2) Fundamental concepts of algebra, including quadratics, systems of equations, clever factorizations, complex numbers, functions, graphing, sequences and series, special functions, exponents and logarithms, and more.
Required text: Introduction to Algebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

Introduction to Geometry

Fundamentals of geometry, including angles, triangle similarity and congruence, complicated area problems, mastering the triangle, special quadrilaterals, polygons, the art of angle chasing, power of a point, 3-dimensional geometry, transformations, analytic geometry, basic trigonometry, geometric proof, and more.
Required text: Introduction to Geometry: Text and Solutions
24 weeks
Are you ready?Do you need this?

Intermediate Algebra

(Formerly called Algebra 3) Algebraic subjects covered include advanced quadratics, polynomials, conics, general functions, logarithms, clever factorizations and substitutions, systems of equations, sequences and series, symmetric sums, advanced factoring methods, classical inequalities, functional equations, and more.
Required text: Intermediate Algebra: Text and Solutions
24 weeks
Are you ready?Do you need this?

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.
Required text: Introduction to Counting & Probability: Text and Solutions
12 weeks
Are you ready?Do you need this?

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.
Required text: Introduction to Number Theory: Text and Solutions
12 weeks
Are you ready?Do you need this?

After Algebra 2

For students in grades 8-10 who have completed algebra 2

The student should take the “Do you need this?” diagnostic test for Introduction to Geometry, even if they have already taken a geometry course. It is essential that students master Introduction to Geometry before proceeding to our intermediate-level courses. Students who do not pass the diagnostic test should begin with Introduction to Geometry. Students who pass the diagnostic test should begin with Intermediate Algebra.

We also encourage all new students to “go back” and take Introduction to Counting & Probability or Introduction to Number Theory if desired.

Introduction to Geometry

Fundamentals of geometry, including angles, triangle similarity and congruence, complicated area problems, mastering the triangle, special quadrilaterals, polygons, the art of angle chasing, power of a point, 3-dimensional geometry, transformations, analytic geometry, basic trigonometry, geometric proof, and more.
Required text: Introduction to Geometry: Text and Solutions
24 weeks
Are you ready?Do you need this?

Intermediate Algebra

(Formerly called Algebra 3) Algebraic subjects covered include advanced quadratics, polynomials, conics, general functions, logarithms, clever factorizations and substitutions, systems of equations, sequences and series, symmetric sums, advanced factoring methods, classical inequalities, functional equations, and more.
Required text: Intermediate Algebra: Text and Solutions
24 weeks
Are you ready?Do you need this?

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.
Required text: Introduction to Counting & Probability: Text and Solutions
12 weeks
Are you ready?Do you need this?

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.
Required text: Introduction to Number Theory: Text and Solutions
12 weeks
Are you ready?Do you need this?

After Precalculus

For students in grades 9-12 who have completed all regular high school math including precalculus

The student should take the “Are you ready?” and “Do you need this?” diagnostic tests for our Precalculus course. Our Precalculus contains much more content and is much more rigorous than most high-school courses, so most students who have taken regular high-school math through precalculus will want to start with our Precalculus course. If the student does not pass the “Are you ready?” diagnostic, start with Intermediate Algebra. If they pass the “Do you need this?” diagnostic, they may take Calculus.

We also encourage all new students to “go back” and take Introduction to Counting & Probability or Introduction to Number Theory if desired, and to continue with Intermediate Counting & Probability or Intermediate Number Theory when ready.

Intermediate Algebra

(Formerly called Algebra 3) Algebraic subjects covered include advanced quadratics, polynomials, conics, general functions, logarithms, clever factorizations and substitutions, systems of equations, sequences and series, symmetric sums, advanced factoring methods, classical inequalities, functional equations, and more.
Required text: Intermediate Algebra: Text and Solutions
24 weeks
Are you ready?Do you need this?

Precalculus

Introduction and evaluation of trigonometric functions, trigonometric identities, geometry with trigonometry, parametric equations, special coordinate systems, complex numbers, exponential form of complex numbers, De Moivre's Theorem, roots of unity, geometry with complex numbers, two-dimensional and three-dimensional vectors and matrices, determinants, dot and cross product, applications of vectors and matrices to geometry.
Required text: Precalculus: Text and Solutions
22 weeks
Are you ready?Do you need this?

Calculus

A course in single-variable calculus. This course covers limits, continuity, derivatives and their applications, definite and indefinite integrals, infinite sequences and series, plane curves, polar coordinates, and basic differential equations. While "test preparation" is not the main focus, this course is approved by the College Board as an AP Calculus BC class for students in grades 9-12 and goes beyond a standard Calculus BC curriculum.
Required text: Calculus: Text and Solutions
25 weeks
Are you ready?

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.
Required text: Introduction to Counting & Probability: Text and Solutions
12 weeks
Are you ready?Do you need this?

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.
Required text: Introduction to Number Theory: Text and Solutions
12 weeks
Are you ready?Do you need this?

Intermediate Counting & Probability

Topics in discrete mathematics, including clever one-to-one correspondences, principle of inclusion-exclusion, generating functions, distributions, the pigeonhole principle, induction, constructive counting and expectation, combinatorics, systems with states, recursion, conditional probability, and introductory graph theory.
Required text: Intermediate Counting & Probability: Text and Solutions
18 weeks
Are you ready?Do you need this?

Intermediate Number Theory

Number theory using algebraic techniques, multiplicative functions, Diophantine equations, modular arithmetic, Fermat's/Euler's Theorem, primitive roots, and quadratic residues. Much of the first half of the class emphasizes using the basic tools of the Introduction class in clever ways to solve difficult problems. In the second half, more theory will be developed, leading students to the beginning Olympiad level.
12 weeks
Are you ready?Do you need this?

Beyond Calculus

For students who have completed calculus

Because our curriculum has more depth and rigor than a typical curriculum, the student might benefit from “retaking” some of our core courses. The student should take the “Do you need this?” diagnostic from our Precalculus course. If they are unsuccessful, work backwards through our core curriculum, using the diagnostic tests to find the appropriate course. If they are successful with the Precalculus “Do you need this?” diagnostic, then any of our Advanced courses should be appropriate for that student.

Our Calculus course also contains much more material and a much higher level of formalism than most high-school “AP-style” calculus courses, so we recommend our Calculus course to a post-calculus student who wants a deeper understanding of the subject.

We also encourage all new students to “go back” and take Introduction to Counting & Probability or Introduction to Number Theory if desired, and to continue with Intermediate Counting & Probability or Intermediate Number Theory when ready.

Precalculus

Introduction and evaluation of trigonometric functions, trigonometric identities, geometry with trigonometry, parametric equations, special coordinate systems, complex numbers, exponential form of complex numbers, De Moivre's Theorem, roots of unity, geometry with complex numbers, two-dimensional and three-dimensional vectors and matrices, determinants, dot and cross product, applications of vectors and matrices to geometry.
Required text: Precalculus: Text and Solutions
22 weeks
Are you ready?Do you need this?

Calculus

A course in single-variable calculus. This course covers limits, continuity, derivatives and their applications, definite and indefinite integrals, infinite sequences and series, plane curves, polar coordinates, and basic differential equations. While "test preparation" is not the main focus, this course is approved by the College Board as an AP Calculus BC class for students in grades 9-12 and goes beyond a standard Calculus BC curriculum.
Required text: Calculus: Text and Solutions
25 weeks
Are you ready?

Olympiad Geometry

Covers numerous topics of geometry useful for Olympiad-level geometric proofs, including similar triangles, cyclic quadrilaterals, power of a point, homothety, inversion, transformations, collinearity, concurrence, construction, locus, and three-dimensional geometry.
12 weeks
Are you ready?Do you need this?

Group Theory

Group theory is the study of symmetry. Objects in nature (physics, chemistry, music, etc.) as well as objects in mathematics itself have beautiful symmetries, and group theory is the algebraic language we use to unlock that beauty. Group theory is the gateway to abstract algebra and tells us (among many other things) that you can't trisect an angle with a straightedge and compass, that there are finitely many perfectly symmetric tiling patterns, and that there is no closed formula for solving a quintic polynomial. In this class we will get a glimpse of the mathematics underlying these famous questions. This course will focus concretely on building groups from other groups, exploring groups as symmetries of geometric objects, and using the tools of group theory to construct fields. The overarching goal of the course is to learn how modern mathematicians understand a topic as general and seemingly fuzzy as “symmetry”.
14 weeks
Are you ready?

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.
Required text: Introduction to Counting & Probability: Text and Solutions
12 weeks
Are you ready?Do you need this?

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.
Required text: Introduction to Number Theory: Text and Solutions
12 weeks
Are you ready?Do you need this?

Intermediate Counting & Probability

Topics in discrete mathematics, including clever one-to-one correspondences, principle of inclusion-exclusion, generating functions, distributions, the pigeonhole principle, induction, constructive counting and expectation, combinatorics, systems with states, recursion, conditional probability, and introductory graph theory.
Required text: Intermediate Counting & Probability: Text and Solutions
18 weeks
Are you ready?Do you need this?

Intermediate Number Theory

Number theory using algebraic techniques, multiplicative functions, Diophantine equations, modular arithmetic, Fermat's/Euler's Theorem, primitive roots, and quadratic residues. Much of the first half of the class emphasizes using the basic tools of the Introduction class in clever ways to solve difficult problems. In the second half, more theory will be developed, leading students to the beginning Olympiad level.
12 weeks
Are you ready?Do you need this?

Contest Preparation Recommendations

Our contest preparation courses are designed for students seeking to improve their results in math competitions. They are intended as supplementary practice and as a way to learn general problem-solving skills, rather than as a complete mathematics curriculum. Students who wish to more thoroughly cover the content and problem-solving skills on these contests should take the overlapping subject classes from our course map above.

Please select the specific contest below for advice on which contest prep course to take.

MATHCOUNTS/AMC 8

For students preparing for Middle School math competitions

Students who have not yet completed prealgebra are not yet ready for our contest prep courses, and should consider our Prealgebra 1 and Prealgebra 2 courses instead. All middle-school students should also consider our Introduction to Counting & Probability and Introduction to Number Theory courses -- both of these are very well-suited for middle-school contest preparation, as are the rest of our Introductory-level subject courses.

Students just getting started with middle-school math contests should consider our MATHCOUNTS/AMC 8 Basics course. Students with more consistent success in these contests (in particular, students who score 15+ on the AMC 8 or 25+ on Chapter-level MATHCOUNTS competitions) should consider our MATHCOUNTS/AMC 8 Advanced course. We also offer a one-weekend Special AMC 8 Problem Seminar.

MATHCOUNTS/AMC 8 Basics

This course is an introduction to the problem solving strategies required for success on MATHCOUNTS and the AMC 8 tests. This class is intended for less experienced students who are just getting started on middle school math contests. Experienced MATHCOUNTS and AMC 8 students should consider our Advanced MATHCOUNTS/AMC 8 class.
12 weeks

MATHCOUNTS/AMC 8 Advanced

Designed for students preparing for State and National MATHCOUNTS, the premier middle school mathematics contest in the US. This course will also help with the harder problems on the AMC 8. The class is designed for experienced MATHCOUNTS students; less experienced students should consider our MATHCOUNTS/AMC 8 Basics course.
12 weeks

Special AMC 8 Problem Seminar A

This course is a special two-day, 5-hour seminar to prepare for the AMC 8 and other middle school level math contests. The AMC 8 is the premier fall math contest for middle school students, and also gives students early problem-solving experience that is valuable towards the high-school level AMC 10 and AMC 12 contests. In this course, students learn problem solving strategies and test-taking tactics over two lessons — during each lesson, class will meet over a 3-hour period, with a half-hour break in the middle. The course also includes a practice AMC 8 test. This course covers entirely different problems than the Special AMC 8 Problem Seminar B.
2 days

Prealgebra 1

Prealgebra 1 includes a thorough exploration of the fundamentals of arithmetic, including fractions, exponents, and decimals. We introduce beginning topics in number theory and algebra, including common divisors and multiples, primes and prime factorizations, basic equations and inequalities, and ratios.
Required text: Prealgebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

Prealgebra 2

Prealgebra 2 includes percent, square roots, a thorough exploration of geometric tools and strategies, an introduction to topics in discrete mathematics and statistics, and a discussion of general problem-solving strategies.
Required text: Prealgebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

Introduction to Algebra A

(Formerly called Algebra 1) Fundamental concepts of algebra, including exponents and radicals, linear equations and inequalities, ratio and proportion, systems of linear equations, factoring quadratics, complex numbers, completing the square, and the quadratic formula.
Required text: Introduction to Algebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.
Required text: Introduction to Counting & Probability: Text and Solutions
12 weeks
Are you ready?Do you need this?

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.
Required text: Introduction to Number Theory: Text and Solutions
12 weeks
Are you ready?Do you need this?

Introduction to Algebra B

(Formerly called Algebra 2) Fundamental concepts of algebra, including quadratics, systems of equations, clever factorizations, complex numbers, functions, graphing, sequences and series, special functions, exponents and logarithms, and more.
Required text: Introduction to Algebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

Introduction to Geometry

Fundamentals of geometry, including angles, triangle similarity and congruence, complicated area problems, mastering the triangle, special quadrilaterals, polygons, the art of angle chasing, power of a point, 3-dimensional geometry, transformations, analytic geometry, basic trigonometry, geometric proof, and more.
Required text: Introduction to Geometry: Text and Solutions
24 weeks
Are you ready?Do you need this?

AMC 10

For students preparing for the AMC 10

Our AMC 10 Problem Series course is designed for students in grade 10 or below who have completed an algebra course and can currently score 60+ on the AMC 10 contest. For students looking to ramp up their problem-solving skills on the final five problems of the AMC 10, we now offer the four-week AMC 10 Final Fives course. We also offer a one-weekend Special AMC 10 Problem Seminar.

Students not yet meeting this standard should instead consider Introduction to Algebra B, Introduction to Counting & Probability, or Introduction to Number Theory. Students who consistently score 100+ on the AMC 10 would probably not benefit from this course and should instead consider our AMC 12 Problem Series or Seminar, AIME A or AIME B Problem Series, Special AIME Seminar A, Special AIME Seminar B, Introduction to Geometry, or Intermediate Algebra courses.

AMC 10 Problem Series

Preparation for the AMC 10, the first test in the series of contests that determine the United States team for the International Mathematics Olympiad. Many top colleges also request AMC scores as part of the college application process. The course consists of discussion of problems from past exams, as well as strategies for taking the test. The course also includes a practice AMC 10 test.
12 weeks

AMC 10 Final Fives

This course is designed specifically to tackle the most challenging problems of the AMC 10, the first in the series of contests that determine the United States team for the International Mathematics Olympiad. Many prestigious universities also consider AMC scores as part of the college application process. This course teaches you the tactics needed for the last five problems, which often determine the high scorers in the exam. Our sessions will include in-depth discussions of these types of problems, as well as unique, effective strategies to approach them. By the end of the course, students will have a clear understanding of these complex problems. This course includes a practice competition focusing on the last five problems of the AMC 10.
4 weeks

Special AMC 10 Problem Seminar A

This course is a special 5-hour weekend seminar to prepare for the AMC 10, which is the first step in qualifying for the United States Junior Math Olympiad. Many top colleges also request AMC scores as part of the college application process. In this course, students learn problem solving strategies and test-taking tactics. The course also includes a practice AMC 10 test. This course is entirely different from the Special AMC 10 Problem Seminar B, but is the same as the Special AMC 10 Problem Seminar offered prior to 2019.
2 days

Special AMC 10 Problem Seminar B

This course is a special two-day, 5-hour seminar to prepare for the AMC 10, which is the first step in qualifying for the United States Junior Math Olympiad. Many top colleges also request AMC scores as part of the college application process. In this course, students learn problem solving strategies and test-taking tactics. The course also includes a practice AMC 10 test. This course is entirely different from the Special AMC 10 Problem Seminar A.
2 days

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.
Required text: Introduction to Counting & Probability: Text and Solutions
12 weeks
Are you ready?Do you need this?

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.
Required text: Introduction to Number Theory: Text and Solutions
12 weeks
Are you ready?Do you need this?

Introduction to Algebra B

(Formerly called Algebra 2) Fundamental concepts of algebra, including quadratics, systems of equations, clever factorizations, complex numbers, functions, graphing, sequences and series, special functions, exponents and logarithms, and more.
Required text: Introduction to Algebra: Text and Solutions
16 weeks
Are you ready?Do you need this?

AMC 12

For students preparing for the AMC 12

Our AMC 12 Problem Series course is designed for high-school students who have completed an algebra and geometry course and can currently score 60+ on the AMC 12 contest. For students looking to ramp up their problem-solving skills on the final five problems of the AMC 12, we now offer the four-week AMC 12 Final Fives course. We also offer a one-weekend Special AMC 12 Problem Seminar.

Students not yet meeting this standard should instead consider Introduction to Geometry, Introduction to Counting & Probability, Introduction to Number Theory, or one of our Intermediate courses. Students who consistently score 90+ on the AMC 12 would probably not benefit from this course and should instead consider our AIME A and AIME B Problem Series courses and our Special AIME Seminar A and Special AIME Seminar B courses.

AMC 12 Problem Series

Preparation for the AMC 12, the first test in the series of contests that determine the United States team for the International Mathematics Olympiad. Many top colleges also request AMC scores as part of the college application process. The course consists of discussion of problems from past exams, as well as strategies for taking the test. The course also includes a practice AMC 12 test.
12 weeks

AMC 12 Final Fives

This course is designed specifically to tackle the challenging final five problems of the AMC 12, the first in the series of contests that determine the United States team for the International Mathematics Olympiad. Many prestigious universities also consider AMC scores as part of the college application process. This course teaches you the tactics needed for the last five problems, which often determine the high scorers in the exam. Our sessions will include in-depth discussions of these types of problems, as well as unique, effective strategies to approach them. By the end of the course, students will not only have a clear understanding of these complex problems. This course includes a practice competition focusing on the last five problems of the AMC 12.
4 weeks

Special AMC 12 Problem Seminar A

This course is a special 5-hour weekend seminar to prepare for the AMC 12, which is the first in the series of tests used to determine the United States team at the International Math Olympiad. Many top colleges also request AMC scores as part of the college application process. In this course, students learn problem solving strategies and test-taking tactics. The course also includes a practice AMC 12 test. This course is entirely different from the Special AMC 12 Problem Seminar B, but is the same as the Special AMC 12 Problem Seminar offered prior to 2019.
2 days

Special AMC 12 Problem Seminar B

This course is a special 5-hour weekend seminar to prepare for the AMC 12, which is the first in the series of tests used to determine the United States team at the International Math Olympiad. Many top colleges also request AMC scores as part of the college application process. In this course, students learn problem solving strategies and test-taking tactics. The course also includes a practice AMC 12 test. This course is entirely different from the Special AMC 12 Problem Seminar A.
2 days

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.
Required text: Introduction to Counting & Probability: Text and Solutions
12 weeks
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Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.
Required text: Introduction to Number Theory: Text and Solutions
12 weeks
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Introduction to Geometry

Fundamentals of geometry, including angles, triangle similarity and congruence, complicated area problems, mastering the triangle, special quadrilaterals, polygons, the art of angle chasing, power of a point, 3-dimensional geometry, transformations, analytic geometry, basic trigonometry, geometric proof, and more.
Required text: Introduction to Geometry: Text and Solutions
24 weeks
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AIME

For students preparing for the AIME

Our AIME A and AIME B Problem Series courses are designed for students who are very confident that they will qualify for the AIME contest. We also offer two one-weekend seminars: Special AIME Problem Seminar A and Special AIME Problem Seminar B.

Students who consistently expect to score 5 or more on the AIME may instead wish to consider our MathWOOT program. AIME-qualifying students would also benefit from any of our Intermediate-level subject courses.

Note: the AIME A and AIME B Problem Series classes cover mostly the same topics but use entirely different problems. Students can take either or both classes, in either order. The same is true for the Special AIME Problem Seminar A and Special AIME Problem Seminar B.

AIME Problem Series A

Preparation for the AIME, the second in the series of tests used to determine the United States team at the International Math Olympiad. Many top colleges also request AIME scores as part of the college application process. The course also includes a practice AIME test.
12 lessons

AIME Problem Series B

Preparation for the AIME, the second in the series of tests used to determine the United States team at the International Math Olympiad. Many top colleges also request AIME scores as part of the college application process. The course also includes a practice AIME test.
12 lessons

Special AIME Problem Seminar A

This class is a special 5-hour weekend seminar to prepare for the AIME, which is the second in the series of tests used to determine the United States team at the International Math Olympiad. Many top colleges also request AIME scores as part of the college application process. In this course, students learn problem solving strategies and test-taking tactics relevant to the AIME. The course also includes a practice AIME test.
2 days

Special AIME Problem Seminar B

This class is a special 5-hour weekend seminar to prepare for the AIME, which is the second in the series of tests used to determine the United States team at the International Math Olympiad. Many top colleges also request AIME scores as part of the college application process. In this course, students learn problem solving strategies and test-taking tactics relevant to the AIME. The course also includes a practice AIME test.
2 days

Intermediate Algebra

(Formerly called Algebra 3) Algebraic subjects covered include advanced quadratics, polynomials, conics, general functions, logarithms, clever factorizations and substitutions, systems of equations, sequences and series, symmetric sums, advanced factoring methods, classical inequalities, functional equations, and more.
Required text: Intermediate Algebra: Text and Solutions
24 weeks
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Intermediate Counting & Probability

Topics in discrete mathematics, including clever one-to-one correspondences, principle of inclusion-exclusion, generating functions, distributions, the pigeonhole principle, induction, constructive counting and expectation, combinatorics, systems with states, recursion, conditional probability, and introductory graph theory.
Required text: Intermediate Counting & Probability: Text and Solutions
18 weeks
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Intermediate Number Theory

Number theory using algebraic techniques, multiplicative functions, Diophantine equations, modular arithmetic, Fermat's/Euler's Theorem, primitive roots, and quadratic residues. Much of the first half of the class emphasizes using the basic tools of the Introduction class in clever ways to solve difficult problems. In the second half, more theory will be developed, leading students to the beginning Olympiad level.
12 weeks
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Precalculus

Introduction and evaluation of trigonometric functions, trigonometric identities, geometry with trigonometry, parametric equations, special coordinate systems, complex numbers, exponential form of complex numbers, De Moivre's Theorem, roots of unity, geometry with complex numbers, two-dimensional and three-dimensional vectors and matrices, determinants, dot and cross product, applications of vectors and matrices to geometry.
Required text: Precalculus: Text and Solutions
22 weeks
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MathWOOT

Master Olympiad-level problem solving with AoPS’s 7-month math Olympiad training program. Join the world’s top students and former Olympians as you prepare for national and international math competitions. Level 1 is designed for AIME qualifiers ready to make the jump to Olympiads. This course focuses on proof-writing and gives students contest-specific skills in all subjects to qualify for national Olympiads, including the USAMO. Includes live class sessions and practice Olympiad tests.
7 months

USAMO

For students preparing for the USAMO

Students who have a strong chance of qualifying for the USA Junior Math Olympiad (USAJMO) or USA Math Olympiad (USAMO) may wish to consider our year-round Worldwide Online Olympiad Training (MathWOOT) program. We strongly recommend that student complete our entire core curriculum or its equivalent, except for Calculus, before considering MathWOOT.

MathWOOT

Master Olympiad-level problem solving with AoPS’s 7-month math Olympiad training program. Join the world’s top students and former Olympians as you prepare for national and international math competitions. Level 1 is designed for AIME qualifiers ready to make the jump to Olympiads. This course focuses on proof-writing and gives students contest-specific skills in all subjects to qualify for national Olympiads, including the USAMO. Includes live class sessions and practice Olympiad tests.
7 months

Precalculus

Introduction and evaluation of trigonometric functions, trigonometric identities, geometry with trigonometry, parametric equations, special coordinate systems, complex numbers, exponential form of complex numbers, De Moivre's Theorem, roots of unity, geometry with complex numbers, two-dimensional and three-dimensional vectors and matrices, determinants, dot and cross product, applications of vectors and matrices to geometry.
Required text: Precalculus: Text and Solutions
22 weeks
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Computer Programming

Please select the box below that most accurately describes the student's programming experience.

Little or No Experience

For students in grades 6-12 with little or no experience in programming

A student with little or no programming experience should start with our Introduction to Programming with Python course. This course assumes no prior programming experience; however, the student should have completed a prealgebra course.

Introduction to Programming with Python

A first course in computer programming using the Python programming language. This course covers basic programming concepts such as variables, for loop iterations, and control flow involving if statements. Students can also expect to build strong foundations in functions, input/output, and arrays as well as other data types.
12 weeks
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Some Experience

For students in grades 6-12 with some programming experience

A student with some programming experience should consider our Intermediate Programming with Python course. See the “Are You Ready?” diagnostic for this course to determine if the student has sufficient programming experience for this course; if not, consider our Introduction to Programming with Python instead. A student whose programming experience is in a language other than Python might have to learn some basic Python on their own before starting Intermediate Programming with Python.

Introduction to Programming with Python

A first course in computer programming using the Python programming language. This course covers basic programming concepts such as variables, for loop iterations, and control flow involving if statements. Students can also expect to build strong foundations in functions, input/output, and arrays as well as other data types.
12 weeks
Are you ready?Do you need this?

Intermediate Programming with Python

This course covers intermediate programming concepts such as recursion, object-oriented programming, graphical user interfaces, and event-driven programming.
12 weeks
Are you ready?Do you need this?

A student with some coding experience, and interest in contest preparation, should consider our USACO Bronze Problem Series course. See the “Are You Ready?” diagnostic for this course to determine if the student has sufficient coding experience for this course; if not, consider our other coding options instead.

USACO Bronze Problem Series

This course is an introduction to the USA Computing Olympiad at the Bronze level. By the end of the course, students will be comfortable applying strategies such as binary search, greedy algorithms, and using data structures such as arrays, maps, and sets. The course builds problem-solving skills and strategies that will be helpful along the rest of the USACO pathway: Silver (for which we are developing a class), Gold (the focus of CodeWOOT), Platinum, and even the IOI.
12 weeks
Are you ready?

Extensive Experience

For students in grades 6-12 with extensive programming experience

A student with extensive programming experience should consider our CodeWOOT course, especially if the student has some experience with foundational algorithms (binary search, depth-first search, sorting) and data structures (linked lists, stacks, queues, trees, graphs) and/or has experience in competitive programming contests. This course includes advanced training materials that will help students prepare for competitions such as the USA Computing Olympiad (USACO) and International Olympiad in Informatics (IOI). We encourage you to take the CodeWOOT diagnostic test to see if CodeWOOT is the right level.

CodeWOOT

CodeWOOT is an Olympiad-level computer science and problem solving course modeled after our WOOT program. This course helps ambitious students sharpen their programming skills and prepare for computer science competitions such as the USA Computing Olympiad (USACO)
7 months

Physics Courses

Please select the box below that most accurately describes the student's science experience.

Little or No Experience

For students in grades 6-12 with little or no experience in science

A student with little or no science experience should start with our Introduction to Physics course. This course assumes no prior physics experience; however, the student should have completed the equivalent of Introduction to Algebra A to be successful.

Introduction to Physics

This course creates a foundation for learning advanced physics by focusing on the fundamental tools used in high school physics and beyond. For example, students will learn how physicists apply tools such as dimensional analysis, extreme case reasoning, and symmetries to understand the relationship between mathematical models and the real world. They’ll also learn the elements of experimental physics, including designing experiments, measuring uncertainty, and analyzing data. Learning core physics practices, like estimation and techniques for physics problem solving, are built into the course curriculum as well.
12 weeks
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A student with little or no science experience that is interested in exploring a fun physics topic could take our Physics Seminar: Relativity course. This course is a special 5 hour weekend class that introduces students to relativity. No prior physics background is required.

Physics Seminar: Relativity

Imagine this: You can fit a 10 m pole in a barn half the size. Your twin is now 10 years older than you, but you didn't use a time machine. And no matter how fast you run, you can never reach the speed of light. How can you explain these scenarios? In this class, we use thought experiments like these and other tools to explore Einstein's theory of special relativity. We introduce Einstein's two postulates and explore the counterintuitive effects of time dilation, length contraction, and relativity of simultaneity. The class concludes with a look at several challenging paradoxes of relativity.
2 days

A student with a little science experience that is interested in learning mechanics and Newton's laws, or taking the AP Physics 1 exam could take Physics 1: Mechanics. This course assumes some background in scientific reasoning, but no specific physics knowledge is required. Knowledge of algebra at a level equivalent to Introduction to Algebra A is needed.

Physics 1: Mechanics

Physics 1: Mechanics brings together advanced problem solvers to explore key concepts in Newtonian Mechanics. Experienced instructors guide students to creatively solve problems in kinematics, forces, Newton's laws, Newtonian gravity, fluid statics and dynamics, rotational motion, and more. Course materials include handouts and homework sets. Instructions for optional at-home lab activities will also be provided. While test preparation is not the main focus, this course is approved by the College Board as an AP Physics 1 class for students in grades 9-12 and students who complete this course are well prepared for all topics on the AP Physics 1 exam.
24 weeks
Are you ready?Do you need this?

Some Experience

For students in grades 6-12 with some science experience

A student with some science experience can start with our Physics 1: Mechanics class. This course assumes some background in scientific reasoning, but no specific physics knowledge is required. This course will cover all topics needed for the AP Physics 1 exam.

Physics 1: Mechanics

Physics 1: Mechanics brings together advanced problem solvers to explore key concepts in Newtonian Mechanics. Experienced instructors guide students to creatively solve problems in kinematics, forces, Newton's laws, Newtonian gravity, fluid statics and dynamics, rotational motion, and more. Course materials include handouts and homework sets. Instructions for optional at-home lab activities will also be provided. While test preparation is not the main focus, this course is approved by the College Board as an AP Physics 1 class for students in grades 9-12 and students who complete this course are well prepared for all topics on the AP Physics 1 exam.
24 weeks
Are you ready?Do you need this?

A student with some physics experience, and interest in contest preparation, should consider our F=ma course. See the “Are You Ready?” diagnostic for this course to determine if the student has sufficient physics experience for this course; if not, consider our Introduction to Physics instead.

F=ma Problem Series

Students use the classical mechanics they have learned to solve the types of problems that appear on the F=ma exam, learning and mastering valuable problem solving techniques in each class. This course both analyzes problems from past exams and has many original problems not available elsewhere. We’ll also cover strategies for taking the test, and students will have an opportunity to complete a practice F=ma test featuring exclusive problems written by our esteemed AoPS curriculum team.
12 weeks
Are you ready?

Extensive Experience

For students preparing for the USPhO or USNCO

These are our most advanced science courses aimed at ambitious science students that are preparing for national or international Olympiads. PhysicsWOOT and ChemWOOT are also for the advanced math student with an interest in science.

ChemWOOT

Art of Problem Solving Chemistry Worldwide Online Olympiad Training is a 7-month training program targeted at national and international chemistry Olympiad contests. ChemWOOT is designed to help prepare students for the USNCO and to bridge the large difficulty gap between the USNCO and the study camp.
7 months

PhysicsWOOT

PhysicsWOOT is an online training program in Olympiad-level physics and problem solving. PhysicsWOOT is modeled after WOOT (Worldwide Online Olympiad Training), the math Olympiad preparation course that we’ve been teaching at AoPS since 2005. PhysicsWOOT is a good class to take whether you’re preparing for the F=ma exam, the US National Physics Olympiad (USAPhO), the Sir Isaac Newton exam (SIN), the Physics Team Training Camp, or the International Physics Olympiad (IPhO).
7 months