Recommendations

Course Map

For recommendations in computer science, click here. For information about Chemistry WOOT, click here.

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

6
Introductory
Intermediate
Advanced
Core Subject Courses Prealgebra 1 Prealgebra 2 Intro Algebra A Intro Counting & Probability Intro Algebra B Intro Geometry Intermediate Algebra Precalculus Calculus
Other Subject Courses Intro Number Theory Intermediate Count & Prob Olympiad Geometry Group Theory
Intermediate Number Theory Mathematical Tapas
Contest Prep Courses MC/AMC 8 Basics MC/AMC 8 Advanced AMC 12
AMC 10 AIME A/B WOOT
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 his or her 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.

Ready for Prealgebra

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

A student who has 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 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.

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.

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.

After Prealgebra

For students who have completed prealgebra (or equivalent middle-school math curriculum)

A student who has 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 his or her 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.

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.

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.

Some Algebra 1

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

A student who has 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.

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.

After Algebra 1

For students who have completed an honors algebra 1 course

A student who has 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.

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.

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.

After Geometry

For students who have completed geometry

A student who has 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.

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.

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.

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.

After Algebra 2

For students who have completed algebra 2

A student who has completed algebra 2: The student should take the “Do you need this?” diagnostic test for Introduction to Geometry, even if he or she has 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.

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.

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.

After Precalculus

For students who have completed all regular high school math including precalculus

A student who has 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 he or she passes the “Do you need this?” diagnostic, he or she 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.

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.

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. At the conclusion of the course, students should have sufficient preparation to take the AP Calculus BC exam; however, "AP exam preparation" is not the main focus of the course.

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.

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.

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.

Beyond Calculus

For students who have completed calculus

A student who has 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 he or she is unsuccessful, work backwards through our core curriculum, using the diagnostic tests to find the appropriate course. If he or she is 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.

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. At the conclusion of the course, students should have sufficient preparation to take the AP Calculus BC exam; however, "AP exam preparation" is not the main focus of the course.

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.

Mathematical Tapas

Colloquium-style seminar. In this class we will be studying living mathematics: concepts people care about today. Most students "graduate" from AoPS into a world of tremendous variety and specializations. Mathematical Tapas will be a sampling of some of these realms and is meant to introduce the student to the various and beautiful flavors of mathematics.

Group Theory Seminar

This 7-week seminar is an introduction to the basics of group theory. In this seminar we will focus on defining and understanding groups: how they are constructed and how they interact with the rest of the world. This seminar is not intended to be a complete group theory course (which is a core component of a college undergraduate mathematics curriculum), but rather is intended to give strong high school students a first look at the most important concepts and examples of this very vast subject.

Group Theory

Group theory is the study of symmetry. Objects in nature (math, physics, chemistry, etc.) have beautiful symmetries and group theory is the algebraic language we use to unlock that beauty. Group theory is the gateway to abstract algebra which is what tells us (among many other things) that you can't trisect an angle, that there are finitely many regular polyhedra, and that there is no closed form for solving a quintic. In this class we will get a glimpse of the mathematics underlying these famous questions. This course will focus specifically on building groups from other groups, exploring groups as symmetries of other objects, and using the tools of group theory to construct fields.

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.

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.

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.

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

MATHCOUNTS and AMC 8 (and other middle school contests): 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.

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.

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.

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.

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.

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.

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.

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.

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.

AMC 10

For students preparing for the AMC 10

Our AMC 10 course is designed for students in grade 10 or below who have completed an algebra course and can currently score 80+ on the AMC 10 contest. 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 120+ on the AMC 10 would probably not benefit from this course and should instead consider our AMC 12, AIME A, AIME 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.

Special AMC 10 Problem Seminar

This course is a special 5-hour weekend seminar to prepare for the AMC 10, 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 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 the same as the Special AMC 10 Problem Seminar offered last year.

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.

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.

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.

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.

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.

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.

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.

AMC 12

For students preparing for the AMC 12

Our AMC 12 course is designed for high-school students who have completed an algebra and geometry course and can currently score 80+ on the AMC 12 contest. 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 120+ on the AMC 12 would probably not benefit from this course and should instead consider our AIME A and AIME 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.

Special AMC 12 Problem Seminar

This course is a special 5-hour weekend seminar to prepare for the AMC 12, 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 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 the same as the Special AMC 12 Problem Seminar offered last year.

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.

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.

Introduction to Counting & Probability

Fundamentals of counting and probability, including casework, multiplication, permutations, combinations, Pascal's triangle, probability, combinatorial identities, and the Binomial Theorem.

Introduction to Number Theory

Fundamental principles of number theory, including primes and composites, divisors and multiples, divisibility, remainders, modular arithmetic, and number bases.

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.

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.

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.

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.

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.

AIME

For students preparing for the AIME

Our AIME A and AIME B courses are designed for students who are very confident that they will qualify for the AIME contest. Students who consistently expect to score 8 or more on the AIME may instead wish to consider our WOOT program. AIME-qualifying students would also benefit from any of our Intermediate-level subject courses. Note: the AIME A and AIME B classes cover mostly the same topics but use entirely different problems. Students can take either or both classes, in either order.

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.

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.

Special AIME Problem Seminar

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. This course is a repeat of the weekend seminar we offered in 2014 and is completely different from the March 14 and 15 Special AIME Problem Seminar B class.

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.

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.

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.

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.

WOOT

Art of Problem Solving Worldwide Online Olympiad Training is a 7-month Olympiad training program consisting of classes and Olympiad testing. Due to sponsorship from D. E. Shaw group, Jane Street Capital, and Two Sigma Investments, all 2015 Math Olympiad Program participants are invited to join WOOT for free. Therefore, WOOT participants will be training with the top students in the United States.

USAMO

For students preparing for the USAMO

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

WOOT

Art of Problem Solving Worldwide Online Olympiad Training is a 7-month Olympiad training program consisting of classes and Olympiad testing. Due to sponsorship from D. E. Shaw group, Jane Street Capital, and Two Sigma Investments, all 2015 Math Olympiad Program participants are invited to join WOOT for free. Therefore, WOOT participants will be training with the top students in the United States.

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.

Computer Programming

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

Little or No Experience

For students 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, data types, iteration, flow of control, input/output, and functions.

Some experience

For students 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 his or her own before starting Intermediate Programming with Python.

A student who is also more mathematically-experienced (at least through our Intermediate Algebra course or equivalent) can also consider our Java Programming 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, data types, iteration, flow of control, input/output, and functions.

Intermediate Programming with Python

This course covers intermediate programming concepts such as recursion, object-oriented programming, graphical user interfaces, and event-driven programming.

Java Programming with Data Structures

An introduction to object-oriented programming and data structures using the Java programming language. Students who complete this course will be prepared for college-level courses in computer science. Some programming experience (such as Art of Problem Solving's Intermediate Programming course) is required.

Extensive experience

For students with extensive programming experience

A student with extensive programming experience might consider our Intermediate Programming with Python or Java Programming courses, especially if the student does not have experience with object-oriented programming or advanced data structures such as linked lists, stacks, queues, trees, and hash tables. Otherwise, advanced programmers would likely not benefit from our courses and should instead consider advanced training materials such as those on the USA Computing Olympiad website.

Intermediate Programming with Python

This course covers intermediate programming concepts such as recursion, object-oriented programming, graphical user interfaces, and event-driven programming.

Java Programming with Data Structures

An introduction to object-oriented programming and data structures using the Java programming language. Students who complete this course will be prepared for college-level courses in computer science. Some programming experience (such as Art of Problem Solving's Intermediate Programming course) is required.
ACS WASC
ACCREDITED
SCHOOL

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