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# Course Catalog

Choose from our introductory math, intermediate math, advanced math, or contest prep series. In addition to advanced online math, AoPS Online also offers courses in computer science and programming.

Click on any course for more details, including the dates and times of upcoming classes. For help choosing the right level, please consult our course map and recommended sequencing.

### Introductory Math

# 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.

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# 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.

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# 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.

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# Introduction to Counting & Probability

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

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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.

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# 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.

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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.

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# Paradoxes and Infinity Seminar

In this class we'll explore several popular paradoxes and attempt to wrap our brains around the world of infinity. For example, we'll discover a hotel that's never full: somehow, this hotel can always add another guest, or two, or three. We'll also run into paradoxes about goats, haystacks, pop-quizzes and more. If you're interested in mind-bending ideas and theories and have a background in basic algebra, this class is for you!

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### Intermediate Math

# 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.

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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.

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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.

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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.

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### Advanced Math

# 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.

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# 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.

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# 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”.

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### WOOT Courses

# 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.

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# 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.

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# 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)

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# 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).

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### Contest Preparation

# 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.

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# 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.

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# 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.

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# 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.

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# Special AMC 8 Problem Seminar B

This course is a special two-day, 5-hour seminar to prepare for the AMC 8, which is the premier fall math contest for middle school students. The AMC 8 also gives students early problem-solving experience that is valuable towards the high-school level AMC 10 and AMC 12 contests, which are the first stage in determining the United States team for the International Math Olympiad. 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 A.

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# 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.

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# 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.

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# 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.

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# 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.

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# 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.

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# 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.

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# 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.

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# 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.

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# 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.

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# 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.

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# 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.

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# 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.

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# 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.

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### Computer Science / Programming

# 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.

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# Intermediate Programming with Python

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

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# 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.

View Course

# 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)

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### Science Courses

# 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.

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# 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.

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# 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.

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# 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 spacetime diagrams and several challenging paradoxes of relativity.

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# 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.

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# 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.

View Course

# 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).

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