Art of Problem Solving

Math texts, online classes, and more for students in grades 5-12.

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Engaging math books and online learning for students ages 6-13.

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Small live classes for advanced math
and language arts learners in grades 1-12.

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Course Catalog

Below are the courses we offer for high-performing students in mathematics, language arts, and science. We offer courses during the academic year and during the summer. Click on any course for more information about that course. Visit the Course Schedule to learn when the courses are offered or to enroll in courses, and read About AoPS Academy to learn more about our educational philosophy.

Academic Year Mathematics

Courses during the school year for high-performing math students in grades 1–12. Before enrolling in Academic Year courses, you will need to request a consultation.

Math Level 1

Students develop their number sense and begin to learn about place value. They are introduced to addition and subtraction and are encouraged to approach numerical problems in clever ways. Additionally, they manipulate shapes, compare numbers, and examine ways to measure physical objects. We use puzzles and games to build skills and establish student understanding of mathematical concepts and problem solving.

Math Level 2

Students build foundational problem-solving skills which they will use throughout their math education. They will expand their understanding of the number system and place value, develop fluency adding and subtracting multi-digit numbers, and explore the properties of special types of numbers such as odds and evens. Each lesson includes challenging word problems and engaging puzzles that guide students toward a deep understanding of the material.

Math Level 3

Students develop fluency with multiplication and division, including using the distributive property to simplify calculations. They are also introduced to fractions to expand their understanding of numbers. In addition, students explore two-dimensional shapes, estimation, the use of variables to write expressions and equations, and other topics. We regularly incorporate word problems to teach students how to translate between writing and mathematics, and puzzles to teach higher-order strategic thinking.

Math Level 4

Students master multiplication and division of multi-digit numbers and build upon their understanding of addition and multiplication to include fractions. They also explore a wide variety of other topics, including properties of special two-dimensional shapes, symmetry, logic, factors, and probability. Students expand their understanding of numbers to include decimals and negative integers, and they learn to create and employ mathematical models via challenging word problems.

Math Level 5

Students master the key topics they'll need to succeed in an AoPS Prealgebra course. They will complete their study of the arithmetic of fractions, decimals, and negative integers. They are also introduced to topics in geometry, number theory, statistics, and beginning algebra through lessons on three-dimensional solids, factors and multiples, statistics, sequences, and ratios. Critical problem-solving skills, mathematical modeling, and deductive reasoning are reinforced with thought-provoking word problems and puzzles.

Prealgebra

Prealgebra begins by formalizing the rules of arithmetic that students learned in elementary school, building on a rigorous foundation as they move into algebra. We then survey a wide range of topics, including number theory, algebra, geometry, counting, statistics, and probability. Each topic is introduced with compelling problems, including many drawn from major national math contests such as MATHCOUNTS and AMC 8. We place special emphasis on challenging word problems throughout the course.

Algebra 1

In Algebra 1, students engage with various expressions from an algebraic and geometric perspective. They learn to solve linear and quadratic equations as well as how to represent expressions in the Cartesian plane. Students are imbued with a deep understanding of the general concept behind functions and are introduced to several important types of functions. Students are also introduced to the rich field of complex numbers. As with previous courses, we continue to emphasize challenging word problems to train students how to apply their new tools. Advanced problems from contests such as MATHCOUNTS, AMC 8, and AMC 10 are included throughout the course.

Geometry

Geometry introduces students to spatial thinking. Students learn to dissect complex geometrical configurations, applying what they've learned to arrive at key insights and novel understandings. Geometry problems are also tackled analytically by placing them on the Cartesian plane. In addition, we build the foundations for precalculus and calculus by introducing students to trigonometry. Many of the challenging problems from this course come from contests such as MATHCOUNTS, AMC 10, and AMC 12, with a few problems coming from even more advanced contests to stretch the strongest students.

Algebra 2

In Algebra 2, students continue their study of algebraic functions and applications. We begin by reviewing key concepts from Algebra 1, then expand upon them to solve even more challenging problems. Students explore the rich field of polynomials and build foundations for calculus through the study of sequences and series. They are exposed to a variety of important algebraic forms and functions, and are equipped with the tools necessary for understanding new forms and functions they'll encounter in the future. We also lay the groundwork for navigating optimization problems with a study of inequalities. Many challenging problems in this course are drawn from contests such as AMC 10, AMC 12, AIME, and the Harvard-MIT Math Tournament.

Precalculus

Our Precalculus class prepares students for a variety of college-level courses. Precalculus provides a deep exploration of trigonometry, complex numbers, and two- and three-dimensional vector spaces, with a special focus on how these areas of mathematics are related. This gives students a solid foundation for collegiate courses in calculus, linear algebra, multi-variable calculus, complex analysis, and physics. Many of the challenging problems of Precalculus come from contests such as AMC 12, AIME, and the Harvard-MIT Math Tournament.

Calculus

Our calculus class goes well beyond mechanics and calculators, and provides students a rigorous understanding of the fundamental operations of calculus, delivering a first-year calculus course like those students would find at a top-tier university. Students completing our calculus course will be in an excellent position to apply their new skills to physics, economics, engineering, and more advanced mathematics.

Middle School Contest Math *

Middle school math contests such as MATHCOUNTS are a launching pad for many of the best math students. In this course, we draw problems from premiere middle school contests such as MATHCOUNTS and the American Mathematics Competitions 8 (AMC 8), as well as beginning high school contests like the American Mathematics Competitions 10 (AMC 10). Students explore important new topics in counting, probability, and number theory, and learn to apply topics in algebra and geometry to advanced problems. Students should either have completed an Algebra 1 course or be currently enrolled in one to be successful in this course.

High School Contest Math *

AoPS has prepared students for the most prestigious high school competitions since 1993. Over the last decade, most winners of the USA Mathematical Olympiad (USAMO) have been AoPS students, including 15 USAMO winners in 2020, as well as the US team members that won the International Math Olympiad (IMO) in 2015, 2016, 2018, and 2019. In this course, students study strategies crucial for success on the American Mathematics Competitions 10 and 12 (AMC 10 and 12), the American Invitational Math Exam (AIME), the Harvard-MIT Math Tournament, and other major high school contests. This course is a challenge which builds on foundational knowledge that students should already have from their high school math courses. Students should expect to encounter difficult problems and topics. Students should either have completed an Algebra 2 course or be currently enrolled in one to be successful in this course.

* Note for students who have previously taken this course: We alternate between two different versions of this course from one year to the next. The two versions are roughly the same difficulty, but include different lessons, practice contests, and homework. Therefore, students taking this course for two consecutive years will see different material in the second year than in the first.

Academic Year Language Arts

Courses during the school year for high-performing language arts students in grades 2–12. Before enrolling in Academic Year courses, you will need to request a consultation.

Language Arts Level 2

The Level 2 course engages students with a fantasy narrative as they practice fundamental grammar concepts and high-level reading and writing strategies. Students apply advanced language skills in order to complete each unit’s spell-busting writing project. Throughout the course, Greenie, a grammar-loving lizard, helps students as they discover the power of their words, beginning the course working on well-crafted sentences and culminating at the end of the year with detailed multi-paragraph pieces.

Language Arts Level 3

The Level 3 course builds the foundation students need to become independent problem solvers in language arts. The course is divided into four quarters: mythology, history, theater, and storytelling. In each unit, students tackle a challenging language arts problem. As they work to solve the problem, students develop deep reading, writing, and critical thinking skills. The thematic focus of the course is ancient Greece, giving students a rich introduction to characters and stories that are central to the Western literary tradition.

Language Arts Level 4

In the Level 4 course, students exercise their critical thinking skills in the study of language across American history. Each quarter, students engage with high-level texts to increase comprehension, and address authentic scenarios that cultivate problem-solving skills and hone each student's development of purposeful, quality writing.

Language Arts Level 5

In the Level 5 course, students expand upon their critical abilities in creating masterful writing: discerning research, composing arguments, building theories, and imagining what's missing -- all within the context of exploring some of history's most enduring mysteries. Students will gain skills in independent research and source evaluation, experience in text analysis and drafting plausible theories, and foster their emerging expertise in crafting the complex, nuanced writing required in upper-level coursework.

Foundations in Middle School Language Arts

This course prepares sixth grade and beginning middle school students for an advanced middle school language arts curriculum. The course has four units: critical thinking and communication, creative writing and language, research, and literary studies. In each unit, students develop new skills that contribute toward a final project that encapsulates the unit theme. Students who complete this course will be prepared for advanced middle school classes and have a competitive edge as they get ready for high school.

Rhetoric: Persuasion in Reading, Writing, and Critical Thinking

In this course for 7th through 9th graders, students will learn how to apply classic rhetorical techniques to real-world writing, speaking, and critical thinking scenarios. The course is divided into four units: Classic Rhetoric, Marketing, Literary Mystery, and Global Problem Solving. With each unit, students develop new skills that contribute toward a final project that encapsulates the unit theme. By the end of the course, students will have become savvy masters of persuasion.

Exposition: Informational Writing and Public Speaking

This course teaches students in grades 7-9 to present information clearly and effectively by introducing them to four of the most important modes of real-world expository writing: investigative journalism, the personal essay, historical documentary, and scientific writing. The course includes a deep focus on both writing and public speaking, training students to become masters of written and oratorical communication.

Advanced Language Arts Seminar

This course introduces students to the craft of literary studies at the college level. Through close reading of challenging texts, students learn to form their own critical interpretation, to write and speak with sophistication, and to build well-crafted arguments one piece of evidence, one claim, and one draft at a time. Over the course of the year, students polish their style, grammar, and vocabulary as they produce creative texts, and develop the research skills integral to successful academic writing and public speaking.

Academic Year Science

Courses during the school year for high-performing science students in grades 3-9. Before enrolling in Academic Year courses, you will need to request a consultation.

Science Level 3

Students will explore topics in earth science, physical science, and life science, using problem solving and a hands-on approach. They will be encouraged to ask questions about the world around them and will learn about scientific tools and processes which can help answer these questions. Classes will include lab activities, demonstrations, and games focused on real life phenomena.

Introductory Physics: Applied Math of Motion

Students learn physics at an introductory level. With a hands-on, experimental approach, they study the fundamentals of Newtonian mechanics: motion, forces, and energy. Students will develop strong skills in critical thinking and scientific reasoning, and will learn to recognize and apply physics in their everyday, real-world experiences. This course is designed for students interested in physics who have completed at least an Algebra 1 class.

Summer Mathematics

Courses during the summer for high-performing math students entering grades 2-12. No consultation required: enroll directly through our course schedule.

Math Beasts Camp 2

Math Beasts Camp 2 is designed for students entering a second grade math class in the fall. This course helps students practice math skills over the summer as well as providing a fun environment where students can get excited about learning mathematics.

Math Beasts Camp 3

Math Beasts Camp 3 is designed for students entering a third grade math class in the fall. The course keeps students' math skills sharp over the summer while introducing new avenues of mathematical discovery, with a focus on number sense and spatial reasoning.

Math Beasts Camp 4

Math Beasts Camp 4 is designed for students entering a fourth grade math class in the fall. The course reviews key concepts from third grade and provides early practice with ideas students will master in the upcoming year. Students also gain the powerful insight of viewing problems through multiple lenses by exploring visual reconceptualizations of numbers.

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