THE MATHEMATICS COURSE MAP
Start with foundations, then explore algebra, geometry, number theory and counting. Each course has its own levels and smaller knowledge stages.
PA · Foundation
Number MeadowBuild a foundation in number structure, algebra, geometry and mathematical reasoning.
15 topic levels, from signed numbers to a problem-solving toolkit.
15 levels · 48 stages · 384 library problems · 2356 checked variations
Preparation: Whole-number arithmetic and a willingness to explain your thinking.
Explore this course →ALG · Introduction
Equation CanyonTurn numerical patterns into equations, functions and models.
Four core-skills levels: linear relationships, quadratics, functions, and algebraic models.
4 levels · 12 stages · 96 library problems · 432 checked variations
Preparation: Signed arithmetic, fractions, powers and basic equations.
Explore this course →GEO · Introduction
Shape HarborReason about angles, shape, similarity, measurement and coordinates.
12 core stages: angle reasoning, congruence, similarity, circles, coordinates and solids.
4 levels · 12 stages · 96 library problems · 432 checked variations
Preparation: Fractions, ratios, basic equations and square roots.
Explore this course →NT · Introduction
Prime PeaksDiscover structure in divisibility, primes, representations and remainders.
12 core stages from Euclid’s algorithm through congruences and coprime counting.
4 levels · 12 stages · 96 library problems · 432 checked variations
Preparation: Integer arithmetic, prime factorization and fractions.
Explore this course →CP · Introduction
Chance CarnivalCount systematically and build probability models with explicit sample spaces.
12 core stages covering counting rules, combinations, probability and binomial identities.
4 levels · 12 stages · 96 library problems · 432 checked variations
Preparation: Fractions, factorial notation and basic algebra.
Explore this course →IA · Intermediate
Algebra GalaxyConnect complex arithmetic, polynomial structure, sequences and inequalities.
12 core stages on complex numbers, polynomials, conics, series and inequalities.
4 levels · 12 stages · 96 library problems · 432 checked variations
Preparation: Linear and quadratic equations, factoring and introductory functions.
Explore this course →IC · Intermediate
Probability LabDevelop counting arguments using distributions, recurrences, conditioning and graphs.
12 core stages including inclusion–exclusion, Catalan counts, Bayes and graph invariants.
4 levels · 12 stages · 96 library problems · 432 checked variations
Preparation: Combinations, elementary probability, binomial coefficients and algebra.
Explore this course →PC · Advanced
Orbit ObservatoryConnect functions, trigonometry, complex numbers, vectors and linear transformations.
12 core stages covering domains, trigonometric identities, polar coordinates and 2D/3D vector methods.
4 levels · 12 stages · 96 library problems · 432 checked variations
Preparation: Intermediate algebra, coordinate geometry, radicals and function notation.
Explore this course →PS · Synthesis
Summit ChallengeChoose representations and arguments that turn difficult-looking problems into tractable ones.
12 strategy stages: reversal, invariants, extremal reasoning, telescoping, induction and connections.
4 levels · 12 stages · 96 library problems · 432 checked variations
Preparation: Algebra, geometry, counting and the logarithm definition. Later stages combine subjects.
Explore this course →Clear a stage by independently solving two different routine problems and one application in a new context. Hints help you learn; hinted answers and repeated solves do not count toward that target. Clear every stage to clear a level.
Every stage includes an explanation, two worked examples and eight library practice problems, plus checked variations with changing numbers and applications. Each level also has a separate unit test and a later review form. Parents see actual attempts, hint use and results.
These are independently authored core-skills courses, with the current scope listed for each course. They do not reproduce complete textbook contents. Difficulty describes the teaching sequence within each course; course preparation matters when comparing subjects. This site is not affiliated with or endorsed by AoPS. Results reflect these exercises and are not standardized scores. Content release math-courses-2026.09.08-v4.