THE MATHEMATICS COURSE MAP
Pick a world. Find your spark.
Start with foundations, then explore algebra, geometry, number theory and counting. Each course has its own levels and smaller knowledge stages.
PA · Foundation
Number MeadowPrealgebra
Build 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 CanyonIntroduction to Algebra
Turn 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 HarborIntroduction to Geometry
Reason 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 PeaksIntroduction to Number Theory
Discover 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 CarnivalIntroduction to Counting and Probability
Count 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 GalaxyIntermediate Algebra
Connect 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 LabIntermediate Counting and Probability
Develop 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 ObservatoryPrecalculus
Connect 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 ChallengeProblem-Solving Strategies
Choose 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 →PSAT · Intermediate
Discovery LabPSAT/NMSQT Math
Targeted practice in algebra, advanced math, data analysis, geometry and trigonometry.
4 domains, 20 focused lessons, original practice and two checkpoint forms per domain.
4 levels · 20 stages · 160 library problems · 560 checked variations
Preparation: Comfort with fractions, signed numbers and basic equations. Use foundation links whenever you need a smaller step.
Explore this course →SAT · Intermediate
Number MeadowSAT Math: Extension Workshops
Add statistical evidence and circle reasoning to the shared SAT / PSAT core.
2 extension levels, 5 focused lessons, original practice and two checkpoint forms per level.
2 levels · 5 stages · 40 library problems · 140 checked variations
Preparation: Use the SAT skill map to review the shared algebra, data and geometry foundations.
Explore this course →Progress earned through practice
Earn two independent practice stars and one application star, then complete the library skill check for that stage. The check covers the stage’s library prompts, so changing numbers alone is not enough. Hints help you learn; your existing stars and earned rewards stay yours. 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-2026.09.27-university-guides-v2.