Curriculum

Explore the curriculum

Every branch of mathematics, from foundations to research-level topics. Domains marked coming soonare mapped in the knowledge graph but don’t have published concepts yet.

Knowledge graph →

Foundations

Numbers, counting, and the logical bedrock everything else is built on.

9 concepts →

Algebra

Pre-Algebra

Variables, expressions, exponents, and the bridge from arithmetic to algebra.

10 concepts →

Algebra I

Linear and quadratic equations, polynomials, and functions.

19 concepts →

Algebra II

Exponentials, logarithms, complex numbers, sequences and series.

18 concepts →

Geometry

Euclidean geometry — points, lines, triangles, circles, and proof.

20 concepts →

Trigonometry

The unit circle, trigonometric functions, and their identities.

22 concepts →

Analytic Geometry

Conic sections and coordinate-based geometry.

19 concepts →

Calculus

Calculus I

Limits, continuity, derivatives, and their applications.

16 concepts →

Calculus II

Integration techniques, infinite series, and parametric/polar calculus.

16 concepts →

Calculus III

Multivariable and vector calculus — gradients, multiple integrals, and Green's/Stokes'/Divergence theorems.

18 concepts →

Linear Algebra

Vector spaces, matrices, eigenvalues, and linear transformations.

19 concepts →

Differential Equations

Equations relating functions to their derivatives.

26 concepts →

Probability

Randomness, distributions, and expectation.

19 concepts →

Statistics

Inference, hypothesis testing, and regression.

20 concepts →

Number Theory

Divisibility, primes, and modular arithmetic.

28 concepts →

Discrete Mathematics

Combinatorics, recurrence relations, and discrete structures.

20 concepts →

Graph Theory

Networks, trees, and traversal algorithms.

21 concepts →

Combinatorics

Counting, permutations, and combinations.

21 concepts →

Set Theory

The foundational language of modern mathematics.

22 concepts →

Mathematical Logic

Formal reasoning, proof, and the foundations of mathematics itself.

28 concepts →

Abstract Algebra

Abstract Algebra I

Groups, subgroups, cyclic groups, homomorphisms, and permutation groups.

20 concepts →

Abstract Algebra II

Rings, ideals, polynomial rings, fields, and Galois theory.

29 concepts →

Topology

Continuity and shape without rigid distance.

34 concepts →

Real Analysis

The rigorous theory underlying calculus.

33 concepts →

Complex Analysis

Calculus over the complex numbers.

31 concepts →

Theory of Computation

Automata, computability, and computational complexity — the mathematical foundations of computer science.

21 concepts →

Numerical Analysis

Approximating solutions to continuous problems — root finding, interpolation, numerical integration, and finite-element/finite-difference methods for differential equations.

22 concepts →

Measure Theory

The rigorous theory of size, integration, and probability that generalizes Riemann integration and underlies modern analysis.

22 concepts →

Category Theory

The abstract study of mathematical structure and structure-preserving maps — a unifying language spanning algebra, topology, and logic.

17 concepts →