Mathematics
Study pure and applied mathematics at all levels with curated textbooks, courses, and problem sets. From basic arithmetic to advanced calculus and beyond.
31 Subcategories
Arithmetic & Pre-Algebra
The essentials before algebra: fractions, decimals, integers, exponents, and number sense.
Geometry & Trigonometry
Shapes, angles, and space: Euclidean and analytic geometry, circles, and the trigonometry that measures them.
Numerical Analysis & Topology
Numerical methods and topology, where computation meets abstract structure.
Abstract Algebra
Groups, rings, and fields: the abstract structures underlying modern mathematics, up to Galois theory.
Algebra
From linear equations to functions, logarithms, and inequalities: the algebra that unlocks higher math.
Algebraic Geometry
Where algebra meets geometry: varieties, curves, schemes, and cohomology.
Algebraic Topology
Topology through algebraic eyes: fundamental groups, homology, cohomology, and fiber bundles.
Calculus
Limits, derivatives, and integrals: the mathematics of change and the theorems that hold it together.
Category Theory
The mathematics of mathematics: categories, functors, limits, and adjunctions.
Combinatorics
The art of counting: permutations, combinations, generating functions, and combinatorial designs.
Complex Analysis
Calculus over the complex numbers: analytic functions, Cauchy's theorem, and conformal mapping.
Differential Equations
Equations that describe change: ODEs, boundary value problems, Laplace transforms, and numerical solutions.
Differential Geometry
Geometry with calculus: manifolds, curvature, geodesics, and Lie groups.
Differential Topology
Smooth manifolds and their global structure: tangent spaces, vector bundles, and de Rham cohomology.
Discrete Math
The math of computer science: logic, graphs, combinatorics, number theory, and recurrences.
Dynamical Systems
How systems evolve over time: stability, bifurcations, attractors, and chaos.
Functional Analysis
Analysis in infinite dimensions: Banach and Hilbert spaces, operators, and distributions.
Graph Theory
Networks in the abstract: connectivity, coloring, matchings, and flows.
Harmonic Analysis
Decomposing functions into waves: Fourier series and transforms, convolution, and Sobolev spaces.
Linear Algebra
Vectors, matrices, and linear maps: eigenvalues, determinants, and the workhorse of applied math.
Mathematical Logic
The foundations of reasoning: formal systems, model theory, computability, and Godel's theorems.
Mathematical Physics
The mathematics behind physics: classical and quantum mechanics, relativity, and electrodynamics.
Mathematics
Cross-cutting mathematical topics spanning algebra, analysis, probability, and number theory.
Measure Theory
The rigorous theory of size and integration: Lebesgue measure, Lp spaces, and Fubini's theorem.
Number Theory
The study of the integers: divisibility, congruences, primes, and the math behind cryptography.
Numerical Linear Algebra
Matrix computation at scale: factorizations, iterative and Krylov methods, and numerical stability.
Probability & Statistics
Chance made rigorous: probability theory, hypothesis testing, Bayesian methods, and statistical inference.
Real Analysis
Calculus made rigorous: sequences, limits, continuity, and Lebesgue integration.
Representation Theory
Groups as matrices: characters, irreducible representations, and Lie algebras.
Set Theory
The foundation of mathematics: sets, cardinality, ordinals, the axiom of choice, and the continuum hypothesis.
Applied Mathematics
Mathematics at work: modeling, optimization, numerical methods, and financial and cryptographic math.