---
title: Mathematics
description: Study pure and applied mathematics at all levels with curated textbooks, courses, and problem sets. From basic arithmetic to advanced calculus and beyond.
url: /category/mathematics
---

# Mathematics

Study pure and applied mathematics at all levels with curated textbooks, courses, and problem sets. From basic arithmetic to advanced calculus and beyond.

## Topics in this Category

### Arithmetic & Pre-Algebra

The essentials before algebra: fractions, decimals, integers, exponents, and number sense.

[Explore Arithmetic & Pre-Algebra](/subcategory/mathematics/arithmetic-and-pre-algebra)

### Geometry & Trigonometry

Shapes, angles, and space: Euclidean and analytic geometry, circles, and the trigonometry that measures them.

[Explore Geometry & Trigonometry](/subcategory/mathematics/geometry-and-trigonometry)

### Numerical Analysis & Topology

Numerical methods and topology, where computation meets abstract structure.

[Explore Numerical Analysis & Topology](/subcategory/mathematics/numerical-analysis-and-topology)

### Abstract Algebra

Groups, rings, and fields: the abstract structures underlying modern mathematics, up to Galois theory.

[Explore Abstract Algebra](/subcategory/mathematics/abstract-algebra)

### Algebra

From linear equations to functions, logarithms, and inequalities: the algebra that unlocks higher math.

[Explore Algebra](/subcategory/mathematics/algebra)

### Algebraic Geometry

Where algebra meets geometry: varieties, curves, schemes, and cohomology.

[Explore Algebraic Geometry](/subcategory/mathematics/algebraic-geometry)

### Algebraic Topology

Topology through algebraic eyes: fundamental groups, homology, cohomology, and fiber bundles.

[Explore Algebraic Topology](/subcategory/mathematics/algebraic-topology)

### Calculus

Limits, derivatives, and integrals: the mathematics of change and the theorems that hold it together.

[Explore Calculus](/subcategory/mathematics/calculus)

### Category Theory

The mathematics of mathematics: categories, functors, limits, and adjunctions.

[Explore Category Theory](/subcategory/mathematics/category-theory)

### Combinatorics

The art of counting: permutations, combinations, generating functions, and combinatorial designs.

[Explore Combinatorics](/subcategory/mathematics/combinatorics)

### Complex Analysis

Calculus over the complex numbers: analytic functions, Cauchy's theorem, and conformal mapping.

[Explore Complex Analysis](/subcategory/mathematics/complex-analysis)

### Differential Equations

Equations that describe change: ODEs, boundary value problems, Laplace transforms, and numerical solutions.

[Explore Differential Equations](/subcategory/mathematics/differential-equations)

### Differential Geometry

Geometry with calculus: manifolds, curvature, geodesics, and Lie groups.

[Explore Differential Geometry](/subcategory/mathematics/differential-geometry)

### Differential Topology

Smooth manifolds and their global structure: tangent spaces, vector bundles, and de Rham cohomology.

[Explore Differential Topology](/subcategory/mathematics/differential-topology)

### Discrete Math

The math of computer science: logic, graphs, combinatorics, number theory, and recurrences.

[Explore Discrete Math](/subcategory/mathematics/discrete-math)

### Dynamical Systems

How systems evolve over time: stability, bifurcations, attractors, and chaos.

[Explore Dynamical Systems](/subcategory/mathematics/dynamical-systems)

### Functional Analysis

Analysis in infinite dimensions: Banach and Hilbert spaces, operators, and distributions.

[Explore Functional Analysis](/subcategory/mathematics/functional-analysis)

### Graph Theory

Networks in the abstract: connectivity, coloring, matchings, and flows.

[Explore Graph Theory](/subcategory/mathematics/graph-theory)

### Harmonic Analysis

Decomposing functions into waves: Fourier series and transforms, convolution, and Sobolev spaces.

[Explore Harmonic Analysis](/subcategory/mathematics/harmonic-analysis)

### Linear Algebra

Vectors, matrices, and linear maps: eigenvalues, determinants, and the workhorse of applied math.

[Explore Linear Algebra](/subcategory/mathematics/linear-algebra)

### Mathematical Logic

The foundations of reasoning: formal systems, model theory, computability, and Godel's theorems.

[Explore Mathematical Logic](/subcategory/mathematics/mathematical-logic)

### Mathematical Physics

The mathematics behind physics: classical and quantum mechanics, relativity, and electrodynamics.

[Explore Mathematical Physics](/subcategory/mathematics/mathematical-physics)

### Mathematics

Cross-cutting mathematical topics spanning algebra, analysis, probability, and number theory.

[Explore Mathematics](/subcategory/mathematics/mathematics)

### Measure Theory

The rigorous theory of size and integration: Lebesgue measure, Lp spaces, and Fubini's theorem.

[Explore Measure Theory](/subcategory/mathematics/measure-theory)

### Number Theory

The study of the integers: divisibility, congruences, primes, and the math behind cryptography.

[Explore Number Theory](/subcategory/mathematics/number-theory)

### Numerical Linear Algebra

Matrix computation at scale: factorizations, iterative and Krylov methods, and numerical stability.

[Explore Numerical Linear Algebra](/subcategory/mathematics/numerical-linear-algebra)

### Probability & Statistics

Chance made rigorous: probability theory, hypothesis testing, Bayesian methods, and statistical inference.

[Explore Probability & Statistics](/subcategory/mathematics/probability-theory)

### Real Analysis

Calculus made rigorous: sequences, limits, continuity, and Lebesgue integration.

[Explore Real Analysis](/subcategory/mathematics/real-analysis)

### Representation Theory

Groups as matrices: characters, irreducible representations, and Lie algebras.

[Explore Representation Theory](/subcategory/mathematics/representation-theory)

### Set Theory

The foundation of mathematics: sets, cardinality, ordinals, the axiom of choice, and the continuum hypothesis.

[Explore Set Theory](/subcategory/mathematics/set-theory)

### Applied Mathematics

Mathematics at work: modeling, optimization, numerical methods, and financial and cryptographic math.

[Explore Applied Mathematics](/subcategory/mathematics/applied-mathematics)

---

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