The Mathematics Encyclopedia

Contents

MathKnow currently has 523 articles organized into 9 categories. Browse the full contents below.

Categories

Algebra Calculus Geometry Number Theory Statistics Discrete Mathematics Topology Analysis Applied Mathematics

Algebra

Study of mathematical symbols and rules for manipulating these symbols

Algebraic Expression

Associative Property

Basis (Linear Algebra)

Cayley-Hamilton Theorem

Characteristic Polynomial

Commutative Property

Completing the Square

Diagonalizable Matrix

Dimension (Vector Space)

Distributive Property

Eigenvalues and Eigenvectors

Euclidean Domain

Floor and Ceiling Functions

Fundamental Theorem of Algebra

Gaussian Elimination

Gram-Schmidt Process

Ideal (Ring Theory)

Inner Product Space

Integral Domain

Inverse Function

Invertible Matrix

Jordan Normal Form

Kernel (Algebra)

Linear Combination

Linear Equation

Linear Independence

Linear Transformation

LU Decomposition

Matrix Multiplication

Normal Subgroup

Orthonormal Basis

Polynomial Long Division

Polynomial Ring

Principal Ideal

Product (Mathematics)

QR Decomposition

Quadratic Equation

Quadratic Formula

Quartic Equation

Quintic Equation

Rank (Linear Algebra)

Rational Root Theorem

Remainder Theorem

Row Echelon Form

Singular Value Decomposition

Symmetric Group

Synthetic Division

System of Linear Equations

Unique Factorization Domain

Vieta's Formulas

Calculus

Mathematical study of continuous change

Concave Function

Conservative Vector Field

Definite Integral

Differentiability

Directional Derivative

Divergence Theorem

Double Integral

Epsilon-Delta Definition

Fundamental Theorem of Calculus

Green's Theorem

Implicit Differentiation

Improper Integral

Indefinite Integral

Inflection Point

Integration by Parts

Integration by Substitution

Jacobian Matrix

L'Hopital's Rule

Lagrange Multiplier

Maclaurin Series

Mean Value Theorem

Multivariable Calculus

Optimization (Calculus)

Partial Derivative

Partial Fractions

Riemann Integral

Rolle's Theorem

Solid of Revolution

Squeeze Theorem

Stokes' Theorem

Surface Integral

Surface of Revolution

Trigonometric Substitution

Triple Integral

Geometry

Study of shapes, sizes, and properties of space

Affine Geometry

Algebraic Geometry

Cartesian Coordinates

Chord (Geometry)

Circular Sector

Congruence (Geometry)

Coordinate System

Differential Geometry

Elliptic Geometry

Euclidean Geometry

Gaussian Curvature

Heron's Formula

Hyperbolic Geometry

Inscribed Angle

Line (Geometry)

Parametric Curve

Perpendicular Lines

Point (Geometry)

Polar Coordinates

Prism (Geometry)

Projective Geometry

Pyramid (Geometry)

Pythagorean Theorem

Regular Polygon

Riemannian Geometry

Similarity (Geometry)

Sine and Cosine

Spherical Geometry

Number Theory

Study of integers and integer-valued functions

Algebraic Integer

Algebraic Number

Apery's Constant

Catalan's Constant

Chinese Remainder Theorem

Composite Number

Continued Fraction

Coprime Integers

Diophantine Equation

Dirichlet Series

e (Euler's Number)

Euclidean Algorithm

Euler-Mascheroni Constant

Euler's Theorem

Euler's Totient Function

Fermat's Last Theorem

Fermat's Little Theorem

Fibonacci Number

Fundamental Theorem of Arithmetic

Greatest Common Divisor

Irrational Number

Khinchin's Constant

Least Common Multiple

Legendre Symbol

Modular Arithmetic

Modulo Operation

Pell's Equation

Prime Counting Function

Prime Number Theorem

Quadratic Reciprocity

Quadratic Residue

Rational Number

Riemann Hypothesis

Riemann Zeta Function

Transcendental Number

Statistics

Collection, analysis, and interpretation of data

Analysis of Variance

Bayesian Inference

Beta Distribution

Binomial Distribution

Central Limit Theorem

Chi-squared Distribution

Chi-squared Test

Conditional Probability

Confidence Interval

Cumulative Distribution Function

Exponential Distribution

Gamma Distribution

Geometric Distribution

Hypergeometric Distribution

Hypothesis Testing

Independence (Probability)

Interquartile Range

Joint Probability Distribution

Law of Large Numbers

Linear Regression

Logistic Regression

Marginal Distribution

Maximum Likelihood Estimation

Mode (Statistics)

Multiple Regression

Multivariate Normal Distribution

Negative Binomial Distribution

Normal Distribution

Null Hypothesis

Pearson Correlation Coefficient

Poisson Distribution

Probability Density Function

Probability Distribution

Random Variable

Range (Statistics)

Regression Analysis

Sampling Distribution

Spearman's Rank Correlation

Standard Deviation

Student's t-distribution

Student's t-test

Type I and Type II Errors

Uniform Distribution

Discrete Mathematics

Study of discrete mathematical structures

Adjacency Matrix

Axiom of Choice

Binomial Coefficient

Bipartite Graph

Boolean Algebra

Cantor's Diagonal Argument

Cardinal Number

Cartesian Product

Chromatic Number

Complement (Set Theory)

Connected Graph

Continuum Hypothesis

Cycle (Graph Theory)

Degree (Graph Theory)

Dijkstra's Algorithm

Edge (Graph Theory)

Equivalence Relation

Euler's Formula (Graph Theory)

Existential Quantification

Four Color Theorem

Generating Function

Godel's Incompleteness Theorems

Hamiltonian Path

Inclusion-Exclusion Principle

Intersection (Set Theory)

Logical Conjunction

Logical Disjunction

Material Implication

Mathematical Induction

Mathematical Proof

Partition (Number Theory)

Pascal's Triangle

Path (Graph Theory)

Pigeonhole Principle

Predicate Logic

Proof by Contradiction

Propositional Logic

Recurrence Relation

Relation (Mathematics)

Shortest Path Problem

Stirling Number

Tautology (Logic)

Tree (Graph Theory)

Union (Set Theory)

Universal Quantification

Vertex (Graph Theory)

Topology

Study of properties preserved under continuous deformation

Connected Space

Fundamental Group

Topological Space

Analysis

Rigorous study of limits, continuity, and infinite processes

Applied Mathematics

Application of mathematics to real-world problems

Bifurcation Theory

Bisection Method

Boundary Value Problem

Convex Optimization

Data Compression

Differential Equation

Digital Signature

Dynamic Programming

Dynamical System

Elliptic Curve Cryptography

Entropy (Information Theory)

Error Detection and Correction

Finite Difference Method

Finite Element Method

General Relativity

Genetic Algorithm

Gradient Descent

Hamilton's Equations

Homogeneous Differential Equation

Information Theory

Initial Value Problem

Integer Programming

Lagrangian Mechanics

Linear Differential Equation

Linear Programming

Lyapunov Exponent

Mathematical Optimization

Mathematical Physics

Maxwell's Equations

Monte Carlo Method

Mutual Information

Nash Equilibrium

Navier-Stokes Equations

Newton's Method

Numerical Analysis

Numerical Integration

Ordinary Differential Equation

Partial Differential Equation

Polynomial Interpolation

Prisoner's Dilemma

Public-key Cryptography

Quantum Mechanics

Root-finding Algorithm

RSA Cryptosystem

Runge-Kutta Methods

Schrodinger Equation

Separable Differential Equation

Shannon Entropy

Simplex Algorithm

Simulated Annealing

Special Relativity

Spline Interpolation

Stability Theory

Strange Attractor

Trapezoidal Rule