Wikipedia:Vital articles/Level 5/Mathematics

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Level 5 Sublists

Vital articles is a list of subjects for which Wikipedia should have corresponding high-quality articles. It serves as a centralized watchlist to track the status of Wikipedia's most essential articles. This is one of the sub-lists of the fifty thousand article Vital articles/Level 5 and is currently under construction.

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The progress bar is auto-updated via category count, and the symbols and article counts are updated daily by User:cewbot. Please read the FAQ before modifying the article list.

See also: People: Mathematicians

Quota 1,200 articles.

Total 1,213 articles.

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Mathematics

This section contains 1213 articles.

Basics

This section contains 100 articles.

  1. Mathematics (Level 1)
    1. Mathematician
      1. Fields Medal
    2. Pure mathematics (Level 4)
    3. Recreational mathematics
  2. Approximation
    1. Estimation
    2. Extrapolation
  3. Constant (mathematics)
  4. Mathematical constant (Level 4)
    1. Pi (Level 3)
    2. e (mathematical constant) (Level 3)
    3. Imaginary unit (Level 4)
    4. Golden ratio (Level 4)
    5. −1
    6. 0 (Level 3)
    7. 1 (Level 4)
    8. Square root of 2
    9. Euler's constant
    10. Feigenbaum constants
  5. Equation (Level 3)
    1. Equation solving (Level 4)
    2. Polynomial (Level 4)
      1. Monomial
      2. Binomial (polynomial)
      3. Trinomial
    3. Equality (mathematics) (Level 4)
  6. Infinity (Level 3)
    1. Transfinite number
  7. Mathematical model
  8. Mathematical notation
    1. Scientific notation (Level 4)
  9. Mathematical problem
    1. Hilbert's problems (Level 4)
    2. Mathematical puzzle
  10. Mathematical proof (Level 3)
    1. Formula (Level 4)
    2. Identity (mathematics)
    3. Theorem (Level 4)
      1. Corollary
      2. Lemma (mathematics)
    4. Conjecture (Level 4)
  11. Operation (mathematics)
    1. Order of operations (Level 4)
  12. Variable (mathematics) (Level 3)
  13. Recursion

Number systems

This section contains 20 articles.

  1. Number (Level 2)
  2. Natural number (Level 3)
  3. Integer (Level 3)
    1. Negative number (Level 4)
    2. Parity (mathematics) (Level 4)
    3. Sign (mathematics)
  4. Real number (Level 3)
    1. Normal number
  5. Complex number (Level 3)
    1. Gaussian integer
    2. Imaginary number (Level 4)
  6. Rational number (Level 4)
    1. Rate (mathematics)
    2. Ratio
    3. Repeating decimal
    4. Irrational number (Level 4)
  7. Algebraic number
    1. Transcendental number
    2. Constructible number
  8. Computable number

Number notation

This section contains 14 articles.

  1. Positional notation (Level 4)
  2. Numerical digit (Level 4)
  3. Decimal (Level 4)
    1. Decimal separator
  4. Numeral system
    1. Hindu–Arabic numeral system
      1. Arabic numerals (Level 3)
    2. Chinese numerals
    3. Egyptian numerals
    4. Maya numerals
    5. Roman numerals (Level 4)
  5. Binary number (Level 4)
  6. Hexadecimal
  7. Sexagesimal

Arithmetic

This section contains 20 articles.

  1. Arithmetic (Level 2)
  2. Counting
    1. Tally marks
  3. Addition (Level 4)
  4. Subtraction (Level 4)
  5. Multiplication (Level 4)
    1. Multiplicative inverse
    2. Multiplication table
    3. Product (mathematics)
  6. Division (mathematics) (Level 4)
    1. Euclidean algorithm (Level 4)
    2. Long division
    3. Division by zero
    4. Divisibility rule
  7. Fraction (Level 3)
    1. Percentage (Level 4)
    2. Continued fraction
    3. Egyptian fraction
  8. Modular arithmetic (Level 4)
    1. Modulo

Functions

See also Calculus and analysis This section contains 80 articles.

Functions: General

This section contains 34 articles.

  1. Function (mathematics) (Level 3)
  2. Algebraic function
  3. Function of a real variable
    1. Function of several real variables
    2. Vector-valued function
  4. Arithmetic function
    1. Additive function
    2. Multiplicative function
  5. Inverse function (Level 4)
  6. Implicit function
  7. Function composition (Level 4)
  8. Graph of a function (Level 4)
  9. Parametric equation (Level 4)
    1. Parameter
  10. Even and odd functions
  11. Piecewise function
  12. Bijection, injection and surjection
    1. Injective function
    2. Surjective function
    3. Bijection
  13. Domain of a function
  14. Range of a function
  15. Zero of a function
  16. Fixed point (mathematics)
    1. Fixed-point theorem
  17. Multivalued function
  18. Partial function
  19. Bounded function
  20. Real-valued function
  21. Analytic function
    1. Entire function
  22. Elliptic function
  23. Periodic function
  24. Map (mathematics)

Specific functions

This section contains 46 articles.

  1. Elementary function
  2. Rational function
    1. Linear function (calculus)
      1. Constant function
      2. Identity function
    2. Quadratic function
      1. Square (algebra)
    3. Cubic function
  3. Exponentiation (Level 3)
    1. Exponential function (Level 4)
    2. Exponential growth
    3. Gaussian function
  4. Logarithm (Level 3)
    1. Common logarithm
    2. Natural logarithm
    3. Binary logarithm
    4. Complex logarithm
  5. nth root (Level 4)
    1. Square root (Level 4)
    2. Cube root
  6. Trigonometric functions (Level 4)
    1. Sine and cosine
    2. Inverse trigonometric functions
  7. Hyperbolic functions (Level 4)
    1. Inverse hyperbolic functions
  8. Bessel function
  9. Floor and ceiling functions
  10. Gamma function (Level 4)
    1. Factorial (Level 4)
      1. Stirling's approximation
  11. Prime-counting function
    1. Euler's totient function
    2. Möbius function
    3. Riemann zeta function
  12. Weierstrass function
  13. Error function
  14. Step function
    1. Heaviside step function
    2. Rectangular function
    3. Sign function
  15. Dirac delta function
  16. Kronecker delta
  17. Absolute value
  18. Lambert W function
  19. Exponential integral
  20. Likelihood function

Geometry

This section contains 177 articles.

Geometry: General

This section contains 24 articles.

  1. Geometry (Level 2)
  2. Coordinate system (Level 4)
    1. Cartesian coordinate system (Level 4)
    2. Cylindrical coordinate system
    3. Polar coordinate system (Level 4)
    4. Spherical coordinate system
  3. Dimension (Level 4)
  4. Zero-dimensional space
    1. Point (geometry) (Level 4)
  5. One-dimensional space
    1. Line (geometry) (Level 3)
    2. Curve (Level 4)
  6. Direction (geometry)
  7. Congruence (geometry)
  8. Similarity (geometry)
  9. Transformation (function)
    1. Invariant (mathematics)
    2. Isometry
      1. Motion (geometry)
    3. Reflection (mathematics)
    4. Rotation (mathematics)
    5. Scaling (geometry)
    6. Shear mapping
    7. Translation (geometry)

Two-dimensional space

This section contains 43 articles.

  1. Two-dimensional space
  2. Euclidean plane (Level 4)
    1. Plane (mathematics) (Level 4)
    2. Coplanarity
  3. Angle (Level 3)
    1. Right angle (Level 4)
    2. Dihedral angle
    3. Internal and external angles
  4. Conic section (Level 4)
    1. Circle (Level 3)
      1. Circumference
      2. Radius
    2. Ellipse (Level 4)
    3. Parabola (Level 4)
    4. Hyperbola (Level 4)
  5. Cardioid
  6. Cycloid
    1. Brachistochrone curve
  7. Lemniscate
  8. Elliptic curve
  9. Catenary
  10. Parallel (geometry)
  11. Perpendicular
    1. Tangent
  12. Line–line intersection

Polygons

This section contains 18 articles.

  1. Polygon (Level 3)
  2. Triangle (Level 3)
    1. Equilateral triangle
    2. Isosceles triangle
    3. Reuleaux triangle
    4. Right triangle
  3. Quadrilateral (Level 4)
    1. Square (Level 4)
    2. Rectangle
    3. Parallelogram
      1. Rhombus
    4. Trapezoid
  4. Pentagon
  5. Hexagon
  6. Octagon
  7. Decagon
  8. Regular polygon
  9. Star polygon

Three-dimensional space

This section contains 25 articles.

  1. Three-dimensional space (Level 3)
  2. Solid geometry
    1. Shape (Level 4)
    2. Size
    3. Surface (mathematics)
      1. Surface of revolution
      2. Torus
  3. Cone
  4. Cylinder
  5. Möbius strip
  6. Sphere (Level 4)
  7. Solid angle
  8. Skew lines

Polyhedra

This section contains 12 articles.

  1. Polyhedron (Level 4)
  2. Regular polyhedron
    1. Platonic solid
  3. Cube (Level 4)
  4. Pyramid (geometry)
    1. Tetrahedron
  5. Octahedron
  6. Dodecahedron
    1. Regular dodecahedron
  7. Icosahedron
    1. Regular icosahedron
  8. Prism (geometry)

Four-dimensional space

This section contains 7 articles.

  1. Four-dimensional space
  2. Rotations in 4-dimensional Euclidean space
  3. 3-sphere
  4. 5-cell
  5. Tesseract
  6. 16-cell
  7. 24-cell

Trigonometry

This section contains 4 articles.

  1. Trigonometry (Level 3)
  2. Law of cosines
  3. Law of sines
  4. Unit circle

Topology

This section contains 21 articles.

  1. Topology (Level 3)
  2. Brouwer fixed-point theorem
  3. General topology (Level 4)
  4. Topological space (Level 4)
  5. Compact space (Level 4)
  6. Connected space
  7. Manifold (Level 4)
    1. Surface (topology)
    2. 3-manifold
    3. 4-manifold
    4. Differentiable manifold
  8. Open set (Level 4)
    1. Neighbourhood (mathematics)
  9. Homology (mathematics) (Level 4)
  10. Homeomorphism
  11. Homotopy (Level 4)
  12. Euler characteristic (Level 4)
  13. Knot theory (Level 4)
  14. Orientability
  15. Poincaré conjecture (Level 4)
  16. Winding number

Measurement

This section contains 10 articles.

  1. Area (Level 3)
    1. Surface area
  2. Volume (Level 3)
  3. Length (Level 4)
    1. Arc length
    2. Perimeter
  4. Height
  5. Distance (Level 4)
    1. Metric space (Level 4)
    2. Ball (mathematics)

Euclidean geometry

This section contains 7 articles.

  1. Euclidean geometry (Level 4)
    1. Euclidean space
    2. Convex set (Level 4)
    3. Pythagorean theorem (Level 4)
  2. Parallel postulate
  3. Straightedge and compass construction
    1. Squaring the circle

Non-Euclidean geometry

This section contains 14 articles.

  1. Non-Euclidean geometry (Level 4)
  2. Affine geometry
    1. Affine transformation
  3. Elliptic geometry
    1. Spherical geometry
    2. Stereographic projection
  4. Hyperbolic geometry
    1. Hyperbolic angle
    2. Hyperbolic triangle
  5. Inversive geometry
  6. Projective geometry
    1. Homography
    2. Projective plane
    3. Projective space

Fractals

This section contains 6 articles.

  1. Fractal (Level 4)
  2. Cantor set
  3. Julia set
  4. Koch snowflake
  5. Mandelbrot set
  6. Sierpiński triangle

Differential geometry

This section contains 6 articles.

  1. Differential geometry (Level 4)
  2. Curvature
  3. Riemannian geometry (Level 4)
    1. Riemannian manifold (Level 4)
  4. Systolic geometry
  5. Theorema Egregium

Other

This section contains 10 articles.

  1. Bisection
  2. Lattice (group)
    1. Minkowski's theorem
  3. Locus (mathematics)
    1. Field line
  4. Symmetry (Level 4)
    1. Symmetry (geometry)
    2. Symmetry in mathematics (Level 4)
  5. Analytic geometry (Level 4)
  6. Tessellation (Level 4)

Algebra

This section contains 110 articles.

Algebra: General

This section contains 2 articles.

  1. Algebra (Level 2)
  2. Algebraic expression

Elementary algebra

This section contains 9 articles.

  1. Elementary algebra (Level 4)
  2. Algebraic equation
    1. Linear equation (Level 4)
    2. Quadratic equation (Level 4)
      1. Quadratic formula
    3. Binomial theorem
    4. Fundamental theorem of algebra (Level 4)
  3. Factorization
  4. Horner's method

Linear algebra

This section contains 43 articles.

  1. Linear algebra (Level 3)
  2. Basis (linear algebra)
  3. Linear combination
  4. Linear independence
  5. Linear map
    1. Projection (linear algebra)
  6. System of linear equations
    1. Cramer's rule
    2. Gaussian elimination (Level 4)
    3. Gauss–Seidel method
    4. Jacobi method
    5. Successive over-relaxation
  7. Scalar (mathematics)
    1. Scalar multiplication
  8. Vector (mathematics and physics)
    1. Vector notation
  9. Tensor (Level 4)
    1. Einstein notation
    2. Metric tensor

Matrices

This section contains 11 articles.

  1. Matrix (mathematics) (Level 4)
  2. Matrix multiplication
  3. Transpose
  4. Determinant (Level 4)
  5. Eigenvalues and eigenvectors (Level 4)
  6. Rank (linear algebra)
    1. Rank–nullity theorem
  7. Diagonal matrix
  8. Identity matrix
  9. Triangular matrix
    1. LU decomposition

Vector spaces

This section contains 13 articles.

  1. Vector space (Level 4)
  2. Banach space
  3. Euclidean vector (Level 4)
  4. Magnitude (mathematics)
    1. Cross product (Level 4)
    2. Dot product (Level 4)
    3. Tensor product
  5. Inner product space
    1. Cauchy–Schwarz inequality
  6. Lie algebra
  7. Norm (mathematics)
    1. Triangle inequality
  8. Quaternion

Abstract algebra

This section contains 48 articles.

  1. Abstract algebra (Level 3)
  2. Algebraic structure
  3. Algebraic topology (Level 4)
    1. Sheaf (mathematics) (Level 4)
  4. Associative property (Level 4)
  5. Commutative algebra (Level 4)
  6. Commutative property (Level 4)
  7. Distributive property (Level 4)
  8. Galois theory (Level 4)
    1. Galois group
  9. Homogeneous polynomial
    1. Quadratic form
  10. Homological algebra (Level 4)
  11. Homomorphism
    1. Isomorphism (Level 4)
      1. Isomorphism theorems
    2. Kernel (algebra)
  12. Identity element
  13. Inverse element
  14. Module (mathematics) (Level 4)
  15. Monoid
  16. Representation theory (Level 4)

Group theory

This section contains 15 articles.

  1. Group theory (Level 4)
  2. Group (mathematics) (Level 4)
  3. Abelian group (Level 4)
  4. Alternating group
  5. Conjugacy class
  6. Cyclic group
  7. Fundamental group (Level 4)
  8. Group representation (Level 4)
  9. Lagrange's theorem (group theory)
  10. Lie group
  11. Modular group
  12. Normal subgroup
  13. Simple group
    1. Classification of finite simple groups
    2. Sporadic group

Ring theory

This section contains 11 articles.

  1. Ring theory (Level 4)
  2. Ring (mathematics) (Level 4)
  3. Algebra over a field
  4. Commutative ring (Level 4)
  5. Field (mathematics) (Level 4)
    1. Finite field
    2. Field extension
  6. Polynomial ring
    1. Hilbert's basis theorem
    2. Hilbert's Nullstellensatz
  7. Ideal (ring theory)

Other algebra topics

This section contains 8 articles.

  1. Affine space
  2. Algebraic geometry (Level 4)
    1. Algebraic variety (Level 4)
    2. Exterior algebra
    3. Modularity theorem
    4. Moduli space
  3. Inequality (mathematics) (Level 4)
  4. Resultant

Statistics and probability

This section contains 122 articles.

Probability

This section contains 48 articles.

  1. Probability (Level 3)
  2. Probability theory (Level 4)
  3. Probability space
    1. Event (probability theory)
      1. Independence (probability theory)
    2. Sample space
      1. Outcome (probability)
  4. Bayes' theorem (Level 4)
  5. Central limit theorem (Level 4)
  6. Chebyshev's inequality
  7. Conditional probability
  8. Covariance (Level 4)
    1. Coefficient of determination
    2. Correlation coefficient
  9. Law of large numbers (Level 4)
  10. Moment (mathematics)
    1. Expected value (Level 4)
    2. Variance (Level 4)
    3. Skewness
    4. Kurtosis
    5. Moment generating function
  11. Random variable (Level 4)
    1. Random walk
  12. Stochastic process (Level 4)
    1. Markov chain (Level 4)
      1. Viterbi algorithm
    2. Poisson point process
    3. Wiener process
  13. Monty Hall problem
  14. Randomness

Probability distributions

This section contains 18 articles.

  1. Probability distribution (Level 4)
  2. Cumulative distribution function
  3. Probability density function (Level 4)
  4. Probability mass function
Specific continuous probability distributions

This section contains 9 articles.

  1. Beta distribution
  2. Chi-squared distribution
  3. Continuous uniform distribution
  4. Exponential distribution (Level 4)
  5. F-distribution
  6. Gamma distribution
  7. Normal distribution (Level 4)
    1. Multivariate normal distribution
  8. Student's t-distribution
Specific discrete probability distributions

This section contains 5 articles.

  1. Bernoulli distribution
  2. Binomial distribution (Level 4)
  3. Discrete uniform distribution (Level 4)
  4. Geometric distribution
  5. Poisson distribution (Level 4)

Statistics

This section contains 74 articles.

  1. Statistics (Level 2)
  2. Autocorrelation
  3. Bayesian inference (Level 4)
    1. Maximum a posteriori estimation
  4. Bayesian statistics
    1. Credible interval
    2. Posterior probability
    3. Prior probability
  5. Coincidence
  6. Confidence interval
  7. Descriptive statistics
  8. Design of experiments (Level 4)
    1. Randomized controlled trial (Level 4)
    2. Factorial experiment
    3. A/B testing
  9. Estimator
  10. Frequentist inference
    1. Frequency (statistics)
  11. Index (statistics)
  12. Kriging
  13. Mathematical statistics
  14. Mean (Level 4)
    1. Arithmetic mean
    2. Geometric mean
    3. Harmonic mean
  15. Maximum likelihood estimation
    1. Expectation–maximization algorithm
  16. Median (Level 4)
  17. Meta-analysis (Level 4)
  18. Mode (statistics) (Level 4)
  19. Observational study (Level 4)
  20. Principal component analysis
  21. Sample mean and covariance
  22. Standard deviation (Level 4)
  23. Standard error (Level 4)
  24. Statistical inference
  25. Time series
  26. Type I and type II errors
  27. Analysis of variance
  28. Correlation does not imply causation
  29. Modifiable areal unit problem
  30. Ecological fallacy
  31. Modifiable temporal unit problem

Correlation

This section contains 7 articles.

  1. Correlation (Level 4)
  2. Regression analysis (Level 4)
    1. Least squares
      1. Ordinary least squares (Level 4)
      2. Non-linear least squares
    2. Linear regression
    3. Logistic regression

Statistical hypothesis test

This section contains 6 articles.

  1. Statistical hypothesis test (Level 4)
  2. Null hypothesis
  3. p-value (Level 4)
  4. Statistical significance
  5. Chi-squared test (Level 4)
  6. Student's t-test (Level 4)

Survey methodology

This section contains 7 articles.

  1. Survey methodology (Level 4)
  2. Statistical population (Level 4)
  3. Sampling (statistics) (Level 4)
    1. Monte Carlo method
    2. Margin of error
    3. Sample size determination
    4. Sampling error

Data and information visualization

This section contains 11 articles.

  1. Data and information visualization (Level 4)
  2. Box plot
  3. Candlestick chart
  4. Correlogram
  5. Histogram
  6. Bar chart
  7. Pie chart
  8. Radar chart
  9. Scatter plot
  10. Stem-and-leaf display
  11. Violin plot

Foundations

This section contains 150 articles.

  1. Foundations of mathematics

Mathematical logic

This section contains 32 articles.

  1. Mathematical logic (Level 4)
  2. Axiom (Level 4)
  3. Rule of inference
  4. Well-formed formula
    1. Atomic formula
  5. Higher-order logic
  6. Intuitionistic logic
  7. Type theory

Propositional logic

This section contains 17 articles.

  1. Propositional logic (Level 4)
  2. Boolean algebra (Level 4)
    1. De Morgan's laws
    2. Karnaugh map
    3. Truth table
  3. Logical connective
    1. If and only if
    2. Material conditional
    3. Negation
    4. Sheffer stroke
  4. Contradiction
    1. Reductio ad absurdum
  5. Contraposition
  6. Modus ponens
  7. Modus tollens
  8. Principle of explosion
  9. Tautology (logic)

First-order logic

This section contains 7 articles.

  1. First-order logic (Level 4)
  2. Free variables and bound variables
  3. Quantifier (logic)
    1. Existential quantification
    2. Universal quantification
  4. Prenex normal form
    1. Skolem normal form

Set theory

This section contains 40 articles.

  1. Set theory (Level 4)
    1. Naive set theory (Level 4)
      1. Russell's paradox (Level 4)
    2. Venn diagram (Level 4)
  2. Set (mathematics) (Level 3)
    1. Complement (set theory)
    2. Element of a set
    3. Empty set (Level 4)
    4. Intersection (set theory) (Level 4)
    5. Partition of a set
      1. Equivalence class
    6. Subset (Level 4)
      1. Closure (mathematics)
    7. Union (set theory) (Level 4)
    8. Universe (mathematics)
  3. Tuple
    1. Cartesian product
    2. Ordered pair
    3. Binary relation
      1. Reflexive relation
      2. Symmetric relation
      3. Transitive relation
      4. Equivalence relation (Level 4)
  4. Class (set theory)
  5. Multiset
  6. Mathematical structure
    1. Space (mathematics)
  7. Cardinality (Level 4)
    1. Cardinal number
    2. Aleph number
    3. Cantor's theorem
      1. Cantor's diagonal argument
    4. Cardinality of the continuum
    5. Continuum hypothesis
    6. Power set
  8. Ordinal number
    1. Transfinite induction
    2. Von Neumann universe
  9. Forcing (mathematics)
  10. Large cardinal

Axiomatic systems

This section contains 19 articles.

  1. Axiomatic system
  2. Zermelo–Fraenkel set theory
    1. Axiom of extensionality
    2. Axiom of regularity
    3. Axiom schema of specification
    4. Axiom of pairing
    5. Axiom of union
    6. Axiom schema of replacement
    7. Axiom of infinity
    8. Axiom of power set
  3. Axiom of choice (Level 4)
    1. Banach–Tarski paradox
    2. Well-ordering theorem
    3. Zorn's lemma
  4. New Foundations
  5. Peano axioms
    1. Mathematical induction (Level 4)
  6. Hilbert's axioms
  7. Tarski's axioms

Computability theory

This section contains 22 articles.

  1. Computability theory (Level 4)
    1. Church–Turing thesis
  2. Model of computation
    1. Combinatory logic
    2. Lambda calculus
    3. Turing machine
  3. Computable function (Level 4)
    1. General recursive function
      1. Primitive recursive function
      2. Mu operator
    2. Gödel numbering
  4. Decision problem
    1. Entscheidungsproblem
      1. Halting problem
      2. Rice's theorem
      3. Turing's proof
      4. Universal Turing machine
    2. Computably enumerable set
      1. Computable set
  5. Oracle machine
    1. Turing reduction
      1. Turing degree

Proof theory

This section contains 2 articles.

  1. Proof theory
  2. Gödel's incompleteness theorems (Level 4)

Model theory

This section contains 12 articles.

  1. Model theory
    1. Compactness theorem
    2. Gödel's completeness theorem
    3. Löwenheim–Skolem theorem
      1. Skolem's paradox
  2. Structure (mathematical logic)
    1. Elementary equivalence
    2. Signature (logic)
    3. Type (model theory)
    4. Ultraproduct
  3. Theory (mathematical logic)
    1. Quantifier elimination

Category theory

This section contains 22 articles.

  1. Category theory (Level 4)
  2. Commutative diagram
    1. Five lemma
    2. Snake lemma
  3. Morphism
  4. Category (mathematics)
    1. Cartesian closed category
    2. Concrete category
    3. Opposite category
    4. Subcategory
  5. Functor
    1. Adjoint functors
    2. Forgetful functor
    3. Hom functor
    4. Yoneda lemma
  6. Universal property
    1. Free object
    2. Limit (category theory)
      1. Coproduct
      2. Initial and terminal objects
      3. Product (category theory)
  7. Natural transformation

Discrete mathematics

This section contains 123 articles.

  1. Discrete mathematics (Level 3)

Combinatorics

This section contains 23 articles.

  1. Combinatorics (Level 4)
    1. Algebraic combinatorics
    2. Enumerative combinatorics
    3. Ramsey theory
      1. Ramsey's theorem
  2. Combinatorial principles
    1. Addition principle
    2. Rule of product
    3. Inclusion–exclusion principle
    4. Pigeonhole principle
  3. Double counting (proof technique)
  4. Latin square
    1. Mutually orthogonal Latin squares
  5. Twelvefold way
    1. Combination (Level 4)
      1. Binomial coefficient
      2. Pascal's triangle
    2. Permutation (Level 4)
      1. Partial permutation
    3. Stirling number
      1. Stirling numbers of the first kind
      2. Stirling numbers of the second kind
      3. Lah number

Graph theory

This section contains 76 articles.

  1. Graph theory (Level 4)
  2. Clique (graph theory)
    1. Clique problem
  3. Graph coloring
    1. Bipartite graph
    2. Chromatic polynomial
    3. Four color theorem
    4. Vizing's theorem
  4. Connectivity (graph theory)
    1. Bridge (graph theory)
    2. Component (graph theory)
    3. Tree (graph theory)
      1. Kruskal's algorithm
      2. Prim's algorithm
  5. Degree (graph theory)
    1. Regular graph
      1. Cage (graph theory)
      2. Coxeter graph
  6. Edge cover
    1. FKT algorithm
  7. Flow network
    1. Ford–Fulkerson algorithm
    2. Max-flow min-cut theorem
    3. Maximum flow problem
    4. Minimum-cost flow problem
    5. Push–relabel maximum flow algorithm
  8. Graph (discrete mathematics) (Level 4)
    1. Complete graph
    2. Directed graph
    3. Multigraph
  9. Graph homomorphism
    1. Edge contraction
      1. Graph minor
    2. Graph automorphism
      1. Cayley graph
    3. Graph isomorphism
      1. Graph isomorphism problem
    4. Homeomorphism (graph theory)
  10. Hypergraph
  11. Intersection graph
  12. Line graph
  13. Matching (graph theory)
    1. Matching polynomial
      1. Hosoya index
    2. Maximum-cardinality matching
      1. Blossom algorithm
      2. Kőnig's theorem (graph theory)
      3. Vertex cover
  14. Planar graph
    1. Crossing number (graph theory)
      1. Three utilities problem
      2. Turán's brick factory problem
    2. Kuratowski's theorem
  15. Snark (graph theory)
    1. Generalized Petersen graph
      1. Petersen graph
  16. Spectral graph theory
    1. Adjacency matrix
    2. Degree matrix
    3. Laplacian matrix

Paths in graphs

This section contains 16 articles.

  1. Path (graph theory)
  2. Cycle (graph theory)
    1. Directed acyclic graph
    2. Girth (graph theory)
  3. Eulerian path
    1. Handshaking lemma
    2. Seven Bridges of Königsberg
  4. Hamiltonian path
    1. Hamiltonian path problem
    2. Held–Karp algorithm
    3. Herschel graph
    4. Travelling salesman problem
  5. Shortest path problem
    1. Bellman–Ford algorithm
    2. Dijkstra's algorithm
    3. Floyd–Warshall algorithm

Order theory

This section contains 23 articles.

  1. Order theory
  2. Domain theory
  3. Preorder
  4. Partially ordered set
    1. Antichain
    2. Antisymmetric relation
    3. Filter (mathematics)
      1. Ultrafilter
    4. Hasse diagram
    5. Ideal (order theory)
    6. Lattice (order)
      1. Boolean algebra (structure)
      2. Join and meet
  5. Stable matching problem
    1. Gale–Shapley algorithm
    2. Stable roommates problem
  6. Total order
    1. Connected relation
    2. Well-order
      1. Well-founded relation
  7. Upper and lower bounds
    1. Greatest element and least element
    2. Infimum and supremum

Calculus and analysis

See also Functions This section contains 196 articles.

Basics

This section contains 11 articles.

  1. Calculus (Level 3)
  2. Limit (mathematics) (Level 3)
    1. Limit of a function (Level 4)
    2. Indeterminate form
  3. Fundamental theorem of calculus (Level 4)
  4. Continuous function (Level 4)
  5. Infinitesimal
    1. Differential (mathematics)
  6. Series expansion
  7. Linear approximation
    1. Linearization

Differential calculus

This section contains 15 articles.

  1. Differential calculus (Level 4)
  2. Differentiable function
  3. Differential operator
  4. Derivative (Level 4)
    1. Second derivative
    2. Time derivative
  5. Differentiation rules
    1. Product rule
    2. Chain rule
    3. Power rule
    4. Quotient rule
    5. Differentiation of trigonometric functions
  6. L'Hôpital's rule
  7. Taylor's theorem
  8. Related rates

Integral calculus

This section contains 12 articles.

  1. Integral (Level 4)
  2. Antiderivative
  3. Lebesgue integral
  4. Numerical integration (Level 4)
  5. Riemann integral
  6. Constant of integration
  7. Improper integral
  8. Integration by parts
  9. Integration by substitution
  10. Jensen's inequality
  11. Limits of integration
  12. Riemann sum

Multivariable and vector calculus

This section contains 30 articles.

  1. Multivariable calculus (Level 4)
  2. Vector calculus (Level 4)
    1. Ricci calculus
  3. Multiple integral (Level 4)
  4. Iterated integral
    1. Fubini's theorem
  5. Partial derivative (Level 4)
  6. Derivative (multivariable calculus)
  7. Directional derivative
  8. Differential form
  9. Vector field
    1. Conservative vector field
    2. Solenoidal vector field
  10. Del (Level 4)
    1. Gradient
    2. Divergence
    3. Curl (mathematics)
    4. Laplace operator
  11. Poisson's equation
    1. Laplace's equation (Level 4)
  12. Line integral
  13. Surface integral
  14. Volume integral
  15. Stokes' theorem
    1. Green's theorem
    2. Gradient theorem
    3. Divergence theorem
  16. Jacobian matrix and determinant
  17. Lagrange multiplier
  18. Helmholtz decomposition

Differential equations

This section contains 42 articles.

  1. Differential equation (Level 4)
  2. Ordinary differential equation (Level 4)
  3. Partial differential equation (Level 4)
    1. Parabolic partial differential equation
    2. Hyperbolic partial differential equation
    3. Elliptic partial differential equation
  4. Linear differential equation
  5. Homogeneous differential equation
  6. Boundary value problem
  7. Convolution
  8. Separation of variables
  9. Integrating factor
  10. Numerical methods for ordinary differential equations
    1. Euler method
    2. Runge–Kutta methods
    3. Shooting method
  11. Numerical methods for partial differential equations
    1. Crank–Nicolson method
    2. Finite element method
    3. Method of lines
  12. Dirichlet problem
  13. Elliptic operator
  14. System of differential equations

Dynamical systems

This section contains 19 articles.

  1. Dynamical systems theory (Level 4)
  2. Dynamical system (Level 4)
    1. Linear dynamical system
    2. Nonlinear system
  3. Phase space
  4. Stability theory
  5. Chaos theory (Level 4)
    1. Bifurcation theory
    2. Butterfly effect
    3. Edge of chaos
  6. Multibody system
    1. Three-body problem
  7. Initial condition
  8. Conserved quantity
  9. Dynamical system simulation
  10. Flow (mathematics)
  11. Lyapunov exponent
  12. Attractor
    1. Limit cycle

Sequences and series

This section contains 19 articles.

  1. Sequence (Level 4)
    1. Limit of a sequence (Level 4)
    2. Generating function
  2. Series (mathematics) (Level 3)
    1. Summation
  3. Taylor series (Level 4)
  4. Laurent series
  5. Convergent series
    1. Absolute convergence
    2. Cauchy sequence
    3. Convergence tests
    4. Radius of convergence
  6. Divergent series
  7. Geometric series
  8. Power series
  9. Dirichlet series
  10. Binomial series
  11. Harmonic series (mathematics)
  12. Multipole expansion

Mathematical analysis

This section contains 67 articles.

  1. Mathematical analysis (Level 3)
  2. Approximation theory (Level 4)
  3. Numerical analysis (Level 4)
  4. Functional analysis (Level 4)
    1. Hilbert space (Level 4)
    2. Lp space
      1. Hölder's inequality
    3. Operator theory
      1. Operator (mathematics)
    4. Sequence space
    5. Uniform convergence
  5. Measure (mathematics)
  6. Calculus of variations (Level 4)
  7. Asymptotic analysis
    1. Asymptote
  8. Interpolation

Real analysis

This section contains 19 articles.

  1. Real analysis (Level 4)
  2. Number line
    1. Completeness of the real numbers
    2. Extended real number line
    3. Interval (mathematics)
  3. Extreme value theorem
  4. Intermediate value theorem
    1. Root-finding algorithm
      1. Newton's method
      2. Bisection method
      3. Regula falsi
      4. Secant method
  5. Mean value theorem
  6. Squeeze theorem
  7. Critical point (mathematics)
    1. Stationary point
      1. Maximum and minimum
      2. Saddle point
    2. Inflection point

Complex analysis

This section contains 22 articles.

  1. Complex analysis (Level 4)
  2. Complex plane
    1. Riemann sphere
  3. Contour integration
    1. Cauchy's integral formula (Level 4)
    2. Cauchy's integral theorem
  4. Euler's formula (Level 4)
    1. De Moivre's formula
  5. Euler's identity (Level 4)
  6. Holomorphic function (Level 4)
  7. Riemann surface (Level 4)
  8. Liouville's theorem (complex analysis)
  9. Cauchy–Riemann equations
  10. Cauchy principal value
  11. Conformal map
  12. Singularity (mathematics)
    1. Zeros and poles
  13. Picard theorem
  14. Residue (complex analysis)
    1. Residue theorem
  15. Branch point
  16. Root of unity

Harmonic analysis

This section contains 10 articles.

  1. Harmonic analysis (Level 4)
  2. Fourier analysis (Level 4)
    1. Fourier series (Level 4)
    2. Fourier transform (Level 4)
      1. Convolution theorem
      2. Fast Fourier transform
  3. Laplace transform (Level 4)
  4. Harmonic function
  5. Potential theory
  6. Wavelet

Number theory

This section contains 55 articles.

  1. Number theory (Level 3)

Divisibility

This section contains 21 articles.

  1. Divisor
  2. Greatest common divisor
  3. Least common multiple
    1. Lowest common denominator
  4. Composite number
  5. Fundamental theorem of arithmetic (Level 4)
  6. Highly composite number

Prime numbers

This section contains 14 articles.

  1. Prime number (Level 3)
    1. Fermat number
    2. Mersenne prime
    3. Semiprime
    4. Twin prime
  2. Coprime integers
    1. abc conjecture
  3. Euclid's theorem (Level 4)
  4. p-adic number
  5. Primality test
    1. AKS primality test
    2. Pseudoprime
    3. Sieve of Eratosthenes
  6. Prime number theorem (Level 4)

Sums and products

This section contains 7 articles.

  1. Aliquot sum
    1. Perfect number
  2. Collatz conjecture
  3. Integer partition
    1. Goldbach's conjecture
    2. Young tableau
  4. Magic square

Modular arithmetic

This section contains 8 articles.

  1. Chinese remainder theorem
  2. Discrete logarithm
  3. Fermat's little theorem
  4. Quadratic residue
    1. Jacobi symbol
    2. Legendre symbol
    3. Quadratic reciprocity
  5. Wilson's theorem

Sequences

This section contains 7 articles.

  1. Arithmetic progression
    1. Dirichlet's theorem on arithmetic progressions
  2. Bell number
  3. Catalan number
  4. Lucky number
  5. Recurrence relation
    1. Fibonacci sequence (Level 4)

Diophantine equations

This section contains 4 articles.

  1. Diophantine equation (Level 4)
  2. Extended Euclidean algorithm
    1. Bézout's identity
  3. Fermat's Last Theorem (Level 4)

Subdisciplines of number theory

This section contains 7 articles.

  1. Algebraic number theory (Level 4)
    1. Algebraic number field (Level 4)
    2. Class field theory (Level 4)
  2. Analytic number theory (Level 4)
    1. Dirichlet character
    2. Möbius inversion formula
    3. Riemann hypothesis (Level 4)

Applied mathematics

This section contains 45 articles.

  1. Applied mathematics (Level 4)
    1. Control theory (Level 4)
    2. Decision theory
    3. Music and mathematics

Game theory

This section contains 18 articles.

  1. Game theory (Level 4)
  2. Extensive-form game
  3. Information set (game theory)
    1. Common knowledge (logic)
    2. Perfect information
  4. Normal-form game
    1. Battle of the sexes (game theory)
    2. Prisoner's dilemma
    3. Zero-sum game
  5. Repeated game
  6. Strategy (game theory)
    1. Minimax
    2. Nash equilibrium
    3. Strategic dominance

Social choice theory

This section contains 4 articles.

  1. Social choice theory
  2. Condorcet paradox
  3. Arrow's impossibility theorem
  4. Gibbard–Satterthwaite theorem

Information theory

This section contains 7 articles.

  1. Information theory (Level 4)
    1. Entropy (information theory)
  2. Coding theory (Level 4)
    1. Data compression (Level 4)
    2. Error detection and correction (Level 4)
    3. Hamming code
    4. Reed–Solomon error correction

Optimization

This section contains 16 articles.

  1. Mathematical optimization (Level 4)
  2. Dynamic programming
  3. Gradient descent
  4. Linear programming (Level 4)
    1. Duality (optimization)
    2. Feasible region
    3. Ellipsoid method
    4. Simplex algorithm
  5. Loss function
  6. Nonlinear programming (Level 4)
    1. Karush–Kuhn–Tucker conditions
  7. Transportation theory (mathematics)
    1. Assignment problem
    2. Hungarian algorithm
  8. Operations research (Level 4)
    1. Optimal facility location

Theoretical computer science

This section contains 55 articles. For topics in applied computer science, see Technology: Computing and information technology

  1. Theoretical computer science (Level 4)
  2. Abstract machine (Level 4)
    1. Nondeterministic Turing machine
  3. Computation
  4. Theory of computation (Level 4)

Algorithms

This section contains 16 articles.

  1. Algorithm (Level 3)
  2. Analysis of algorithms
    1. Big O notation
    2. Deterministic algorithm
    3. Divide-and-conquer algorithm
  3. Cache replacement policies
  4. Search algorithm
    1. Binary search
    2. Breadth-first search
    3. Brute-force search
    4. Depth-first search
    5. String-searching algorithm
  5. Sorting algorithm
    1. Heapsort
    2. Merge sort
    3. Quicksort

Automata theory

This section contains 7 articles.

  1. Automata theory
    1. Cellular automaton
      1. Conway's Game of Life
    2. Finite-state machine
    3. Pushdown automaton
  2. Formal language (Level 4)
    1. Chomsky hierarchy

Complexity theory

This section contains 12 articles.

  1. Computational complexity theory (Level 4)
    1. Blum axioms
    2. Constructible function
  2. Kolmogorov complexity
  3. Space complexity
  4. Time complexity
    1. NP (complexity)
    2. P (complexity)
    3. P versus NP problem (Level 4)
      1. Boolean satisfiability problem
      2. NP-hardness
    4. Time hierarchy theorem

Data structures and types

This section contains 15 articles.

  1. Abstract data type
    1. Associative array
    2. Graph (abstract data type)
    3. Queue (abstract data type)
    4. Stack (abstract data type)
  2. Data model
  3. Data structure (Level 4)
    1. Hash table
    2. Heap (data structure)
    3. Linked list
    4. Array (data structure)
    5. Tree (abstract data type)
      1. B-tree
      2. Binary search tree
      3. Red–black tree