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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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See also: People: Mathematicians

Quota 1,200 articles.

Total 1,204 articles.

Class #Articles
FA 6
GA 36
B 338
C 543
LIST 1
FFA 12
DGA 13
FFLC 1
Start 278
Stub 1

Basics

[edit]

This section contains 121 articles.

  1. Mathematics (Level 1)
    1. Mathematical notation
      1. Scientific notation (Level 4)
    2. Mathematician
      1. Fields Medal
    3. Pure mathematics (Level 4)
    4. Recreational mathematics
  2. Approximation
    1. Estimation
    2. Extrapolation
  3. Arithmetic (Level 2)
    1. Counting
      1. Cardinal number
      2. Tally marks
    2. Addition (Level 4)
      1. Plus and minus signs
    3. Subtraction (Level 4)
    4. Multiplication (Level 4)
      1. Multiplicative inverse
      2. Multiplication sign
      3. Multiplication table
      4. Product (mathematics)
    5. Division (mathematics) (Level 4)
      1. Division sign
      2. Euclidean algorithm (Level 4)
      3. Long division
      4. Division by zero
      5. Divisibility rule
    6. Fraction (Level 3)
      1. Percentage (Level 4)
        1. Percent sign
      2. Continued fraction
      3. Egyptian fraction
    7. Modular arithmetic (Level 4)
      1. Modulo
    8. Divisor
      1. Greatest common divisor
      2. Lowest common denominator
    9. Multiple (mathematics)
      1. Least common multiple
  4. Constant (mathematics) (Level 4)
    1. Mathematical constant
    2. Pi (Level 3)
    3. e (mathematical constant) (Level 3)
    4. Imaginary unit (Level 4)
    5. Golden ratio (Level 4)
    6. −1 (Level 4)
    7. 0 (Level 3)
    8. One half (½)
    9. 1 (Level 4)
    10. 2
    11. 3
    12. 4
    13. 5
    14. 6
    15. 7
    16. 8
    17. 9
    18. 10
    19. 100
    20. 1000 (number)
    21. Square root of 2
    22. Euler's constant
    23. Feigenbaum constants
  5. Equation (Level 3)
    1. Equation solving (Level 4)
    2. Polynomial (Level 4)
      1. Monomial
      2. Binomial (polynomial)
      3. Trinomial
  6. Infinity (Level 3)
    1. Infinity symbol
    2. Transfinite number
  7. Mathematical model
  8. Mathematical problem
    1. Hilbert's problems (Level 4)
    2. Mathematical puzzle
  9. Mathematical proof (Level 3)
    1. Formula (Level 4)
    2. Identity (mathematics)
    3. Theorem (Level 4)
      1. Corollary
      2. Lemma (mathematics)
    4. Conjecture (Level 4)
  10. Number (Level 2)
    1. Natural number (Level 3)
    2. Integer (Level 3)
      1. Negative number (Level 4)
      2. Parity (mathematics) (Level 4)
      3. Sign (mathematics)
    3. Real number (Level 3)
    4. Complex number (Level 3)
      1. Gaussian integer
    5. Rational number (Level 4)
      1. Rate (mathematics)
      2. Ratio
      3. Repeating decimal
    6. Irrational number (Level 4)
    7. Imaginary number (Level 4)
    8. Algebraic number
    9. Transcendental number
    10. Constructible number
    11. Computable number
    12. Normal number
  11. Operation (mathematics)
    1. Order of operations (Level 4)
  12. Positional notation (Level 4)
    1. Numerical digit (Level 4)
    2. Decimal (Level 4)
      1. Decimal separator
    3. 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)
    4. Binary number (Level 4)
    5. Hexadecimal
    6. Sexagesimal
  13. Variable (mathematics) (Level 3)

Functions

[edit]

This section contains 89 articles.

Functions: General

[edit]

This section contains 41 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 (Level 4)
  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. Critical point (mathematics)
    1. Stationary point
      1. Maximum and minimum
      2. Saddle point
    2. Inflection point
  18. Limit of a function (Level 4)
  19. Multivalued function
  20. Partial function
  21. Bounded function
  22. Real-valued function
  23. Analytic function
    1. Entire function
  24. Elliptic function
  25. Periodic function
  26. Curvature
  27. Map (mathematics)

Specific functions

[edit]

This section contains 48 articles.

  1. Elementary function
  2. Rational function
    1. Linear function (calculus)
      1. Negation
      2. Constant function
      3. 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. Knuth's up-arrow notation
  4. Logarithm (Level 3)
    1. Common logarithm
    2. Natural logarithm
    3. Binary logarithm
    4. Complex logarithm
  5. nth root (Level 3)
    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

[edit]

This section contains 171 articles.

Geometry: General

[edit]

This section contains 23 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. Congruence (geometry)
  7. Similarity (geometry)
  8. 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

[edit]

This section contains 41 articles.

  1. Euclidean plane (Level 4)
    1. Plane (mathematics) (Level 4)
    2. Coplanarity
  2. Angle (Level 3)
    1. Right angle (Level 4)
    2. Dihedral angle
    3. Internal and external angles
  3. Polygon (Level 3)
    1. Triangle (Level 3)
      1. Equilateral triangle
      2. Isosceles triangle
      3. Reuleaux triangle
      4. Right triangle
    2. Quadrilateral (Level 4)
      1. Square (Level 4)
      2. Rectangle
      3. Parallelogram
        1. Rhombus
      4. Trapezoid
    3. Pentagon
    4. Hexagon
    5. Octagon
    6. Decagon
    7. Regular polygon
  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

Three-dimensional space

[edit]

This section contains 24 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. Sphere (Level 4)
  6. Polyhedron (Level 4)
    1. Regular polyhedron
    2. 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)
  7. Solid angle
  8. Skew lines

Four-dimensional space

[edit]

This section contains 8 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
  8. 120-cell

Trigonometry

[edit]

This section contains 4 articles.

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

Topology

[edit]

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. Manifold (Level 4)
    1. Surface (topology)
    2. 3-manifold
    3. 4-manifold
    4. Differentiable manifold
  7. Open set (Level 4)
    1. Clopen set
    2. Neighbourhood (mathematics)
  8. Homology (mathematics) (Level 4)
  9. Homeomorphism
  10. Homotopy (Level 4)
  11. Euler characteristic (Level 4)
  12. Knot theory (Level 4)
  13. Orientability
  14. Poincaré conjecture (Level 4)
  15. Winding number

Measurement

[edit]

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

[edit]

This section contains 6 articles.

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

Non-Euclidean geometry

[edit]

This section contains 14 articles.

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

Other

[edit]

This section contains 20 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. Differential geometry (Level 4)
    1. Riemannian geometry (Level 4)
    2. Systolic geometry
    3. Theorema Egregium
  7. Fractal (Level 4)
    1. Cantor set
    2. Julia set
    3. Koch snowflake
    4. Mandelbrot set
    5. Sierpiński triangle
  8. Tessellation (Level 4)

Algebra

[edit]

This section contains 104 articles.

Algebra: General

[edit]

This section contains 2 articles.

  1. Algebra (Level 3)
  2. Algebraic expression

Elementary algebra

[edit]

This section contains 6 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

Linear algebra

[edit]

This section contains 42 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. Matrix (mathematics) (Level 4)
    1. Matrix addition
    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
  8. Scalar (mathematics)
    1. Scalar multiplication
  9. Vector (mathematics and physics)
    1. Vector notation
  10. Vector space (Level 4)
    1. Banach space
    2. Euclidean vector (Level 4)
    3. Magnitude (mathematics)
      1. Cross product (Level 4)
      2. Dot product (Level 4)
      3. Tensor product
    4. Inner product space
    5. Lie algebra
    6. Norm (mathematics)
      1. Triangle inequality
  11. Tensor (Level 4)
    1. Einstein notation
    2. Metric tensor

Abstract algebra

[edit]

This section contains 42 articles.

  1. Abstract algebra (Level 4)
  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. Field (mathematics) (Level 4)
    1. Finite field
    2. Field extension
  9. Fundamental theorem of algebra (Level 4)
  10. Galois theory (Level 4)
  11. Group (mathematics) (Level 4)
    1. Abelian group (Level 4)
    2. Classification of finite simple groups (Level 4)
    3. Fundamental group (Level 4)
    4. Galois group
    5. Group representation (Level 4)
    6. Group theory (Level 4)
      1. Conjugacy class
      2. Lagrange's theorem (group theory)
    7. Lie group
    8. Modular group
    9. Normal subgroup
  12. Homogeneous polynomial
    1. Quadratic form
  13. Homological algebra (Level 4)
  14. Homomorphism
    1. Isomorphism (Level 4)
      1. Isomorphism theorems
    2. Kernel (algebra)
  15. Module (mathematics) (Level 4)
  16. Representation theory (Level 4)
  17. Ring theory (Level 4)
    1. Algebra over a field
    2. Commutative ring (Level 4)
    3. Polynomial ring
      1. Hilbert's basis theorem
      2. Hilbert's Nullstellensatz
    4. Ring (mathematics) (Level 4)
      1. Ideal (ring theory)

Other algebra topics

[edit]

This section contains 12 articles.

  1. Affine space
  2. Algebraic geometry (Level 4)
    1. Algebraic variety (Level 4)
    2. Exterior algebra
    3. Moduli space
  3. Equality (mathematics)
  4. Horner's method
  5. Inequality (mathematics) (Level 4)
    1. Cauchy–Schwarz inequality
    2. Hölder's inequality
    3. Jensen's inequality
  6. Resultant

Statistics and probability

[edit]

This section contains 100 articles.

Statistics

[edit]

This section contains 60 articles.

  1. Statistics (Level 2)
  2. Bayesian inference (Level 4)
    1. Maximum a posteriori estimation
  3. Bayesian statistics
    1. Credible interval
    2. Posterior probability
    3. Prior probability
  4. Confidence interval
  5. Correlation (Level 4)
    1. Regression analysis (Level 4)
      1. Least squares
        1. Ordinary least squares (Level 4)
        2. Non-linear least squares
      2. Linear regression
      3. Logistic regression
  6. Data and information visualization (Level 4)
    1. Box plot
    2. Histogram
    3. Bar chart
    4. Pie chart
    5. Scatter plot
  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. Mathematical statistics
  12. Mean (Level 4)
    1. Arithmetic mean
    2. Geometric mean
    3. Harmonic mean
  13. Maximum likelihood estimation
    1. Expectation–maximization algorithm
  14. Median (Level 4)
  15. Meta-analysis (Level 4)
  16. Mode (statistics) (Level 4)
  17. Observational study (Level 4)
  18. Principal component analysis
  19. Sample mean and covariance
  20. Standard deviation (Level 4)
  21. Standard error (Level 4)
  22. Statistical hypothesis test (Level 4)
    1. p-value (Level 4)
    2. Statistical significance
    3. Chi-squared test (Level 4)
    4. Student's t-test (Level 4)
  23. Statistical inference
  24. Survey methodology (Level 4)
    1. Statistical population (Level 4)
    2. Sampling (statistics) (Level 4)
      1. Monte Carlo method
      2. Margin of error
      3. Sample size determination
      4. Sampling error
  25. Time series
  26. Type I and type II errors
  27. Analysis of variance

Probability

[edit]

This section contains 40 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. Conditional probability
  7. Covariance (Level 4)
  8. Law of large numbers (Level 4)
  9. Moment (mathematics)
    1. Expected value (Level 4)
    2. Variance (Level 4)
    3. Skewness
    4. Kurtosis
    5. Moment-generating function
  10. Probability distribution (Level 4)
    1. Cumulative distribution function
    2. Probability density function (Level 4)
      1. Chi-squared distribution
      2. Continuous uniform distribution
      3. Exponential distribution (Level 4)
      4. Normal distribution (Level 4)
    3. Probability mass function
      1. Binomial distribution (Level 4)
      2. Discrete uniform distribution (Level 4)
      3. Geometric distribution
      4. Poisson distribution (Level 4)
    4. Student's t-distribution
  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

Foundations

[edit]

This section contains 154 articles.

  1. Foundations of mathematics

Mathematical logic

[edit]

This section contains 32 articles.

  1. Mathematical logic (Level 4)
    1. Axiom (Level 4)
      1. Axiom schema
    2. Rule of inference
    3. Well-formed formula
      1. Atomic formula
  2. Propositional calculus (Level 4)
    1. Boolean algebra (Level 4)
      1. De Morgan's laws
      2. Karnaugh map
      3. Truth table
    2. Logical connective
      1. Material conditional
      2. Sheffer stroke
    3. Contraposition
    4. If and only if
    5. Modus ponens
    6. Modus tollens
    7. Principle of explosion
    8. Proof by contradiction
  3. First-order logic (Level 4)
    1. Free variables and bound variables
    2. Quantifier (logic)
      1. Existential quantification
      2. Universal quantification
    3. Prenex normal form
      1. Skolem normal form
    4. Arithmetical hierarchy
      1. Analytical hierarchy
  4. Higher-order logic
  5. Intuitionistic logic
  6. Type theory

Set theory

[edit]

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 (mathematics)
    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
      1. Multiset
      2. Pointed set
    3. Binary relation
      1. Reflexive relation
      2. Symmetric relation
      3. Transitive relation
      4. Equivalence relation (Level 4)
  4. Class (set theory)
    1. Indexed family
  5. Mathematical structure
    1. Space (mathematics)
  6. Cardinality
    1. Aleph number
    2. Cantor's theorem (Level 4)
      1. Cantor's diagonal argument
    3. Cardinality of the continuum
    4. Continuum hypothesis
      1. Forcing (mathematics)
    5. Power set
  7. Ordinal number
    1. Transfinite induction
    2. Von Neumann universe

Axiomatic systems

[edit]

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

[edit]

This section contains 23 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. μ operator
    2. Gödel numbering
      1. Gödel's incompleteness theorems (Level 4)
  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

Model theory

[edit]

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

[edit]

This section contains 27 articles.

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

Discrete mathematics

[edit]

This section contains 126 articles.

  1. Discrete mathematics (Level 4)

Combinatorics

[edit]

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. 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
  5. Latin square
    1. Mutually orthogonal Latin squares

Graph theory

[edit]

This section contains 79 articles.

  1. Graph theory (Level 4)
    1. Graph (discrete mathematics) (Level 4)
      1. Complete graph
      2. Degree (graph theory)
      3. Directed graph
      4. Multigraph
    2. Hypergraph
  2. Clique (graph theory)
    1. Bipartite graph
    2. Clique problem
    3. Graph coloring
      1. Chromatic polynomial
      2. Four color theorem
      3. Vizing's theorem
    4. Regular graph
      1. Cage (graph theory)
      2. Coxeter graph
  3. Connectivity (graph theory)
    1. Bridge (graph theory)
    2. Component (graph theory)
    3. Tree (graph theory)
      1. Kruskal's algorithm
      2. Prim's algorithm
  4. 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
  5. 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)
    5. Intersection graph
    6. Line graph
  6. 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
    3. Rainbow matching
  7. Edge cover
    1. FKT algorithm
  8. Path (graph theory)
    1. Cycle (graph theory)
      1. Directed acyclic graph
      2. Girth (graph theory)
    2. Eulerian path
      1. BEST theorem
      2. Handshaking lemma
      3. Seven Bridges of Königsberg
    3. Hamiltonian path
      1. Hamiltonian path problem
      2. Held–Karp algorithm
      3. Herschel graph
      4. Travelling salesman problem
    4. Shortest path problem
      1. Bellman–Ford algorithm
      2. Dijkstra's algorithm
      3. Floyd–Warshall algorithm
  9. Planar graph
    1. Crossing number (graph theory)
      1. Three utilities problem
      2. Turán's brick factory problem
    2. Kuratowski's theorem
  10. Snark (graph theory)
    1. Generalized Petersen graph
      1. Dürer graph
      2. Petersen graph
  11. Spectral graph theory
    1. Adjacency matrix
    2. Degree matrix
    3. Laplacian matrix

Order theory

[edit]

This section contains 23 articles.

  1. Order theory
    1. Domain theory
    2. Upper and lower bounds
      1. Greatest element and least element
      2. Infimum and supremum
  2. Preorder
  3. 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
  4. Stable marriage problem
    1. Gale–Shapley algorithm
    2. Stable roommates problem
  5. Total order
    1. Connected relation
    2. Well-order
      1. Well-founded relation

Calculus and analysis

[edit]

This section contains 188 articles.

Basics

[edit]

This section contains 10 articles.

  1. Calculus (Level 3)
  2. Limit (mathematics) (Level 3)
    1. 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

[edit]

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

[edit]

This section contains 11 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. Limits of integration
  11. Riemann sum

Multivariable and vector calculus

[edit]

This section contains 30 articles.

  1. Multivariable calculus (Level 4)
  2. Vector calculus (Level 4)
    1. Tensor calculus
  3. Multiple integral (Level 4)
  4. Iterated integral
    1. Fubini's theorem
  5. Partial derivative (Level 4)
  6. Total derivative
  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

[edit]

This section contains 42 articles.

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

Dynamical systems

[edit]

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. Dynamic simulation
  10. Flow (mathematics)
  11. Lyapunov exponent
  12. Attractor
    1. Limit cycle

Sequences and series

[edit]

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

[edit]

This section contains 61 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
    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

[edit]

This section contains 14 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

Complex analysis

[edit]

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

[edit]

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

[edit]

This section contains 53 articles.

  1. Number theory (Level 3)

Prime numbers

[edit]

This section contains 14 articles.

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

Sums and products

[edit]

This section contains 10 articles.

  1. Aliquot sum
    1. Perfect number
  2. Composite number
    1. Fundamental theorem of arithmetic (Level 4)
    2. Highly composite number
  3. Collatz conjecture
  4. Magic square
  5. Integer partition
    1. Goldbach's conjecture
    2. Young tableau

Modular arithmetic

[edit]

This section contains 8 articles.

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

Sequences

[edit]

This section contains 8 articles.

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

Diophantine equations

[edit]

This section contains 5 articles.

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

Subdisciplines

[edit]

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

[edit]

This section contains 43 articles.

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

Game theory

[edit]

This section contains 18 articles.

  1. Game theory (Level 4)
    1. Extensive-form game
    2. Information set (game theory)
      1. Common knowledge (logic)
      2. Perfect information
    3. Normal-form game
      1. Battle of the sexes (game theory)
      2. Prisoner's dilemma
      3. Zero-sum game
    4. Repeated game
    5. Strategy (game theory)
      1. Minimax
      2. Nash equilibrium
      3. Strategic dominance
  2. Social choice theory
    1. Condorcet paradox
    2. Arrow's impossibility theorem
    3. Gibbard–Satterthwaite theorem

Information theory

[edit]

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

[edit]

This section contains 14 articles.

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

Theoretical computer science

[edit]

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

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

Algorithms

[edit]

This section contains 16 articles.

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

Automata theory

[edit]

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

[edit]

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

[edit]

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


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