Wikipedia:Vital articles/Level/5/Mathematics

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.


 * See also: People: Mathematicians

Quota 1,200 articles.

Total 1,201 articles.

Basics

 * 1)   Mathematics (Level 1)
 * 2)  Mathematical notation
 * 3)  Scientific notation (Level 4)
 * 4)  Mathematician
 * 5)  Fields Medal
 * 6)  Pure mathematics (Level 4)
 * 7)  Recreational mathematics
 * 8)  Approximation
 * 9)  Estimation
 * 10)  Extrapolation
 * 11)  Arithmetic (Level 2)
 * 12)  Counting
 * 13)  Cardinal number
 * 14)  Tally marks
 * 15)  Addition (Level 4)
 * 16)  Plus and minus signs
 * 17)  Subtraction (Level 4)
 * 18)  Multiplication (Level 4)
 * 19)  Multiplication sign
 * 20)  Multiplication table
 * 21)  Product (mathematics)
 * 22)  Division (mathematics) (Level 4)
 * 23)  Division sign
 * 24)  Euclidean algorithm (Level 4)
 * 25)  Long division
 * 26)  Division by zero
 * 27)  Divisibility rule
 * 28)  Fraction (Level 3)
 * 29)  Percentage (Level 4)
 * 30)  Percent sign
 * 31)  Continued fraction
 * 32)  Egyptian fraction
 * 33)  Modular arithmetic (Level 4)
 * 34)  Modulo
 * 35)  Divisor
 * 36)  Greatest common divisor
 * 37)  Lowest common denominator
 * 38)  Multiple (mathematics)
 * 39)  Least common multiple
 * 40)  Constant (mathematics) (Level 4)
 * 41)  Mathematical constant
 * 42)  Pi (Level 3)
 * 43)  $e$ (mathematical constant) (Level 3)
 * 44)  Imaginary unit (Level 4)
 * 45)  Golden ratio (Level 4)
 * 46)  −1 (Level 4)
 * 47)  0 (Level 3)
 * 48)  One half (½)
 * 49)  1 (Level 4)
 * 50)  2
 * 51)  3
 * 52)  4
 * 53)  5
 * 54)  6
 * 55)  7
 * 56)  8
 * 57)  9
 * 58)  10
 * 59)  100
 * 60)  1000 (number)
 * 61)  Square root of 2
 * 62)  Euler's constant
 * 63)  Feigenbaum constants
 * 64)  Equation (Level 3)
 * 65)  Equation solving (Level 4)
 * 66)  Polynomial (Level 4)
 * 67)  Monomial
 * 68)  Binomial (polynomial)
 * 69)  Trinomial
 * 70)  Infinity (Level 3)
 * 71)  Infinity symbol
 * 72)  Transfinite number
 * 73)  Mathematical model
 * 74)  Mathematical problem
 * 75)   Hilbert's problems (Level 4)
 * 76)  Mathematical puzzle
 * 77)  Mathematical proof (Level 3)
 * 78)  Formula (Level 4)
 * 79)  Identity (mathematics)
 * 80)  Theorem (Level 4)
 * 81)  Corollary
 * 82)  Lemma (mathematics)
 * 83)  Conjecture (Level 4)
 * 84)  Number (Level 2)
 * 85)  Natural number (Level 3)
 * 86)  Integer (Level 3)
 * 87)  Negative number (Level 4)
 * 88)  Parity (mathematics) (Level 4)
 * 89)  Sign (mathematics)
 * 90)  Real number (Level 3)
 * 91)  Complex number (Level 3)
 * 92)  Gaussian integer
 * 93)  Rational number (Level 4)
 * 94)  Rate (mathematics)
 * 95)  Ratio
 * 96)  Repeating decimal
 * 97)  Irrational number (Level 4)
 * 98)  Imaginary number (Level 4)
 * 99)  Algebraic number
 * 100)  Transcendental number
 * 101)  Constructible number
 * 102)  Computable number
 * 103)  Normal number
 * 104)  Operation (mathematics)
 * 105)  Order of operations (Level 4)
 * 106)  Positional notation (Level 4)
 * 107)  Numerical digit (Level 4)
 * 108)  Decimal (Level 4)
 * 109)  Decimal separator
 * 110)  Numeral system
 * 111)  Hindu–Arabic numeral system
 * 112)  Arabic numerals (Level 3)
 * 113)  Chinese numerals
 * 114)  Egyptian numerals
 * 115)  Maya numerals
 * 116)  Roman numerals (Level 4)
 * 117)  Binary number (Level 4)
 * 118)  Hexadecimal
 * 119)  Sexagesimal
 * 120)  Variable (mathematics) (Level 3)

Functions: General

 * 1)  Function (mathematics) (Level 3)
 * 2)  Algebraic function
 * 3)  Function of a real variable
 * 4)  Function of several real variables
 * 5)  Vector-valued function
 * 6)  Arithmetic function
 * 7)  Additive function
 * 8)  Multiplicative function
 * 9)  Inverse function (Level 4)
 * 10)  Implicit function (Level 4)
 * 11)  Function composition (Level 4)
 * 12)  Graph of a function (Level 4)
 * 13)  Parametric equation (Level 4)
 * 14)  Parameter
 * 15)  Even and odd functions
 * 16)  Piecewise
 * 17)  Bijection, injection and surjection
 * 18)  Injective function
 * 19)  Surjective function
 * 20)  Bijection
 * 21)  Domain of a function
 * 22)  Range of a function
 * 23)  Zero of a function
 * 24)  Fixed point (mathematics)
 * 25)  Fixed-point theorem
 * 26)  Critical point (mathematics)
 * 27)  Stationary point
 * 28)  Maximum and minimum
 * 29)  Saddle point
 * 30)  Inflection point
 * 31)  Limit of a function (Level 4)
 * 32)  Multivalued function
 * 33)  Partial function
 * 34)  Bounded function
 * 35)  Real-valued function
 * 36)  Analytic function
 * 37)  Entire function
 * 38)  Elliptic function
 * 39)  Periodic function
 * 40)  Curvature
 * 41)  Map (mathematics)

Specific functions

 * 1)  Elementary function
 * 2)  Rational function
 * 3)  Linear function (calculus)
 * 4)  Negation
 * 5)  Constant function
 * 6)  Identity function
 * 7)  Quadratic function
 * 8)  Square (algebra)
 * 9)  Cubic function
 * 10)  Exponentiation (Level 3)
 * 11)  Exponential function (Level 4)
 * 12)  Exponential growth
 * 13)  Gaussian function
 * 14)  Knuth's up-arrow notation
 * 15)  Logarithm (Level 3)
 * 16)  Common logarithm
 * 17)  Natural logarithm
 * 18)  Binary logarithm
 * 19)  Complex logarithm
 * 20)  nth root (Level 3)
 * 21)  Square root (Level 4)
 * 22)  Cube root
 * 23)   Trigonometric functions (Level 4)
 * 24)  Sine and cosine
 * 25)  Inverse trigonometric functions
 * 26)  Hyperbolic functions (Level 4)
 * 27)  Inverse hyperbolic functions
 * 28)  Bessel function
 * 29)  Floor and ceiling functions
 * 30)  Gamma function (Level 4)
 * 31)  Factorial (Level 4)
 * 32)  Stirling's approximation
 * 33)  Prime-counting function
 * 34)  Euler's totient function
 * 35)  Möbius function
 * 36)  Riemann zeta function
 * 37)  Weierstrass function
 * 38)  Error function
 * 39)  Step function
 * 40)  Heaviside step function
 * 41)  Rectangular function
 * 42)  Sign function
 * 43)  Dirac delta function
 * 44)  Kronecker delta
 * 45)  Absolute value
 * 46)  Lambert W function
 * 47)  Exponential integral
 * 48)  Likelihood function

Geometry: General

 * 1)  Geometry (Level 2)
 * 2)  Coordinate system (Level 4)
 * 3)  Cartesian coordinate system (Level 4)
 * 4)  Cylindrical coordinate system
 * 5)   Polar coordinate system (Level 4)
 * 6)  Spherical coordinate system
 * 7)  Dimension (Level 4)
 * 8)  Zero-dimensional space
 * 9)  Point (geometry) (Level 4)
 * 10)  One-dimensional space
 * 11)  Line (geometry) (Level 3)
 * 12)  Curve (Level 4)
 * 13)  Congruence (geometry)
 * 14)  Similarity (geometry)
 * 15)  Transformation (function)
 * 16)  Invariant (mathematics)
 * 17)  Isometry
 * 18)  Motion (geometry)
 * 19)  Reflection (mathematics)
 * 20)  Rotation (mathematics)
 * 21)  Scaling (geometry)
 * 22)  Shear mapping
 * 23)  Translation (geometry)

Two-dimensional space

 * 1)  Euclidean plane (Level 4)
 * 2)  Plane (mathematics) (Level 4)
 * 3)  Coplanarity
 * 4)  Angle (Level 3)
 * 5)  Right angle (Level 4)
 * 6)  Dihedral angle
 * 7)  Internal and external angles
 * 8)  Polygon (Level 3)
 * 9)   Triangle (Level 3)
 * 10)  Equilateral triangle
 * 11)  Isosceles triangle
 * 12)  Reuleaux triangle
 * 13)  Right triangle
 * 14)  Quadrilateral (Level 4)
 * 15)  Square (Level 4)
 * 16)  Rectangle
 * 17)  Parallelogram
 * 18)  Rhombus
 * 19)  Trapezoid
 * 20)  Pentagon
 * 21)  Hexagon
 * 22)  Octagon
 * 23)  Decagon
 * 24)  Regular polygon
 * 25)  Conic section (Level 4)
 * 26)  Circle (Level 3)
 * 27)  Circumference
 * 28)  Radius
 * 29)  Ellipse (Level 4)
 * 30)  Parabola (Level 4)
 * 31)  Hyperbola (Level 4)
 * 32)  Cardioid
 * 33)  Cycloid
 * 34)  Brachistochrone curve
 * 35)  Lemniscate
 * 36)  Elliptic curve
 * 37)  Catenary
 * 38)  Parallel (geometry)
 * 39)  Perpendicular
 * 40)  Tangent
 * 41)  Line–line intersection

Three-dimensional space

 * 1)  Three-dimensional space (Level 3)
 * 2)  Solid geometry
 * 3)  Shape (Level 4)
 * 4)  Size
 * 5)  Surface (mathematics)
 * 6)  Surface of revolution
 * 7)  Torus
 * 8)  Cone
 * 9)  Cylinder
 * 10)  Sphere (Level 4)
 * 11)  Polyhedron (Level 4)
 * 12)  Regular polyhedron
 * 13)  Platonic solid
 * 14)  Cube (Level 4)
 * 15)  Pyramid (geometry)
 * 16)  Tetrahedron
 * 17)  Octahedron
 * 18)  Dodecahedron
 * 19)  Regular dodecahedron
 * 20)  Icosahedron
 * 21)  Regular icosahedron
 * 22)  Prism (geometry)
 * 23)  Solid angle
 * 24)  Skew lines

Four-dimensional space

 * 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

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

Topology

 * 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)
 * 7)  Surface (topology)
 * 8)  3-manifold
 * 9)  4-manifold
 * 10)  Differentiable manifold
 * 11)  Open set (Level 4)
 * 12)  Clopen set
 * 13)  Neighbourhood (mathematics)
 * 14)  Homology (mathematics) (Level 4)
 * 15)  Homeomorphism
 * 16)  Homotopy (Level 4)
 * 17)  Euler characteristic (Level 4)
 * 18)  Knot theory (Level 4)
 * 19)  Orientability
 * 20)  Poincaré conjecture (Level 4)
 * 21)  Winding number

Measurement

 * 1)  Area (Level 3)
 * 2)  Surface area
 * 3)  Volume (Level 3)
 * 4)  Length (Level 4)
 * 5)  Arc length
 * 6)  Perimeter
 * 7)  Height
 * 8)  Distance (Level 4)
 * 9)  Metric space (Level 4)
 * 10)  Ball (mathematics)

Euclidean geometry

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

Non-Euclidean geometry

 * 1)  Non-Euclidean geometry (Level 4)
 * 2)  Affine geometry
 * 3)  Affine transformation
 * 4)  Elliptic geometry
 * 5)  Spherical geometry
 * 6)  Stereographic projection
 * 7)  Hyperbolic geometry
 * 8)  Hyperbolic angle
 * 9)  Hyperbolic triangle
 * 10)  Inversive geometry
 * 11)  Projective geometry
 * 12)  Homography
 * 13)  Projective plane
 * 14)  Projective space

Other

 * 1)  Bisection
 * 2)  Lattice (group)
 * 3)  Minkowski's theorem
 * 4)  Locus (mathematics)
 * 5)  Field line
 * 6)  Symmetry (Level 4)
 * 7)  Symmetry (geometry)
 * 8)  Symmetry in mathematics (Level 4)
 * 9)  Analytic geometry (Level 4)
 * 10)  Differential geometry (Level 4)
 * 11)  Riemannian geometry (Level 4)
 * 12)  Systolic geometry
 * 13)  Theorema Egregium
 * 14)   Fractal (Level 4)
 * 15)  Cantor set
 * 16)  Julia set
 * 17)  Koch snowflake
 * 18)  Mandelbrot set
 * 19)  Sierpiński triangle
 * 20)  Tessellation (Level 4)

Algebra: General

 * 1)  Algebra (Level 3)
 * 2)  Algebraic expression

Elementary algebra

 * 1)  Elementary algebra (Level 4)
 * 2)  Algebraic equation
 * 3)   Quadratic equation (Level 4)
 * 4)  Quadratic formula
 * 5)  Binomial theorem

Linear algebra

 * 1)   Linear algebra (Level 3)
 * 2)  Basis (linear algebra)
 * 3)  Linear combination
 * 4)  Linear independence
 * 5)  Linear map
 * 6)  Projection (linear algebra)
 * 7)  Linear equation (Level 4)
 * 8)  System of linear equations
 * 9)  Gaussian elimination (Level 4)
 * 10)  Jacobi method
 * 11)  Gauss–Seidel method
 * 12)  Cramer's rule
 * 13)  Successive over-relaxation
 * 14)  LU decomposition
 * 15)  Matrix (mathematics) (Level 4)
 * 16)  Matrix addition
 * 17)  Matrix multiplication
 * 18)  Transpose
 * 19)  Determinant (Level 4)
 * 20)   Eigenvalues and eigenvectors (Level 4)
 * 21)  Rank (linear algebra)
 * 22)  Rank–nullity theorem
 * 23)  Diagonal matrix
 * 24)  Identity matrix
 * 25)  Triangular matrix
 * 26)  Operator theory
 * 27)  Operator (mathematics)
 * 28)  Scalar (mathematics)
 * 29)  Scalar multiplication
 * 30)  Vector (mathematics and physics)
 * 31)  Vector notation
 * 32)  Vector space (Level 4)
 * 33)  Banach space
 * 34)  Euclidean vector (Level 4)
 * 35)  Magnitude (mathematics)
 * 36)  Cross product (Level 4)
 * 37)  Dot product (Level 4)
 * 38)  Tensor product
 * 39)  Inner product space
 * 40)  Lie algebra
 * 41)  Norm (mathematics)
 * 42)  Triangle inequality
 * 43)  Tensor (Level 4)
 * 44)  Einstein notation
 * 45)  Metric tensor

Abstract algebra

 * 1)  Abstract algebra (Level 4)
 * 2)  Algebraic structure
 * 3)  Algebraic topology (Level 4)
 * 4)  Sheaf (mathematics) (Level 4)
 * 5)  Associative property (Level 4)
 * 6)  Commutative algebra (Level 4)
 * 7)  Commutative property (Level 4)
 * 8)  Distributive property (Level 4)
 * 9)  Field (mathematics) (Level 4)
 * 10)  Finite field
 * 11)  Field extension
 * 12)  Fundamental theorem of algebra (Level 4)
 * 13)  Galois theory (Level 4)
 * 14)  Group (mathematics) (Level 4)
 * 15)  Abelian group (Level 4)
 * 16)  Classification of finite simple groups (Level 4)
 * 17)  Fundamental group (Level 4)
 * 18)  Galois group
 * 19)  Group representation (Level 4)
 * 20)  Group theory (Level 4)
 * 21)  Conjugacy class
 * 22)  Lagrange's theorem (group theory)
 * 23)  Lie group
 * 24)  Modular group
 * 25)  Normal subgroup
 * 26)  Homogeneous polynomial
 * 27)  Quadratic form
 * 28)  Homological algebra (Level 4)
 * 29)  Homomorphism
 * 30)  Isomorphism (Level 4)
 * 31)  Isomorphism theorems
 * 32)  Kernel (algebra)
 * 33)  Module (mathematics) (Level 4)
 * 34)  Multiplicative inverse
 * 35)  Representation theory (Level 4)
 * 36)  Ring theory (Level 4)
 * 37)  Algebra over a field
 * 38)  Commutative ring (Level 4)
 * 39)  Polynomial ring
 * 40)  Hilbert's basis theorem
 * 41)  Hilbert's Nullstellensatz
 * 42)  Ring (mathematics) (Level 4)
 * 43)  Ideal (ring theory)

Other algebra topics

 * 1)  Affine space
 * 2)  Algebraic geometry (Level 4)
 * 3)  Algebraic variety (Level 4)
 * 4)  Exterior algebra
 * 5)  Moduli space
 * 6)  Equality (mathematics)
 * 7)  Horner's method
 * 8)  Inequality (mathematics) (Level 4)
 * 9)  Cauchy–Schwarz inequality
 * 10)  Hölder's inequality
 * 11)  Jensen's inequality
 * 12)  Resultant

Statistics

 * 1)   Statistics (Level 2)
 * 2)  Bayesian inference (Level 4)
 * 3)  Maximum a posteriori estimation
 * 4)  Bayesian statistics
 * 5)  Credible interval
 * 6)  Posterior probability
 * 7)  Prior probability
 * 8)  Confidence interval
 * 9)  Correlation (Level 4)
 * 10)  Regression analysis (Level 4)
 * 11)  Ordinary least squares (Level 4)
 * 12)  Non-linear least squares
 * 13)  Linear regression
 * 14)  Logistic regression
 * 15)  Data and information visualization (Level 4)
 * 16)  Box plot
 * 17)  Histogram
 * 18)  Bar chart
 * 19)  Pie chart
 * 20)  Scatter plot
 * 21)  Descriptive statistics
 * 22)  Design of experiments (Level 4)
 * 23)  Randomized controlled trial (Level 4)
 * 24)  Factorial experiment
 * 25)  A/B testing
 * 26)  Estimator
 * 27)  Frequentist inference
 * 28)  Frequency (statistics)
 * 29)  Mean (Level 4)
 * 30)  Arithmetic mean
 * 31)  Geometric mean
 * 32)  Harmonic mean
 * 33)  Maximum likelihood estimation
 * 34)  Expectation–maximization algorithm
 * 35)  Median (Level 4)
 * 36)  Meta-analysis (Level 4)
 * 37)  Mode (statistics) (Level 4)
 * 38)  Observational study (Level 4)
 * 39)  Principal component analysis
 * 40)  Sample mean and covariance
 * 41)  Standard deviation (Level 4)
 * 42)  Standard error (Level 4)
 * 43)  Statistical hypothesis test (Level 4)
 * 44)  p-value (Level 4)
 * 45)  Statistical significance
 * 46)  Chi-squared test (Level 4)
 * 47)  Student's t-test (Level 4)
 * 48)  Statistical inference
 * 49)  Survey methodology (Level 4)
 * 50)  Statistical population (Level 4)
 * 51)  Sampling (statistics) (Level 4)
 * 52)  Monte Carlo method
 * 53)   Margin of error
 * 54)  Sample size determination
 * 55)  Sampling error
 * 56)  Time series
 * 57)  Type I and type II errors
 * 58)  Analysis of variance

Probability

 * 1)  Probability (Level 3)
 * 2)   Probability theory (Level 4)
 * 3)  Probability space
 * 4)  Event (probability theory)
 * 5)  Independence (probability theory)
 * 6)  Sample space
 * 7)  Outcome (probability)
 * 8)  Bayes' theorem (Level 4)
 * 9)  Central limit theorem (Level 4)
 * 10)  Conditional probability
 * 11)  Covariance (Level 4)
 * 12)  Law of large numbers (Level 4)
 * 13)  Moment (mathematics)
 * 14)  Expected value (Level 4)
 * 15)  Variance (Level 4)
 * 16)  Skewness
 * 17)  Kurtosis
 * 18)  Moment-generating function
 * 19)  Probability distribution (Level 4)
 * 20)  Cumulative distribution function
 * 21)  Probability density function (Level 4)
 * 22)  Chi-squared distribution
 * 23)  Continuous uniform distribution
 * 24)  Exponential distribution (Level 4)
 * 25)  Normal distribution (Level 4)
 * 26)  Probability mass function
 * 27)  Binomial distribution (Level 4)
 * 28)  Discrete uniform distribution (Level 4)
 * 29)  Geometric distribution
 * 30)  Poisson distribution (Level 4)
 * 31)  Student's t-distribution
 * 32)  Random variable (Level 4)
 * 33)  Random walk
 * 34)  Stochastic process (Level 4)
 * 35)  Markov chain (Level 4)
 * 36)  Viterbi algorithm
 * 37)  Poisson point process
 * 38)  Wiener process
 * 39)   Monty Hall problem
 * 40)  Randomness

Foundations

 * 1)  Foundations of mathematics

Mathematical logic

 * 1)  Mathematical logic (Level 4)
 * 2)  Axiom (Level 4)
 * 3)  Axiom schema
 * 4)  Rule of inference
 * 5)  Well-formed formula
 * 6)  Atomic formula
 * 7)  Propositional calculus (Level 4)
 * 8)  Boolean algebra (Level 4)
 * 9)  De Morgan's laws
 * 10)  Karnaugh map
 * 11)  Truth table
 * 12)  Logical connective
 * 13)  Material conditional
 * 14)  Sheffer stroke
 * 15)  Contraposition
 * 16)  If and only if
 * 17)  Modus ponens
 * 18)  Modus tollens
 * 19)  Principle of explosion
 * 20)  Proof by contradiction
 * 21)  First-order logic (Level 4)
 * 22)  Free variables and bound variables
 * 23)  Quantifier (logic)
 * 24)  Existential quantification
 * 25)  Universal quantification
 * 26)  Prenex normal form
 * 27)  Skolem normal form
 * 28)  Arithmetical hierarchy
 * 29)  Analytical hierarchy
 * 30)  Higher-order logic
 * 31)  Intuitionistic logic
 * 32)  Type theory

Set theory

 * 1)  Set theory (Level 4)
 * 2)  Naive set theory (Level 4)
 * 3)  Russell's paradox (Level 4)
 * 4)  Venn diagram (Level 4)
 * 5)  Set (mathematics) (Level 3)
 * 6)  Complement (set theory)
 * 7)  Element (mathematics)
 * 8)  Empty set (Level 4)
 * 9)  Intersection (set theory) (Level 4)
 * 10)  Partition of a set
 * 11)  Equivalence class
 * 12)  Subset (Level 4)
 * 13)  Closure (mathematics)
 * 14)  Union (set theory) (Level 4)
 * 15)  Universe (mathematics)
 * 16)  Tuple
 * 17)  Cartesian product
 * 18)  Ordered pair
 * 19)  Multiset
 * 20)  Pointed set
 * 21)  Binary relation
 * 22)  Reflexive relation
 * 23)  Symmetric relation
 * 24)  Transitive relation
 * 25)  Equivalence relation (Level 4)
 * 26)  Class (set theory)
 * 27)  Indexed family
 * 28)  Mathematical structure
 * 29)  Space (mathematics)
 * 30)  Cardinality
 * 31)  Aleph number
 * 32)  Cantor's theorem (Level 4)
 * 33)  Cantor's diagonal argument
 * 34)  Cardinality of the continuum
 * 35)  Continuum hypothesis
 * 36)  Forcing (mathematics)
 * 37)  Power set
 * 38)   Ordinal number
 * 39)  Transfinite induction
 * 40)  Von Neumann universe

Axiomatic systems

 * 1)  Axiomatic system
 * 2)  Zermelo–Fraenkel set theory
 * 3)  Axiom of extensionality
 * 4)  Axiom of regularity
 * 5)  Axiom schema of specification
 * 6)  Axiom of pairing
 * 7)  Axiom of union
 * 8)  Axiom schema of replacement
 * 9)  Axiom of infinity
 * 10)  Axiom of power set
 * 11)  Axiom of choice (Level 4)
 * 12)  Banach–Tarski paradox
 * 13)  Well-ordering theorem
 * 14)  Zorn's lemma
 * 15)  New Foundations
 * 16)  Peano axioms
 * 17)  Mathematical induction (Level 4)
 * 18)  Hilbert's axioms
 * 19)  Tarski's axioms

Computability theory

 * 1)  Computability theory (Level 4)
 * 2)  Church–Turing thesis
 * 3)  Model of computation
 * 4)  Combinatory logic
 * 5)  Lambda calculus
 * 6)  Turing machine
 * 7)  Computable function (Level 4)
 * 8)  General recursive function
 * 9)  Primitive recursive function
 * 10)  μ operator
 * 11)  Gödel numbering
 * 12)   Gödel's incompleteness theorems (Level 4)
 * 13)  Decision problem
 * 14)  Entscheidungsproblem
 * 15)  Halting problem
 * 16)  Rice's theorem
 * 17)  Turing's proof
 * 18)  Universal Turing machine
 * 19)  Computably enumerable set
 * 20)  Computable set
 * 21)  Oracle machine
 * 22)  Turing reduction
 * 23)  Turing degree

Model theory

 * 1)  Model theory
 * 2)  Compactness theorem
 * 3)  Gödel's completeness theorem
 * 4)  Löwenheim–Skolem theorem
 * 5)  Skolem's paradox
 * 6)  Structure (mathematical logic)
 * 7)  Elementary equivalence
 * 8)  Signature (logic)
 * 9)  Type (model theory)
 * 10)  Ultraproduct
 * 11)  Theory (mathematical logic)
 * 12)  Quantifier elimination

Category theory

 * 1)  Category theory (Level 4)
 * 2)  Commutative diagram
 * 3)  Five lemma
 * 4)  Snake lemma
 * 5)  Morphism
 * 6)  Category (mathematics)
 * 7)  Cartesian closed category
 * 8)  Comma category
 * 9)  Concrete category
 * 10)  Opposite category
 * 11)  Subcategory
 * 12)  Functor
 * 13)  Adjoint functors
 * 14)  Forgetful functor
 * 15)  Hom functor
 * 16)  Yoneda lemma
 * 17)  Universal property
 * 18)  Free object
 * 19)  Limit (category theory)
 * 20)  Coproduct
 * 21)  Initial and terminal objects
 * 22)  Kan extension
 * 23)  Product (category theory)
 * 24)  Pullback (category theory)
 * 25)  Pushout (category theory)
 * 26)  Monad (category theory)
 * 27)  Natural transformation

Discrete mathematics

 * 1)  Discrete mathematics (Level 4)

Combinatorics

 * 1)  Combinatorics (Level 4)
 * 2)  Algebraic combinatorics
 * 3)  Enumerative combinatorics
 * 4)  Ramsey theory
 * 5)  Ramsey's theorem
 * 6)  Combinatorial principles
 * 7)  Addition principle
 * 8)  Rule of product
 * 9)  Inclusion–exclusion principle
 * 10)  Pigeonhole principle
 * 11)  Double counting (proof technique)
 * 12)  Twelvefold way
 * 13)  Combination (Level 4)
 * 14)  Binomial coefficient
 * 15)  Pascal's triangle
 * 16)  Permutation (Level 4)
 * 17)  Partial permutation
 * 18)  Stirling number
 * 19)  Stirling numbers of the first kind
 * 20)  Stirling numbers of the second kind
 * 21)  Lah number
 * 22)  Latin square
 * 23)  Mutually orthogonal Latin squares

Graph theory

 * 1)  Graph theory (Level 4)
 * 2)  Graph (discrete mathematics) (Level 4)
 * 3)  Complete graph
 * 4)  Degree (graph theory)
 * 5)  Directed graph
 * 6)  Multigraph
 * 7)  Hypergraph
 * 8)  Clique (graph theory)
 * 9)  Bipartite graph
 * 10)  Clique problem
 * 11)  Graph coloring
 * 12)  Chromatic polynomial
 * 13)  Four color theorem
 * 14)  Vizing's theorem
 * 15)  Regular graph
 * 16)  Cage (graph theory)
 * 17)  Coxeter graph
 * 18)  Connectivity (graph theory)
 * 19)  Bridge (graph theory)
 * 20)  Component (graph theory)
 * 21)  Tree (graph theory)
 * 22)  Kruskal's algorithm
 * 23)  Prim's algorithm
 * 24)  Flow network
 * 25)  Ford–Fulkerson algorithm
 * 26)  Max-flow min-cut theorem
 * 27)  Maximum flow problem
 * 28)  Minimum-cost flow problem
 * 29)  Push–relabel maximum flow algorithm
 * 30)  Graph homomorphism
 * 31)  Edge contraction
 * 32)  Graph minor
 * 33)  Graph automorphism
 * 34)  Cayley graph
 * 35)  Graph isomorphism
 * 36)  Graph isomorphism problem
 * 37)  Homeomorphism (graph theory)
 * 38)  Intersection graph
 * 39)  Line graph
 * 40)  Matching (graph theory)
 * 41)  Matching polynomial
 * 42)  Hosoya index
 * 43)  Maximum cardinality matching
 * 44)  Blossom algorithm
 * 45)  Kőnig's theorem (graph theory)
 * 46)  Vertex cover
 * 47)  Rainbow matching
 * 48)  Edge cover
 * 49)  FKT algorithm
 * 50)  Path (graph theory)
 * 51)  Cycle (graph theory)
 * 52)  Directed acyclic graph
 * 53)  Girth (graph theory)
 * 54)  Eulerian path
 * 55)  BEST theorem
 * 56)  Handshaking lemma
 * 57)  Seven Bridges of Königsberg
 * 58)  Hamiltonian path
 * 59)  Hamiltonian path problem
 * 60)  Held–Karp algorithm
 * 61)  Herschel graph
 * 62)  Travelling salesman problem
 * 63)  Shortest path problem
 * 64)  Bellman–Ford algorithm
 * 65)  Dijkstra's algorithm
 * 66)  Floyd–Warshall algorithm
 * 67)  Planar graph
 * 68)  Crossing number (graph theory)
 * 69)  Three utilities problem
 * 70)  Turán's brick factory problem
 * 71)  Kuratowski's theorem
 * 72)  Snark (graph theory)
 * 73)  Generalized Petersen graph
 * 74)  Dürer graph
 * 75)  Petersen graph
 * 76)  Spectral graph theory
 * 77)  Adjacency matrix
 * 78)  Degree matrix
 * 79)  Laplacian matrix

Order theory

 * 1)   Order theory
 * 2)  Domain theory
 * 3)  Upper and lower bounds
 * 4)  Greatest element and least element
 * 5)  Infimum and supremum
 * 6)  Preorder
 * 7)  Partially ordered set
 * 8)  Antichain
 * 9)  Antisymmetric relation
 * 10)  Filter (mathematics)
 * 11)  Ultrafilter
 * 12)  Hasse diagram
 * 13)  Ideal (order theory)
 * 14)  Lattice (order)
 * 15)  Boolean algebra (structure)
 * 16)  Join and meet
 * 17)  Stable marriage problem
 * 18)  Gale–Shapley algorithm
 * 19)  Stable roommates problem
 * 20)  Total order
 * 21)  Connected relation
 * 22)  Well-order
 * 23)  Well-founded relation

Basics

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

Differential calculus

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

Integral calculus

 * 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

 * 1)  Multivariable calculus (Level 4)
 * 2)  Vector calculus (Level 4)
 * 3)  Tensor calculus
 * 4)  Multiple integral (Level 4)
 * 5)  Iterated integral
 * 6)  Fubini's theorem
 * 7)  Partial derivative (Level 4)
 * 8)  Total derivative
 * 9)  Directional derivative
 * 10)  Differential form
 * 11)  Vector field
 * 12)  Conservative vector field
 * 13)  Solenoidal vector field
 * 14)  Del (Level 4)
 * 15)  Gradient
 * 16)  Divergence
 * 17)  Curl (mathematics)
 * 18)  Laplace operator
 * 19)  Poisson's equation
 * 20)  Laplace's equation (Level 4)
 * 21)  Line integral
 * 22)  Surface integral
 * 23)  Volume integral
 * 24)  Stokes' theorem
 * 25)  Green's theorem
 * 26)  Gradient theorem
 * 27)  Divergence theorem
 * 28)  Jacobian matrix and determinant
 * 29)  Lagrange multiplier
 * 30)  Helmholtz decomposition

Differential equations

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

Dynamical systems

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

Sequences and series

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

Mathematical analysis

 * 1)   Mathematical analysis (Level 3)
 * 2)  Approximation theory (Level 4)
 * 3)  Numerical analysis (Level 4)
 * 4)  Functional analysis (Level 4)
 * 5)  Hilbert space (Level 4)
 * 6)  Lp space
 * 7)  Sequence space
 * 8)  Uniform convergence
 * 9)   Measure (mathematics)
 * 10)  Calculus of variations (Level 4)
 * 11)  Asymptotic analysis
 * 12)  Asymptote
 * 13)  Interpolation

Real analysis

 * 1)  Real analysis (Level 4)
 * 2)  Number line
 * 3)  Completeness of the real numbers
 * 4)  Extended real number line
 * 5)  Interval (mathematics)
 * 6)  Extreme value theorem
 * 7)  Intermediate value theorem
 * 8)  Root-finding algorithms
 * 9)  Newton's method
 * 10)  Bisection method
 * 11)  Regula falsi
 * 12)  Secant method
 * 13)  Mean value theorem
 * 14)  Squeeze theorem

Complex analysis

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

Harmonic analysis

 * 1)  Harmonic analysis (Level 4)
 * 2)  Fourier analysis (Level 4)
 * 3)  Fourier series (Level 4)
 * 4)  Fourier transform (Level 4)
 * 5)  Convolution theorem
 * 6)  Fast Fourier transform
 * 7)  Laplace transform (Level 4)
 * 8)  Harmonic function
 * 9)  Potential theory
 * 10)  Wavelet

Number theory

 * 1)  Number theory (Level 3)

Prime numbers

 * 1)  Prime number (Level 3)
 * 2)  Fermat number
 * 3)  Mersenne prime
 * 4)  Semiprime
 * 5)  Twin prime
 * 6)  Primality test
 * 7)  AKS primality test
 * 8)  Pseudoprime
 * 9)  Sieve of Eratosthenes
 * 10)  Coprime integers
 * 11)  abc conjecture
 * 12)  Euclid's theorem (Level 4)
 * 13)  Prime number theorem (Level 4)
 * 14)  $p$-adic number

Sums and products

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

Modular arithmetic

 * 1)  Chinese remainder theorem
 * 2)  Discrete logarithm
 * 3)  Fermat's little theorem
 * 4)  Quadratic residue
 * 5)  Quadratic reciprocity
 * 6)  Legendre symbol
 * 7)  Jacobi symbol
 * 8)  Wilson's theorem

Sequences

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

Diophantine equations

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

Subdisciplines

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

Applied mathematics

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

Game theory

 * 1)   Game theory (Level 4)
 * 2)  Extensive-form game
 * 3)  Information set (game theory)
 * 4)  Common knowledge (logic)
 * 5)  Perfect information
 * 6)  Normal-form game
 * 7)  Battle of the sexes (game theory)
 * 8)   Prisoner's dilemma
 * 9)  Zero-sum game
 * 10)  Repeated game
 * 11)  Strategy (game theory)
 * 12)  Minimax
 * 13)   Nash equilibrium
 * 14)  Strategic dominance
 * 15)  Social choice theory
 * 16)  Condorcet paradox
 * 17)  Arrow's impossibility theorem
 * 18)  Gibbard–Satterthwaite theorem

Information theory

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

Optimization

 * 1)  Mathematical optimization (Level 4)
 * 2)  Dynamic programming
 * 3)  Linear programming (Level 4)
 * 4)  Duality (optimization)
 * 5)  Feasible region
 * 6)  Ellipsoid method
 * 7)  Simplex algorithm
 * 8)  Loss function
 * 9)  Nonlinear programming (Level 4)
 * 10)  Karush–Kuhn–Tucker conditions
 * 11)  Transportation theory (mathematics)
 * 12)  Assignment problem
 * 13)  Hungarian algorithm
 * 14)  Operations research (Level 4)

Theoretical computer science
For topics in applied computer science, see Technology: Computing and information technology


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

Algorithms

 * 1)   Algorithm (Level 3)
 * 2)  Analysis of algorithms
 * 3)  Big O notation
 * 4)  Deterministic algorithm
 * 5)  Divide-and-conquer algorithm
 * 6)  Cache replacement policies
 * 7)  Search algorithm
 * 8)  Binary search
 * 9)  Breadth-first search
 * 10)  Brute-force search
 * 11)  Depth-first search
 * 12)  String-searching algorithm
 * 13)  Sorting algorithm
 * 14)  Heapsort
 * 15)  Merge sort
 * 16)  Quicksort

Automata theory

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

Complexity theory

 * 1)   Computational complexity theory (Level 4)
 * 2)  Blum axioms
 * 3)  Constructible function
 * 4)  Kolmogorov complexity
 * 5)  Space complexity
 * 6)  Time complexity
 * 7)  NP (complexity)
 * 8)  P (complexity)
 * 9)  P versus NP problem (Level 4)
 * 10)  Boolean satisfiability problem
 * 11)  NP-hardness
 * 12)  Time hierarchy theorem

Data structures and types

 * 1)  Abstract data type
 * 2)  Associative array
 * 3)  Graph (abstract data type)
 * 4)  Queue (abstract data type)
 * 5)  Stack (abstract data type)
 * 6)  Data model
 * 7)  Data structure (Level 4)
 * 8)  Hash table
 * 9)  Heap (data structure)
 * 10)  Linked list
 * 11)  Array (data structure)
 * 12)  Tree (data structure)
 * 13)  B-tree
 * 14)  Binary search tree
 * 15)  Red–black tree