利用者:佐藤なにが/5万の記事/数学

Basics

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

Functions: General

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
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

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

Geometry: General

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

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

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

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)
   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

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

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

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

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

Algebra: General

1. Algebra (Level 3)
2. Algebraic expression

Elementary algebra

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

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

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

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

Statistics

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. Ordinary least squares (Level 4)
      2. Non-linear least squares
      3. Linear regression
      4. 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. Mean (Level 4)
    1. Arithmetic mean
    2. Geometric mean
    3. Harmonic mean
12. Maximum likelihood estimation
    1. Expectation–maximization algorithm
13. Median (Level 4)
14. Meta-analysis (Level 4)
15. Mode (statistics) (Level 4)
16. Observational study (Level 4)
17. Principal component analysis
18. Sample mean and covariance
19. Standard deviation (Level 4)
20. Standard error (Level 4)
21. 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)
22. Statistical inference
23. 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
24. Time series
25. Type I and type II errors
26. Analysis of variance

Probability

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

1. Foundations of mathematics

Mathematical logic

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

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

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

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

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

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

1. Discrete mathematics (Level 4)

Combinatorics

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

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

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

Basics

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

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

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)
   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

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. Separation of variables
4. Integrating factor
5. Numerical methods for ordinary differential equations
   1. Euler method
   2. Runge–Kutta methods
   3. Shooting method
6. Numerical methods for partial differential equations
   1. Crank–Nicolson method
   2. Finite element method
   3. Method of lines
7. Dirichlet problem
8. Elliptic operator
9. System of differential equations

Dynamical systems

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

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

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

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

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

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

1. Number theory (Level 3)

Prime numbers

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

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

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

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

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

Subdisciplines

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

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

Game theory

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

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

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

Template:Vital article count 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

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

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

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

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 (data structure)
      1. B-tree
      2. Binary search tree
      3. Red–black tree