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Mathematics

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. Constant (mathematics)
4. Mathematical constant (Level 4)
   1. Pi (Level 3)
   2. e (mathematical constant) (Level 3)
   3. Imaginary unit (Level 4)
   4. Golden ratio (Level 4)
   5. −1
   6. 0 (Level 3)
   7. 1 (Level 4)
   8. Square root of 2
   9. Euler's constant
   10. Feigenbaum constants
5. Equation (Level 3)
   1. Equation solving (Level 4)
   2. Polynomial (Level 4)
      1. Monomial
      2. Binomial (polynomial)
      3. Trinomial
   3. Equality (mathematics)
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. Operation (mathematics)
    1. Order of operations (Level 4)
11. Variable (mathematics) (Level 3)

This section contains 20 articles.

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

This section contains 14 articles.

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

This section contains 29 articles.

1. Arithmetic (Level 2)
2. Counting
   1. Tally marks
3. Addition (Level 4)
   1. Plus and minus signs
4. Subtraction (Level 4)
5. Multiplication (Level 4)
   1. Multiplicative inverse
   2. Multiplication sign
   3. Multiplication table
   4. Product (mathematics)
6. Division (mathematics) (Level 4)
   1. Division sign
   2. Euclidean algorithm (Level 4)
   3. Long division
   4. Division by zero
   5. Divisibility rule
7. Fraction (Level 3)
   1. Percentage (Level 4)
      1. Percent sign
   2. Continued fraction
   3. Egyptian fraction
8. Modular arithmetic (Level 4)
   1. Modulo
9. Divisor
   1. Greatest common divisor
   2. Lowest common denominator
10. Multiple (mathematics)
    1. Least common multiple

Functions

This section contains 34 articles.

1. Function (mathematics) (Level 3)
2. Algebraic function
3. Function of a real variable
   1. Function of several real variables
   2. Vector-valued function
4. Arithmetic function
   1. Additive function
   2. Multiplicative function
5. Inverse function (Level 4)
6. Implicit function (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. Multivalued function
18. Partial function
19. Bounded function
20. Real-valued function
21. Analytic function
    1. Entire function
22. Elliptic function
23. Periodic function
24. Map (mathematics)

This section contains 47 articles.

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

Geometry

This section contains 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)

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. Conic section (Level 4)
   1. Circle (Level 3)
      1. Circumference
      2. Radius
   2. Ellipse (Level 4)
   3. Parabola (Level 4)
   4. Hyperbola (Level 4)
4. Cardioid
5. Cycloid
   1. Brachistochrone curve
6. Lemniscate
7. Elliptic curve
8. Catenary
9. Parallel (geometry)
10. Perpendicular
    1. Tangent
11. Line–line intersection

This section contains 17 articles.

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

This section contains 25 articles.

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

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

This section contains 7 articles.

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

This section contains 4 articles.

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

This section contains 21 articles.

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

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)

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

This section contains 14 articles.

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

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

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

This section contains 22 articles.

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

Algebra

This section contains 2 articles.

1. Algebra (Level 2)
2. Algebraic expression

This section contains 7 articles.

1. Elementary algebra (Level 4)
2. Algebraic equation
   1. Linear equation (Level 4)
   2. Quadratic equation (Level 4)
      1. Quadratic formula
   3. Binomial theorem
   4. Fundamental theorem of algebra (Level 4)

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. Scalar (mathematics)
   1. Scalar multiplication
8. Vector (mathematics and physics)
   1. Vector notation
9. Tensor (Level 4)
   1. Einstein notation
   2. Metric tensor

This section contains 11 articles.

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

This section contains 12 articles.

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

This section contains 47 articles.

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

This section contains 15 articles.

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

This section contains 11 articles.

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

Statistics and probability

This section contains 70 articles.

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

This section contains 44 articles.

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

This section contains 14 articles.

1. Probability distribution (Level 4)
2. Cumulative distribution function
3. Probability density function (Level 4)
   1. Chi-squared distribution
   2. Continuous uniform distribution
   3. Exponential distribution (Level 4)
   4. Normal distribution (Level 4)
   5. Student's t-distribution
4. Probability mass function
   1. Bernoulli distribution
   2. Binomial distribution (Level 4)
   3. Discrete uniform distribution (Level 4)
   4. Geometric distribution
   5. Poisson distribution (Level 4)

Foundations

1. Foundations of mathematics

This section contains 30 articles.

1. Mathematical logic (Level 4)
2. Axiom (Level 4)
3. Rule of inference
4. Well-formed formula
   1. Atomic formula
5. Propositional logic (Level 4)
   1. Boolean algebra (Level 4)
      1. De Morgan's laws
      2. Karnaugh map
      3. Truth table
   2. Logical connective
      1. If and only if
      2. Material conditional
      3. Negation
      4. Sheffer stroke
   3. Contraposition
   4. Modus ponens
   5. Modus tollens
   6. Principle of explosion
   7. Proof by contradiction
6. 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
7. Higher-order logic
8. Intuitionistic logic
9. Type theory

This section contains 40 articles.

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

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

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

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

This section contains 22 articles.

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

Discrete mathematics

1. Discrete mathematics (Level 4)

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

This section contains 79 articles.

1. Graph theory (Level 4)
2. Graph (discrete mathematics) (Level 4)
   1. Complete graph
   2. Degree (graph theory)
   3. Directed graph
   4. Multigraph
3. Hypergraph
4. 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
5. Connectivity (graph theory)
   1. Bridge (graph theory)
   2. Component (graph theory)
   3. Tree (graph theory)
      1. Kruskal's algorithm
      2. Prim's algorithm
6. 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
7. 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
8. 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
9. Edge cover
   1. FKT algorithm
10. 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
11. Planar graph
    1. Crossing number (graph theory)
       1. Three utilities problem
       2. Turán's brick factory problem
    2. Kuratowski's theorem
12. Snark (graph theory)
    1. Generalized Petersen graph
       1. Dürer graph
       2. Petersen graph
13. Spectral graph theory
    1. Adjacency matrix
    2. Degree matrix
    3. Laplacian matrix

This section contains 23 articles.

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

Calculus and analysis

This section contains 11 articles.

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

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

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

This section contains 30 articles.

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

This section contains 42 articles.

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

This section contains 19 articles.

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

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

This section contains 66 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

This section contains 19 articles.

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

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

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

1. Number theory (Level 3)

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

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

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

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

This section contains 5 articles.

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

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

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

This section contains 18 articles.

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

This section contains 4 articles.

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

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

This section contains 15 articles.

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

Theoretical computer science

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

This section contains 16 articles.

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

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