Wikipedia:Vital articles/Level 4/Mathematics

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Vital articles is a list of subjects for which Wikipedia should have corresponding high-quality articles. It serves as a centralized watchlist to track the status of Wikipedia's most essential articles. This is one of eleven Level 4 sub-lists of ten thousand articles and is currently under construction.

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Mathematics

This section contains 299 articles.

For mathematicians, see: People: Mathematicians.

Basics

This section contains 58 articles.

  1. Mathematics (Level 1)
  2. Arithmetic (Level 2)
    1. Addition
    2. Subtraction
    3. Multiplication
    4. Division
      1. Euclidean algorithm
    5. Fraction (Level 3)
      1. Percentage
    6. Modular arithmetic
  3. Number (Level 2)
    1. Integer (Level 3)
      1. Natural number (Level 3)
      2. Parity
    2. Real number (Level 3)
      1. Rational number
      2. Irrational number
      3. Negative number
    3. Complex number (Level 3)
      1. Imaginary number
  4. Positional notation
    1. Numerical digit
    2. Decimal
    3. Arabic numerals (Level 3)
    4. Roman numerals
    5. Binary number
  5. Scientific notation
  6. Order of operations
  7. Function (Level 3)
    1. Exponentiation (Level 3)
    2. Logarithm (Level 3)
    3. nth root
      1. Square root
    4. Exponential function
    5. Polynomial
    6. Inverse function
    7. Implicit function
    8. Function composition
    9. Graph of a function
    10. Parametric equation
  8. Equation (Level 3)
    1. Equality
    2. Equation solving
  9. Variable (Level 3)
  10. Mathematical constant
    1. π (Level 3)
    2. e (Level 3)
    3. i
    4. 0 (Level 3)
    5. 1
    6. Golden ratio
  11. Inequality
  12. Formula
  13. Theorem
  14. Conjecture
  15. Factorial
    1. Gamma function
  16. Hilbert's problems

Geometry

This section contains 58 articles.

  1. Geometry (Level 2)
  2. Coordinate system
    1. Cartesian coordinate system
    2. Polar coordinate system
  3. Dimension
  4. Point
  5. Line (Level 3)
  6. Curve
  7. Euclidean plane
    1. Plane (mathematics)
    2. Angle (Level 3)
      1. Right angle
    3. Area (Level 3)
    4. Shape
    5. Polygon (Level 3)
      1. Triangle (Level 3)
      2. Quadrilateral
        1. Square
    6. Conic section
      1. Circle (Level 3)
      2. Ellipse
      3. Parabola
      4. Hyperbola
  8. Three-dimensional space (Level 3)
    1. Volume (Level 3)
    2. Sphere
    3. Polyhedron
      1. Cube
  9. Trigonometry (Level 3)
    1. Trigonometric functions
    2. Hyperbolic functions
  10. Topology (Level 3)
    1. General topology
    2. Topological space
    3. Compact space
    4. Manifold
    5. Open set
    6. Homology
    7. Homotopy
    8. Euler characteristic
    9. Knot theory
    10. Poincaré conjecture
  11. Length
  12. Distance
    1. Metric space
  13. Symmetry
    1. Symmetry in mathematics
  14. Analytic geometry
  15. Differential geometry
    1. Riemannian geometry
      1. Riemannian manifold
  16. Euclidean geometry
    1. Convex set
    2. Pythagorean theorem
  17. Non-Euclidean geometry
  18. Fractal
  19. Tensor
  20. Tessellation

Algebra

This section contains 38 articles.

  1. Algebra (Level 2)
    1. Elementary algebra
  2. Linear algebra (Level 3)
    1. Linear equation
    2. Gaussian elimination
    3. Matrix
      1. Determinant
      2. Eigenvalues and eigenvectors
    4. Vector space
      1. Euclidean vector
        1. Cross product
        2. Dot product
  3. Algebraic geometry
    1. Algebraic variety
  4. Boolean algebra
  5. Quadratic equation
  6. Abstract algebra (Level 3)
    1. Algebraic topology
      1. Sheaf
    2. Associative property
    3. Commutative algebra
    4. Commutative property
    5. Distributive property
    6. Field (mathematics)
    7. Fundamental theorem of algebra
    8. Galois theory
    9. Group
      1. Abelian group
      2. Fundamental group
      3. Group representation
      4. Group theory
    10. Homological algebra
    11. Isomorphism
    12. Module
    13. Representation theory
    14. Ring theory
      1. Commutative ring
      2. Ring

Statistics and probability

This section contains 40 articles.

  1. Statistics (Level 2)
    1. Bayesian inference
    2. Correlation
      1. Regression
        1. Least squares
    3. Covariance
    4. Data and information visualization
    5. Design of experiments
      1. Randomized controlled trial
    6. Mean
    7. Median
    8. Meta-analysis
    9. Mode
    10. Observational study
    11. Standard deviation
    12. Standard error
    13. Statistical hypothesis test
      1. p-value
      2. Chi-squared test
      3. Student's t-test
    14. Survey methodology
      1. Statistical population
      2. Sampling
  2. Probability (Level 3)
    1. Probability theory
    2. Bayes' theorem
    3. Central limit theorem
    4. Expected value
    5. Law of large numbers
    6. Markov chain
    7. Probability density function
    8. Probability distribution
      1. Binomial distribution
      2. Exponential distribution
      3. Normal distribution
      4. Poisson distribution
      5. Discrete uniform distribution
    9. Random variable
    10. Stochastic process
    11. Variance

Discrete mathematics

This section contains 51 articles.

For topics in applied computer science, see Technology: Computing and information technology.
  1. Discrete mathematics (Level 3)
  2. Number theory (Level 3)
    1. Prime number (Level 3)
      1. Prime number theorem
      2. Euclid's theorem
    2. Fundamental theorem of arithmetic
    3. Algebraic number theory
      1. Algebraic number field
      2. Class field theory
    4. Analytic number theory
      1. Riemann hypothesis
    5. Diophantine equation
      1. Fermat's Last Theorem
  3. Mathematical logic
    1. Mathematical proof (Level 3)
    2. Axiom
    3. Computability theory
      1. Computable function
    4. First-order logic
    5. Gödel's incompleteness theorems
    6. Mathematical induction
    7. Propositional logic
  4. Combinatorics
    1. Combination
    2. Permutation
  5. Theoretical computer science
    1. Algorithm (Level 3)
    2. Abstract machine
      1. Numerical integration
    3. Coding theory
      1. Data compression
      2. Error detection and correction
    4. Computational complexity theory
      1. P versus NP problem
    5. Data structure
    6. Formal language
    7. Theory of computation
  6. Set theory
    1. Set (Level 3)
      1. Empty set
      2. Subset
    2. Axiom of choice
    3. Cardinality
    4. Equivalence relation
    5. Intersection (set theory)
    6. Naive set theory
      1. Russell's paradox
    7. Union (set theory)
    8. Venn diagram
  7. Graph theory
    1. Graph (discrete mathematics)

Calculus and analysis

This section contains 41 articles.

  1. Calculus (Level 3)
    1. Series (Level 3)
    2. Limit (Level 3)
      1. Infinity (Level 3)
      2. Limit of a function
      3. Limit of a sequence
      4. Sequence
        1. Fibonacci sequence
    3. Fundamental theorem of calculus
    4. Continuous function
    5. Differential calculus
      1. Derivative
      2. Differential equation
      3. Ordinary differential equation
    6. Integral
      1. Laplace transform
    7. Multivariable calculus
      1. Multiple integral
      2. Partial derivative
        1. Laplace's equation
        2. Partial differential equation
      3. Vector calculus
        1. Del
    8. Taylor series
  2. Mathematical analysis (Level 3)
    1. Approximation theory
    2. Numerical analysis
    3. Complex analysis
      1. Cauchy's integral formula
      2. Euler's formula
      3. Euler's identity
      4. Holomorphic function
      5. Riemann surface
    4. Functional analysis
      1. Hilbert space
    5. Harmonic analysis
      1. Fourier analysis
      2. Fourier series
      3. Fourier transform
    6. Real analysis
    7. Calculus of variations

Other

This section contains 13 articles.

  1. Applied mathematics
    1. Mathematical optimization
      1. Linear programming
      2. Nonlinear programming
      3. Operations research
    2. Game theory
    3. Information theory
  2. Dynamical systems theory
    1. Dynamical system
    2. Control theory
    3. Chaos theory
  3. Category theory
  4. Pure mathematics

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