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വിക്കിപീഡിയ:Vital articles/Expanded/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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This list is tailored to the English-language Wikipedia. There is also a list of one thousand articles considered vital to Wikipedias of all languages.

For more information on this list and the process for adding articles, please see the Frequently Asked Questions (FAQ) page.

Mathematics (296 articles)

തിരുത്തുക
See also: Mathematicians

Basics (60 articles)

തിരുത്തുക
  1.     Mathematics (Level 1)
    1.   Mathematician
  2.   Arithmetic (Level 2)
    1.   Addition (Level 3)
    2.   Subtraction (Level 3)
    3.   Multiplication (Level 3)
    4.   Division (Level 3)
      1.   Euclidean algorithm
    5.   Fraction (Level 3)
      1.   Percentage
    6.   Modular arithmetic
  3.   Number (Level 2)
    1.   Natural number (Level 3)
    2.   Integer (Level 3)
    3.   Rational number
    4.   Real number (Level 3)
    5.   Complex number (Level 3)
    6.   Irrational number
    7.   Imaginary number
  4.   Function (Level 3)
    1.   Exponentiation (Level 3)
    2.   Logarithm (Level 3)
    3.   nth root (Level 3)
    4.   Square root
    5.   Exponential function
    6.   Inverse function
    7.   Implicit function
    8.   Function composition
    9.   Graph of a function
  5.   Equation (Level 3)
    1.   Series (Level 3)
    2.   Equation solving
    3.   Polynomial
    4.     Quadratic equation
  6.   Trigonometry (Level 3)
    1.   Inverse trigonometric functions
    2.     Trigonometric functions
    3.   Hyperbolic function
  7.   Variable (Level 3)
  8.   Constant
    1.   0 (Level 3)
    2.   Pi (Level 3)
    3.   e (Level 3)
    4.   1
    5.   −1
    6.   Imaginary unit
    7.   Golden ratio
  9.   Positional notation
    1.   Numerical digit
    2.   Decimal
    3.   Arabic numerals
    4.   Roman numerals
    5.   Binary number
  10.   Formula
  11.   Theorem
    1.     Pythagorean theorem
  12.   Conjecture
  13.   Factorial
    1.   Gamma function
  14.   Hilbert's problems

Geometry (55 articles)

തിരുത്തുക
  1.   Geometry (Level 2)
  2.   Coordinate system (Level 3)
    1.   Cartesian coordinate system
    2.   Polar coordinate system
  3.   Dimension (Level 3)
  4.   Point
  5.   Line (Level 3)
  6.   Two-dimensional space
    1.   Plane (Level 3)
    2.   Angle (Level 3)
    3.   Area (Level 3)
    4.   Shape (Level 3)
    5.   Polygon (Level 3)
      1.       Triangle (Level 3)
      2.   Quadrilateral
        1.   Square
    6.   Conic section (Level 3)
      1.   Circle (Level 3)
      2.   Ellipse
      3.   Parabola
      4.   Hyperbola
  7.   Three-dimensional space
    1.   Volume (Level 3)
    2.   Sphere (Level 3)
    3.   Polyhedron (Level 3)
      1.   Cube
  8.   Topology (Level 3)
    1.   Compact space
    2.   Euler characteristic
    3.   General topology
    4.   Homology
    5.   Homotopy
    6.   Knot theory
    7.   Manifold
    8.   Open set
    9.   Poincaré conjecture
    10.   Topological space
  9.   Length
    1.   Ruler
    2.   Calipers
  10.   Distance
    1.   Metric space
  11.   Analytic geometry
  12.   Differential geometry
    1.   Atiyah–Singer index theorem
    2.   Riemannian geometry
  13.     Euclidean geometry
    1.   Euclidean space
    2.   Convex set
  14.   Non-Euclidean geometry
  15.   Symmetry
    1.   Symmetry in mathematics
  16.     Fractal
  17.   Parametric equation
  18.   Tensor

Algebra (39 articles)

തിരുത്തുക
  1.   Algebra (Level 3)
    1.   Elementary algebra
  2.     Linear algebra
    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.   Inequality
  6.   Abstract algebra
    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.   Classification of finite simple groups
      3.   Fundamental group
      4.   Group representation
      5.   Group theory
    10.   Homological algebra
    11.   Isomorphism
    12.   Module
    13.   Representation theory
    14.   Ring theory
      1.   Commutative ring
      2.   Ring

Discrete mathematics (36 articles)

തിരുത്തുക

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

  1.   Discrete mathematics
  2.   Combinatorics (Level 3)
    1.   Combination
    2.   Permutation
  3.   Set theory
    1.   Set (Level 3)
    2.   Axiom of choice
    3.   Cantor's theorem
    4.   Empty set
    5.   Equivalence relation
    6.   Naive set theory
      1.   Russell's paradox
    7.   Union (set theory)
    8.   Intersection (set theory)
  4.   Graph theory
    1.   Four color theorem
    2.   Graph
  5.   Mathematical logic
    1.   Mathematical proof (Level 3)
    2.   Axiom
    3.   Computability theory
      1.   Computable function
    4.     Gödel's incompleteness theorems
    5.   Mathematical induction
    6.   Propositional calculus
  6.   Theoretical computer science
    1.   Abstract machine
    2.       Algorithm (Level 3)
      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.   Theory of computation

Probability and statistics (41 articles)

തിരുത്തുക
  1.   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.   Uniform distribution (discrete)
    9.   Random variable
    10.   Stochastic process
    11.   Variance
  2.     Statistics (Level 2)
    1.   Bayesian inference
    2.   Correlation and dependence
      1.   Regression
        1.   Least squares
    3.   Data visualization
    4.   Design of experiments
      1.   Randomized controlled trial
    5.   Mean
      1.   Arithmetic mean
    6.   Median
    7.   Mode
    8.   Observational study
    9.   Sample mean and sample covariance
    10.   Standard deviation
    11.   Standard error
    12.   Statistical hypothesis testing
      1.   p-value
      2.   Chi-square test
      3.   Student's t-test
    13.   Survey methodology
      1.   Accidental sampling
      2.   Statistical population
      3.   Sampling

Calculus and analysis (39 articles)

തിരുത്തുക
  1.     Calculus (Level 3)
    1.   Limit (Level 3)
      1.   Infinity (Level 3)
      2.   Limit of a function
      3.   Limit of a sequence
      4.   Sequence
        1.   Fibonacci number
    2.   Fundamental theorem of calculus
    3.   Differential calculus
      1.   Derivative
      2.   Differential equation
      3.   Ordinary differential equation
    4.   Integral
      1.   Laplace transform
    5.   Multivariable calculus
      1.   Multiple integral
      2.   Partial derivative
        1.   Laplace's equation
        2.   Partial differential equation
      3.   Vector calculus
        1.   Del
    6.   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 (26 articles)

തിരുത്തുക
  1.   Number theory (Level 3)
    1.   Prime number (Level 3)
      1.   Prime number theorem
      2.   Euclid's theorem
    2.   Algebraic number theory
      1.   Algebraic number field
      2.   Class field theory
    3.   Analytic number theory
      1.     Riemann hypothesis
    4.   Diophantine equation
      1.   Fermat's Last Theorem
    5.   Fundamental theorem of arithmetic
  2.   Applied mathematics
    1.   Mathematical optimization (Level 3)
      1.   Linear programming
      2.   Nonlinear programming
      3.   Operations research
    2.     Game theory
    3.   Information theory
  3.   Dynamical systems theory
    1.   Dynamical system
      1.   Linear dynamical system
      2.   Nonlinear system
    2.   Control theory
  4.   Category theory
  5.   Pure mathematics


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