User:Kusnir/VitalMathematics

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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.

Articles are labelled as:

• Featured articles
• Former featured articles
• A-class articles
• Good articles
• Delisted good articles
• B-class articles
• C-class articles
• Start-class articles
• Stub-class articles
• A full list is at Template:Icon/doc

These symbols are updated manually and may be out of date; you are encouraged to fix any errors you discover.

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 (298 articles)

See also: People: Mathematicians

Basics (56 articles)

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. Real number (Level 3)
   4. Complex number (Level 3)
   5. Rational number
   6. Irrational number
   7. Imaginary number
4. Function (Level 3)
   1. Exponentiation (Level 3)
   2. Logarithm (Level 3)
   3. nth root (Level 3)
      1. Square root
   4. Exponential function
   5. Inverse function
   6. Implicit function
   7. Function composition
   8. Graph of a function
   9. Parametric equation
5. Equation (Level 3)
   1. Series (Level 3)
   2. Equation solving
   3. Polynomial
   4. Quadratic equation
6. Variable (Level 3)
7. Constant
   1. Pi (Level 3)
   2. e (Level 3)
   3. 0 (Level 3)
   4. 1
   5. −1
   6. Imaginary unit
   7. Golden ratio
8. Positional notation
   1. Numerical digit
   2. Decimal
   3. Arabic numerals
   4. Roman numerals
   5. Binary number
9. Formula
10. Theorem
11. Conjecture
12. Factorial
    1. Gamma function
13. Hilbert's problems

Geometry (61 articles)

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)
      1. Right angle
   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. Trigonometry (Level 3)
   1. Trigonometric functions
   2. Inverse trigonometric functions
   3. Hyperbolic function
9. 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
10. Length
    1. Ruler
    2. Calipers
11. Distance
    1. Metric space
12. Symmetry
    1. Symmetry in mathematics
13. Analytic geometry
14. Differential geometry
    1. Atiyah–Singer index theorem
    2. Riemannian geometry
15. Euclidean geometry
    1. Euclidean space
    2. Convex set
    3. Pythagorean theorem
16. Non-Euclidean geometry
17. Fractal
18. Tensor
19. Tessellation

Algebra (39 articles)

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

Statistics and probability (40 articles)

1. 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
   6. Median
   7. Meta-analysis
   8. Mode
   9. Observational study
   10. Sample mean and covariance
   11. Standard deviation
   12. Standard error
   13. Statistical hypothesis testing
       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 (37 articles)

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

1. Discrete mathematics
2. 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
3. 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
4. Combinatorics (Level 3)
   1. Combination
   2. Permutation
5. Set theory
   1. Set (Level 3)
      1. Empty set
      2. Subset
   2. Axiom of choice
   3. Cantor's theorem
   4. Equivalence relation
   5. Intersection (set theory)
   6. Naive set theory
      1. Russell's paradox
   7. Union (set theory)
6. Graph theory
   1. Graph (discrete mathematics)

Calculus and analysis (39 articles)

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)

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