Wiki143: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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Total 299 articles.

Class	#Articles
FA	5
GA	15
B	144
C	129
FFA	9
DGA	10
FFLC	1
Start	6

Mathematics

For mathematicians, see: People: Mathematicians.

Basics

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 (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
8. Equation (Level 3)
   1. Series (Level 3)
   2. Equation solving
   3. Polynomial
9. Variable (Level 3)
10. Constant
    1. [[Pi|Template:Pi]] (Level 3)
    2. [[E (mathematical constant)|Template:Mvar]] (Level 3)
    3. [[Imaginary unit|Template:Mvar]]
    4. 0 (Level 3)
    5. 1
    6. Golden ratio
11. Formula
12. Theorem
13. Conjecture
14. Factorial
    1. Gamma function
15. Hilbert's problems

Geometry

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

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. Inequality
6. Quadratic equation
7. 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

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

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. First-order logic
   5. Gödel's incompleteness theorems
   6. Mathematical induction
   7. Propositional calculus
3. Combinatorics
   1. Combination
   2. Permutation
4. 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
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)
   8. Venn diagram
6. Graph theory
   1. Graph (discrete mathematics)

Calculus and analysis

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 sequence
   2. Fundamental theorem of calculus
   3. Continuous function
   4. Differential calculus
      1. Derivative
      2. Differential equation
      3. Ordinary differential equation
   5. Integral
      1. Laplace transform
   6. Multivariable calculus
      1. Multiple integral
      2. Partial derivative
         1. Laplace's equation
         2. Partial differential equation
      3. Vector calculus
         1. Del
   7. 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

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