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Wikipedia:Vital articles/Level/4/Mathematics#Basics (58 articles)

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{{center|{{Clickable button 2|Improve a random level 4 vital article in Mathematics|class=mw-ui-progressive|url=https://randomincategory.toolforge.org/?category=Wikipedia%20level-4%20vital%20articles%20in%20Mathematics&server=en.wikipedia.org&cmnamespace=&cmtype=&returntype=subject}}}}

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.

{{Wikipedia:Vital articles/Labels}}

This list is tailored to the English-language Wikipedia. There is also a list of ten 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.

{{TOC limit|4}}

Total 299 articles.

class="wikitable sortable"
Class#Articles
{{Icon|FA}} FA5
{{Icon|GA}} GA15
{{Icon|B}} B146
{{Icon|C}} C127
{{Icon|FFA}} FFA9
{{Icon|DGA}} DGA10
{{Icon|FFLC}} FFLC1
{{Icon|Start}} Start6

Mathematics

{{Vital article count|299}}

:For mathematicians, see: People: Mathematicians.

=Basics =

{{Vital article count|57}}

{{Div col|colwidth=15em}}

  1. {{Icon|B}} {{Icon|DGA}} Mathematics (Level 1)
  2. {{Icon|GA}} Arithmetic (Level 2)
  3. {{Icon|GA}} Addition
  4. {{Icon|B}} Subtraction
  5. {{Icon|C}} Multiplication
  6. {{Icon|C}} Division
  7. {{Icon|FA}} Euclidean algorithm
  8. {{Icon|C}} Fraction (Level 3)
  9. {{Icon|B}} Percentage
  10. {{Icon|C}} Modular arithmetic
  11. {{Icon|C}} Number (Level 2)
  12. {{Icon|C}} Integer (Level 3)
  13. {{Icon|C}} Natural number (Level 3)
  14. {{Icon|C}} Parity
  15. {{Icon|C}} Real number (Level 3)
  16. {{Icon|C}} Rational number
  17. {{Icon|B}} Irrational number
  18. {{Icon|B}} Negative number
  19. {{Icon|B}} Complex number (Level 3)
  20. {{Icon|C}} Imaginary number
  21. {{Icon|C}} Positional notation
  22. {{Icon|B}} Numerical digit
  23. {{Icon|C}} Decimal
  24. {{Icon|C}} Arabic numerals (Level 3)
  25. {{Icon|C}} Roman numerals
  26. {{Icon|B}} Binary number
  27. {{Icon|B}} Scientific notation
  28. {{Icon|B}} Order of operations
  29. {{Icon|C}} Function (Level 3)
  30. {{Icon|C}} {{Icon|DGA}} Exponentiation (Level 3)
  31. {{Icon|FA}} Logarithm (Level 3)
  32. {{Icon|C}} nth root (Level 3)
  33. {{Icon|B}} Square root
  34. {{Icon|C}} Exponential function
  35. {{Icon|C}} Inverse function
  36. {{Icon|C}} Implicit function
  37. {{Icon|B}} Function composition
  38. {{Icon|C}} Graph of a function
  39. {{Icon|C}} Parametric equation
  40. {{Icon|C}} Equation (Level 3)
  41. {{Icon|C}} Series (Level 3)
  42. {{Icon|C}} Equation solving
  43. {{Icon|C}} Polynomial
  44. {{Icon|C}} Variable (Level 3)
  45. {{Icon|C}} Constant
  46. {{Icon|FA}} {{pi}} (Level 3)
  47. {{Icon|GA}} E (mathematical constant) (Level 3)
  48. {{Icon|B}} Imaginary unit
  49. {{Icon|C}} 0 (Level 3)
  50. {{Icon|GA}} 1
  51. {{Icon|B}} Golden ratio
  52. {{Icon|B}} Formula
  53. {{Icon|B}} Theorem
  54. {{Icon|B}} Conjecture
  55. {{Icon|GA}} Factorial
  56. {{Icon|B}} Gamma function
  57. {{Icon|B}} {{Icon|FFLC}} Hilbert's problems

{{Div col end}}

=Geometry =

{{Vital article count|58}}

{{Div col|colwidth=15em}}

  1. {{Icon|B}} Geometry (Level 2)
  2. {{Icon|C}} Coordinate system
  3. {{Icon|B}} Cartesian coordinate system
  4. {{Icon|C}} {{Icon|FFA}} Polar coordinate system
  5. {{Icon|C}} Dimension
  6. {{Icon|C}} Point
  7. {{Icon|C}} Line (Level 3)
  8. {{Icon|C}} Curve
  9. {{Icon|C}} Euclidean plane
  10. {{Icon|Start}} Plane (mathematics)
  11. {{Icon|C}} Angle (Level 3)
  12. {{Icon|C}} Right angle
  13. {{Icon|B}} Area (Level 3)
  14. {{Icon|C}} Shape
  15. {{Icon|C}} Polygon (Level 3)
  16. {{Icon|C}} {{Icon|FFA}} Triangle (Level 3)
  17. {{Icon|C}} Quadrilateral
  18. {{Icon|B}} Square
  19. {{Icon|C}} Conic section
  20. {{Icon|C}} Circle (Level 3)
  21. {{Icon|C}} Ellipse
  22. {{Icon|B}} Parabola
  23. {{Icon|B}} Hyperbola
  24. {{Icon|C}} Three-dimensional space (Level 3)
  25. {{Icon|C}} Volume (Level 3)
  26. {{Icon|B}} Sphere
  27. {{Icon|C}} Polyhedron
  28. {{Icon|B}} Cube
  29. {{Icon|B}} Trigonometry (Level 3)
  30. {{Icon|B}} {{Icon|FFA}} Trigonometric functions
  31. {{Icon|C}} Hyperbolic functions
  32. {{Icon|B}} Topology (Level 3)
  33. {{Icon|B}} General topology
  34. {{Icon|B}} Topological space
  35. {{Icon|B}} Compact space
  36. {{Icon|C}} Manifold
  37. {{Icon|C}} Open set
  38. {{Icon|C}} Homology
  39. {{Icon|C}} Homotopy
  40. {{Icon|C}} Euler characteristic
  41. {{Icon|B}} Knot theory
  42. {{Icon|C}} Poincaré conjecture
  43. {{Icon|Start}} Length
  44. {{Icon|C}} Distance
  45. {{Icon|B}} Metric space
  46. {{Icon|C}} Symmetry
  47. {{Icon|B}} Symmetry in mathematics
  48. {{Icon|B}} Analytic geometry
  49. {{Icon|B}} Differential geometry
  50. {{Icon|B}} Riemannian geometry
  51. {{Icon|C}} Riemannian manifold
  52. {{Icon|C}} {{Icon|DGA}} Euclidean geometry
  53. {{Icon|C}} Convex set
  54. {{Icon|GA}} {{Icon|FFA}} Pythagorean theorem
  55. {{Icon|B}} Non-Euclidean geometry
  56. {{Icon|B}} {{Icon|FFA}} Fractal
  57. {{Icon|C}} Tensor
  58. {{Icon|GA}} Tessellation

{{Div col end}}

=Algebra =

{{Vital article count|40}}

{{Div col|colwidth=20em}}

  1. {{Icon|FA}} Algebra (Level 3)
  2. {{Icon|B}} Elementary algebra
  3. {{Icon|C}} {{Icon|DGA}} Linear algebra (Level 3)
  4. {{Icon|B}} Linear equation
  5. {{Icon|B}} Gaussian elimination
  6. {{Icon|GA}} Matrix
  7. {{Icon|B}} Determinant
  8. {{Icon|B}} {{Icon|FFA}} Eigenvalues and eigenvectors
  9. {{Icon|GA}} Vector space
  10. {{Icon|B}} Euclidean vector
  11. {{Icon|B}} Cross product
  12. {{Icon|C}} Dot product
  13. {{Icon|B}} Algebraic geometry
  14. {{Icon|B}} Algebraic variety
  15. {{Icon|C}} Boolean algebra
  16. {{Icon|C}} Inequality
  17. {{Icon|B}} {{Icon|DGA}} Quadratic equation
  18. {{Icon|C}} Abstract algebra
  19. {{Icon|B}} Algebraic topology
  20. {{Icon|B}} Sheaf
  21. {{Icon|C}} Associative property
  22. {{Icon|B}} Commutative algebra
  23. {{Icon|GA}} Commutative property
  24. {{Icon|C}} Distributive property
  25. {{Icon|GA}} Field (mathematics)
  26. {{Icon|B}} Fundamental theorem of algebra
  27. {{Icon|C}} Galois theory
  28. {{Icon|FA}} Group
  29. {{Icon|B}} Abelian group
  30. {{Icon|B}} Classification of finite simple groups
  31. {{Icon|B}} Fundamental group
  32. {{Icon|B}} Group representation
  33. {{Icon|B}} Group theory
  34. {{Icon|B}} Homological algebra
  35. {{Icon|C}} Isomorphism
  36. {{Icon|B}} Module
  37. {{Icon|B}} Representation theory
  38. {{Icon|B}} Ring theory
  39. {{Icon|B}} Commutative ring
  40. {{Icon|B}} Ring

{{Div col end}}

=Statistics and probability =

{{Vital article count|40}}

{{Div col|colwidth=20em}}

  1. {{Icon|B}} {{Icon|DGA}} Statistics (Level 2)
  2. {{Icon|B}} Bayesian inference
  3. {{Icon|B}} Correlation
  4. {{Icon|C}} Regression
  5. {{Icon|B}} Least squares
  6. {{Icon|C}} Covariance
  7. {{Icon|C}} Data and information visualization
  8. {{Icon|C}} Design of experiments
  9. {{Icon|B}} Randomized controlled trial
  10. {{Icon|B}} Mean
  11. {{Icon|B}} Median
  12. {{Icon|C}} Meta-analysis
  13. {{Icon|B}} Mode
  14. {{Icon|Start}} Observational study
  15. {{Icon|B}} Standard deviation
  16. {{Icon|C}} Standard error
  17. {{Icon|B}} Statistical hypothesis test
  18. {{Icon|B}} p-value
  19. {{Icon|C}} Chi-squared test
  20. {{Icon|B}} Student's t-test
  21. {{Icon|C}} Survey methodology
  22. {{Icon|Start}} Statistical population
  23. {{Icon|B}} Sampling
  24. {{Icon|B}} Probability (Level 3)
  25. {{Icon|B}} {{Icon|DGA}} Probability theory
  26. {{Icon|B}} Bayes' theorem
  27. {{Icon|B}} Central limit theorem
  28. {{Icon|C}} Expected value
  29. {{Icon|C}} Law of large numbers
  30. {{Icon|B}} Markov chain
  31. {{Icon|B}} Probability density function
  32. {{Icon|C}} Probability distribution
  33. {{Icon|B}} Binomial distribution
  34. {{Icon|B}} Exponential distribution
  35. {{Icon|B}} Normal distribution
  36. {{Icon|B}} Poisson distribution
  37. {{Icon|Start}} Discrete uniform distribution
  38. {{Icon|B}} Random variable
  39. {{Icon|B}} Stochastic process
  40. {{Icon|B}} Variance

{{Div col end}}

=Discrete mathematics =

{{Vital article count|39}}

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

{{Div col|colwidth=15em}}

  1. {{Icon|B}} Discrete mathematics
  2. {{Icon|B}} Mathematical logic
  3. {{Icon|C}} Mathematical proof (Level 3)
  4. {{Icon|C}} Axiom
  5. {{Icon|B}} Computability theory
  6. {{Icon|B}} Computable function
  7. {{Icon|B}} First-order logic
  8. {{Icon|B}} {{Icon|DGA}} Gödel's incompleteness theorems
  9. {{Icon|B}} Mathematical induction
  10. {{Icon|B}} Propositional calculus
  11. {{Icon|C}} Combinatorics
  12. {{Icon|B}} Combination
  13. {{Icon|B}} Permutation
  14. {{Icon|B}} Theoretical computer science
  15. {{Icon|C}} {{Icon|FFA}} Algorithm (Level 3)
  16. {{Icon|C}} Abstract machine
  17. {{Icon|B}} Numerical integration
  18. {{Icon|C}} Coding theory
  19. {{Icon|B}} Data compression
  20. {{Icon|C}} Error detection and correction
  21. {{Icon|B}} {{Icon|FFA}} Computational complexity theory
  22. {{Icon|B}} P versus NP problem
  23. {{Icon|C}} Data structure
  24. {{Icon|C}} Formal language
  25. {{Icon|C}} Theory of computation
  26. {{Icon|B}} Set theory
  27. {{Icon|B}} Set (Level 3)
  28. {{Icon|C}} Empty set
  29. {{Icon|C}} Subset
  30. {{Icon|B}} Axiom of choice
  31. {{Icon|B}} Cantor's theorem
  32. {{Icon|B}} Equivalence relation
  33. {{Icon|C}} Intersection (set theory)
  34. {{Icon|C}} Naive set theory
  35. {{Icon|C}} Russell's paradox
  36. {{Icon|Start}} Union (set theory)
  37. {{Icon|B}} Venn diagram
  38. {{Icon|B}} Graph theory
  39. {{Icon|C}} Graph (discrete mathematics)

{{Div col end}}

=Calculus and analysis =

{{Vital article count|40}}

{{Div col|colwidth=20em}}

  1. {{Icon|C}} Calculus (Level 3)
  2. {{Icon|C}} Limit (Level 3)
  3. {{Icon|C}} Infinity (Level 3)
  4. {{Icon|C}} Limit of a function
  5. {{Icon|C}} Limit of a sequence
  6. {{Icon|C}} Sequence
  7. {{Icon|B}} Fibonacci sequence
  8. {{Icon|C}} Fundamental theorem of calculus
  9. {{Icon|B}} Continuous function
  10. {{Icon|B}} Differential calculus
  11. {{Icon|GA}} Derivative
  12. {{Icon|B}} Differential equation
  13. {{Icon|B}} Ordinary differential equation
  14. {{Icon|B}} Integral
  15. {{Icon|B}} Laplace transform
  16. {{Icon|C}} Multivariable calculus
  17. {{Icon|C}} Multiple integral
  18. {{Icon|C}} Partial derivative
  19. {{Icon|B}} Laplace's equation
  20. {{Icon|C}} Partial differential equation
  21. {{Icon|B}} Vector calculus
  22. {{Icon|C}} Del
  23. {{Icon|GA}} Taylor series
  24. {{Icon|C}} {{Icon|DGA}} Mathematical analysis (Level 3)
  25. {{Icon|C}} Approximation theory
  26. {{Icon|B}} Numerical analysis
  27. {{Icon|C}} Complex analysis
  28. {{Icon|B}} Cauchy's integral formula
  29. {{Icon|B}} Euler's formula
  30. {{Icon|C}} Euler's identity
  31. {{Icon|C}} Holomorphic function
  32. {{Icon|B}} Riemann surface
  33. {{Icon|C}} Functional analysis
  34. {{Icon|GA}} Hilbert space
  35. {{Icon|C}} Harmonic analysis
  36. {{Icon|B}} Fourier analysis
  37. {{Icon|B}} Fourier series
  38. {{Icon|B}} Fourier transform
  39. {{Icon|C}} Real analysis
  40. {{Icon|B}} Calculus of variations

{{Div col end}}

=Other =

{{Vital article count|25}}

{{Div col|colwidth=20em}}

  1. {{Icon|B}} Number theory (Level 3)
  2. {{Icon|GA}} Prime number (Level 3)
  3. {{Icon|B}} Prime number theorem
  4. {{Icon|C}} Euclid's theorem
  5. {{Icon|C}} Fundamental theorem of arithmetic
  6. {{Icon|B}} Algebraic number theory
  7. {{Icon|B}} Algebraic number field
  8. {{Icon|C}} Class field theory
  9. {{Icon|B}} Analytic number theory
  10. {{Icon|B}} {{Icon|DGA}} Riemann hypothesis
  11. {{Icon|C}} Diophantine equation
  12. {{Icon|C}} Fermat's Last Theorem
  13. {{Icon|B}} Applied mathematics
  14. {{Icon|B}} Mathematical optimization
  15. {{Icon|B}} Linear programming
  16. {{Icon|C}} Nonlinear programming
  17. {{Icon|C}} Operations research
  18. {{Icon|C}} {{Icon|FFA}} Game theory
  19. {{Icon|B}} Information theory
  20. {{Icon|C}} Dynamical systems theory
  21. {{Icon|B}} Dynamical system
  22. {{Icon|B}} Control theory
  23. {{Icon|B}} Chaos theory
  24. {{Icon|B}} Category theory
  25. {{Icon|B}} Pure mathematics

{{Div col end}}

{{Core topics}}

All languages should have

Vital articles