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Wikipedia:Vital articles/Level/5/Mathematics#Theoretical computer science

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{{center|{{Clickable button 2|Improve a random level 5 vital article in Mathematics|class=mw-ui-progressive|url=https://randomincategory.toolforge.org/?category=Wikipedia%20level-5%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 the sub-lists of the fifty thousand article Vital articles/Level 5 and is currently under construction.

{{Wikipedia:Vital articles 5/Labels}}

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:See also: People: Mathematicians

Quota 1,200 articles.

Total 1,195 articles.

class="wikitable sortable"
Class#Articles
{{Icon|FA}} FA6
{{Icon|GA}} GA39
{{Icon|B}} B333
{{Icon|C}} C546
{{Icon|LIST}} LIST1
{{Icon|FFA}} FFA12
{{Icon|DGA}} DGA14
{{Icon|FFLC}} FFLC1
{{Icon|Start}} Start270

=Mathematics=

{{Vital article count|1195}}

Basics

{{Vital article count|110}}

{{Div col|colwidth=15em}}

  1. {{Icon|B}} {{Icon|DGA}} Mathematics (Level 1)
  2. {{Icon|Start}} Mathematical notation
  3. {{Icon|B}} Scientific notation (Level 4)
  4. {{Icon|B}} Mathematician
  5. {{Icon|B}} Fields Medal
  6. {{Icon|B}} Pure mathematics (Level 4)
  7. {{Icon|Start}} Recreational mathematics
  8. {{Icon|C}} Approximation
  9. {{Icon|Start}} Estimation
  10. {{Icon|Start}} Extrapolation
  11. {{Icon|GA}} Arithmetic (Level 2)
  12. {{Icon|Start}} Counting
  13. {{Icon|B}} Cardinal number
  14. {{Icon|C}} Tally marks
  15. {{Icon|GA}} Addition (Level 4)
  16. {{Icon|C}} Plus and minus signs
  17. {{Icon|B}} Subtraction (Level 4)
  18. {{Icon|C}} Multiplication (Level 4)
  19. {{Icon|C}} Multiplicative inverse
  20. {{Icon|C}} Multiplication sign
  21. {{Icon|Start}} Multiplication table
  22. {{Icon|B}} Product (mathematics)
  23. {{Icon|C}} Division (mathematics) (Level 4)
  24. {{Icon|Start}} Division sign
  25. {{Icon|FA}} Euclidean algorithm (Level 4)
  26. {{Icon|C}} Long division
  27. {{Icon|B}} Division by zero
  28. {{Icon|C}} Divisibility rule
  29. {{Icon|C}} Fraction (Level 3)
  30. {{Icon|B}} Percentage (Level 4)
  31. {{Icon|C}} Percent sign
  32. {{Icon|B}} Continued fraction
  33. {{Icon|C}} Egyptian fraction
  34. {{Icon|C}} Modular arithmetic (Level 4)
  35. {{Icon|Start}} Modulo
  36. {{Icon|C}} Divisor
  37. {{Icon|C}} Greatest common divisor
  38. {{Icon|Start}} Lowest common denominator
  39. {{Icon|Start}} Multiple (mathematics)
  40. {{Icon|C}} Least common multiple
  41. {{Icon|C}} Constant (mathematics) (Level 4)
  42. {{Icon|C}} Mathematical constant
  43. {{Icon|FA}} Pi (Level 3)
  44. {{Icon|GA}} E (mathematical constant) (Level 3)
  45. {{Icon|B}} Imaginary unit (Level 4)
  46. {{Icon|B}} Golden ratio (Level 4)
  47. {{Icon|C}} −1
  48. {{Icon|C}} 0 (Level 3)
  49. {{Icon|GA}} 1 (Level 4)
  50. {{Icon|B}} Square root of 2
  51. {{Icon|B}} Euler's constant
  52. {{Icon|C}} Feigenbaum constants
  53. {{Icon|C}} Equation (Level 3)
  54. {{Icon|C}} Equation solving (Level 4)
  55. {{Icon|C}} Polynomial (Level 4)
  56. {{Icon|Start}} Monomial
  57. {{Icon|Start}} Binomial (polynomial)
  58. {{Icon|Start}} Trinomial
  59. {{Icon|GA}} Equality (mathematics)
  60. {{Icon|C}} Infinity (Level 3)
  61. {{Icon|GA}} Infinity symbol
  62. {{Icon|Start}} Transfinite number
  63. {{Icon|C}} Mathematical model
  64. {{Icon|Start}} Mathematical problem
  65. {{Icon|B}} {{Icon|FFLC}} Hilbert's problems (Level 4)
  66. {{Icon|Start}} Mathematical puzzle
  67. {{Icon|C}} Mathematical proof (Level 3)
  68. {{Icon|B}} Formula (Level 4)
  69. {{Icon|C}} Identity (mathematics)
  70. {{Icon|B}} Theorem (Level 4)
  71. {{Icon|Start}} Corollary
  72. {{Icon|Start}} Lemma (mathematics)
  73. {{Icon|B}} Conjecture (Level 4)
  74. {{Icon|C}} Number (Level 2)
  75. {{Icon|C}} Natural number (Level 3)
  76. {{Icon|C}} Integer (Level 3)
  77. {{Icon|B}} Negative number (Level 4)
  78. {{Icon|C}} Parity (mathematics) (Level 4)
  79. {{Icon|C}} Sign (mathematics)
  80. {{Icon|C}} Real number (Level 3)
  81. {{Icon|B}} Complex number (Level 3)
  82. {{Icon|C}} Gaussian integer
  83. {{Icon|C}} Rational number (Level 4)
  84. {{Icon|Start}} Rate (mathematics)
  85. {{Icon|C}} Ratio
  86. {{Icon|C}} Repeating decimal
  87. {{Icon|B}} Irrational number (Level 4)
  88. {{Icon|C}} Imaginary number (Level 4)
  89. {{Icon|C}} Algebraic number
  90. {{Icon|B}} Transcendental number
  91. {{Icon|GA}} Constructible number
  92. {{Icon|Start}} Computable number
  93. {{Icon|B}} Normal number
  94. {{Icon|Start}} Operation (mathematics)
  95. {{Icon|B}} Order of operations (Level 4)
  96. {{Icon|C}} Positional notation (Level 4)
  97. {{Icon|B}} Numerical digit (Level 4)
  98. {{Icon|C}} Decimal (Level 4)
  99. {{Icon|C}} Decimal separator
  100. {{Icon|B}} Numeral system
  101. {{Icon|C}} Hindu–Arabic numeral system
  102. {{Icon|C}} Arabic numerals (Level 3)
  103. {{Icon|C}} Chinese numerals
  104. {{Icon|C}} Egyptian numerals
  105. {{Icon|Start}} Maya numerals
  106. {{Icon|C}} Roman numerals (Level 4)
  107. {{Icon|B}} Binary number (Level 4)
  108. {{Icon|B}} Hexadecimal
  109. {{Icon|C}} Sexagesimal
  110. {{Icon|C}} Variable (mathematics) (Level 3)

{{Div col end}}

Functions

{{Vital article count|89}}

{{Div col|colwidth=15em}}

=Functions: General=

{{Vital article count|41}}

  1. {{Icon|C}} Function (mathematics) (Level 3)
  2. {{Icon|Start}} Algebraic function
  3. {{Icon|C}} Function of a real variable
  4. {{Icon|C}} Function of several real variables
  5. {{Icon|Start}} Vector-valued function
  6. {{Icon|B}} Arithmetic function
  7. {{Icon|Start}} Additive function
  8. {{Icon|Start}} Multiplicative function
  9. {{Icon|C}} Inverse function (Level 4)
  10. {{Icon|C}} Implicit function (Level 4)
  11. {{Icon|B}} Function composition (Level 4)
  12. {{Icon|C}} Graph of a function (Level 4)
  13. {{Icon|C}} Parametric equation (Level 4)
  14. {{Icon|B}} Parameter
  15. {{Icon|C}} Even and odd functions
  16. {{Icon|Start}} Piecewise function
  17. {{Icon|B}} Bijection, injection and surjection
  18. {{Icon|C}} Injective function
  19. {{Icon|B}} Surjective function
  20. {{Icon|C}} Bijection
  21. {{Icon|Start}} Domain of a function
  22. {{Icon|C}} Range of a function
  23. {{Icon|C}} Zero of a function
  24. {{Icon|Start}} Fixed point (mathematics)
  25. {{Icon|C}} Fixed-point theorem
  26. {{Icon|C}} Critical point (mathematics)
  27. {{Icon|B}} Stationary point
  28. {{Icon|C}} Maximum and minimum
  29. {{Icon|Start}} Saddle point
  30. {{Icon|C}} Inflection point
  31. {{Icon|C}} Limit of a function (Level 4)
  32. {{Icon|Start}} Multivalued function
  33. {{Icon|B}} Partial function
  34. {{Icon|Start}} Bounded function
  35. {{Icon|Start}} Real-valued function
  36. {{Icon|C}} Analytic function
  37. {{Icon|C}} Entire function
  38. {{Icon|C}} Elliptic function
  39. {{Icon|C}} Periodic function
  40. {{Icon|C}} Curvature
  41. {{Icon|C}} Map (mathematics)

=Specific functions =

{{Vital article count|48}}

  1. {{Icon|Start}} Elementary function
  2. {{Icon|C}} Rational function
  3. {{Icon|C}} Linear function (calculus)
  4. {{Icon|C}} Negation
  5. {{Icon|Start}} Constant function
  6. {{Icon|C}} Identity function
  7. {{Icon|C}} Quadratic function
  8. {{Icon|C}} Square (algebra)
  9. {{Icon|C}} Cubic function
  10. {{Icon|C}} {{Icon|DGA}} Exponentiation (Level 3)
  11. {{Icon|C}} Exponential function (Level 4)
  12. {{Icon|B}} Exponential growth
  13. {{Icon|C}} Gaussian function
  14. {{Icon|Start}} Knuth's up-arrow notation
  15. {{Icon|FA}} Logarithm (Level 3)
  16. {{Icon|C}} Common logarithm
  17. {{Icon|C}} Natural logarithm
  18. {{Icon|GA}} Binary logarithm
  19. {{Icon|B}} Complex logarithm
  20. {{Icon|C}} nth root (Level 3)
  21. {{Icon|B}} Square root (Level 4)
  22. {{Icon|C}} Cube root
  23. {{Icon|B}} {{Icon|FFA}} Trigonometric functions (Level 4)
  24. {{Icon|C}} Sine and cosine
  25. {{Icon|B}} Inverse trigonometric functions
  26. {{Icon|C}} Hyperbolic functions (Level 4)
  27. {{Icon|Start}} Inverse hyperbolic functions
  28. {{Icon|B}} Bessel function
  29. {{Icon|B}} Floor and ceiling functions
  30. {{Icon|B}} Gamma function (Level 4)
  31. {{Icon|GA}} Factorial (Level 4)
  32. {{Icon|C}} Stirling's approximation
  33. {{Icon|C}} Prime-counting function
  34. {{Icon|B}} Euler's totient function
  35. {{Icon|C}} Möbius function
  36. {{Icon|B}} Riemann zeta function
  37. {{Icon|Start}} Weierstrass function
  38. {{Icon|C}} Error function
  39. {{Icon|C}} Step function
  40. {{Icon|Start}} Heaviside step function
  41. {{Icon|C}} Rectangular function
  42. {{Icon|C}} Sign function
  43. {{Icon|GA}} Dirac delta function
  44. {{Icon|C}} Kronecker delta
  45. {{Icon|C}} Absolute value
  46. {{Icon|B}} Lambert W function
  47. {{Icon|C}} Exponential integral
  48. {{Icon|C}} Likelihood function

{{Div col end}}

Geometry

{{Vital article count|172}}

{{Div col|colwidth=15em}}

=Geometry: General=

{{Vital article count|23}}

  1. {{Icon|B}} Geometry (Level 2)
  2. {{Icon|C}} Coordinate system (Level 4)
  3. {{Icon|B}} Cartesian coordinate system (Level 4)
  4. {{Icon|C}} Cylindrical coordinate system
  5. {{Icon|C}} {{Icon|FFA}} Polar coordinate system (Level 4)
  6. {{Icon|B}} Spherical coordinate system
  7. {{Icon|C}} Dimension (Level 4)
  8. {{Icon|Start}} Zero-dimensional space
  9. {{Icon|C}} Point (geometry) (Level 4)
  10. {{Icon|Start}} One-dimensional space
  11. {{Icon|C}} Line (geometry) (Level 3)
  12. {{Icon|C}} Curve (Level 4)
  13. {{Icon|C}} Congruence (geometry)
  14. {{Icon|C}} Similarity (geometry)
  15. {{Icon|Start}} Transformation (function)
  16. {{Icon|C}} Invariant (mathematics)
  17. {{Icon|C}} Isometry
  18. {{Icon|C}} Motion (geometry)
  19. {{Icon|Start}} Reflection (mathematics)
  20. {{Icon|C}} Rotation (mathematics)
  21. {{Icon|Start}} Scaling (geometry)
  22. {{Icon|Start}} Shear mapping
  23. {{Icon|Start}} Translation (geometry)

=Two-dimensional space =

{{Vital article count|41}}

  1. {{Icon|C}} Euclidean plane (Level 4)
  2. {{Icon|Start}} Plane (mathematics) (Level 4)
  3. {{Icon|Start}} Coplanarity
  4. {{Icon|C}} Angle (Level 3)
  5. {{Icon|C}} Right angle (Level 4)
  6. {{Icon|C}} Dihedral angle
  7. {{Icon|Start}} Internal and external angles
  8. {{Icon|C}} Polygon (Level 3)
  9. {{Icon|C}} {{Icon|FFA}} Triangle (Level 3)
  10. {{Icon|C}} Equilateral triangle
  11. {{Icon|GA}} Isosceles triangle
  12. {{Icon|GA}} Reuleaux triangle
  13. {{Icon|C}} Right triangle
  14. {{Icon|C}} Quadrilateral (Level 4)
  15. {{Icon|B}} Square (Level 4)
  16. {{Icon|C}} Rectangle
  17. {{Icon|C}} Parallelogram
  18. {{Icon|C}} Rhombus
  19. {{Icon|C}} Trapezoid
  20. {{Icon|Start}} Pentagon
  21. {{Icon|C}} Hexagon
  22. {{Icon|Start}} Octagon
  23. {{Icon|Start}} Decagon
  24. {{Icon|C}} Regular polygon
  25. {{Icon|C}} Conic section (Level 4)
  26. {{Icon|C}} Circle (Level 3)
  27. {{Icon|Start}} Circumference
  28. {{Icon|C}} Radius
  29. {{Icon|C}} Ellipse (Level 4)
  30. {{Icon|B}} Parabola (Level 4)
  31. {{Icon|B}} Hyperbola (Level 4)
  32. {{Icon|C}} Cardioid
  33. {{Icon|C}} Cycloid
  34. {{Icon|C}} Brachistochrone curve
  35. {{Icon|C}} Lemniscate
  36. {{Icon|B}} Elliptic curve
  37. {{Icon|B}} Catenary
  38. {{Icon|C}} Parallel (geometry)
  39. {{Icon|Start}} Perpendicular
  40. {{Icon|C}} Tangent
  41. {{Icon|C}} Line–line intersection

=Three-dimensional space =

{{Vital article count|25}}

  1. {{Icon|C}} Three-dimensional space (Level 3)
  2. {{Icon|Start}} Solid geometry
  3. {{Icon|C}} Shape (Level 4)
  4. {{Icon|Start}} Size
  5. {{Icon|C}} Surface (mathematics)
  6. {{Icon|C}} Surface of revolution
  7. {{Icon|B}} Torus
  8. {{Icon|Start}} Cone
  9. {{Icon|C}} Cylinder
  10. {{Icon|GA}} Möbius strip
  11. {{Icon|B}} Sphere (Level 4)
  12. {{Icon|C}} Polyhedron (Level 4)
  13. {{Icon|C}} Regular polyhedron
  14. {{Icon|C}} Platonic solid
  15. {{Icon|B}} Cube (Level 4)
  16. {{Icon|C}} Pyramid (geometry)
  17. {{Icon|C}} Tetrahedron
  18. {{Icon|Start}} Octahedron
  19. {{Icon|C}} Dodecahedron
  20. {{Icon|C}} Regular dodecahedron
  21. {{Icon|Start}} Icosahedron
  22. {{Icon|B}} Regular icosahedron
  23. {{Icon|Start}} Prism (geometry)
  24. {{Icon|C}} Solid angle
  25. {{Icon|Start}} Skew lines

=Four-dimensional space =

{{Vital article count|7}}

  1. {{Icon|C}} Four-dimensional space
  2. {{Icon|C}} Rotations in 4-dimensional Euclidean space
  3. {{Icon|C}} 3-sphere
  4. {{Icon|C}} 5-cell
  5. {{Icon|C}} Tesseract
  6. {{Icon|Start}} 16-cell
  7. {{Icon|C}} 24-cell

=Trigonometry =

{{Vital article count|4}}

  1. {{Icon|B}} Trigonometry (Level 3)
  2. {{Icon|C}} Law of cosines
  3. {{Icon|C}} Law of sines
  4. {{Icon|Start}} Unit circle

=Topology =

{{Vital article count|21}}

  1. {{Icon|B}} Topology (Level 3)
  2. {{Icon|B}} Brouwer fixed-point theorem
  3. {{Icon|B}} General topology (Level 4)
  4. {{Icon|B}} Topological space (Level 4)
  5. {{Icon|B}} Compact space (Level 4)
  6. {{Icon|B}} Connected space
  7. {{Icon|C}} Manifold (Level 4)
  8. {{Icon|B}} Surface (topology)
  9. {{Icon|C}} 3-manifold
  10. {{Icon|B}} 4-manifold
  11. {{Icon|B}} Differentiable manifold
  12. {{Icon|C}} Open set (Level 4)
  13. {{Icon|C}} Neighbourhood (mathematics)
  14. {{Icon|C}} Homology (mathematics) (Level 4)
  15. {{Icon|B}} Homeomorphism
  16. {{Icon|C}} Homotopy (Level 4)
  17. {{Icon|C}} Euler characteristic (Level 4)
  18. {{Icon|B}} Knot theory (Level 4)
  19. {{Icon|C}} Orientability
  20. {{Icon|C}} Poincaré conjecture (Level 4)
  21. {{Icon|B}} Winding number

=Measurement =

{{Vital article count|10}}

  1. {{Icon|B}} Area (Level 3)
  2. {{Icon|C}} Surface area
  3. {{Icon|C}} Volume (Level 3)
  4. {{Icon|Start}} Length (Level 4)
  5. {{Icon|B}} Arc length
  6. {{Icon|C}} Perimeter
  7. {{Icon|C}} Height
  8. {{Icon|C}} Distance (Level 4)
  9. {{Icon|B}} Metric space (Level 4)
  10. {{Icon|C}} Ball (mathematics)

=Euclidean geometry =

{{Vital article count|6}}

  1. {{Icon|C}} {{Icon|DGA}} Euclidean geometry (Level 4)
  2. {{Icon|B}} Euclidean space
  3. {{Icon|C}} Convex set (Level 4)
  4. {{Icon|GA}} {{Icon|FFA}} Pythagorean theorem (Level 4)
  5. {{Icon|C}} Parallel postulate
  6. {{Icon|GA}} Squaring the circle

=Non-Euclidean geometry =

{{Vital article count|14}}

  1. {{Icon|B}} Non-Euclidean geometry (Level 4)
  2. {{Icon|C}} Affine geometry
  3. {{Icon|Start}} Affine transformation
  4. {{Icon|B}} Elliptic geometry
  5. {{Icon|Start}} Spherical geometry
  6. {{Icon|B}} Stereographic projection
  7. {{Icon|C}} Hyperbolic geometry
  8. {{Icon|B}} Hyperbolic angle
  9. {{Icon|Start}} Hyperbolic triangle
  10. {{Icon|C}} Inversive geometry
  11. {{Icon|C}} Projective geometry
  12. {{Icon|Start}} Homography
  13. {{Icon|C}} Projective plane
  14. {{Icon|B}} Projective space

=Other =

{{Vital article count|21}}

  1. {{Icon|C}} Bisection
  2. {{Icon|C}} Lattice (group)
  3. {{Icon|C}} Minkowski's theorem
  4. {{Icon|C}} Locus (mathematics)
  5. {{Icon|Start}} Field line
  6. {{Icon|C}} Symmetry (Level 4)
  7. {{Icon|B}} Symmetry (geometry)
  8. {{Icon|B}} Symmetry in mathematics (Level 4)
  9. {{Icon|B}} Analytic geometry (Level 4)
  10. {{Icon|B}} Differential geometry (Level 4)
  11. {{Icon|B}} Riemannian geometry (Level 4)
  12. {{Icon|C}} Riemannian manifold (Level 4)
  13. {{Icon|B}} Systolic geometry
  14. {{Icon|Start}} Theorema Egregium
  15. {{Icon|B}} {{Icon|FFA}} Fractal (Level 4)
  16. {{Icon|C}} Cantor set
  17. {{Icon|C}} Julia set
  18. {{Icon|C}} Koch snowflake
  19. {{Icon|C}} Mandelbrot set
  20. {{Icon|C}} Sierpiński triangle
  21. {{Icon|GA}} Tessellation (Level 4)

{{Div col end}}

Algebra

{{Vital article count|105}}

{{Div col|colwidth=15em}}

=Algebra: General=

{{Vital article count|2}}

  1. {{Icon|FA}} Algebra (Level 3)
  2. {{Icon|Start}} Algebraic expression

=Elementary algebra =

{{Vital article count|7}}

  1. {{Icon|B}} Elementary algebra (Level 4)
  2. {{Icon|C}} Algebraic equation
  3. {{Icon|B}} Linear equation (Level 4)
  4. {{Icon|B}} {{Icon|DGA}} Quadratic equation (Level 4)
  5. {{Icon|B}} Quadratic formula
  6. {{Icon|C}} Binomial theorem
  7. {{Icon|B}} Fundamental theorem of algebra (Level 4)

=Linear algebra =

{{Vital article count|42}}

  1. {{Icon|C}} {{Icon|DGA}} Linear algebra (Level 3)
  2. {{Icon|C}} Basis (linear algebra)
  3. {{Icon|C}} Linear combination
  4. {{Icon|C}} Linear independence
  5. {{Icon|C}} Linear map
  6. {{Icon|C}} Projection (linear algebra)
  7. {{Icon|B}} System of linear equations
  8. {{Icon|C}} Cramer's rule
  9. {{Icon|B}} Gaussian elimination (Level 4)
  10. {{Icon|C}} Gauss–Seidel method
  11. {{Icon|C}} Jacobi method
  12. {{Icon|C}} Successive over-relaxation
  13. {{Icon|GA}} Matrix (mathematics) (Level 4)
  14. {{Icon|B}} Matrix multiplication
  15. {{Icon|C}} Transpose
  16. {{Icon|B}} Determinant (Level 4)
  17. {{Icon|B}} {{Icon|FFA}} Eigenvalues and eigenvectors (Level 4)
  18. {{Icon|C}} Rank (linear algebra)
  19. {{Icon|C}} Rank–nullity theorem
  20. {{Icon|Start}} Diagonal matrix
  21. {{Icon|Start}} Identity matrix
  22. {{Icon|C}} Triangular matrix
  23. {{Icon|C}} LU decomposition
  24. {{Icon|C}} Scalar (mathematics)
  25. {{Icon|C}} Scalar multiplication
  26. {{Icon|C}} Vector (mathematics and physics)
  27. {{Icon|C}} Vector notation
  28. {{Icon|GA}} Vector space (Level 4)
  29. {{Icon|B}} Banach space
  30. {{Icon|B}} Euclidean vector (Level 4)
  31. {{Icon|C}} Magnitude (mathematics)
  32. {{Icon|B}} Cross product (Level 4)
  33. {{Icon|C}} Dot product (Level 4)
  34. {{Icon|C}} Tensor product
  35. {{Icon|B}} Inner product space
  36. {{Icon|C}} Lie algebra
  37. {{Icon|C}} Norm (mathematics)
  38. {{Icon|B}} Triangle inequality
  39. {{Icon|B}} Quaternion
  40. {{Icon|C}} Tensor (Level 4)
  41. {{Icon|B}} Einstein notation
  42. {{Icon|B}} Metric tensor

=Abstract algebra =

{{Vital article count|43}}

  1. {{Icon|C}} Abstract algebra (Level 4)
  2. {{Icon|C}} Algebraic structure
  3. {{Icon|B}} Algebraic topology (Level 4)
  4. {{Icon|B}} Sheaf (mathematics) (Level 4)
  5. {{Icon|C}} Associative property (Level 4)
  6. {{Icon|B}} Commutative algebra (Level 4)
  7. {{Icon|GA}} Commutative property (Level 4)
  8. {{Icon|C}} Distributive property (Level 4)
  9. {{Icon|GA}} Field (mathematics) (Level 4)
  10. {{Icon|B}} Finite field
  11. {{Icon|C}} Field extension
  12. {{Icon|B}} Group theory (Level 4)
  13. {{Icon|FA}} Group (mathematics) (Level 4)
  14. {{Icon|B}} Abelian group (Level 4)
  15. {{Icon|B}} Cyclic group
  16. {{Icon|B}} Fundamental group (Level 4)
  17. {{Icon|B}} Group representation (Level 4)
  18. {{Icon|B}} Conjugacy class
  19. {{Icon|B}} Lagrange's theorem (group theory)
  20. {{Icon|B}} Lie group
  21. {{Icon|C}} Modular group
  22. {{Icon|C}} Normal subgroup
  23. {{Icon|C}} Simple group
  24. {{Icon|B}} Classification of finite simple groups (Level 4)
  25. {{Icon|C}} Galois theory (Level 4)
  26. {{Icon|C}} Galois group
  27. {{Icon|Start}} Homogeneous polynomial
  28. {{Icon|C}} Quadratic form
  29. {{Icon|B}} Homological algebra (Level 4)
  30. {{Icon|C}} Homomorphism
  31. {{Icon|C}} Isomorphism (Level 4)
  32. {{Icon|C}} Isomorphism theorems
  33. {{Icon|B}} Kernel (algebra)
  34. {{Icon|B}} Module (mathematics) (Level 4)
  35. {{Icon|B}} Representation theory (Level 4)
  36. {{Icon|B}} Ring theory (Level 4)
  37. {{Icon|C}} Algebra over a field
  38. {{Icon|B}} Commutative ring (Level 4)
  39. {{Icon|C}} Polynomial ring
  40. {{Icon|C}} Hilbert's basis theorem
  41. {{Icon|C}} Hilbert's Nullstellensatz
  42. {{Icon|B}} Ring (mathematics) (Level 4)
  43. {{Icon|C}} Ideal (ring theory)

=Other algebra topics =

{{Vital article count|11}}

  1. {{Icon|B}} Affine space
  2. {{Icon|B}} Algebraic geometry (Level 4)
  3. {{Icon|B}} Algebraic variety (Level 4)
  4. {{Icon|B}} Exterior algebra
  5. {{Icon|C}} Moduli space
  6. {{Icon|Start}} Horner's method
  7. {{Icon|C}} Inequality (mathematics) (Level 4)
  8. {{Icon|B}} Cauchy–Schwarz inequality
  9. {{Icon|C}} Hölder's inequality
  10. {{Icon|B}} Jensen's inequality
  11. {{Icon|C}} Resultant

{{Div col end}}

Statistics and probability

{{Vital article count|109}}

{{Div col|colwidth=15em}}

=Statistics =

{{Vital article count|66}}

  1. {{Icon|B}} {{Icon|DGA}} Statistics (Level 2)
  2. {{Icon|C}} Autocorrelation
  3. {{Icon|B}} Bayesian inference (Level 4)
  4. {{Icon|Start}} Maximum a posteriori estimation
  5. {{Icon|C}} Bayesian statistics
  6. {{Icon|Start}} Credible interval
  7. {{Icon|Start}} Posterior probability
  8. {{Icon|C}} Prior probability
  9. {{Icon|C}} Confidence interval
  10. {{Icon|B}} Correlation (Level 4)
  11. {{Icon|C}} Regression analysis (Level 4)
  12. {{Icon|B}} Least squares
  13. {{Icon|B}} Ordinary least squares (Level 4)
  14. {{Icon|C}} Non-linear least squares
  15. {{Icon|B}} Linear regression
  16. {{Icon|C}} Logistic regression
  17. {{Icon|C}} Data and information visualization (Level 4)
  18. {{Icon|C}} Box plot
  19. {{Icon|Start}} Candlestick chart
  20. {{Icon|B}} Histogram
  21. {{Icon|Start}} Bar chart
  22. {{Icon|C}} Pie chart
  23. {{Icon|Start}} Scatter plot
  24. {{Icon|Start}} Descriptive statistics
  25. {{Icon|C}} Design of experiments (Level 4)
  26. {{Icon|B}} Randomized controlled trial (Level 4)
  27. {{Icon|C}} Factorial experiment
  28. {{Icon|C}} A/B testing
  29. {{Icon|C}} Estimator
  30. {{Icon|Start}} Frequentist inference
  31. {{Icon|C}} Frequency (statistics)
  32. {{Icon|C}} Mathematical statistics
  33. {{Icon|B}} Mean (Level 4)
  34. {{Icon|C}} Arithmetic mean
  35. {{Icon|C}} Geometric mean
  36. {{Icon|C}} Harmonic mean
  37. {{Icon|B}} Maximum likelihood estimation
  38. {{Icon|C}} Expectation–maximization algorithm
  39. {{Icon|B}} Median (Level 4)
  40. {{Icon|C}} Meta-analysis (Level 4)
  41. {{Icon|B}} Mode (statistics) (Level 4)
  42. {{Icon|Start}} Observational study (Level 4)
  43. {{Icon|B}} Principal component analysis
  44. {{Icon|Start}} Sample mean and covariance
  45. {{Icon|B}} Standard deviation (Level 4)
  46. {{Icon|C}} Standard error (Level 4)
  47. {{Icon|B}} Statistical hypothesis test (Level 4)
  48. {{Icon|C}} Null hypothesis
  49. {{Icon|B}} p-value (Level 4)
  50. {{Icon|C}} Statistical significance
  51. {{Icon|C}} Chi-squared test (Level 4)
  52. {{Icon|B}} Student's t-test (Level 4)
  53. {{Icon|C}} Statistical inference
  54. {{Icon|C}} Survey methodology (Level 4)
  55. {{Icon|Start}} Statistical population (Level 4)
  56. {{Icon|B}} Sampling (statistics) (Level 4)
  57. {{Icon|B}} Monte Carlo method
  58. {{Icon|B}} {{Icon|FFA}} Margin of error
  59. {{Icon|C}} Sample size determination
  60. {{Icon|Start}} Sampling error
  61. {{Icon|C}} Time series
  62. {{Icon|B}} Type I and type II errors
  63. {{Icon|C}} Analysis of variance
  64. {{Icon|C}} Correlation does not imply causation
  65. {{Icon|Start}} Modifiable areal unit problem
  66. {{Icon|Start}} Ecological fallacy

=Probability =

{{Vital article count|43}}

  1. {{Icon|B}} Probability (Level 3)
  2. {{Icon|B}} {{Icon|DGA}} Probability theory (Level 4)
  3. {{Icon|B}} Probability space
  4. {{Icon|C}} Event (probability theory)
  5. {{Icon|C}} Independence (probability theory)
  6. {{Icon|C}} Sample space
  7. {{Icon|Start}} Outcome (probability)
  8. {{Icon|B}} Bayes' theorem (Level 4)
  9. {{Icon|B}} Central limit theorem (Level 4)
  10. {{Icon|C}} Conditional probability
  11. {{Icon|C}} Covariance (Level 4)
  12. {{Icon|B}} Coefficient of determination
  13. {{Icon|Start}} Correlation coefficient
  14. {{Icon|C}} Law of large numbers (Level 4)
  15. {{Icon|C}} Moment (mathematics)
  16. {{Icon|C}} Expected value (Level 4)
  17. {{Icon|B}} Variance (Level 4)
  18. {{Icon|B}} Skewness
  19. {{Icon|B}} Kurtosis
  20. {{Icon|Start}} Moment-generating function
  21. {{Icon|C}} Probability distribution (Level 4)
  22. {{Icon|C}} Cumulative distribution function
  23. {{Icon|B}} Probability density function (Level 4)
  24. {{Icon|C}} Chi-squared distribution
  25. {{Icon|B}} Continuous uniform distribution
  26. {{Icon|B}} Exponential distribution (Level 4)
  27. {{Icon|B}} Normal distribution (Level 4)
  28. {{Icon|Start}} Probability mass function
  29. {{Icon|Start}} Bernoulli distribution
  30. {{Icon|B}} Binomial distribution (Level 4)
  31. {{Icon|Start}} Discrete uniform distribution (Level 4)
  32. {{Icon|C}} Geometric distribution
  33. {{Icon|B}} Poisson distribution (Level 4)
  34. {{Icon|B}} Student's t-distribution
  35. {{Icon|B}} Random variable (Level 4)
  36. {{Icon|C}} Random walk
  37. {{Icon|B}} Stochastic process (Level 4)
  38. {{Icon|B}} Markov chain (Level 4)
  39. {{Icon|C}} Viterbi algorithm
  40. {{Icon|B}} Poisson point process
  41. {{Icon|C}} Wiener process
  42. {{Icon|B}} {{Icon|FFA}} Monty Hall problem
  43. {{Icon|B}} Randomness

{{Div col end}}

Foundations

{{Vital article count|145}}

{{Div col|colwidth=15em}}

  1. {{Icon|C}} Foundations of mathematics

=Mathematical logic =

{{Vital article count|29}}

  1. {{Icon|B}} Mathematical logic (Level 4)
  2. {{Icon|C}} Axiom (Level 4)
  3. {{Icon|GA}} Rule of inference
  4. {{Icon|Start}} Well-formed formula
  5. {{Icon|Start}} Atomic formula
  6. {{Icon|B}} Propositional calculus (Level 4)
  7. {{Icon|C}} Boolean algebra (Level 4)
  8. {{Icon|C}} De Morgan's laws
  9. {{Icon|B}} Karnaugh map
  10. {{Icon|Start}} Truth table
  11. {{Icon|Start}} Logical connective
  12. {{Icon|Start}} If and only if
  13. {{Icon|Start}} Material conditional
  14. {{Icon|Start}} Sheffer stroke
  15. {{Icon|C}} Contraposition
  16. {{Icon|Start}} Modus ponens
  17. {{Icon|Start}} Modus tollens
  18. {{Icon|Start}} Principle of explosion
  19. {{Icon|Start}} Proof by contradiction
  20. {{Icon|B}} First-order logic (Level 4)
  21. {{Icon|Start}} Free variables and bound variables
  22. {{Icon|C}} Quantifier (logic)
  23. {{Icon|Start}} Existential quantification
  24. {{Icon|Start}} Universal quantification
  25. {{Icon|B}} Prenex normal form
  26. {{Icon|Start}} Skolem normal form
  27. {{Icon|Start}} Higher-order logic
  28. {{Icon|C}} Intuitionistic logic
  29. {{Icon|C}} Type theory

=Set theory =

{{Vital article count|39}}

  1. {{Icon|B}} Set theory (Level 4)
  2. {{Icon|C}} Naive set theory (Level 4)
  3. {{Icon|C}} Russell's paradox (Level 4)
  4. {{Icon|B}} Venn diagram (Level 4)
  5. {{Icon|B}} Set (mathematics) (Level 3)
  6. {{Icon|Start}} Complement (set theory)
  7. {{Icon|Start}} Element (mathematics)
  8. {{Icon|C}} Empty set (Level 4)
  9. {{Icon|C}} Intersection (set theory) (Level 4)
  10. {{Icon|C}} Partition of a set
  11. {{Icon|C}} Equivalence class
  12. {{Icon|C}} Subset (Level 4)
  13. {{Icon|C}} Closure (mathematics)
  14. {{Icon|Start}} Union (set theory) (Level 4)
  15. {{Icon|Start}} Universe (mathematics)
  16. {{Icon|C}} Tuple
  17. {{Icon|C}} Cartesian product
  18. {{Icon|C}} Ordered pair
  19. {{Icon|C}} Multiset
  20. {{Icon|C}} Binary relation
  21. {{Icon|Start}} Reflexive relation
  22. {{Icon|Start}} Symmetric relation
  23. {{Icon|Start}} Transitive relation
  24. {{Icon|B}} Equivalence relation (Level 4)
  25. {{Icon|Start}} Class (set theory)
  26. {{Icon|C}} Indexed family
  27. {{Icon|Start}} Mathematical structure
  28. {{Icon|C}} Space (mathematics)
  29. {{Icon|C}} Cardinality
  30. {{Icon|C}} Aleph number
  31. {{Icon|B}} Cantor's theorem (Level 4)
  32. {{Icon|B}} Cantor's diagonal argument
  33. {{Icon|B}} Cardinality of the continuum
  34. {{Icon|B}} Continuum hypothesis
  35. {{Icon|B}} Forcing (mathematics)
  36. {{Icon|C}} Power set
  37. {{Icon|B}} {{Icon|DGA}} Ordinal number
  38. {{Icon|C}} Transfinite induction
  39. {{Icon|C}} Von Neumann universe

=Axiomatic systems =

{{Vital article count|19}}

  1. {{Icon|C}} Axiomatic system
  2. {{Icon|C}} Zermelo–Fraenkel set theory
  3. {{Icon|Start}} Axiom of extensionality
  4. {{Icon|B}} Axiom of regularity
  5. {{Icon|B}} Axiom schema of specification
  6. {{Icon|B}} Axiom of pairing
  7. {{Icon|Start}} Axiom of union
  8. {{Icon|B}} Axiom schema of replacement
  9. {{Icon|C}} Axiom of infinity
  10. {{Icon|Start}} Axiom of power set
  11. {{Icon|B}} Axiom of choice (Level 4)
  12. {{Icon|B}} Banach–Tarski paradox
  13. {{Icon|Start}} Well-ordering theorem
  14. {{Icon|B}} Zorn's lemma
  15. {{Icon|B}} New Foundations
  16. {{Icon|C}} Peano axioms
  17. {{Icon|B}} Mathematical induction (Level 4)
  18. {{Icon|C}} Hilbert's axioms
  19. {{Icon|Start}} Tarski's axioms

=Computability theory =

{{Vital article count|23}}

  1. {{Icon|B}} Computability theory (Level 4)
  2. {{Icon|C}} Church–Turing thesis
  3. {{Icon|Start}} Model of computation
  4. {{Icon|B}} Combinatory logic
  5. {{Icon|B}} Lambda calculus
  6. {{Icon|B}} Turing machine
  7. {{Icon|B}} Computable function (Level 4)
  8. {{Icon|B}} General recursive function
  9. {{Icon|B}} Primitive recursive function
  10. {{Icon|B}} μ operator
  11. {{Icon|C}} Gödel numbering
  12. {{Icon|B}} {{Icon|DGA}} Gödel's incompleteness theorems (Level 4)
  13. {{Icon|Start}} Decision problem
  14. {{Icon|C}} Entscheidungsproblem
  15. {{Icon|C}} Halting problem
  16. {{Icon|C}} Rice's theorem
  17. {{Icon|B}} Turing's proof
  18. {{Icon|C}} Universal Turing machine
  19. {{Icon|Start}} Computably enumerable set
  20. {{Icon|Start}} Computable set
  21. {{Icon|C}} Oracle machine
  22. {{Icon|B}} Turing reduction
  23. {{Icon|B}} Turing degree

=Model theory =

{{Vital article count|12}}

  1. {{Icon|B}} Model theory
  2. {{Icon|Start}} Compactness theorem
  3. {{Icon|Start}} Gödel's completeness theorem
  4. {{Icon|B}} Löwenheim–Skolem theorem
  5. {{Icon|GA}} Skolem's paradox
  6. {{Icon|B}} Structure (mathematical logic)
  7. {{Icon|Start}} Elementary equivalence
  8. {{Icon|B}} Signature (logic)
  9. {{Icon|B}} Type (model theory)
  10. {{Icon|C}} Ultraproduct
  11. {{Icon|Start}} Theory (mathematical logic)
  12. {{Icon|Start}} Quantifier elimination

=Category theory =

{{Vital article count|22}}

  1. {{Icon|C}} Category theory (Level 4)
  2. {{Icon|C}} Commutative diagram
  3. {{Icon|Start}} Five lemma
  4. {{Icon|Start}} Snake lemma
  5. {{Icon|C}} Morphism
  6. {{Icon|B}} Category (mathematics)
  7. {{Icon|C}} Cartesian closed category
  8. {{Icon|B}} Concrete category
  9. {{Icon|Start}} Opposite category
  10. {{Icon|C}} Subcategory
  11. {{Icon|B}} Functor
  12. {{Icon|B}} Adjoint functors
  13. {{Icon|Start}} Forgetful functor
  14. {{Icon|B}} Hom functor
  15. {{Icon|Start}} Yoneda lemma
  16. {{Icon|C}} Universal property
  17. {{Icon|Start}} Free object
  18. {{Icon|Start}} Limit (category theory)
  19. {{Icon|C}} Coproduct
  20. {{Icon|Start}} Initial and terminal objects
  21. {{Icon|C}} Product (category theory)
  22. {{Icon|C}} Natural transformation

{{div col end}}

Discrete mathematics

{{Vital article count|126}}

{{Div col|colwidth=15em}}

  1. {{Icon|B}} Discrete mathematics (Level 4)

=Combinatorics =

{{Vital article count|23}}

  1. {{Icon|C}} Combinatorics (Level 4)
  2. {{Icon|C}} Algebraic combinatorics
  3. {{Icon|Start}} Enumerative combinatorics
  4. {{Icon|Start}} Ramsey theory
  5. {{Icon|B}} Ramsey's theorem
  6. {{Icon|Start}} Combinatorial principles
  7. {{Icon|C}} Addition principle
  8. {{Icon|C}} Rule of product
  9. {{Icon|C}} Inclusion–exclusion principle
  10. {{Icon|B}} Pigeonhole principle
  11. {{Icon|Start}} Double counting (proof technique)
  12. {{Icon|Start}} Twelvefold way
  13. {{Icon|B}} Combination (Level 4)
  14. {{Icon|C}} Binomial coefficient
  15. {{Icon|C}} Pascal's triangle
  16. {{Icon|B}} Permutation (Level 4)
  17. {{Icon|Start}} Partial permutation
  18. {{Icon|B}} Stirling number
  19. {{Icon|C}} Stirling numbers of the first kind
  20. {{Icon|C}} Stirling numbers of the second kind
  21. {{Icon|Start}} Lah number
  22. {{Icon|C}} Latin square
  23. {{Icon|C}} Mutually orthogonal Latin squares

=Graph theory =

{{Vital article count|79}}

  1. {{Icon|B}} Graph theory (Level 4)
  2. {{Icon|C}} Graph (discrete mathematics) (Level 4)
  3. {{Icon|B}} Complete graph
  4. {{Icon|Start}} Degree (graph theory)
  5. {{Icon|C}} Directed graph
  6. {{Icon|Start}} Multigraph
  7. {{Icon|C}} Hypergraph
  8. {{Icon|C}} Clique (graph theory)
  9. {{Icon|B}} Bipartite graph
  10. {{Icon|GA}} Clique problem
  11. {{Icon|B}} Graph coloring
  12. {{Icon|B}} Chromatic polynomial
  13. {{Icon|B}} Four color theorem
  14. {{Icon|C}} Vizing's theorem
  15. {{Icon|Start}} Regular graph
  16. {{Icon|Start}} Cage (graph theory)
  17. {{Icon|Start}} Coxeter graph
  18. {{Icon|C}} Connectivity (graph theory)
  19. {{Icon|Start}} Bridge (graph theory)
  20. {{Icon|GA}} Component (graph theory)
  21. {{Icon|C}} Tree (graph theory)
  22. {{Icon|Start}} Kruskal's algorithm
  23. {{Icon|C}} Prim's algorithm
  24. {{Icon|C}} Flow network
  25. {{Icon|C}} Ford–Fulkerson algorithm
  26. {{Icon|Start}} Max-flow min-cut theorem
  27. {{Icon|C}} Maximum flow problem
  28. {{Icon|Start}} Minimum-cost flow problem
  29. {{Icon|C}} Push–relabel maximum flow algorithm
  30. {{Icon|GA}} Graph homomorphism
  31. {{Icon|Start}} Edge contraction
  32. {{Icon|B}} Graph minor
  33. {{Icon|B}} Graph automorphism
  34. {{Icon|Start}} Cayley graph
  35. {{Icon|Start}} Graph isomorphism
  36. {{Icon|C}} Graph isomorphism problem
  37. {{Icon|Start}} Homeomorphism (graph theory)
  38. {{Icon|C}} Intersection graph
  39. {{Icon|B}} Line graph
  40. {{Icon|B}} Matching (graph theory)
  41. {{Icon|Start}} Matching polynomial
  42. {{Icon|Start}} Hosoya index
  43. {{Icon|Start}} Maximum cardinality matching
  44. {{Icon|C}} Blossom algorithm
  45. {{Icon|C}} Kőnig's theorem (graph theory)
  46. {{Icon|C}} Vertex cover
  47. {{Icon|Start}} Rainbow matching
  48. {{Icon|Start}} Edge cover
  49. {{Icon|C}} FKT algorithm
  50. {{Icon|Start}} Path (graph theory)
  51. {{Icon|Start}} Cycle (graph theory)
  52. {{Icon|GA}} Directed acyclic graph
  53. {{Icon|Start}} Girth (graph theory)
  54. {{Icon|C}} Eulerian path
  55. {{Icon|Start}} BEST theorem
  56. {{Icon|GA}} Handshaking lemma
  57. {{Icon|B}} Seven Bridges of Königsberg
  58. {{Icon|C}} Hamiltonian path
  59. {{Icon|C}} Hamiltonian path problem
  60. {{Icon|C}} Held–Karp algorithm
  61. {{Icon|GA}} Herschel graph
  62. {{Icon|B}} Travelling salesman problem
  63. {{Icon|C}} Shortest path problem
  64. {{Icon|C}} Bellman–Ford algorithm
  65. {{Icon|C}} Dijkstra's algorithm
  66. {{Icon|B}} Floyd–Warshall algorithm
  67. {{Icon|B}} Planar graph
  68. {{Icon|B}} Crossing number (graph theory)
  69. {{Icon|GA}} Three utilities problem
  70. {{Icon|GA}} Turán's brick factory problem
  71. {{Icon|C}} Kuratowski's theorem
  72. {{Icon|GA}} Snark (graph theory)
  73. {{Icon|Start}} Generalized Petersen graph
  74. {{Icon|Start}} Dürer graph
  75. {{Icon|C}} Petersen graph
  76. {{Icon|C}} Spectral graph theory
  77. {{Icon|C}} Adjacency matrix
  78. {{Icon|Start}} Degree matrix
  79. {{Icon|Start}} Laplacian matrix

=Order theory =

{{Vital article count|23}}

  1. {{Icon|B}} {{Icon|DGA}} Order theory
  2. {{Icon|Start}} Domain theory
  3. {{Icon|Start}} Upper and lower bounds
  4. {{Icon|Start}} Greatest element and least element
  5. {{Icon|Start}} Infimum and supremum
  6. {{Icon|C}} Preorder
  7. {{Icon|C}} Partially ordered set
  8. {{Icon|C}} Antichain
  9. {{Icon|Start}} Antisymmetric relation
  10. {{Icon|C}} Filter (mathematics)
  11. {{Icon|B}} Ultrafilter
  12. {{Icon|Start}} Hasse diagram
  13. {{Icon|Start}} Ideal (order theory)
  14. {{Icon|B}} Lattice (order)
  15. {{Icon|B}} Boolean algebra (structure)
  16. {{Icon|C}} Join and meet
  17. {{Icon|C}} Stable matching problem
  18. {{Icon|GA}} Gale–Shapley algorithm
  19. {{Icon|Start}} Stable roommates problem
  20. {{Icon|B}} Total order
  21. {{Icon|B}} Connected relation
  22. {{Icon|B}} Well-order
  23. {{Icon|Start}} Well-founded relation

{{Div col end}}

Calculus and analysis

{{Vital article count|188}}

{{Div col|colwidth=15em}}

=Basics =

{{Vital article count|10}}

  1. {{Icon|C}} Calculus (Level 3)
  2. {{Icon|C}} Limit (mathematics) (Level 3)
  3. {{Icon|Start}} Indeterminate form
  4. {{Icon|C}} Fundamental theorem of calculus (Level 4)
  5. {{Icon|B}} Continuous function (Level 4)
  6. {{Icon|C}} Infinitesimal
  7. {{Icon|LIST}} Differential (mathematics)
  8. {{Icon|Start}} Series expansion
  9. {{Icon|C}} Linear approximation
  10. {{Icon|Start}} Linearization

=Differential calculus =

{{Vital article count|15}}

  1. {{Icon|B}} Differential calculus (Level 4)
  2. {{Icon|Start}} Differentiable function
  3. {{Icon|C}} Differential operator
  4. {{Icon|GA}} Derivative (Level 4)
  5. {{Icon|Start}} Second derivative
  6. {{Icon|C}} Time derivative
  7. {{Icon|Start}} Differentiation rules
  8. {{Icon|B}} Product rule
  9. {{Icon|C}} Chain rule
  10. {{Icon|Start}} Power rule
  11. {{Icon|C}} Quotient rule
  12. {{Icon|Start}} Differentiation of trigonometric functions
  13. {{Icon|C}} L'Hôpital's rule
  14. {{Icon|B}} Taylor's theorem
  15. {{Icon|Start}} Related rates

=Integral calculus =

{{Vital article count|11}}

  1. {{Icon|B}} Integral (Level 4)
  2. {{Icon|Start}} Antiderivative
  3. {{Icon|B}} Lebesgue integral
  4. {{Icon|B}} Numerical integration (Level 4)
  5. {{Icon|B}} Riemann integral
  6. {{Icon|Start}} Constant of integration
  7. {{Icon|C}} Improper integral
  8. {{Icon|C}} Integration by parts
  9. {{Icon|C}} Integration by substitution
  10. {{Icon|Start}} Limits of integration
  11. {{Icon|C}} Riemann sum

=Multivariable and vector calculus =

{{Vital article count|30}}

  1. {{Icon|C}} Multivariable calculus (Level 4)
  2. {{Icon|B}} Vector calculus (Level 4)
  3. {{Icon|B}} Ricci calculus
  4. {{Icon|C}} Multiple integral (Level 4)
  5. {{Icon|Start}} Iterated integral
  6. {{Icon|C}} Fubini's theorem
  7. {{Icon|C}} Partial derivative (Level 4)
  8. {{Icon|B}} Total derivative
  9. {{Icon|Start}} Directional derivative
  10. {{Icon|C}} Differential form
  11. {{Icon|C}} Vector field
  12. {{Icon|C}} Conservative vector field
  13. {{Icon|Start}} Solenoidal vector field
  14. {{Icon|C}} Del (Level 4)
  15. {{Icon|C}} Gradient
  16. {{Icon|C}} Divergence
  17. {{Icon|B}} Curl (mathematics)
  18. {{Icon|C}} Laplace operator
  19. {{Icon|Start}} Poisson's equation
  20. {{Icon|B}} Laplace's equation (Level 4)
  21. {{Icon|C}} Line integral
  22. {{Icon|C}} Surface integral
  23. {{Icon|Start}} Volume integral
  24. {{Icon|B}} Stokes' theorem
  25. {{Icon|C}} Green's theorem
  26. {{Icon|Start}} Gradient theorem
  27. {{Icon|C}} Divergence theorem
  28. {{Icon|C}} Jacobian matrix and determinant
  29. {{Icon|B}} Lagrange multiplier
  30. {{Icon|Start}} Helmholtz decomposition

=Differential equations =

{{Vital article count|42}}

  1. {{Icon|B}} Differential equation (Level 4)
  2. {{Icon|B}} Ordinary differential equation (Level 4)
  3. {{Icon|C}} Partial differential equation (Level 4)
  4. {{Icon|Start}} Parabolic partial differential equation
  5. {{Icon|Start}} Hyperbolic partial differential equation
  6. {{Icon|Start}} Elliptic partial differential equation
  7. {{Icon|C}} Linear differential equation
  8. {{Icon|Start}} Homogeneous differential equation
  9. {{Icon|C}} Boundary value problem
  10. {{Icon|C}} Convolution
  11. {{Icon|C}} Separation of variables
  12. {{Icon|Start}} Integrating factor
  13. {{Icon|B}} Numerical methods for ordinary differential equations
  14. {{Icon|B}} Euler method
  15. {{Icon|C}} Runge–Kutta methods
  16. {{Icon|Start}} Shooting method
  17. {{Icon|C}} Numerical methods for partial differential equations
  18. {{Icon|C}} Crank–Nicolson method
  19. {{Icon|C}} Finite element method
  20. {{Icon|Start}} Method of lines
  21. {{Icon|C}} Dirichlet problem
  22. {{Icon|C}} Elliptic operator
  23. {{Icon|Start}} System of differential equations

==Dynamical systems ==

{{Vital article count|19}}

  1. {{Icon|C}} Dynamical systems theory (Level 4)
  2. {{Icon|B}} Dynamical system (Level 4)
  3. {{Icon|Start}} Linear dynamical system
  4. {{Icon|C}} Nonlinear system
  5. {{Icon|C}} Phase space
  6. {{Icon|Start}} Stability theory
  7. {{Icon|B}} Chaos theory (Level 4)
  8. {{Icon|Start}} Bifurcation theory
  9. {{Icon|B}} Butterfly effect
  10. {{Icon|Start}} Edge of chaos
  11. {{Icon|C}} Multibody system
  12. {{Icon|C}} Three-body problem
  13. {{Icon|Start}} Initial condition
  14. {{Icon|Start}} Conserved quantity
  15. {{Icon|Start}} Dynamical system simulation
  16. {{Icon|Start}} Flow (mathematics)
  17. {{Icon|C}} Lyapunov exponent
  18. {{Icon|C}} Attractor
  19. {{Icon|C}} Limit cycle

=Sequences and series =

{{Vital article count|19}}

  1. {{Icon|C}} Sequence (Level 4)
  2. {{Icon|C}} Limit of a sequence (Level 4)
  3. {{Icon|C}} Generating function
  4. {{Icon|C}} Series (mathematics) (Level 3)
  5. {{Icon|C}} Summation
  6. {{Icon|GA}} Taylor series (Level 4)
  7. {{Icon|C}} Laurent series
  8. {{Icon|C}} Convergent series
  9. {{Icon|B}} Absolute convergence
  10. {{Icon|B}} Cauchy sequence
  11. {{Icon|Start}} Convergence tests
  12. {{Icon|B}} Radius of convergence
  13. {{Icon|B}} Divergent series
  14. {{Icon|C}} Geometric series
  15. {{Icon|B}} Power series
  16. {{Icon|C}} Dirichlet series
  17. {{Icon|B}} Binomial series
  18. {{Icon|GA}} Harmonic series (mathematics)
  19. {{Icon|C}} Multipole expansion

=Mathematical analysis =

{{Vital article count|61}}

  1. {{Icon|C}} {{Icon|DGA}} Mathematical analysis (Level 3)
  2. {{Icon|C}} Approximation theory (Level 4)
  3. {{Icon|B}} Numerical analysis (Level 4)
  4. {{Icon|C}} Functional analysis (Level 4)
  5. {{Icon|GA}} Hilbert space (Level 4)
  6. {{Icon|B}} Lp space
  7. {{Icon|C}} Operator theory
  8. {{Icon|C}} Operator (mathematics)
  9. {{Icon|C}} Sequence space
  10. {{Icon|C}} Uniform convergence
  11. {{Icon|C}} {{Icon|DGA}} Measure (mathematics)
  12. {{Icon|B}} Calculus of variations (Level 4)
  13. {{Icon|C}} Asymptotic analysis
  14. {{Icon|C}} Asymptote
  15. {{Icon|B}} Interpolation

==Real analysis ==

{{Vital article count|14}}

  1. {{Icon|C}} Real analysis (Level 4)
  2. {{Icon|C}} Number line
  3. {{Icon|C}} Completeness of the real numbers
  4. {{Icon|C}} Extended real number line
  5. {{Icon|B}} Interval (mathematics)
  6. {{Icon|C}} Extreme value theorem
  7. {{Icon|Start}} Intermediate value theorem
  8. {{Icon|C}} Root-finding algorithm
  9. {{Icon|C}} Newton's method
  10. {{Icon|Start}} Bisection method
  11. {{Icon|C}} Regula falsi
  12. {{Icon|C}} Secant method
  13. {{Icon|C}} Mean value theorem
  14. {{Icon|Start}} Squeeze theorem

==Complex analysis ==

{{Vital article count|22}}

  1. {{Icon|C}} Complex analysis (Level 4)
  2. {{Icon|B}} Complex plane
  3. {{Icon|B}} Riemann sphere
  4. {{Icon|C}} Contour integration
  5. {{Icon|B}} Cauchy's integral formula (Level 4)
  6. {{Icon|C}} Cauchy's integral theorem
  7. {{Icon|B}} Euler's formula (Level 4)
  8. {{Icon|C}} De Moivre's formula
  9. {{Icon|C}} Euler's identity (Level 4)
  10. {{Icon|C}} Holomorphic function (Level 4)
  11. {{Icon|B}} Riemann surface (Level 4)
  12. {{Icon|C}} Liouville's theorem (complex analysis)
  13. {{Icon|C}} Cauchy–Riemann equations
  14. {{Icon|Start}} Cauchy principal value
  15. {{Icon|Start}} Conformal map
  16. {{Icon|Start}} Singularity (mathematics)
  17. {{Icon|C}} Zeros and poles
  18. {{Icon|Start}} Picard theorem
  19. {{Icon|Start}} Residue (complex analysis)
  20. {{Icon|Start}} Residue theorem
  21. {{Icon|Start}} Branch point
  22. {{Icon|B}} Root of unity

==Harmonic analysis ==

{{Vital article count|10}}

  1. {{Icon|C}} Harmonic analysis (Level 4)
  2. {{Icon|B}} Fourier analysis (Level 4)
  3. {{Icon|B}} Fourier series (Level 4)
  4. {{Icon|B}} Fourier transform (Level 4)
  5. {{Icon|Start}} Convolution theorem
  6. {{Icon|C}} Fast Fourier transform
  7. {{Icon|B}} Laplace transform (Level 4)
  8. {{Icon|B}} Harmonic function
  9. {{Icon|Start}} Potential theory
  10. {{Icon|B}} Wavelet

{{Div col end}}

Number theory

{{Vital article count|53}}

{{Div col|colwidth=15em}}

  1. {{Icon|B}} Number theory (Level 3)

=Prime numbers =

{{Vital article count|14}}

  1. {{Icon|GA}} Prime number (Level 3)
  2. {{Icon|C}} Fermat number
  3. {{Icon|C}} Mersenne prime
  4. {{Icon|C}} Semiprime
  5. {{Icon|C}} Twin prime
  6. {{Icon|Start}} Primality test
  7. {{Icon|C}} AKS primality test
  8. {{Icon|Start}} Pseudoprime
  9. {{Icon|C}} Sieve of Eratosthenes
  10. {{Icon|C}} Coprime integers
  11. {{Icon|C}} abc conjecture
  12. {{Icon|C}} Euclid's theorem (Level 4)
  13. {{Icon|B}} Prime number theorem (Level 4)
  14. {{Icon|B}} p-adic number

=Sums and products =

{{Vital article count|10}}

  1. {{Icon|Start}} Aliquot sum
  2. {{Icon|B}} Perfect number
  3. {{Icon|Start}} Composite number
  4. {{Icon|C}} Fundamental theorem of arithmetic (Level 4)
  5. {{Icon|Start}} Highly composite number
  6. {{Icon|C}} Collatz conjecture
  7. {{Icon|B}} Magic square
  8. {{Icon|C}} Integer partition
  9. {{Icon|C}} Goldbach's conjecture
  10. {{Icon|C}} Young tableau

=Modular arithmetic =

{{Vital article count|8}}

  1. {{Icon|C}} Chinese remainder theorem
  2. {{Icon|C}} Discrete logarithm
  3. {{Icon|C}} Fermat's little theorem
  4. {{Icon|C}} Quadratic residue
  5. {{Icon|B}} Quadratic reciprocity
  6. {{Icon|Start}} Legendre symbol
  7. {{Icon|Start}} Jacobi symbol
  8. {{Icon|Start}} Wilson's theorem

=Sequences =

{{Vital article count|8}}

  1. {{Icon|Start}} Arithmetic progression
  2. {{Icon|Start}} Dirichlet's theorem on arithmetic progressions
  3. {{Icon|B}} Recurrence relation
  4. {{Icon|B}} Fibonacci sequence (Level 4)
  5. {{Icon|GA}} Telephone number (mathematics)
  6. {{Icon|B}} Bell number
  7. {{Icon|C}} Catalan number
  8. {{Icon|Start}} Lucky number

=Diophantine equations =

{{Vital article count|5}}

  1. {{Icon|C}} Diophantine equation (Level 4)
  2. {{Icon|C}} Fermat's Last Theorem (Level 4)
  3. {{Icon|C}} Modularity theorem
  4. {{Icon|C}} Extended Euclidean algorithm
  5. {{Icon|Start}} Bézout's identity

=Subdisciplines =

{{Vital article count|7}}

  1. {{Icon|B}} Algebraic number theory (Level 4)
  2. {{Icon|B}} Algebraic number field (Level 4)
  3. {{Icon|C}} Class field theory (Level 4)
  4. {{Icon|B}} Analytic number theory (Level 4)
  5. {{Icon|C}} Dirichlet character
  6. {{Icon|Start}} Möbius inversion formula
  7. {{Icon|B}} {{Icon|DGA}} Riemann hypothesis (Level 4)

{{div col end}}

Applied mathematics

{{Vital article count|43}}

{{Div col|colwidth=15em}}

  1. {{Icon|B}} Applied mathematics (Level 4)
  2. {{Icon|B}} Control theory (Level 4)
  3. {{Icon|C}} Decision theory
  4. {{Icon|C}} Music and mathematics

=Game theory =

{{Vital article count|18}}

  1. {{Icon|C}} {{Icon|FFA}} Game theory (Level 4)
  2. {{Icon|B}} Extensive-form game
  3. {{Icon|Start}} Information set (game theory)
  4. {{Icon|Start}} Common knowledge (logic)
  5. {{Icon|Start}} Perfect information
  6. {{Icon|Start}} Normal-form game
  7. {{Icon|Start}} Battle of the sexes (game theory)
  8. {{Icon|C}} {{Icon|FFA}} Prisoner's dilemma
  9. {{Icon|C}} Zero-sum game
  10. {{Icon|Start}} Repeated game
  11. {{Icon|Start}} Strategy (game theory)
  12. {{Icon|Start}} Minimax
  13. {{Icon|B}} {{Icon|DGA}} Nash equilibrium
  14. {{Icon|Start}} Strategic dominance
  15. {{Icon|Start}} Social choice theory
  16. {{Icon|Start}} Condorcet paradox
  17. {{Icon|B}} Arrow's impossibility theorem
  18. {{Icon|Start}} Gibbard–Satterthwaite theorem

=Information theory =

{{Vital article count|7}}

  1. {{Icon|B}} Information theory (Level 4)
  2. {{Icon|C}} Entropy (information theory)
  3. {{Icon|C}} Coding theory (Level 4)
  4. {{Icon|B}} Data compression (Level 4)
  5. {{Icon|C}} Error detection and correction (Level 4)
  6. {{Icon|C}} Hamming code
  7. {{Icon|C}} Reed–Solomon error correction

=Optimization =

{{Vital article count|14}}

  1. {{Icon|B}} Mathematical optimization (Level 4)
  2. {{Icon|B}} Dynamic programming
  3. {{Icon|B}} Linear programming (Level 4)
  4. {{Icon|C}} Duality (optimization)
  5. {{Icon|Start}} Feasible region
  6. {{Icon|C}} Ellipsoid method
  7. {{Icon|B}} Simplex algorithm
  8. {{Icon|C}} Loss function
  9. {{Icon|C}} Nonlinear programming (Level 4)
  10. {{Icon|C}} Karush–Kuhn–Tucker conditions
  11. {{Icon|Start}} Transportation theory (mathematics)
  12. {{Icon|Start}} Assignment problem
  13. {{Icon|C}} Hungarian algorithm
  14. {{Icon|C}} Operations research (Level 4)

{{Div col end}}

Theoretical computer science

{{Vital article count|55}}

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

{{Div col|colwidth=15em}}

  1. {{Icon|B}} Theoretical computer science (Level 4)
  2. {{Icon|C}} Abstract machine (Level 4)
  3. {{Icon|C}} Nondeterministic Turing machine
  4. {{Icon|Start}} Computation
  5. {{Icon|C}} Theory of computation (Level 4)

=Algorithms =

{{Vital article count|16}}

  1. {{Icon|C}} {{Icon|FFA}} Algorithm (Level 3)
  2. {{Icon|C}} Analysis of algorithms
  3. {{Icon|B}} Big O notation
  4. {{Icon|Start}} Deterministic algorithm
  5. {{Icon|B}} Divide-and-conquer algorithm
  6. {{Icon|C}} Cache replacement policies
  7. {{Icon|Start}} Search algorithm
  8. {{Icon|FA}} Binary search
  9. {{Icon|Start}} Breadth-first search
  10. {{Icon|Start}} Brute-force search
  11. {{Icon|C}} Depth-first search
  12. {{Icon|Start}} String-searching algorithm
  13. {{Icon|B}} Sorting algorithm
  14. {{Icon|B}} Heapsort
  15. {{Icon|C}} Merge sort
  16. {{Icon|B}} Quicksort

=Automata theory =

{{Vital article count|7}}

  1. {{Icon|C}} Automata theory
  2. {{Icon|B}} Cellular automaton
  3. {{Icon|B}} Conway's Game of Life
  4. {{Icon|B}} Finite-state machine
  5. {{Icon|B}} Pushdown automaton
  6. {{Icon|C}} Formal language (Level 4)
  7. {{Icon|C}} Chomsky hierarchy

=Complexity theory =

{{Vital article count|12}}

  1. {{Icon|B}} {{Icon|FFA}} Computational complexity theory (Level 4)
  2. {{Icon|Start}} Blum axioms
  3. {{Icon|Start}} Constructible function
  4. {{Icon|B}} Kolmogorov complexity
  5. {{Icon|Start}} Space complexity
  6. {{Icon|B}} Time complexity
  7. {{Icon|C}} NP (complexity)
  8. {{Icon|C}} P (complexity)
  9. {{Icon|B}} P versus NP problem (Level 4)
  10. {{Icon|C}} Boolean satisfiability problem
  11. {{Icon|C}} NP-hardness
  12. {{Icon|C}} Time hierarchy theorem

=Data structures and types =

{{Vital article count|15}}

  1. {{Icon|C}} Abstract data type
  2. {{Icon|C}} Associative array
  3. {{Icon|C}} Graph (abstract data type)
  4. {{Icon|Start}} Queue (abstract data type)
  5. {{Icon|C}} Stack (abstract data type)
  6. {{Icon|C}} Data model
  7. {{Icon|C}} Data structure (Level 4)
  8. {{Icon|B}} Hash table
  9. {{Icon|C}} Heap (data structure)
  10. {{Icon|C}} Linked list
  11. {{Icon|C}} Array (data structure)
  12. {{Icon|C}} Tree (abstract data type)
  13. {{Icon|C}} B-tree
  14. {{Icon|GA}} Binary search tree
  15. {{Icon|C}} Red–black tree

{{Div col end}}

{{Core topics}}

All languages should have

Vital articles