വിക്കിപീഡിയ:Vital articles/Expanded/Mathematics

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Mathematics (296 articles)

See also: Mathematicians

Basics (60 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. 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)

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)

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)

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)

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)

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