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Mathematics

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See also: Scientists, inventors and mathematicians

Basics

1. Conjecture
   1. Equation solving
   2. Gamma function
2. Hilbert's problems
   1. Arabic numerals
   2. Binary number
3. Multiplication table

Algebra

1. Abstract algebra
   1. Algebraic topology
      1. Sheaf (mathematics)
   2. Commutative algebra
   3. Field (mathematics)
   4. Fundamental theorem of algebra
      1. Classification of finite simple groups
      2. Fundamental group
      3. Group representation
   5. Homological algebra
   6. Isomorphism
   7. Module (mathematics)
   8. Representation theory
   9. Ring theory
      1. Commutative ring
      2. Field theory (mathematics)
      3. Galois theory
   10. Algebraic variety
2. Inequality
   1. Gaussian elimination
3. Multilinear algebra

Calculus and analysis

1. 1. Complex analysis
      1. Cauchy's integral formula
      2. Holomorphic function
      3. Riemann surface
   2. Functional analysis
   3. Harmonic analysis
      1. Fourier analysis
      2. Fourier series
      3. Mathematical optimization
   4. Riemann sphere
   5. Fundamental theorem of calculus
   6. Multivariable calculus
      1. Multiple integral
      2. Partial derivative
         1. Laplace's equation
         2. Partial differential equations
      3. Vector calculus
   7. Calculus of variations
2. Limit (mathematics)
   1. Limit of a sequence
3. Real analysis

Discrete mathematics

1. Graph theory
   1. Graph (mathematics)
2. Mathematical logic
   1. Computability theory
      1. Computable function
   2. Gödel's incompleteness theorems
   3. Mathematical induction
   4. Propositional calculus
   5. Axiom of choice
   6. Cantor's theorem
   7. Naive set theory
      1. Russell's paradox

Geometry

1. Differential geometry
   1. Atiyah–Singer index theorem
2. Dimension (mathematics and physics)
   1. Mandelbrot set
3. Hilbert space
4. Metric space
5. Non-Euclidean geometry
6. Riemannian geometry
7. Tensor
   1. Compact space
   2. Euler characteristic
   3. General topology
   4. Homology
   5. Homotopy
   6. Manifold
   7. Open set
   8. Poincaré conjecture
   9. Topological space

Shape

1. 1. 1. Reuleaux triangle
2. Polyhedron
   1. Prism (geometry)

Other

1. 1. Information entropy
2. Category theory
   1. Category (mathematics)
   2. Commutative diagram
3. Dynamical system
   1. Nonlinear system
   2. Algebraic number theory
      1. Algebraic number field
      2. Class field theory
   3. Analytic number theory
   4. Diophantine equation
   5. Fermat's Last Theorem
      1. Prime number theorem
4. Pure mathematics
5. Theoretical computer science
   1. Computational complexity theory
   2. Theory of computation
6. Linear programming
7. Nonlinear programming
8. P versus NP problem
9. Principal component analysis
10. Econometrics

Probability and statistics

1. 1. Central limit theorem
   2. Law of large numbers
   3. Markov chain
   4. Probability density function
      1. Chi-squared distribution
      2. Exponential distribution
         1. Multivariate normal distribution
      3. Pareto distribution
      4. Poisson distribution
      5. Student's t-distribution
      6. Uniform distribution (continuous)
      7. Uniform distribution (discrete)
   5. Probability space
   6. Stochastic process
   7. Bayesian inference
   8. Chi-squared test
   9. Correlation and dependence
   10. Linear regression
   11. Margin of error
       1. Arithmetic mean
   12. Maximum likelihood
   13. Mode
   14. P-value
   15. Regression analysis
   16. Standard error
   17. Statistical hypothesis testing
   18. Student's t-test
2. Design of experiments
3. Randomized controlled trial
4. Survey methodology
5. Statistical population