Mathematics

| 🗖 nosplit | ↑ parent "Ciro Santilli's Homepage" | 17, 11k, 293

🗖 nosplit | ⇓ toc | ↑ parent "Ciro Santilli's Homepage" | Wikipedia | 17, 11k, 293

The proper precise definition of mathematics can be found at: Section 2. "Formalization of Mathematics".

Table of contents | 17, 11k, 293
- 1. The beauty of mathematics | 257, 548, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 1.1. Lists of mathematical problems | 13, 291, 3 | 🔗 link | 🗖 nosplit | ↑ parent "The beauty of mathematics"
    - 1.1.1. Hilbert's problems | 22 | 🔗 link | 🗖 nosplit | ↑ parent "Lists of mathematical problems"
    - 1.1.2. Millennium Prize Problems | 244, 256, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Lists of mathematical problems"
      - 1.1.2.1. Birch and Swinnerton-Dyer Conjecture | 12 | 🔗 link | 🗖 nosplit | ↑ parent "Millennium Prize Problems"
- 2. Formalization of Mathematics | 439, 829, 21 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 2.1. QED manifesto | 25 | 🔗 link | 🗖 nosplit | ↑ parent "Formalization of Mathematics"
  - 2.2. Formal proof | 15, 144, 8 | 🔗 link | 🗖 nosplit | ↑ parent "Formalization of Mathematics"
    - 2.2.1. Formal system | 0, 39, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Formal proof"
      - 2.2.1.1. Zermelo-Fraenkel set theory (ZF) | 25, 39, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Formal system"
        
        2.2.1.1.1. Metamath | 14 | 🔗 link | 🗖 nosplit | ↑ parent "Zermelo-Fraenkel set theory"
    - 2.2.2. Axiom | 0, 90, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Formal proof"
      - 2.2.2.1. Consistency | 41 | 🔗 link | 🗖 nosplit | ↑ parent "Axiom"
      - 2.2.2.2. Independence (mathematical logic) | 49 | 🔗 link | 🗖 nosplit | ↑ parent "Axiom"
    - 2.2.3. Conjecture | 🔗 link | 🗖 nosplit | ↑ parent "Formal proof"
    - 2.2.4. Theorem | 🔗 link | 🗖 nosplit | ↑ parent "Formal proof"
  - 2.3. Set (mathematics) | 86 | 🔗 link | 🗖 nosplit | ↑ parent "Formalization of Mathematics"
  - 2.4. Function (mathematics) | 25, 77, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Formalization of Mathematics"
    - 2.4.1. Exponential function | 0, 52, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Function"
      - 2.4.1.1. Matrix exponential | 52 | 🔗 link | 🗖 nosplit | ↑ parent "Exponential function"
  - 2.5. Function space | 11 | 🔗 link | 🗖 nosplit | ↑ parent "Formalization of Mathematics"
  - 2.6. Integer | 🔗 link | 🗖 nosplit | ↑ parent "Formalization of Mathematics"
  - 2.7. Real number | 4, 4, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Formalization of Mathematics"
    - 2.7.1. Countable set | 0, 0, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Real number"
      - 2.7.1.1. Cantor's diagonal argument | 🔗 link | 🗖 nosplit | ↑ parent "Countable set"
  - 2.8. Complex number | 43 | 🔗 link | 🗖 nosplit | ↑ parent "Formalization of Mathematics"
  - 2.9. Ordered pair | 🔗 link | 🗖 nosplit | ↑ parent "Formalization of Mathematics"
- 3. Algebra | 0, 1k, 51 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 3.1. Commutator | 🔗 link | 🗖 nosplit | ↑ parent "Algebra"
  - 3.2. Field (mathematics) | 🔗 link | 🗖 nosplit | ↑ parent "Algebra"
  - 3.3. Linear algebra | 0, 226, 19 | 🔗 link | 🗖 nosplit | ↑ parent "Algebra"
    - 3.3.1. Dot product | 🔗 link | 🗖 nosplit | ↑ parent "Linear algebra"
    - 3.3.2. Projection (mathematics) | 🔗 link | 🗖 nosplit | ↑ parent "Linear algebra"
    - 3.3.3. Matrix | 0, 226, 14 | 🔗 link | 🗖 nosplit | ↑ parent "Linear algebra"
      - 3.3.3.1. Matrix multiplication | 11, 150, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Matrix"
        
        3.3.3.1.1. Matrix multiplication algorithm | 2 | 🔗 link | 🗖 nosplit | ↑ parent "Matrix multiplication"
        
        3.3.3.1.2. Linear map (linear operator) | 123, 137, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Matrix multiplication"
        
        3.3.3.1.2.1. Linear operator | 14 | 🔗 link | 🗖 nosplit | ↑ parent "Linear map"
        
        3.3.3.1.2.2. Self-adjoint operator | 🔗 link | 🗖 nosplit | ↑ parent "Linear map"
      - 3.3.3.2. Eigenvalues and eigenvectors | 0, 26, 6 | 🔗 link | 🗖 nosplit | ↑ parent "Matrix"
        
        3.3.3.2.1. Applications of eigenvalues and eigenvectors | 6 | 🔗 link | 🗖 nosplit | ↑ parent "Eigenvalues and eigenvectors"
        
        3.3.3.2.2. Eigenvalue | 9 | 🔗 link | 🗖 nosplit | ↑ parent "Eigenvalues and eigenvectors"
        
        3.3.3.2.3. Eigenvector | 9 | 🔗 link | 🗖 nosplit | ↑ parent "Eigenvalues and eigenvectors"
        
        3.3.3.2.4. Eigenvectors and eigenvalues of the identity matrix | 2 | 🔗 link | 🗖 nosplit | ↑ parent "Eigenvalues and eigenvectors"
        
        3.3.3.2.5. Spectral theorem | 0, 0, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Eigenvalues and eigenvectors"
        
        3.3.3.2.5.1. Hermitian matrix | 🔗 link | 🗖 nosplit | ↑ parent "Spectral theorem"
      - 3.3.3.3. Orthogonal matrix | 11, 50, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Matrix"
        
        3.3.3.3.1. Unitary matrix | 39 | 🔗 link | 🗖 nosplit | ↑ parent "Orthogonal matrix"
    - 3.3.4. Vector space | 0, 0, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Linear algebra"
      - 3.3.4.1. Vector (mathematics) | 🔗 link | 🗖 nosplit | ↑ parent "Vector space"
  - 3.4. Group (mathematics) | 0, 1k, 28 | 🔗 link | 🗖 nosplit | ↑ parent "Algebra"
    - 3.4.1. Abelian group | 30 | 🔗 link | 🗖 nosplit | ↑ parent "Group"
    - 3.4.2. Symmetry | 29 | 🔗 link | 🗖 nosplit | ↑ parent "Group"
    - 3.4.3. Important mathematical groups | 0, 11, 5 | 🔗 link | 🗖 nosplit | ↑ parent "Group"
      - 3.4.3.1. Important discrete mathematical groups | 0, 11, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Important mathematical groups"
        
        3.4.3.1.1. Cyclic group ( $Z_{n}$ ) | 🔗 link | 🗖 nosplit | ↑ parent "Important discrete mathematical groups"
        
        3.4.3.1.2. Alternating group ( $A_{n}$ ) | 🔗 link | 🗖 nosplit | ↑ parent "Important discrete mathematical groups"
        
        3.4.3.1.3. Wallpaper group | 3 | 🔗 link | 🗖 nosplit | ↑ parent "Important discrete mathematical groups"
        
        3.4.3.1.4. Space group | 8 | 🔗 link | 🗖 nosplit | ↑ parent "Important discrete mathematical groups"
    - 3.4.4. Group isomorphism | 0, 124, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Group"
      - 3.4.4.1. Group homomorphism | 95, 124, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Group isomorphism"
        
        3.4.4.1.1. Fundamental theorem on homomorphisms | 29 | 🔗 link | 🗖 nosplit | ↑ parent "Group homomorphism"
        
        3.4.4.1.2. Kernel (algebra) | 🔗 link | 🗖 nosplit | ↑ parent "Group homomorphism"
    - 3.4.5. Direct product of groups | 0, 59, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Group"
      - 3.4.5.1. Semidirect product | 59 | 🔗 link | 🗖 nosplit | ↑ parent "Direct product of groups"
    - 3.4.6. Subgroup | 0, 949, 13 | 🔗 link | 🗖 nosplit | ↑ parent "Group"
      - 3.4.6.1. Subgroup generated by a group | 🔗 link | 🗖 nosplit | ↑ parent "Subgroup"
      - 3.4.6.2. Quotient group | 45, 949, 11 | 🔗 link | 🗖 nosplit | ↑ parent "Subgroup"
        
        3.4.6.2.1. Subquotient | 64 | 🔗 link | 🗖 nosplit | ↑ parent "Quotient group"
        
        3.4.6.2.2. Relationship between the quotient group and direct products | 304 | 🔗 link | 🗖 nosplit | ↑ parent "Quotient group"
        
        3.4.6.2.3. Normal subgroup | 143, 536, 8 | 🔗 link | 🗖 nosplit | ↑ parent "Quotient group"
        
        3.4.6.2.3.1. Simple group | 48 | 🔗 link | 🗖 nosplit | ↑ parent "Normal subgroup"
        
        3.4.6.2.3.2. Classification of finite groups | 71, 345, 6 | 🔗 link | 🗖 nosplit | ↑ parent "Normal subgroup"
        
        3.4.6.2.3.2.1. Classification of finite simple groups | 84, 166, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Classification of finite groups"
        
        3.4.6.2.3.2.1.1. Monster group | 33 | 🔗 link | 🗖 nosplit | ↑ parent "Classification of finite simple groups"
        
        3.4.6.2.3.2.1.2. Group of Lie type | 35 | 🔗 link | 🗖 nosplit | ↑ parent "Classification of finite simple groups"
        
        3.4.6.2.3.2.1.3. Jordan-Holder Theorem | 14 | 🔗 link | 🗖 nosplit | ↑ parent "Classification of finite simple groups"
        
        3.4.6.2.3.2.1.4. Composition series | 🔗 link | 🗖 nosplit | ↑ parent "Classification of finite simple groups"
        
        3.4.6.2.3.2.2. Group extension problem | 108 | 🔗 link | 🗖 nosplit | ↑ parent "Classification of finite groups"
- 4. Calculus | 17, 5k, 136 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 4.1. Mathematical analysis | 17 | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
  - 4.2. Limit (mathematics) | 46, 46, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
    - 4.2.1. Convergent series | 🔗 link | 🗖 nosplit | ↑ parent "Limit"
    - 4.2.2. Continuous function | 🔗 link | 🗖 nosplit | ↑ parent "Limit"
  - 4.3. Derivative | 0, 142, 9 | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
    - 4.3.1. Chain rule | 0, 0, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Derivative"
      - 4.3.1.1. Multivariable chain rule | 🔗 link | 🗖 nosplit | ↑ parent "Chain rule"
    - 4.3.2. Maxima and minima | 0, 2, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Derivative"
      - 4.3.2.1. Lifegard problem | 2 | 🔗 link | 🗖 nosplit | ↑ parent "Maxima and minima"
      - 4.3.2.2. Saddle point | 🔗 link | 🗖 nosplit | ↑ parent "Maxima and minima"
    - 4.3.3. Partial derivative | 0, 70, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Derivative"
      - 4.3.3.1. Partial derivative symbol ( $\partial$ ) | 70 | 🔗 link | 🗖 nosplit | ↑ parent "Partial derivative"
    - 4.3.4. Total derivative | 70 | 🔗 link | 🗖 nosplit | ↑ parent "Derivative"
    - 4.3.5. Directional derivative | 🔗 link | 🗖 nosplit | ↑ parent "Derivative"
  - 4.4. Riemann integral | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
  - 4.5. Lebesgue integral | 31, 851, 12 | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
    - 4.5.1. Lebesgue integral vs Riemann integral | 197, 264, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Lebesgue integral"
      - 4.5.1.1. Real world applications of the Lebesgue integral | 67 | 🔗 link | 🗖 nosplit | ↑ parent "Lebesgue integral vs Riemann integral"
    - 4.5.2. Lebesgue measurable | 🔗 link | 🗖 nosplit | ↑ parent "Lebesgue integral"
    - 4.5.3. Lebesgue integral of $L^{p}$ is complete but Riemann isn't | 89, 547, 7 | 🔗 link | 🗖 nosplit | ↑ parent "Lebesgue integral"
      - 4.5.3.1. Riesz-Fischer theorem | 59, 302, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Lebesgue integral of $L^{p}$ is complete but Riemann isn't"
        
        4.5.3.1.1. $L^{p}$ is complete | 1 | 🔗 link | 🗖 nosplit | ↑ parent "Riesz-Fischer theorem"
        
        4.5.3.1.2. Fourier basis is complete for $L^{2}$ | 60, 242, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Riesz-Fischer theorem"
        
        4.5.3.1.2.1. $L^{p}$ norm sequence convergence does not imply pointwise convergence | 42 | 🔗 link | 🗖 nosplit | ↑ parent "Fourier basis is complete for $L^{2}$ "
        
        4.5.3.1.2.2. Carleson's theorem | 140 | 🔗 link | 🗖 nosplit | ↑ parent "Fourier basis is complete for $L^{2}$ "
      - 4.5.3.2. $L^{p}$ | 30, 156, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Lebesgue integral of $L^{p}$ is complete but Riemann isn't"
        
        4.5.3.2.1. $L^{2}$ | 126 | 🔗 link | 🗖 nosplit | ↑ parent " $L^{p}$ "
    - 4.5.4. Every Riemann integrable function is Lebesgue integrable | 9 | 🔗 link | 🗖 nosplit | ↑ parent "Lebesgue integral"
  - 4.6. Measure theory | 55 | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
  - 4.7. Fourier series | 139, 385, 8 | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
    - 4.7.1. Applications of the Fourier series | 0, 72, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Fourier series"
      - 4.7.1.1. Solving partial differential equations with the Fourier series | 72 | 🔗 link | 🗖 nosplit | ↑ parent "Applications of the Fourier series"
    - 4.7.2. Discrete Fourier transform (DFT) | 🔗 link | 🗖 nosplit | ↑ parent "Fourier series"
    - 4.7.3. Fourier transform | 24, 157, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Fourier series"
      - 4.7.3.1. Multidimensional Fourier transform | 41 | 🔗 link | 🗖 nosplit | ↑ parent "Fourier transform"
      - 4.7.3.2. Fourier inversion theorem | 41 | 🔗 link | 🗖 nosplit | ↑ parent "Fourier transform"
      - 4.7.3.3. Laplace transform | 51 | 🔗 link | 🗖 nosplit | ↑ parent "Fourier transform"
    - 4.7.4. History of the Fourier series | 17 | 🔗 link | 🗖 nosplit | ↑ parent "Fourier series"
  - 4.8. Topology | 72, 575, 16 | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
    - 4.8.1. Neighbourhood (mathematics) | 12 | 🔗 link | 🗖 nosplit | ↑ parent "Topology"
    - 4.8.2. Topological space | 🔗 link | 🗖 nosplit | ↑ parent "Topology"
    - 4.8.3. Manifold | 164, 414, 6 | 🔗 link | 🗖 nosplit | ↑ parent "Topology"
      - 4.8.3.1. Atlas (topology) | 25, 25, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Manifold"
        
        4.8.3.1.1. Coordinate chart | 🔗 link | 🗖 nosplit | ↑ parent "Atlas"
      - 4.8.3.2. Covariant derivative | 39 | 🔗 link | 🗖 nosplit | ↑ parent "Manifold"
      - 4.8.3.3. Tangent space | 128, 140, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Manifold"
        
        4.8.3.3.1. Tangent vector to a manifold | 12 | 🔗 link | 🗖 nosplit | ↑ parent "Tangent space"
      - 4.8.3.4. One-form | 46 | 🔗 link | 🗖 nosplit | ↑ parent "Manifold"
    - 4.8.4. Metric (mathematics) | 0, 10, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Topology"
      - 4.8.4.1. Metric space | 10 | 🔗 link | 🗖 nosplit | ↑ parent "Metric"
    - 4.8.5. Complete metric space | 44 | 🔗 link | 🗖 nosplit | ↑ parent "Topology"
    - 4.8.6. Dense set | 🔗 link | 🗖 nosplit | ↑ parent "Topology"
    - 4.8.7. Real coordinate space ( $R^{n}$ ) | 0, 23, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Topology"
      - 4.8.7.1. Euclidean space | 23, 23, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Real coordinate space"
        
        4.8.7.1.1. Non-Euclidean geometry | 🔗 link | 🗖 nosplit | ↑ parent "Euclidean space"
  - 4.9. Distribution (mathematics) | 56, 131, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
    - 4.9.1. Dirac delta function | 75 | 🔗 link | 🗖 nosplit | ↑ parent "Distribution"
  - 4.10. Complex analysis | 14, 277, 6 | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
    - 4.10.1. Holomorphic function | 69 | 🔗 link | 🗖 nosplit | ↑ parent "Complex analysis"
    - 4.10.2. Analytic continuation | 52, 194, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Complex analysis"
      - 4.10.2.1. Visualizing the Riemann hypothesis and analytic continuation by 3Blue1Brown (2016) | 16 | 🔗 link | 🗖 nosplit | ↑ parent "Analytic continuation"
      - 4.10.2.2. Identity theorem | 92, 126, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Analytic continuation"
        
        4.10.2.2.1. Riemann zeta function | 0, 34, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Identity theorem"
        
        4.10.2.2.1.1. Riemann hypothesis | 34 | 🔗 link | 🗖 nosplit | ↑ parent "Riemann zeta function"
  - 4.11. Hilbert space | 34 | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
  - 4.12. Differential equation | 0, 3k, 60 | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
  - 4.13. Taylor series | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
  - 4.14. Gradient, Divergence, Curl, and Laplacian | 0, 306, 7 | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
  - 4.15. Infinitesimal | 24 | 🔗 link | 🗖 nosplit | ↑ parent "Calculus"
- 5. Discrete mathematics | 0, 0, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 5.1. Graph (discrete mathematics) | 🔗 link | 🗖 nosplit | ↑ parent "Discrete mathematics"
- 6. Functional equation | 0, 13, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 6.1. Cauchy's functional equation | 13 | 🔗 link | 🗖 nosplit | ↑ parent "Functional equation"
- 7. Game theory | 0, 152, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 7.1. Nash equilibrium | 142, 152, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Game theory"
    - 7.1.1. Mixed strategy | 🔗 link | 🗖 nosplit | ↑ parent "Nash equilibrium"
    - 7.1.2. Prisoner's dilemma | 2 | 🔗 link | 🗖 nosplit | ↑ parent "Nash equilibrium"
    - 7.1.3. Bimatrix game | 8 | 🔗 link | 🗖 nosplit | ↑ parent "Nash equilibrium"
- 8. Geometry | 0, 2k, 32 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 8.1. Sphere | 0, 11, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Geometry"
    - 8.1.1. 3-sphere ( $S^{3}$ ) | 11 | 🔗 link | 🗖 nosplit | ↑ parent "Sphere"
  - 8.2. Four-dimensional space (4D) | 10, 38, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Geometry"
    - 8.2.1. Visualizing 4D | 28 | 🔗 link | 🗖 nosplit | ↑ parent "Four-dimensional space"
  - 8.3. Polytope | 0, 256, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Geometry"
    - 8.3.1. Regular polytope | 5, 256, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Polytope"
      - 8.3.1.1. Platonic solid | 38 | 🔗 link | 🗖 nosplit | ↑ parent "Regular polytope"
      - 8.3.1.2. Classification of regular polytopes | 213 | 🔗 link | 🗖 nosplit | ↑ parent "Regular polytope"
  - 8.4. Differential geometry | 10, 1k, 23 | 🔗 link | 🗖 nosplit | ↑ parent "Geometry"
    - 8.4.1. Lie group | 217, 1k, 22 | 🔗 link | 🗖 nosplit | ↑ parent "Differential geometry"
      - 8.4.1.1. Applications of Lie groups to differential equations | 102 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"
      - 8.4.1.2. Lie algebra | 21, 98, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"
        
        8.4.1.2.1. Exponential map (Lie theory) | 70 | 🔗 link | 🗖 nosplit | ↑ parent "Lie algebra"
        
        8.4.1.2.2. Generator of a Lie algebra | 7 | 🔗 link | 🗖 nosplit | ↑ parent "Lie algebra"
      - 8.4.1.3. Continuous symmetry | 18, 308, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"
        
        8.4.1.3.1. Local symmetry | 152, 290, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Continuous symmetry"
        
        8.4.1.3.1.1. Local symmetries of the Lagrangian imply conserved currents | 138 | 🔗 link | 🗖 nosplit | ↑ parent "Local symmetry"
      - 8.4.1.4. Important Lie groups | 0, 693, 13 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"
        
        8.4.1.4.1. General linear group ( $G L (n)$ ) | 44 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
        
        8.4.1.4.2. Special linear group ( $S L (n)$ ) | 18 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
        
        8.4.1.4.3. Orthogonal group ( $O (n)$ ) | 159, 181, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
        
        8.4.1.4.3.1. Special orthogonal group ( $S O (n)$ ) | 22 | 🔗 link | 🗖 nosplit | ↑ parent "Orthogonal group"
        
        8.4.1.4.4. Unitary group ( $U (n)$ ) | 82, 155, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
        
        8.4.1.4.4.1. Unitary group of dimension 2 ( $U (2)$ ) | 5 | 🔗 link | 🗖 nosplit | ↑ parent "Unitary group"
        
        8.4.1.4.4.2. Unit circle | 19 | 🔗 link | 🗖 nosplit | ↑ parent "Unitary group"
        
        8.4.1.4.4.3. Special unitary group ( $S U (n)$ ) | 49 | 🔗 link | 🗖 nosplit | ↑ parent "Unitary group"
        
        8.4.1.4.5. Poincare group | 192, 295, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Important Lie groups"
        
        8.4.1.4.5.1. Galilean transformation | 🔗 link | 🗖 nosplit | ↑ parent "Poincare group"
        
        8.4.1.4.5.2. Lorentz group ( $S O (1, 3)$ ) | 61, 103, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Poincare group"
        
        8.4.1.4.5.2.1. Lorentz boost | 24 | 🔗 link | 🗖 nosplit | ↑ parent "Lorentz group"
        
        8.4.1.4.5.2.2. Indefinite orthogonal group ( $S O (m, n)$ ) | 18 | 🔗 link | 🗖 nosplit | ↑ parent "Lorentz group"
      - 8.4.1.5. Representation theory | 61 | 🔗 link | 🗖 nosplit | ↑ parent "Lie group"
- 9. Mathematician | 115, 786, 6 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 9.1. High flying bird vs gophers (Birds and frogs by Freeman Dyson (2009)) | 621 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematician"
  - 9.2. List of mathematicians | 0, 50, 4 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematician"
    - 9.2.1. James Harris Simons | 50 | 🔗 link | 🗖 nosplit | ↑ parent "List of mathematicians"
    - 9.2.2. Joseph Fourier | 🔗 link | 🗖 nosplit | ↑ parent "List of mathematicians"
    - 9.2.3. Paul Erdos | 0, 0, 1 | 🔗 link | 🗖 nosplit | ↑ parent "List of mathematicians"
      - 9.2.3.1. Erdos number | 🔗 link | 🗖 nosplit | ↑ parent "Paul Erdos"
- 10. Mathematical notation | 0, 25, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 10.1. Mathematical symbol that looks like a Greek letter but isn't | 25 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematical notation"
- 11. Number theory | 0, 14, 12 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 11.1. Modular arithmetic | 0, 14, 3 | 🔗 link | 🗖 nosplit | ↑ parent "Number theory"
    - 11.1.1. Modular multiplication | 0, 0, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Modular arithmetic"
      - 11.1.1.1. Modular multiplicative inverse | 🔗 link | 🗖 nosplit | ↑ parent "Modular multiplication"
    - 11.1.2. Modular exponentiation | 14 | 🔗 link | 🗖 nosplit | ↑ parent "Modular arithmetic"
  - 11.2. Prime number | 0, 0, 7 | 🔗 link | 🗖 nosplit | ↑ parent "Number theory"
- 12. Numerical analysis | 97, 169, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 12.1. Perturbation theory | 72 | 🔗 link | 🗖 nosplit | ↑ parent "Numerical analysis"
- 13. Polynomial | 0, 58, 6 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 13.1. Algebraic equation | 0, 14, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Polynomial"
    - 13.1.1. Algebraic number | 0, 14, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Algebraic equation"
      - 13.1.1.1. Transcendental number | 14 | 🔗 link | 🗖 nosplit | ↑ parent "Algebraic number"
  - 13.2. Galois theory | 🔗 link | 🗖 nosplit | ↑ parent "Polynomial"
  - 13.3. Diophantine equation | 12, 44, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Polynomial"
    - 13.3.1. Undecidable Diophantine equation problems | 32 | 🔗 link | 🗖 nosplit | ↑ parent "Diophantine equation"
- 14. Probability | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
- 15. Mathematics bibliography | 35, 142, 2 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics"
  - 15.1. Mathematics YouTube channels | 0, 107, 1 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics bibliography"
    - 15.1.1. 3Blue1Brown | 107 | 🔗 link | 🗖 nosplit | ↑ parent "Mathematics YouTube channels"

Ancestors

Ciro Santilli's Homepage | 238, 163k, 3k

Incoming links

Art | 110, 16k, 273
The best articles by Ciro Santilli | 2k
Ciro Santilli's bad old event memory | 653
Computer science | 240, 2k, 70
Fields Medal | 17
High flying bird vs gophers | 621
Magic: The Gathering | 1k, 1k, 3
Mathematics illustration software | 35
Numerical analysis | 97, 169, 1
Physics | 276, 33k, 581
Quantum electrodynamics | 676, 3k, 22
Lecture 2 | 108
There is value of tutorials written by early pioneers of the field | 123
Video game | 483, 2k, 38
Website front-end for a mathematical formal proof system | 718