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Mathematics

| nosplit | ↑ parent "Ciro Santilli's Homepage" | words: 17 | descendant words: 35k | descendants: 772

↑ parent "Ciro Santilli's Homepage" | nosplit | ⇓ toc | words: 17 | descendant words: 35k | descendants: 772

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

Table of contents | 17, 35k, 772
- The beauty of mathematics | 405, 853, 9 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - The Hundred Greatest Theorems by Paul and Jack Abad (1999) | 7 | 🔗 link | nosplit | ↑ parent "The beauty of mathematics"
  - Classification (mathematics) | 107 | 🔗 link | nosplit | ↑ parent "The beauty of mathematics"
  - Pathological (mathematics) | 0, 41, 2 | 🔗 link | nosplit | ↑ parent "The beauty of mathematics"
    - Exceptional object | 41, 41, 1 | 🔗 link | nosplit | ↑ parent "Pathological"
      - Exceptional isomorphism | 🔗 link | nosplit | ↑ parent "Exceptional object"
  - Lists of mathematical problems | 13, 293, 3 | 🔗 link | nosplit | ↑ parent "The beauty of mathematics"
    - Hilbert's problems | 22 | 🔗 link | nosplit | ↑ parent "Lists of mathematical problems"
    - Millennium Prize Problems | 244, 258, 1 | 🔗 link | nosplit | ↑ parent "Lists of mathematical problems"
      - Birch and Swinnerton-Dyer Conjecture | 14 | 🔗 link | nosplit | ↑ parent "Millennium Prize Problems"
- Formalization of Mathematics | 458, 3k, 75 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - Proof assistant | 15, 49, 3 | 🔗 link | nosplit | ↑ parent "Formalization of Mathematics"
    - QED manifesto | 26 | 🔗 link | nosplit | ↑ parent "Proof assistant"
    - List of proof assistants | 0, 8, 1 | 🔗 link | nosplit | ↑ parent "Proof assistant"
      - Lean (proof assistant) | 8 | 🔗 link | nosplit | ↑ parent "List of proof assistants"
  - Formal proof | 15, 219, 11 | 🔗 link | nosplit | ↑ parent "Formalization of Mathematics"
    - Mathematical proof | 🔗 link | nosplit | ↑ parent "Formal proof"
    - Formal system | 0, 101, 3 | 🔗 link | nosplit | ↑ parent "Formal proof"
      - Zermelo-Fraenkel set theory (ZF) | 57, 101, 2 | 🔗 link | nosplit | ↑ parent "Formal system"
        
        Set theory | 28 | 🔗 link | nosplit | ↑ parent "Zermelo-Fraenkel set theory"
        
        Metamath | 16 | 🔗 link | nosplit | ↑ parent "Zermelo-Fraenkel set theory"
    - Axiom | 0, 90, 2 | 🔗 link | nosplit | ↑ parent "Formal proof"
      - Consistency | 41 | 🔗 link | nosplit | ↑ parent "Axiom"
      - Independence (mathematical logic) | 49 | 🔗 link | nosplit | ↑ parent "Axiom"
    - Conjecture | 🔗 link | nosplit | ↑ parent "Formal proof"
    - Theorem | 0, 13, 1 | 🔗 link | nosplit | ↑ parent "Formal proof"
      - Corollary | 13 | 🔗 link | nosplit | ↑ parent "Theorem"
  - Set (mathematics) | 86, 188, 2 | 🔗 link | nosplit | ↑ parent "Formalization of Mathematics"
    - Union (set theory, $A ⋃ B$ ) | 🔗 link | nosplit | ↑ parent "Set"
    - Cardinality | 102 | 🔗 link | nosplit | ↑ parent "Set"
  - Function (mathematics) | 24, 1k, 27 | 🔗 link | nosplit | ↑ parent "Formalization of Mathematics"
    - Cartesian product | 15 | 🔗 link | nosplit | ↑ parent "Function"
    - Direct product | 40 | 🔗 link | nosplit | ↑ parent "Function"
    - Domain, codomain and image | 0, 176, 7 | 🔗 link | nosplit | ↑ parent "Function"
      - Bijection | 0, 54, 2 | 🔗 link | nosplit | ↑ parent "Domain, codomain and image"
        
        Injective function | 32 | 🔗 link | nosplit | ↑ parent "Bijection"
        
        Surjective function | 22 | 🔗 link | nosplit | ↑ parent "Bijection"
      - Domain of a function | 🔗 link | nosplit | ↑ parent "Domain, codomain and image"
      - Codomain | 92, 122, 1 | 🔗 link | nosplit | ↑ parent "Domain, codomain and image"
        
        Endofunction | 30 | 🔗 link | nosplit | ↑ parent "Codomain"
      - Image (mathematics) | 🔗 link | nosplit | ↑ parent "Domain, codomain and image"
    - Addition | 🔗 link | nosplit | ↑ parent "Function"
    - Subtraction | 🔗 link | nosplit | ↑ parent "Function"
    - Multiplication | 🔗 link | nosplit | ↑ parent "Function"
    - Division | 🔗 link | nosplit | ↑ parent "Function"
    - Exponentiation ( $x^{y}$ ) | 0, 883, 12 | 🔗 link | nosplit | ↑ parent "Function"
      - nth root | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Exponentiation"
        
        Square root | 🔗 link | nosplit | ↑ parent "nth root"
      - Exponentiation functional equation | 49 | 🔗 link | nosplit | ↑ parent "Exponentiation"
      - Exponential function ( $e^{x}$ ) | 0, 834, 8 | 🔗 link | nosplit | ↑ parent "Exponentiation"
        
        Exponential function differential equation | 71 | 🔗 link | nosplit | ↑ parent "Exponential function"
        
        Definition of the exponential function | 0, 519, 2 | 🔗 link | nosplit | ↑ parent "Exponential function"
        
        Taylor expansion definition of the exponential function | 85 | 🔗 link | nosplit | ↑ parent "Definition of the exponential function"
        
        Product definition of the exponential function | 434 | 🔗 link | nosplit | ↑ parent "Definition of the exponential function"
        
        Logarithm | 🔗 link | nosplit | ↑ parent "Exponential function"
        
        Matrix exponential | 120, 244, 2 | 🔗 link | nosplit | ↑ parent "Exponential function"
        
        Logarithm of a matrix | 0, 124, 1 | 🔗 link | nosplit | ↑ parent "Matrix exponential"
        
        Existence of the matrix logarithm | 124 | 🔗 link | nosplit | ↑ parent "Logarithm of a matrix"
  - Function space | 11 | 🔗 link | nosplit | ↑ parent "Formalization of Mathematics"
  - Integer ( $Z$ ) | 🔗 link | nosplit | ↑ parent "Formalization of Mathematics"
  - Rational number ( $Q$ ) | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Formalization of Mathematics"
    - Fraction | 🔗 link | nosplit | ↑ parent "Rational number"
  - Real number ( $R$ ) | 13, 13, 4 | 🔗 link | nosplit | ↑ parent "Formalization of Mathematics"
    - Dedekind cut | 🔗 link | nosplit | ↑ parent "Real number"
    - Cardinality of the continuum | 0, 0, 2 | 🔗 link | nosplit | ↑ parent "Real number"
      - Countable set | 🔗 link | nosplit | ↑ parent "Cardinality of the continuum"
      - Cantor's diagonal argument | 🔗 link | nosplit | ↑ parent "Cardinality of the continuum"
  - Complex number | 67, 226, 7 | 🔗 link | nosplit | ↑ parent "Formalization of Mathematics"
    - Complex conjugate ( $\overline{x}$ ) | 🔗 link | nosplit | ↑ parent "Complex number"
    - Imaginary number | 🔗 link | nosplit | ↑ parent "Complex number"
    - Imaginary unit ( $i$ ) | 🔗 link | nosplit | ↑ parent "Complex number"
    - Cayley-Dickson construction | 36, 159, 3 | 🔗 link | nosplit | ↑ parent "Complex number"
      - Quaternion ( $H$ , 4) | 103 | 🔗 link | nosplit | ↑ parent "Cayley-Dickson construction"
      - Octonion (8) | 20 | 🔗 link | nosplit | ↑ parent "Cayley-Dickson construction"
      - Sedenion (16) | 🔗 link | nosplit | ↑ parent "Cayley-Dickson construction"
  - Ordered pair | 37 | 🔗 link | nosplit | ↑ parent "Formalization of Mathematics"
  - Logic | 0, 177, 9 | 🔗 link | nosplit | ↑ parent "Formalization of Mathematics"
    - Propositional logic | 52, 52, 2 | 🔗 link | nosplit | ↑ parent "Logic"
      - Modus ponens | 🔗 link | nosplit | ↑ parent "Propositional logic"
      - If and only if (Iff) | 🔗 link | nosplit | ↑ parent "Propositional logic"
    - First-order logic | 22, 125, 5 | 🔗 link | nosplit | ↑ parent "Logic"
      - Existential quantification ( $\exists$ ) | 21, 103, 3 | 🔗 link | nosplit | ↑ parent "First-order logic"
        
        Existence and uniqueness | 82, 82, 2 | 🔗 link | nosplit | ↑ parent "Existential quantification"
        
        Existence | 🔗 link | nosplit | ↑ parent "Existence and uniqueness"
        
        Uniqueness | 🔗 link | nosplit | ↑ parent "Existence and uniqueness"
      - Universal quantification ( $\forall$ ) | 🔗 link | nosplit | ↑ parent "First-order logic"
- Algebra | 27, 11k, 216 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - Abstract algebra | 17 | 🔗 link | nosplit | ↑ parent "Algebra"
  - Algebraic structure | 69, 278, 7 | 🔗 link | nosplit | ↑ parent "Algebra"
    - Commutator | 🔗 link | nosplit | ↑ parent "Algebraic structure"
    - Identity element | 0, 10, 2 | 🔗 link | nosplit | ↑ parent "Algebraic structure"
      - Inverse element | 10, 10, 1 | 🔗 link | nosplit | ↑ parent "Identity element"
        
        Invertible | 🔗 link | nosplit | ↑ parent "Inverse element"
    - Order (algebra) | 72, 199, 2 | 🔗 link | nosplit | ↑ parent "Algebraic structure"
      - Degree (algebra) | 114 | 🔗 link | nosplit | ↑ parent "Order"
      - Finite algebraic structure | 13 | 🔗 link | nosplit | ↑ parent "Order"
  - Linear algebra | 0, 6k, 114 | 🔗 link | nosplit | ↑ parent "Algebra"
    - Linear function | 131 | 🔗 link | nosplit | ↑ parent "Linear algebra"
    - Linear map (linear operator) | 313, 2k, 27 | 🔗 link | nosplit | ↑ parent "Linear algebra"
      - Form (mathematics) | 54 | 🔗 link | nosplit | ↑ parent "Linear map"
      - Linear form | 64, 497, 3 | 🔗 link | nosplit | ↑ parent "Linear map"
        
        Matrix representation of a linear form | 49 | 🔗 link | nosplit | ↑ parent "Linear form"
        
        Dual space ( $V^{*}$ ) | 165, 384, 1 | 🔗 link | nosplit | ↑ parent "Linear form"
        
        Dual vector ( $e^{i}$ ) | 219 | 🔗 link | nosplit | ↑ parent "Dual space"
      - Linear operator | 122, 177, 1 | 🔗 link | nosplit | ↑ parent "Linear map"
        
        Adjoint operator ( $A^{†}$ ) | 55 | 🔗 link | nosplit | ↑ parent "Linear operator"
      - Self-adjoint operator | 🔗 link | nosplit | ↑ parent "Linear map"
      - Multilinear map | 0, 1k, 18 | 🔗 link | nosplit | ↑ parent "Linear map"
        
        Bilinear map | 133 | 🔗 link | nosplit | ↑ parent "Multilinear map"
        
        Bilinear form ( $B (x, y)$ ) | 105, 419, 2 | 🔗 link | nosplit | ↑ parent "Multilinear map"
        
        Matrix representation of a bilinear form | 113, 314, 1 | 🔗 link | nosplit | ↑ parent "Bilinear form"
        
        Effect of a change of basis on the matrix of a bilinear form ( $B_{2} = C^{T} B C$ ) | 201 | 🔗 link | nosplit | ↑ parent "Matrix representation of a bilinear form"
        
        Multilinear form | 59 | 🔗 link | nosplit | ↑ parent "Multilinear map"
        
        Symmetric bilinear map | 63, 578, 9 | 🔗 link | nosplit | ↑ parent "Multilinear map"
        
        Symmetric bilinear form | 18, 120, 1 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear map"
        
        Matrix representation of a symmetric bilinear form | 102 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear form"
        
        Hermitian form | 89, 99, 1 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear map"
        
        Matrix representation of a Hermitian form | 10 | 🔗 link | nosplit | ↑ parent "Hermitian form"
        
        Quadratic form | 223 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear map"
        
        Positive definite symmetric bilinear form | 19, 39, 1 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear map"
        
        Matrix representation of a positive definite symmetric bilinear form | 20 | 🔗 link | nosplit | ↑ parent "Positive definite symmetric bilinear form"
        
        Skew-symmetric bilinear map | 16 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear map"
        
        Skew-symmetric bilinear form | 18 | 🔗 link | nosplit | ↑ parent "Symmetric bilinear map"
        
        Symmetric multilinear map | 8, 16, 1 | 🔗 link | nosplit | ↑ parent "Multilinear map"
        
        Antisymmetric multilinear map | 8 | 🔗 link | nosplit | ↑ parent "Symmetric multilinear map"
        
        Alternating multilinear map | 9 | 🔗 link | nosplit | ↑ parent "Multilinear map"
    - Dot product | 295, 295, 3 | 🔗 link | nosplit | ↑ parent "Linear algebra"
      - Orthogonality | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Dot product"
        
        Orthonormality | 🔗 link | nosplit | ↑ parent "Orthogonality"
      - Angle | 🔗 link | nosplit | ↑ parent "Dot product"
    - Cross product ( $x \times y$ ) | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Linear algebra"
      - Jacobi identity | 🔗 link | nosplit | ↑ parent "Cross product"
    - Index picking function | 0, 158, 3 | 🔗 link | nosplit | ↑ parent "Linear algebra"
      - Kronecker delta ( $δ_{i j}$ ) | 🔗 link | nosplit | ↑ parent "Index picking function"
      - Levi-Civita symbol ( $ε$ ) | 61, 158, 1 | 🔗 link | nosplit | ↑ parent "Index picking function"
        
        Levi-Civita symbol as a tensor | 97 | 🔗 link | nosplit | ↑ parent "Levi-Civita symbol"
    - Projection (mathematics) | 🔗 link | nosplit | ↑ parent "Linear algebra"
    - Matrix | 0, 2k, 44 | 🔗 link | nosplit | ↑ parent "Linear algebra"
      - Matrix operation | 0, 146, 6 | 🔗 link | nosplit | ↑ parent "Matrix"
        
        Determinant ( $d e t$ ) | 30 | 🔗 link | nosplit | ↑ parent "Matrix operation"
        
        Matrix inverse ( $M^{- 1}$ ) | 24, 73, 1 | 🔗 link | nosplit | ↑ parent "Matrix operation"
        
        Invertible matrix | 49 | 🔗 link | nosplit | ↑ parent "Matrix inverse"
        
        Transpose ( $M^{T}$ ) | 0, 43, 2 | 🔗 link | nosplit | ↑ parent "Matrix operation"
        
        Transpose of a matrix multiplication | 22 | 🔗 link | nosplit | ↑ parent "Transpose"
        
        Inverse of the transpose | 21 | 🔗 link | nosplit | ↑ parent "Transpose"
      - Matrix multiplication | 80, 84, 2 | 🔗 link | nosplit | ↑ parent "Matrix"
        
        Matrix multiplication algorithm | 4 | 🔗 link | nosplit | ↑ parent "Matrix multiplication"
        
        Matrix decomposition | 🔗 link | nosplit | ↑ parent "Matrix multiplication"
      - Eigenvalues and eigenvectors | 0, 1k, 18 | 🔗 link | nosplit | ↑ parent "Matrix"
        
        Applications of eigenvalues and eigenvectors | 12 | 🔗 link | nosplit | ↑ parent "Eigenvalues and eigenvectors"
        
        Eigenvalue | 9, 130, 2 | 🔗 link | nosplit | ↑ parent "Eigenvalues and eigenvectors"
        
        Spectrum (functional analysis) | 18, 121, 1 | 🔗 link | nosplit | ↑ parent "Eigenvalue"
        
        Continuous spectrum (functional analysis) | 103 | 🔗 link | nosplit | ↑ parent "Spectrum"
        
        Eigendecomposition of a matrix | 128, 794, 7 | 🔗 link | nosplit | ↑ parent "Eigenvalues and eigenvectors"
        
        Eigendecomposition of a real symmetric matrix | 40 | 🔗 link | nosplit | ↑ parent "Eigendecomposition of a matrix"
        
        Sylvester's law of inertia | 527, 626, 5 | 🔗 link | nosplit | ↑ parent "Eigendecomposition of a matrix"
        
        Congruent matrix | 36, 99, 1 | 🔗 link | nosplit | ↑ parent "Sylvester's law of inertia"
        
        Matrix congruence can be seen as the change of basis of a bilinear form | 63 | 🔗 link | nosplit | ↑ parent "Congruent matrix"
        
        Matrix similarity | 🔗 link | nosplit | ↑ parent "Sylvester's law of inertia"
        
        Metric signature | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Sylvester's law of inertia"
        
        Metric signature matrix | 🔗 link | nosplit | ↑ parent "Metric signature"
        
        Eigenvector | 9 | 🔗 link | nosplit | ↑ parent "Eigenvalues and eigenvectors"
        
        Eigenvectors and eigenvalues of the identity matrix | 4 | 🔗 link | nosplit | ↑ parent "Eigenvalues and eigenvectors"
        
        Spectral theorem | 0, 63, 3 | 🔗 link | nosplit | ↑ parent "Eigenvalues and eigenvectors"
        
        Hermitian matrix | 0, 63, 2 | 🔗 link | nosplit | ↑ parent "Spectral theorem"
        
        Hermitian operator | 63, 63, 1 | 🔗 link | nosplit | ↑ parent "Hermitian matrix"
        
        Riesz representation theorem | 🔗 link | nosplit | ↑ parent "Hermitian operator"
      - Kronecker product | 🔗 link | nosplit | ↑ parent "Matrix"
      - Named matrix | 0, 284, 13 | 🔗 link | nosplit | ↑ parent "Matrix"
        
        Diagonal matrix | 19, 38, 2 | 🔗 link | nosplit | ↑ parent "Named matrix"
        
        Scalar matrix ( $Z (V)$ ) | 19, 19, 1 | 🔗 link | nosplit | ↑ parent "Diagonal matrix"
        
        Identity matrix ( $I_{n}$ ) | 🔗 link | nosplit | ↑ parent "Scalar matrix"
        
        Square matrix | 0, 53, 1 | 🔗 link | nosplit | ↑ parent "Named matrix"
        
        Matrix ring (Matrix ring of degree n, $M_{n}$ , Set of all n-by-y square matrices) | 53 | 🔗 link | nosplit | ↑ parent "Square matrix"
        
        Orthogonal matrix | 11, 56, 1 | 🔗 link | nosplit | ↑ parent "Named matrix"
        
        Unitary matrix | 45 | 🔗 link | nosplit | ↑ parent "Orthogonal matrix"
        
        Triangular matrix | 🔗 link | nosplit | ↑ parent "Named matrix"
        
        Symmetric matrix | 54, 137, 4 | 🔗 link | nosplit | ↑ parent "Named matrix"
        
        Definite matrix | 16, 55, 1 | 🔗 link | nosplit | ↑ parent "Symmetric matrix"
        
        Positive definite matrix | 39 | 🔗 link | nosplit | ↑ parent "Definite matrix"
        
        Skew-symmetric matrix (Antisymmetric matrix) | 28, 28, 1 | 🔗 link | nosplit | ↑ parent "Symmetric matrix"
        
        Skew-symmetric form | 🔗 link | nosplit | ↑ parent "Skew-symmetric matrix"
    - Vector space | 0, 394, 9 | 🔗 link | nosplit | ↑ parent "Linear algebra"
      - Basis (linear algebra) | 0, 235, 4 | 🔗 link | nosplit | ↑ parent "Vector space"
        
        Change of basis | 25, 235, 2 | 🔗 link | nosplit | ↑ parent "Basis"
        
        Change of basis matrix | 165 | 🔗 link | nosplit | ↑ parent "Change of basis"
        
        Change of basis between symmetric matrices | 45 | 🔗 link | nosplit | ↑ parent "Change of basis"
        
        Linear independence | 🔗 link | nosplit | ↑ parent "Basis"
      - Classification of vector spaces | 4 | 🔗 link | nosplit | ↑ parent "Vector space"
      - Underlying field of a vector space | 114 | 🔗 link | nosplit | ↑ parent "Vector space"
      - Vector (mathematics) | 0, 41, 1 | 🔗 link | nosplit | ↑ parent "Vector space"
        
        Scalar (mathematics) | 41 | 🔗 link | nosplit | ↑ parent "Vector"
    - Tensor | 124, 990, 17 | 🔗 link | nosplit | ↑ parent "Linear algebra"
      - A linear map is a (1,1) tensor | 80 | 🔗 link | nosplit | ↑ parent "Tensor"
      - Tensor space ( $T^{(m, n)}$ ) | 5, 11, 1 | 🔗 link | nosplit | ↑ parent "Tensor"
        
        Order of a tensor | 6 | 🔗 link | nosplit | ↑ parent "Tensor space"
      - Einstein notation (Einstein summation convention) | 103, 775, 13 | 🔗 link | nosplit | ↑ parent "Tensor"
        
        Raised and lowered indices | 109, 109, 3 | 🔗 link | nosplit | ↑ parent "Einstein notation"
        
        Raised index | 🔗 link | nosplit | ↑ parent "Raised and lowered indices"
        
        Lowered index | 🔗 link | nosplit | ↑ parent "Raised and lowered indices"
        
        Raising and lowering indices | 🔗 link | nosplit | ↑ parent "Raised and lowered indices"
        
        Implicit metric signature in Einstein notation | 79 | 🔗 link | nosplit | ↑ parent "Einstein notation"
        
        Einstein notation for partial derivatives | 102, 484, 4 | 🔗 link | nosplit | ↑ parent "Einstein notation"
        
        Divergence in Einstein notation | 125 | 🔗 link | nosplit | ↑ parent "Einstein notation for partial derivatives"
        
        Laplacian in Einstein notation ( $\partial_{i} \partial^{i}$ ) | 108, 257, 2 | 🔗 link | nosplit | ↑ parent "Einstein notation for partial derivatives"
        
        D'alembert operator in Einstein notation ( $\partial_{i} \partial^{i}$ ) | 96, 149, 1 | 🔗 link | nosplit | ↑ parent "Laplacian in Einstein notation"
        
        Klein-Gordon equation in Einstein notation | 53 | 🔗 link | nosplit | ↑ parent "D'alembert operator in Einstein notation"
        
        Covariance and contravariance of vectors | 0, 0, 2 | 🔗 link | nosplit | ↑ parent "Einstein notation"
        
        Covariant vector | 🔗 link | nosplit | ↑ parent "Covariance and contravariance of vectors"
        
        Contravariant vector | 🔗 link | nosplit | ↑ parent "Covariance and contravariance of vectors"
    - Linear algebra bibliography | 23 | 🔗 link | nosplit | ↑ parent "Linear algebra"
  - Group (mathematics) | 0, 5k, 90 | 🔗 link | nosplit | ↑ parent "Algebra"
    - Center (group theory) | 🔗 link | nosplit | ↑ parent "Group"
    - Commutative property | 0, 30, 2 | 🔗 link | nosplit | ↑ parent "Group"
      - Abelian group | 30, 30, 1 | 🔗 link | nosplit | ↑ parent "Commutative property"
        
        Non-commutative | 🔗 link | nosplit | ↑ parent "Abelian group"
    - Symmetry | 31 | 🔗 link | nosplit | ↑ parent "Group"
    - Important mathematical group | 0, 438, 19 | 🔗 link | nosplit | ↑ parent "Group"
      - Important discrete mathematical group | 0, 438, 18 | 🔗 link | nosplit | ↑ parent "Important mathematical group"
        
        Cyclic group ( $C_{n}$ ) | 🔗 link | nosplit | ↑ parent "Important discrete mathematical group"
        
        The direct product of two cyclic groups of coprime order is another cyclic group | 72 | 🔗 link | nosplit | ↑ parent "Important discrete mathematical group"
        
        Permutation | 0, 304, 11 | 🔗 link | nosplit | ↑ parent "Important discrete mathematical group"
        
        Cycle notation | 80 | 🔗 link | nosplit | ↑ parent "Permutation"
        
        Parity of a permutation | 0, 0, 2 | 🔗 link | nosplit | ↑ parent "Permutation"
        
        Odd permutation | 🔗 link | nosplit | ↑ parent "Parity of a permutation"
        
        Even permutation | 🔗 link | nosplit | ↑ parent "Parity of a permutation"
        
        Permutation group | 0, 224, 6 | 🔗 link | nosplit | ↑ parent "Permutation"
        
        Stabilizer (group) | 119 | 🔗 link | nosplit | ↑ parent "Permutation group"
        
        Symmetric group | 15, 33, 1 | 🔗 link | nosplit | ↑ parent "Permutation group"
        
        All groups are isomorphic to a subgroup of the symmetric group | 18 | 🔗 link | nosplit | ↑ parent "Symmetric group"
        
        Alternating group ( $A_{n}$ ) | 52, 72, 2 | 🔗 link | nosplit | ↑ parent "Permutation group"
        
        Alternating group of degree 5 | 0, 20, 1 | 🔗 link | nosplit | ↑ parent "Alternating group"
        
        The alternating groups of degree 5 or greater are simple | 20 | 🔗 link | nosplit | ↑ parent "Alternating group of degree 5"
        
        Dihedral group ( $D_{n}$ ) | 48 | 🔗 link | nosplit | ↑ parent "Important discrete mathematical group"
        
        Wallpaper group | 3 | 🔗 link | nosplit | ↑ parent "Important discrete mathematical group"
        
        Space group | 8 | 🔗 link | nosplit | ↑ parent "Important discrete mathematical group"
        
        Klein four-group | 3 | 🔗 link | nosplit | ↑ parent "Important discrete mathematical group"
    - Finite group | 0, 1k, 28 | 🔗 link | nosplit | ↑ parent "Group"
      - Classification of finite groups | 69, 1k, 27 | 🔗 link | nosplit | ↑ parent "Finite group"
        
        List of finite groups | 4, 13, 1 | 🔗 link | nosplit | ↑ parent "Classification of finite groups"
        
        GroupNames | 9 | 🔗 link | nosplit | ↑ parent "List of finite groups"
        
        Classification of finite simple groups | 187, 957, 23 | 🔗 link | nosplit | ↑ parent "Classification of finite groups"
        
        Group of Lie type | 199, 267, 2 | 🔗 link | nosplit | ↑ parent "Classification of finite simple groups"
        
        Chevalley group | 0, 68, 1 | 🔗 link | nosplit | ↑ parent "Group of Lie type"
        
        Chevalley groups $A_{n} (q)$ | 68 | 🔗 link | nosplit | ↑ parent "Chevalley group"
        
        Sporadic group | 8, 489, 17 | 🔗 link | nosplit | ↑ parent "Classification of finite simple groups"
        
        Mathieu group | 245, 433, 13 | 🔗 link | nosplit | ↑ parent "Sporadic group"
        
        k-transitive group | 19, 174, 7 | 🔗 link | nosplit | ↑ parent "Mathieu group"
        
        Classification of k-transitive groups | 22, 155, 6 | 🔗 link | nosplit | ↑ parent "k-transitive group"
        
        2-transitive group | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Classification of k-transitive groups"
        
        Classification of 2-transitive groups | 🔗 link | nosplit | ↑ parent "2-transitive group"
        
        Classification of 3-transitive groups | 9 | 🔗 link | nosplit | ↑ parent "Classification of k-transitive groups"
        
        Classification of 4-transitive groups | 19 | 🔗 link | nosplit | ↑ parent "Classification of k-transitive groups"
        
        Classification of 5-transitive groups | 95 | 🔗 link | nosplit | ↑ parent "Classification of k-transitive groups"
        
        Classification of 6-transitive groups | 10 | 🔗 link | nosplit | ↑ parent "Classification of k-transitive groups"
        
        Mathieu group $M_{1} 1$ | 🔗 link | nosplit | ↑ parent "Mathieu group"
        
        Mathieu group $M_{1} 2$ | 🔗 link | nosplit | ↑ parent "Mathieu group"
        
        Mathieu group $M_{2} 2$ | 🔗 link | nosplit | ↑ parent "Mathieu group"
        
        Mathieu group $M_{2} 3$ | 🔗 link | nosplit | ↑ parent "Mathieu group"
        
        Mathieu group $M_{2} 4$ | 14 | 🔗 link | nosplit | ↑ parent "Mathieu group"
        
        Janko group | 🔗 link | nosplit | ↑ parent "Sporadic group"
        
        Monster group | 34, 48, 1 | 🔗 link | nosplit | ↑ parent "Sporadic group"
        
        Monstrous moonshine | 14 | 🔗 link | nosplit | ↑ parent "Monster group"
        
        Jordan-Holder Theorem | 14 | 🔗 link | nosplit | ↑ parent "Classification of finite simple groups"
        
        Composition series | 🔗 link | nosplit | ↑ parent "Classification of finite simple groups"
        
        Group extension problem | 110 | 🔗 link | nosplit | ↑ parent "Classification of finite groups"
    - Group operation | 🔗 link | nosplit | ↑ parent "Group"
    - Group isomorphism | 0, 246, 4 | 🔗 link | nosplit | ↑ parent "Group"
      - Isomorphism | 120 | 🔗 link | nosplit | ↑ parent "Group isomorphism"
      - Group homomorphism | 95, 126, 2 | 🔗 link | nosplit | ↑ parent "Group isomorphism"
        
        Fundamental theorem on homomorphisms | 31 | 🔗 link | nosplit | ↑ parent "Group homomorphism"
        
        Kernel (algebra) | 🔗 link | nosplit | ↑ parent "Group homomorphism"
    - Generating set of a group | 0, 327, 4 | 🔗 link | nosplit | ↑ parent "Group"
      - Cayley graph | 61, 211, 1 | 🔗 link | nosplit | ↑ parent "Generating set of a group"
        
        Cycle graph (algebra) | 150 | 🔗 link | nosplit | ↑ parent "Cayley graph"
      - Cycle of an element of a group | 98, 116, 1 | 🔗 link | nosplit | ↑ parent "Generating set of a group"
        
        Order of an element of a group | 18 | 🔗 link | nosplit | ↑ parent "Cycle of an element of a group"
    - Direct product of groups ( $G \times H$ ) | 0, 441, 2 | 🔗 link | nosplit | ↑ parent "Group"
      - Product of group subsets | 🔗 link | nosplit | ↑ parent "Direct product of groups"
      - Semidirect product ( $N ⋊ H$ ) | 441 | 🔗 link | nosplit | ↑ parent "Direct product of groups"
    - Subgroup | 0, 653, 7 | 🔗 link | nosplit | ↑ parent "Group"
      - Subgroup generated by a group | 🔗 link | nosplit | ↑ parent "Subgroup"
      - Quotient group | 51, 653, 5 | 🔗 link | nosplit | ↑ parent "Subgroup"
        
        Subquotient | 64 | 🔗 link | nosplit | ↑ parent "Quotient group"
        
        Relationship between the quotient group and direct products | 308 | 🔗 link | nosplit | ↑ parent "Quotient group"
        
        Normal subgroup | 149, 230, 2 | 🔗 link | nosplit | ↑ parent "Quotient group"
        
        Simple group | 48, 81, 1 | 🔗 link | nosplit | ↑ parent "Normal subgroup"
        
        How to show that a group is simple | 33 | 🔗 link | nosplit | ↑ parent "Simple group"
    - Ring (mathematics) | 276, 1k, 13 | 🔗 link | nosplit | ↑ parent "Group"
      - Commutative ring | 🔗 link | nosplit | ↑ parent "Ring"
      - Division ring | 41 | 🔗 link | nosplit | ↑ parent "Ring"
      - Field (mathematics) | 81, 1k, 10 | 🔗 link | nosplit | ↑ parent "Ring"
        
        Distributive property | 50 | 🔗 link | nosplit | ↑ parent "Field"
        
        Finite field ( $G F (n)$ ) | 212, 796, 4 | 🔗 link | nosplit | ↑ parent "Field"
        
        Classification of finite fields | 78 | 🔗 link | nosplit | ↑ parent "Finite field"
        
        Finite field of non-prime order | 131 | 🔗 link | nosplit | ↑ parent "Finite field"
        
        GF(2) | 🔗 link | nosplit | ↑ parent "Finite field"
        
        GF(4) | 375 | 🔗 link | nosplit | ↑ parent "Finite field"
        
        Vector field | 0, 172, 3 | 🔗 link | nosplit | ↑ parent "Field"
        
        Algebra over a field | 113, 172, 2 | 🔗 link | nosplit | ↑ parent "Vector field"
        
        Division algebra | 17, 59, 1 | 🔗 link | nosplit | ↑ parent "Algebra over a field"
        
        Frobenius theorem (real division algebras) | 42 | 🔗 link | nosplit | ↑ parent "Division algebra"
  - Associative property | 🔗 link | nosplit | ↑ parent "Algebra"
- Applied mathematics | 🔗 link | nosplit | ↑ parent "Mathematics"
- Calculus | 17, 9k, 222 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - Mathematical analysis | 17 | 🔗 link | nosplit | ↑ parent "Calculus"
  - Limit (mathematics) | 46, 250, 7 | 🔗 link | nosplit | ↑ parent "Calculus"
    - Convergent series | 🔗 link | nosplit | ↑ parent "Limit"
    - Continuous function | 0, 116, 3 | 🔗 link | nosplit | ↑ parent "Limit"
      - Continuous problems are simpler than discrete ones | 92 | 🔗 link | nosplit | ↑ parent "Continuous function"
      - Discrete | 24, 24, 1 | 🔗 link | nosplit | ↑ parent "Continuous function"
        
        Discretization | 🔗 link | nosplit | ↑ parent "Discrete"
    - Infinity ( $\infty$ ) | 88 | 🔗 link | nosplit | ↑ parent "Limit"
    - L'Hôpital's rule (limit of a ratio) | 🔗 link | nosplit | ↑ parent "Limit"
  - Derivative | 0, 385, 19 | 🔗 link | nosplit | ↑ parent "Calculus"
    - Chain rule | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Derivative"
      - Multivariable chain rule | 🔗 link | nosplit | ↑ parent "Chain rule"
    - Differentiable function | 0, 4, 4 | 🔗 link | nosplit | ↑ parent "Derivative"
      - Smoothness | 🔗 link | nosplit | ↑ parent "Differentiable function"
      - Infinitely differentiable function ( $C^{\infty}$ ) | 0, 4, 2 | 🔗 link | nosplit | ↑ parent "Differentiable function"
        
        Bump function | 0, 4, 1 | 🔗 link | nosplit | ↑ parent "Infinitely differentiable function"
        
        Flat top bump function | 4 | 🔗 link | nosplit | ↑ parent "Bump function"
    - Maxima and minima | 119, 123, 3 | 🔗 link | nosplit | ↑ parent "Derivative"
      - Lifegard problem | 4 | 🔗 link | nosplit | ↑ parent "Maxima and minima"
      - Derivative test | 🔗 link | nosplit | ↑ parent "Maxima and minima"
      - Saddle point | 🔗 link | nosplit | ↑ parent "Maxima and minima"
    - Newton dot notation | 🔗 link | nosplit | ↑ parent "Derivative"
    - Partial derivative | 0, 188, 4 | 🔗 link | nosplit | ↑ parent "Derivative"
      - Partial derivative notation | 0, 188, 3 | 🔗 link | nosplit | ↑ parent "Partial derivative"
        
        Partial derivative symbol ( $\partial$ ) | 99 | 🔗 link | nosplit | ↑ parent "Partial derivative notation"
        
        Partial label partial derivative notation ( $\partial_{x} F$ , $\partial_{y} F$ ) | 🔗 link | nosplit | ↑ parent "Partial derivative notation"
        
        Partial index partial derivative notation ( $\partial_{0} F$ , $\partial_{1} F$ ) | 89 | 🔗 link | nosplit | ↑ parent "Partial derivative notation"
    - Total derivative | 70 | 🔗 link | nosplit | ↑ parent "Derivative"
    - Directional derivative | 🔗 link | nosplit | ↑ parent "Derivative"
  - Integral | 0, 1k, 19 | 🔗 link | nosplit | ↑ parent "Calculus"
    - Area | 0, 15, 1 | 🔗 link | nosplit | ↑ parent "Integral"
      - Volume | 15 | 🔗 link | nosplit | ↑ parent "Area"
    - Riemann integral | 26 | 🔗 link | nosplit | ↑ parent "Integral"
    - Lebesgue integral | 91, 1k, 15 | 🔗 link | nosplit | ↑ parent "Integral"
      - Lebesgue integral vs Riemann integral | 202, 273, 1 | 🔗 link | nosplit | ↑ parent "Lebesgue integral"
        
        Real world applications of the Lebesgue integral | 71 | 🔗 link | nosplit | ↑ parent "Lebesgue integral vs Riemann integral"
      - Lebesgue measurable | 🔗 link | nosplit | ↑ parent "Lebesgue integral"
      - Lebesgue integral of $L^{p}$ is complete but Riemann isn't | 91, 805, 11 | 🔗 link | nosplit | ↑ parent "Lebesgue integral"
        
        Riesz-Fischer theorem | 59, 306, 4 | 🔗 link | nosplit | ↑ parent "Lebesgue integral of $L^{p}$ is complete but Riemann isn't"
        
        $L^{p}$ is complete | 1 | 🔗 link | nosplit | ↑ parent "Riesz-Fischer theorem"
        
        Fourier basis is complete for $L^{2}$ | 62, 246, 2 | 🔗 link | nosplit | ↑ parent "Riesz-Fischer theorem"
        
        $L^{p}$ norm sequence convergence does not imply pointwise convergence | 44 | 🔗 link | nosplit | ↑ parent "Fourier basis is complete for $L^{2}$ "
        
        Carleson's theorem | 140 | 🔗 link | nosplit | ↑ parent "Fourier basis is complete for $L^{2}$ "
        
        Lp space ( $L^{p}$ ) | 30, 408, 5 | 🔗 link | nosplit | ↑ parent "Lebesgue integral of $L^{p}$ is complete but Riemann isn't"
        
        $L^{1}$ | 🔗 link | nosplit | ↑ parent "Lp space"
        
        $L^{2}$ | 130, 378, 3 | 🔗 link | nosplit | ↑ parent "Lp space"
        
        Plancherel theorem | 150, 248, 2 | 🔗 link | nosplit | ↑ parent " $L^{2}$ "
        
        The Fourier transform is a bijection in $L^{2}$ | 87 | 🔗 link | nosplit | ↑ parent "Plancherel theorem"
        
        Every Riemann integrable function is Lebesgue integrable | 11 | 🔗 link | nosplit | ↑ parent "Plancherel theorem"
  - Measure theory | 57 | 🔗 link | nosplit | ↑ parent "Calculus"
  - Fourier series | 144, 558, 8 | 🔗 link | nosplit | ↑ parent "Calculus"
    - Applications of the Fourier series | 0, 74, 1 | 🔗 link | nosplit | ↑ parent "Fourier series"
      - Solving partial differential equations with the Fourier series | 74 | 🔗 link | nosplit | ↑ parent "Applications of the Fourier series"
    - Discrete Fourier transform (DFT) | 🔗 link | nosplit | ↑ parent "Fourier series"
    - Fourier transform | 186, 323, 3 | 🔗 link | nosplit | ↑ parent "Fourier series"
      - Multidimensional Fourier transform | 44 | 🔗 link | nosplit | ↑ parent "Fourier transform"
      - Fourier inversion theorem | 41 | 🔗 link | nosplit | ↑ parent "Fourier transform"
      - Laplace transform | 52 | 🔗 link | nosplit | ↑ parent "Fourier transform"
    - History of the Fourier series | 17 | 🔗 link | nosplit | ↑ parent "Fourier series"
  - Topology | 152, 2k, 62 | 🔗 link | nosplit | ↑ parent "Calculus"
    - Covering space | 84, 84, 1 | 🔗 link | nosplit | ↑ parent "Topology"
      - Double cover | 🔗 link | nosplit | ↑ parent "Covering space"
    - Neighbourhood (mathematics) | 12 | 🔗 link | nosplit | ↑ parent "Topology"
    - Topological space | 🔗 link | nosplit | ↑ parent "Topology"
    - Manifold | 183, 475, 7 | 🔗 link | nosplit | ↑ parent "Topology"
      - Atlas (topology) | 25, 25, 1 | 🔗 link | nosplit | ↑ parent "Manifold"
        
        Coordinate chart | 🔗 link | nosplit | ↑ parent "Atlas"
      - Covariant derivative | 39 | 🔗 link | nosplit | ↑ parent "Manifold"
      - Differentiable manifold | 32 | 🔗 link | nosplit | ↑ parent "Manifold"
      - Tangent space | 136, 148, 1 | 🔗 link | nosplit | ↑ parent "Manifold"
        
        Tangent vector to a manifold | 12 | 🔗 link | nosplit | ↑ parent "Tangent space"
      - One-form | 48 | 🔗 link | nosplit | ↑ parent "Manifold"
    - Metric (mathematics, $d (x, y)$ ) | 106, 473, 10 | 🔗 link | nosplit | ↑ parent "Topology"
      - Metric space | 10, 367, 9 | 🔗 link | nosplit | ↑ parent "Metric"
        
        Metric space vs normed vector space vs inner product space | 93 | 🔗 link | nosplit | ↑ parent "Metric space"
        
        Complete metric space | 44 | 🔗 link | nosplit | ↑ parent "Metric space"
        
        Normed vector space | 0, 49, 2 | 🔗 link | nosplit | ↑ parent "Metric space"
        
        Inner product space | 23, 49, 1 | 🔗 link | nosplit | ↑ parent "Normed vector space"
        
        Inner product | 26 | 🔗 link | nosplit | ↑ parent "Inner product space"
        
        Norm (mathematics, $∣ x ∣$ ) | 78, 145, 2 | 🔗 link | nosplit | ↑ parent "Metric space"
        
        Norm induced by an inner product | 26 | 🔗 link | nosplit | ↑ parent "Norm"
        
        Metric induced by a norm | 41 | 🔗 link | nosplit | ↑ parent "Norm"
        
        Pseudometric space | 26 | 🔗 link | nosplit | ↑ parent "Metric space"
    - Compact space | 🔗 link | nosplit | ↑ parent "Topology"
    - Dense set | 🔗 link | nosplit | ↑ parent "Topology"
    - Connected space | 0, 39, 3 | 🔗 link | nosplit | ↑ parent "Topology"
      - Connected component | 39 | 🔗 link | nosplit | ↑ parent "Connected space"
      - Simply connected space | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Connected space"
        
        Loop (topology) | 🔗 link | nosplit | ↑ parent "Simply connected space"
    - Homotopy | 0, 526, 7 | 🔗 link | nosplit | ↑ parent "Topology"
      - Generalized Poincaré conjecture | 282, 526, 6 | 🔗 link | nosplit | ↑ parent "Homotopy"
        
        Exotic sphere | 🔗 link | nosplit | ↑ parent "Generalized Poincaré conjecture"
        
        Poincaré conjecture | 🔗 link | nosplit | ↑ parent "Generalized Poincaré conjecture"
        
        Classification of closed surfaces | 215, 244, 3 | 🔗 link | nosplit | ↑ parent "Generalized Poincaré conjecture"
        
        Torus | 🔗 link | nosplit | ↑ parent "Classification of closed surfaces"
        
        Möbius strip | 🔗 link | nosplit | ↑ parent "Classification of closed surfaces"
        
        Klein bottle | 29 | 🔗 link | nosplit | ↑ parent "Classification of closed surfaces"
    - Real coordinate space ( $R^{n}$ ) | 0, 214, 24 | 🔗 link | nosplit | ↑ parent "Topology"
      - Real line ( $R^{1}$ ) | 🔗 link | nosplit | ↑ parent "Real coordinate space"
      - Real plane ( $R^{2}$ ) | 🔗 link | nosplit | ↑ parent "Real coordinate space"
      - Real coordinate space of dimension three ( $R^{3}$ ) | 🔗 link | nosplit | ↑ parent "Real coordinate space"
      - Real coordinate space of dimension four ( $R^{4}$ , 4D) | 10, 29, 1 | 🔗 link | nosplit | ↑ parent "Real coordinate space"
        
        Visualizing 4D | 19 | 🔗 link | nosplit | ↑ parent "Real coordinate space of dimension four"
      - Dimension | 0, 4, 2 | 🔗 link | nosplit | ↑ parent "Real coordinate space"
        
        Infinite dimensional | 4, 4, 1 | 🔗 link | nosplit | ↑ parent "Dimension"
        
        Finite dimensional | 🔗 link | nosplit | ↑ parent "Infinite dimensional"
      - Complex coordinate space ( $C^{n}$ ) | 0, 115, 1 | 🔗 link | nosplit | ↑ parent "Real coordinate space"
        
        Complex dot product | 115 | 🔗 link | nosplit | ↑ parent "Complex coordinate space"
      - Euclidean space | 23, 66, 13 | 🔗 link | nosplit | ↑ parent "Real coordinate space"
        
        Euclidean metric signature matrix | 9 | 🔗 link | nosplit | ↑ parent "Euclidean space"
        
        Cartesian coordinate system | 🔗 link | nosplit | ↑ parent "Euclidean space"
        
        Polar coordinate system | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Euclidean space"
        
        Spherical coordinate system | 🔗 link | nosplit | ↑ parent "Polar coordinate system"
        
        Pythagorean theorem | 🔗 link | nosplit | ↑ parent "Euclidean space"
        
        Non-Euclidean geometry | 0, 34, 7 | 🔗 link | nosplit | ↑ parent "Euclidean space"
        
        Elliptic geometry | 0, 34, 2 | 🔗 link | nosplit | ↑ parent "Non-Euclidean geometry"
        
        Model of elliptic geometry | 0, 34, 1 | 🔗 link | nosplit | ↑ parent "Elliptic geometry"
        
        Projective elliptic geometry | 34 | 🔗 link | nosplit | ↑ parent "Model of elliptic geometry"
        
        Hyperbolic gemoetry | 0, 0, 3 | 🔗 link | nosplit | ↑ parent "Non-Euclidean geometry"
        
        Hyperbolic functions | 0, 0, 2 | 🔗 link | nosplit | ↑ parent "Hyperbolic gemoetry"
        
        Hyperbolic sine | 🔗 link | nosplit | ↑ parent "Hyperbolic functions"
        
        Hyperbolic cossine | 🔗 link | nosplit | ↑ parent "Hyperbolic functions"
  - Distribution (mathematics) | 182, 265, 3 | 🔗 link | nosplit | ↑ parent "Calculus"
    - Dirac delta function | 83, 83, 2 | 🔗 link | nosplit | ↑ parent "Distribution"
      - Green's function | 🔗 link | nosplit | ↑ parent "Dirac delta function"
      - Heaviside step function | 🔗 link | nosplit | ↑ parent "Dirac delta function"
  - Complex analysis | 14, 278, 6 | 🔗 link | nosplit | ↑ parent "Calculus"
    - Holomorphic function | 69 | 🔗 link | nosplit | ↑ parent "Complex analysis"
    - Analytic continuation | 52, 195, 4 | 🔗 link | nosplit | ↑ parent "Complex analysis"
      - Visualizing the Riemann hypothesis and analytic continuation by 3Blue1Brown (2016) | 17 | 🔗 link | nosplit | ↑ parent "Analytic continuation"
      - Identity theorem | 92, 126, 2 | 🔗 link | nosplit | ↑ parent "Analytic continuation"
        
        Riemann zeta function | 0, 34, 1 | 🔗 link | nosplit | ↑ parent "Identity theorem"
        
        Riemann hypothesis | 34 | 🔗 link | nosplit | ↑ parent "Riemann zeta function"
  - Hilbert space | 34, 184, 1 | 🔗 link | nosplit | ↑ parent "Calculus"
    - Complete basis | 150 | 🔗 link | nosplit | ↑ parent "Hilbert space"
  - Differential equation | 0, 3k, 73 | 🔗 link | nosplit | ↑ parent "Calculus"
    - Euler number ( $e$ ) | 0, 11, 2 | 🔗 link | nosplit | ↑ parent "Differential equation"
      - Natural logarithm ( $l n (n)$ , $l o g_{e} (n)$ ) | 0, 11, 1 | 🔗 link | nosplit | ↑ parent "Euler number"
        
        Euler-Mascheroni constant | 11 | 🔗 link | nosplit | ↑ parent "Natural logarithm"
    - Linear differential equation | 172, 172, 1 | 🔗 link | nosplit | ↑ parent "Differential equation"
      - Holonomic function | 🔗 link | nosplit | ↑ parent "Linear differential equation"
    - Order of a differential equation | 7 | 🔗 link | nosplit | ↑ parent "Differential equation"
    - Ordinary differential equation (ODE) | 0, 0, 5 | 🔗 link | nosplit | ↑ parent "Differential equation"
      - Existence and uniqueness of solutions of ordinary differential equations | 0, 0, 2 | 🔗 link | nosplit | ↑ parent "Ordinary differential equation"
        
        Peano existence theorem | 🔗 link | nosplit | ↑ parent "Existence and uniqueness of solutions of ordinary differential equations"
        
        Picard-Lindelöf theorem | 🔗 link | nosplit | ↑ parent "Existence and uniqueness of solutions of ordinary differential equations"
      - System of ordinary differential equations | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Ordinary differential equation"
        
        System of linear ordinary differential equations | 🔗 link | nosplit | ↑ parent "System of ordinary differential equations"
    - Partial differential equation (PDE) | 0, 2k, 45 | 🔗 link | nosplit | ↑ parent "Differential equation"
      - Analytical method to solve a partial differential equation | 6, 88, 1 | 🔗 link | nosplit | ↑ parent "Partial differential equation"
        
        Separation of variables | 82 | 🔗 link | nosplit | ↑ parent "Analytical method to solve a partial differential equation"
      - Numerical method to solve a partial differential equation | 20, 79, 3 | 🔗 link | nosplit | ↑ parent "Partial differential equation"
        
        Variational formulation of a partial differential equation | 32, 32, 1 | 🔗 link | nosplit | ↑ parent "Numerical method to solve a partial differential equation"
        
        Weak solution | 🔗 link | nosplit | ↑ parent "Variational formulation of a partial differential equation"
        
        Finite element method | 27 | 🔗 link | nosplit | ↑ parent "Numerical method to solve a partial differential equation"
      - Important partial differential equation | 43, 793, 24 | 🔗 link | nosplit | ↑ parent "Partial differential equation"
        
        Laplace's equation | 83, 188, 5 | 🔗 link | nosplit | ↑ parent "Important partial differential equation"
        
        Legendre polynomials | 46 | 🔗 link | nosplit | ↑ parent "Laplace's equation"
        
        Poisson's equation | 16, 16, 1 | 🔗 link | nosplit | ↑ parent "Laplace's equation"
        
        Uniqueness theorem for Poisson's equation | 🔗 link | nosplit | ↑ parent "Poisson's equation"
        
        Harmonic function | 11, 43, 1 | 🔗 link | nosplit | ↑ parent "Laplace's equation"
        
        Spherical harmonic | 32 | 🔗 link | nosplit | ↑ parent "Harmonic function"
        
        Heat equation | 144 | 🔗 link | nosplit | ↑ parent "Important partial differential equation"
        
        Wave equation | 124, 418, 16 | 🔗 link | nosplit | ↑ parent "Important partial differential equation"
        
        The wave equation can be seen as infinitely many infinitesimal coupled oscillators | 67 | 🔗 link | nosplit | ↑ parent "Wave equation"
        
        Wave | 🔗 link | nosplit | ↑ parent "Wave equation"
        
        Diffraction | 0, 57, 5 | 🔗 link | nosplit | ↑ parent "Wave equation"
        
        Arago spot | 🔗 link | nosplit | ↑ parent "Diffraction"
        
        Huygens-Fresnel principle | 0, 57, 3 | 🔗 link | nosplit | ↑ parent "Diffraction"
        
        Kirchhoff's diffraction formula | 10, 57, 2 | 🔗 link | nosplit | ↑ parent "Huygens-Fresnel principle"
        
        Fraunhofer diffraction | 24 | 🔗 link | nosplit | ↑ parent "Kirchhoff's diffraction formula"
        
        Fresnel diffraction | 23 | 🔗 link | nosplit | ↑ parent "Kirchhoff's diffraction formula"
        
        Refraction | 🔗 link | nosplit | ↑ parent "Wave equation"
        
        Resonance | 8 | 🔗 link | nosplit | ↑ parent "Wave equation"
        
        Wave interference | 0, 33, 1 | 🔗 link | nosplit | ↑ parent "Wave equation"
        
        Interference pattern | 33 | 🔗 link | nosplit | ↑ parent "Wave interference"
        
        2D wave equation on a circular domain | 0, 112, 2 | 🔗 link | nosplit | ↑ parent "Wave equation"
        
        Bessel function | 86, 112, 1 | 🔗 link | nosplit | ↑ parent "2D wave equation on a circular domain"
        
        Fourier-Bessel series | 26 | 🔗 link | nosplit | ↑ parent "Bessel function"
        
        Helmholtz equation | 17 | 🔗 link | nosplit | ↑ parent "Wave equation"
      - Existence and uniqueness of solutions of partial differential equations | 116 | 🔗 link | nosplit | ↑ parent "Partial differential equation"
      - Partial differential equation solver | 0, 1k, 6 | 🔗 link | nosplit | ↑ parent "Partial differential equation"
        
        FreeFem | 648, 691, 3 | 🔗 link | nosplit | ↑ parent "Partial differential equation solver"
        
        FreeFem examples | 0, 43, 2 | 🔗 link | nosplit | ↑ parent "FreeFem"
        
        heat-dirichlet.1d.freefem | 21 | 🔗 link | nosplit | ↑ parent "FreeFem examples"
        
        heat-dirichlet-2d-freefem | 22 | 🔗 link | nosplit | ↑ parent "FreeFem examples"
        
        FEniCS Project | 233, 372, 1 | 🔗 link | nosplit | ↑ parent "Partial differential equation solver"
        
        Hans Petter Langtangen | 139 | 🔗 link | nosplit | ↑ parent "FEniCS Project"
      - System of partial differential equations | 77 | 🔗 link | nosplit | ↑ parent "Partial differential equation"
      - Classification of second order partial differential equations into elliptic, parabolic and hyperbolic | 43, 123, 4 | 🔗 link | nosplit | ↑ parent "Partial differential equation"
        
        Elliptic partial differential equation | 🔗 link | nosplit | ↑ parent "Classification of second order partial differential equations into elliptic, parabolic and hyperbolic"
        
        Parabolic partial differential equation | 🔗 link | nosplit | ↑ parent "Classification of second order partial differential equations into elliptic, parabolic and hyperbolic"
        
        Hyperbolic partial differential equation | 🔗 link | nosplit | ↑ parent "Classification of second order partial differential equations into elliptic, parabolic and hyperbolic"
        
        Which boundary conditions lead to existence and uniqueness of a second order PDE | 80 | 🔗 link | nosplit | ↑ parent "Classification of second order partial differential equations into elliptic, parabolic and hyperbolic"
    - Phase space | 23 | 🔗 link | nosplit | ↑ parent "Differential equation"
    - Boundary condition | 0, 469, 9 | 🔗 link | nosplit | ↑ parent "Differential equation"
      - Initial condition | 29 | 🔗 link | nosplit | ↑ parent "Boundary condition"
      - Boundary value problem | 🔗 link | nosplit | ↑ parent "Boundary condition"
      - Dirichlet boundary condition | 46 | 🔗 link | nosplit | ↑ parent "Boundary condition"
      - Neumann boundary condition | 28, 343, 4 | 🔗 link | nosplit | ↑ parent "Boundary condition"
        
        Cauchy boundary condition | 70 | 🔗 link | nosplit | ↑ parent "Neumann boundary condition"
        
        Robin boundary condition | 117 | 🔗 link | nosplit | ↑ parent "Neumann boundary condition"
        
        Open boundary condition | 115 | 🔗 link | nosplit | ↑ parent "Neumann boundary condition"
        
        Mixed boundary condition | 13 | 🔗 link | nosplit | ↑ parent "Neumann boundary condition"
      - Time dependent boundary condition | 51 | 🔗 link | nosplit | ↑ parent "Boundary condition"
    - Control theory | 104, 104, 3 | 🔗 link | nosplit | ↑ parent "Differential equation"
      - Control engineering | 🔗 link | nosplit | ↑ parent "Control theory"
      - Control system | 🔗 link | nosplit | ↑ parent "Control theory"
      - Feedback loop | 🔗 link | nosplit | ↑ parent "Control theory"
  - Series (mathematics) | 0, 0, 3 | 🔗 link | nosplit | ↑ parent "Calculus"
    - Power series | 0, 0, 2 | 🔗 link | nosplit | ↑ parent "Series"
      - Radius of convergence | 🔗 link | nosplit | ↑ parent "Power series"
      - Taylor series | 🔗 link | nosplit | ↑ parent "Power series"
  - Gradient, Divergence, Curl, and Laplacian | 0, 401, 7 | 🔗 link | nosplit | ↑ parent "Calculus"
    - Curl (mathematics, $\nabla \times$ ) | 11 | 🔗 link | nosplit | ↑ parent "Gradient, Divergence, Curl, and Laplacian"
    - Nabla symbol ( $\nabla$ ) | 96, 149, 1 | 🔗 link | nosplit | ↑ parent "Gradient, Divergence, Curl, and Laplacian"
      - Del | 53 | 🔗 link | nosplit | ↑ parent "Nabla symbol"
    - Divergence ( $\nabla \cdot$ , $d i v ()$ ) | 74 | 🔗 link | nosplit | ↑ parent "Gradient, Divergence, Curl, and Laplacian"
    - Gradient ( $\nabla$ ) | 89 | 🔗 link | nosplit | ↑ parent "Gradient, Divergence, Curl, and Laplacian"
    - Laplace operator ( $Δ$ , $\nabla^{2}$ ) | 39, 78, 1 | 🔗 link | nosplit | ↑ parent "Gradient, Divergence, Curl, and Laplacian"
      - D'alembert operator ( $□$ ) | 39 | 🔗 link | nosplit | ↑ parent "Laplace operator"
  - Infinitesimal | 23 | 🔗 link | nosplit | ↑ parent "Calculus"
- Discrete mathematics | 0, 0, 3 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - Graph (discrete mathematics) | 0, 0, 2 | 🔗 link | nosplit | ↑ parent "Discrete mathematics"
    - Edge (graph) | 🔗 link | nosplit | ↑ parent "Graph"
    - Vertex | 🔗 link | nosplit | ↑ parent "Graph"
- Functional equation | 0, 13, 1 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - Cauchy's functional equation | 13 | 🔗 link | nosplit | ↑ parent "Functional equation"
- Game theory | 0, 163, 6 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - Balance of power | 🔗 link | nosplit | ↑ parent "Game theory"
  - Nash equilibrium | 142, 154, 3 | 🔗 link | nosplit | ↑ parent "Game theory"
    - Mixed strategy | 🔗 link | nosplit | ↑ parent "Nash equilibrium"
    - Prisoner's dilemma | 4 | 🔗 link | nosplit | ↑ parent "Nash equilibrium"
    - Bimatrix game | 8 | 🔗 link | nosplit | ↑ parent "Nash equilibrium"
  - Tit for tat | 9 | 🔗 link | nosplit | ↑ parent "Game theory"
- Geometry | 0, 9k, 154 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - Fractal | 🔗 link | nosplit | ↑ parent "Geometry"
  - Point (geometry) | 0, 53, 3 | 🔗 link | nosplit | ↑ parent "Geometry"
    - Line (geometry) | 🔗 link | nosplit | ↑ parent "Point"
    - Hyperplane | 53, 53, 1 | 🔗 link | nosplit | ↑ parent "Point"
      - Plane (geometry) | 🔗 link | nosplit | ↑ parent "Hyperplane"
  - n-sphere ( $S^{n}$ ) | 0, 10, 7 | 🔗 link | nosplit | ↑ parent "Geometry"
    - Antipodal point | 🔗 link | nosplit | ↑ parent "n-sphere"
    - Diameter | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "n-sphere"
      - Radius | 🔗 link | nosplit | ↑ parent "Diameter"
    - Circle ( $S^{1}$ , 1-sphere) | 🔗 link | nosplit | ↑ parent "n-sphere"
    - Sphere ( $S^{2}$ , 2-sphere) | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "n-sphere"
      - Great circle | 🔗 link | nosplit | ↑ parent "Sphere"
    - 3-sphere ( $S^{3}$ ) | 10 | 🔗 link | nosplit | ↑ parent "n-sphere"
  - Projective geometry | 0, 1k, 12 | 🔗 link | nosplit | ↑ parent "Geometry"
    - Projective space ( $P (V)$ ) | 86, 86, 1 | 🔗 link | nosplit | ↑ parent "Projective geometry"
      - Projective plane | 🔗 link | nosplit | ↑ parent "Projective space"
    - Real projective space ( $R P^{n}$ , $P (R^{n + 1})$ ) | 31, 966, 9 | 🔗 link | nosplit | ↑ parent "Projective geometry"
      - Real projective line ( $R P^{1}$ , $P (R^{2})$ ) | 27 | 🔗 link | nosplit | ↑ parent "Real projective space"
      - Real projective plane ( $R P^{2}$ , $P (R^{3})$ ) | 95, 908, 7 | 🔗 link | nosplit | ↑ parent "Real projective space"
        
        Synthetic geometry of the real projective plane | 405 | 🔗 link | nosplit | ↑ parent "Real projective plane"
        
        Model of the real projective plane | 0, 318, 2 | 🔗 link | nosplit | ↑ parent "Real projective plane"
        
        Lines through origin model of the real projective plane | 5 | 🔗 link | nosplit | ↑ parent "Model of the real projective plane"
        
        Spherical cap model of the real projective plane | 313 | 🔗 link | nosplit | ↑ parent "Model of the real projective plane"
        
        The real projective plane is not simply connected | 90 | 🔗 link | nosplit | ↑ parent "Real projective plane"
        
        Point at infinity | 🔗 link | nosplit | ↑ parent "Real projective plane"
        
        Homogenous coordinates | 🔗 link | nosplit | ↑ parent "Real projective plane"
  - Polytope | 37, 487, 28 | 🔗 link | nosplit | ↑ parent "Geometry"
    - Convex polytope | 🔗 link | nosplit | ↑ parent "Polytope"
    - Regular polytope | 5, 390, 5 | 🔗 link | nosplit | ↑ parent "Polytope"
      - Classification of regular polytopes | 148, 385, 4 | 🔗 link | nosplit | ↑ parent "Regular polytope"
        
        Simplex | 48 | 🔗 link | nosplit | ↑ parent "Classification of regular polytopes"
        
        Hypercube | 112, 132, 1 | 🔗 link | nosplit | ↑ parent "Classification of regular polytopes"
        
        Hyperrectangle | 20 | 🔗 link | nosplit | ↑ parent "Hypercube"
        
        Cross polytope | 57 | 🔗 link | nosplit | ↑ parent "Classification of regular polytopes"
    - Polygon | 0, 15, 12 | 🔗 link | nosplit | ↑ parent "Polytope"
      - Quadrilateral | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Polygon"
        
        Rectangle | 🔗 link | nosplit | ↑ parent "Quadrilateral"
      - Parallelogram | 0, 15, 2 | 🔗 link | nosplit | ↑ parent "Polygon"
        
        Parallelepiped | 15, 15, 1 | 🔗 link | nosplit | ↑ parent "Parallelogram"
        
        Volume of the parallelepiped | 🔗 link | nosplit | ↑ parent "Parallelepiped"
      - Regular polygon | 0, 0, 6 | 🔗 link | nosplit | ↑ parent "Polygon"
        
        Regular convex polygon | 0, 0, 5 | 🔗 link | nosplit | ↑ parent "Regular polygon"
        
        Triangle | 🔗 link | nosplit | ↑ parent "Regular convex polygon"
        
        Square | 🔗 link | nosplit | ↑ parent "Regular convex polygon"
        
        Pentagon | 🔗 link | nosplit | ↑ parent "Regular convex polygon"
        
        Hexagon | 🔗 link | nosplit | ↑ parent "Regular convex polygon"
        
        Octagon | 🔗 link | nosplit | ↑ parent "Regular convex polygon"
    - Polyhedron | 0, 0, 2 | 🔗 link | nosplit | ↑ parent "Polytope"
      - Tetrahedron | 🔗 link | nosplit | ↑ parent "Polyhedron"
      - Octahedron | 🔗 link | nosplit | ↑ parent "Polyhedron"
    - Regular polyhedron | 0, 45, 1 | 🔗 link | nosplit | ↑ parent "Polytope"
      - Platonic solid | 45 | 🔗 link | nosplit | ↑ parent "Regular polyhedron"
    - 4-polytope | 0, 0, 2 | 🔗 link | nosplit | ↑ parent "Polytope"
      - Regular 4-polytope | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "4-polytope"
        
        Tesseract | 🔗 link | nosplit | ↑ parent "Regular 4-polytope"
  - Differential geometry | 12, 7k, 98 | 🔗 link | nosplit | ↑ parent "Geometry"
    - Lie group | 278, 7k, 97 | 🔗 link | nosplit | ↑ parent "Differential geometry"
      - Applications of Lie groups to differential equations (How to use Lie Groups to solve differential equations) | 104 | 🔗 link | nosplit | ↑ parent "Lie group"
      - Lie algebra | 424, 1k, 15 | 🔗 link | nosplit | ↑ parent "Lie group"
        
        Infinitesimal generator | 196 | 🔗 link | nosplit | ↑ parent "Lie algebra"
        
        Lie group-Lie algebra correspondence | 56, 264, 7 | 🔗 link | nosplit | ↑ parent "Lie algebra"
        
        Lie algebra exponential covering problem | 20, 82, 2 | 🔗 link | nosplit | ↑ parent "Lie group-Lie algebra correspondence"
        
        A single exponential map is not enough to recover a simple Lie group from its algebra | 12 | 🔗 link | nosplit | ↑ parent "Lie algebra exponential covering problem"
        
        The product of a exponential of the compact algebra with that of the non-compact algebra recovers a simple Lie from its algebra | 50 | 🔗 link | nosplit | ↑ parent "Lie algebra exponential covering problem"
        
        Two different Lie groups can have the same Lie algebra | 40, 126, 3 | 🔗 link | nosplit | ↑ parent "Lie group-Lie algebra correspondence"
        
        Every Lie algebra has a unique single corresponding simply connected Lie group | 66, 86, 1 | 🔗 link | nosplit | ↑ parent "Two different Lie groups can have the same Lie algebra"
        
        Universal covering group | 20 | 🔗 link | nosplit | ↑ parent "Every Lie algebra has a unique single corresponding simply connected Lie group"
        
        Every Lie group that has a given Lie algebra is the image of an homomorphism from the universal cover group | 🔗 link | nosplit | ↑ parent "Two different Lie groups can have the same Lie algebra"
        
        Lie bracket | 🔗 link | nosplit | ↑ parent "Lie algebra"
        
        Exponential map | 12, 180, 1 | 🔗 link | nosplit | ↑ parent "Lie algebra"
        
        Exponential map (Lie theory) | 168 | 🔗 link | nosplit | ↑ parent "Exponential map"
        
        Baker-Campbell-Hausdorff formula (BCH formula) | 231 | 🔗 link | nosplit | ↑ parent "Lie algebra"
        
        Generator of a Lie algebra | 🔗 link | nosplit | ↑ parent "Lie algebra"
        
        Generators of a Lie algebra | 7 | 🔗 link | nosplit | ↑ parent "Lie algebra"
      - Continuous symmetry | 18, 367, 2 | 🔗 link | nosplit | ↑ parent "Lie group"
        
        Local symmetry | 181, 349, 1 | 🔗 link | nosplit | ↑ parent "Continuous symmetry"
        
        Local symmetries of the Lagrangian imply conserved currents | 168 | 🔗 link | nosplit | ↑ parent "Local symmetry"
      - Important Lie group | 0, 5k, 65 | 🔗 link | nosplit | ↑ parent "Lie group"
        
        Matrix Lie group | 9, 471, 4 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Every closed subgroup of $G L (n, C)$ is a Lie group | 8 | 🔗 link | nosplit | ↑ parent "Matrix Lie group"
        
        Lie algebra of a matrix Lie group | 219, 454, 2 | 🔗 link | nosplit | ↑ parent "Matrix Lie group"
        
        Lie bracket of a matrix Lie group | 119 | 🔗 link | nosplit | ↑ parent "Lie algebra of a matrix Lie group"
        
        One parameter subgroup | 116 | 🔗 link | nosplit | ↑ parent "Lie algebra of a matrix Lie group"
        
        Classical group | 0, 222, 3 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Symplectic group ( $S p (n, F)$ ) | 222, 222, 2 | 🔗 link | nosplit | ↑ parent "Classical group"
        
        Symplectic matrix | 🔗 link | nosplit | ↑ parent "Symplectic group"
        
        Unitary symplectic group ( $S p (n)$ ) | 🔗 link | nosplit | ↑ parent "Symplectic group"
        
        General linear group ( $G L (n)$ , $G L (n, F)$ ) | 91, 170, 1 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Finite general linear group ( $G L (n, F_{m})$ , $G L (n, m)$ ) | 79 | 🔗 link | nosplit | ↑ parent "General linear group"
        
        Lie algebra of $G L (n)$ | 109 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Special linear group ( $S L (n)$ ) | 18, 638, 4 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Special linear group of dimension 2 ( $S L (2)$ ) | 🔗 link | nosplit | ↑ parent "Special linear group"
        
        Lie algebra of $S L (n)$ | 0, 569, 1 | 🔗 link | nosplit | ↑ parent "Special linear group"
        
        Lie algebra of $S L (2)$ | 569 | 🔗 link | nosplit | ↑ parent "Lie algebra of $S L (n)$ "
        
        Finite special general linear group ( $S L (n, m)$ ) | 51 | 🔗 link | nosplit | ↑ parent "Special linear group"
        
        Isometry group | 69, 206, 1 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Lie algebra of a isometry group | 137 | 🔗 link | nosplit | ↑ parent "Isometry group"
        
        Orthogonal group ( $O (n)$ ) | 0, 1k, 22 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Definition of the orthogonal group | 8, 391, 4 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
        
        The orthogonal group is the group of all matrices that preserve the dot product | 72, 244, 1 | 🔗 link | nosplit | ↑ parent "Definition of the orthogonal group"
        
        What happens to the definition of the orthogonal group if we choose other types of symmetric bilinear forms | 172 | 🔗 link | nosplit | ↑ parent "The orthogonal group is the group of all matrices that preserve the dot product"
        
        The orthogonal group is the group of all invertible matrices where the inverse is equal to the transpose | 102 | 🔗 link | nosplit | ↑ parent "Definition of the orthogonal group"
        
        The orthogonal group is the group of all matrices with orthonormal rows and orthonormal columns | 37 | 🔗 link | nosplit | ↑ parent "Definition of the orthogonal group"
        
        Topology of the orthogonal group | 0, 343, 2 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
        
        The orthogonal group is compact | 🔗 link | nosplit | ↑ parent "Topology of the orthogonal group"
        
        Connected components of the orthogonal group (The orthogonal group has two connected components) | 343 | 🔗 link | nosplit | ↑ parent "Topology of the orthogonal group"
        
        Lie algebra of $O (n)$ | 9 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
        
        Special orthogonal group ( $S O (n)$ , Rotation group) | 46, 275, 3 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
        
        Lie algebra of $S O (3)$ | 180, 211, 1 | 🔗 link | nosplit | ↑ parent "Special orthogonal group"
        
        Lie bracket of the rotation group | 31 | 🔗 link | nosplit | ↑ parent "Lie algebra of $S O (3)$ "
        
        3D rotation group ( $S O (3)$ ) | 18 | 🔗 link | nosplit | ↑ parent "Special orthogonal group"
        
        Unitary group ( $U (n)$ ) | 80, 205, 8 | 🔗 link | nosplit | ↑ parent "Orthogonal group"
        
        Unitary group of degree 1 ( $U (1)$ ) | 🔗 link | nosplit | ↑ parent "Unitary group"
        
        Unitary group of degree 2 ( $U (2)$ ) | 5 | 🔗 link | nosplit | ↑ parent "Unitary group"
        
        Unit circle | 19 | 🔗 link | nosplit | ↑ parent "Unitary group"
        
        Special unitary group ( $S U (n)$ ) | 49, 101, 4 | 🔗 link | nosplit | ↑ parent "Unitary group"
        
        Special unitary of degree 2 ( $S U (2)$ ) | 34, 52, 3 | 🔗 link | nosplit | ↑ parent "Special unitary group"
        
        Representations of $S U (2)$ | 0, 18, 2 | 🔗 link | nosplit | ↑ parent "Special unitary of degree 2"
        
        Lie algebra of $S U (2)$ | 10 | 🔗 link | nosplit | ↑ parent "Representations of $S U (2)$ "
        
        2D representation of $S U (2)$ | 8 | 🔗 link | nosplit | ↑ parent "Representations of $S U (2)$ "
        
        Projective linear group | 19, 48, 5 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Finite projective linear group ( $P G L (q, p)$ ) | 🔗 link | nosplit | ↑ parent "Projective linear group"
        
        Projective special linear group | 0, 29, 3 | 🔗 link | nosplit | ↑ parent "Projective linear group"
        
        Finite projective special linear group ( $P S L (p, q)$ ) | 0, 29, 2 | 🔗 link | nosplit | ↑ parent "Projective special linear group"
        
        $P S L (2, p)$ | 0, 29, 1 | 🔗 link | nosplit | ↑ parent "Finite projective special linear group"
        
        PSL(2,7) | 29 | 🔗 link | nosplit | ↑ parent " $P S L (2, p)$ "
        
        Poincaré group | 192, 2k, 16 | 🔗 link | nosplit | ↑ parent "Important Lie group"
        
        Galilean transformation | 0, 610, 5 | 🔗 link | nosplit | ↑ parent "Poincaré group"
        
        Translation (geometry) | 13, 238, 2 | 🔗 link | nosplit | ↑ parent "Galilean transformation"
        
        Translation group | 19, 225, 1 | 🔗 link | nosplit | ↑ parent "Translation"
        
        The derivative is the generator of the translation group | 206 | 🔗 link | nosplit | ↑ parent "Translation group"
        
        Galilean invariance | 285, 372, 1 | 🔗 link | nosplit | ↑ parent "Galilean transformation"
        
        Covariance | 87 | 🔗 link | nosplit | ↑ parent "Galilean invariance"
        
        Lorentz group ( $S O (1, 3)$ ) | 189, 794, 9 | 🔗 link | nosplit | ↑ parent "Poincaré group"
        
        Representation theory of the Lorentz group | 80, 137, 3 | 🔗 link | nosplit | ↑ parent "Lorentz group"
        
        Representation of the Lorentz group | 26, 57, 2 | 🔗 link | nosplit | ↑ parent "Representation theory of the Lorentz group"
        
        Lie algebra of the Lorentz group | 🔗 link | nosplit | ↑ parent "Representation of the Lorentz group"
        
        Spinor | 31 | 🔗 link | nosplit | ↑ parent "Representation of the Lorentz group"
        
        Lorentz boost | 47 | 🔗 link | nosplit | ↑ parent "Lorentz group"
        
        Indefinite orthogonal group ( $O (m, n)$ ) | 38, 421, 3 | 🔗 link | nosplit | ↑ parent "Lorentz group"
        
        Definition of the indefinite orthogonal group | 204, 383, 1 | 🔗 link | nosplit | ↑ parent "Indefinite orthogonal group"
        
        All indefinite orthogonal groups of matrices of equal metric signature are isomorphic | 179 | 🔗 link | nosplit | ↑ parent "Definition of the indefinite orthogonal group"
        
        Indefinite special orthogonal group ( $S O (m, n)$ ) | 🔗 link | nosplit | ↑ parent "Indefinite orthogonal group"
      - Representation theory | 304, 304, 3 | 🔗 link | nosplit | ↑ parent "Lie group"
        
        Irreducible representation | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Representation theory"
        
        Casimir element | 🔗 link | nosplit | ↑ parent "Irreducible representation"
        
        Schur's lemma | 🔗 link | nosplit | ↑ parent "Representation theory"
      - Simple Lie group | 0, 46, 1 | 🔗 link | nosplit | ↑ parent "Lie group"
        
        Classification of simple Lie groups | 46 | 🔗 link | nosplit | ↑ parent "Simple Lie group"
      - Lie group bibliography | 32, 244, 4 | 🔗 link | nosplit | ↑ parent "Lie group"
        
        An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee (2011) | 46 | 🔗 link | nosplit | ↑ parent "Lie group bibliography"
        
        Lie Groups, Physics, and Geometry by Robert Gilmore (2008) | 166 | 🔗 link | nosplit | ↑ parent "Lie group bibliography"
        
        Naive Lie theory by John Stillwell (2008) | 🔗 link | nosplit | ↑ parent "Lie group bibliography"
        
        Lie Algebras In Particle Physics by Howard Georgi (1999) | 🔗 link | nosplit | ↑ parent "Lie group bibliography"
- Mathematician | 118, 1k, 18 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - High flying bird vs gophers (Birds and frogs by Freeman Dyson (2009)) | 625 | 🔗 link | nosplit | ↑ parent "Mathematician"
  - Mathematics Genealogy Project | 🔗 link | nosplit | ↑ parent "Mathematician"
  - List of mathematicians | 0, 313, 15 | 🔗 link | nosplit | ↑ parent "Mathematician"
    - Alexander Grothendieck | 55 | 🔗 link | nosplit | ↑ parent "List of mathematicians"
    - Blaise Pascal (1623-1662) | 12 | 🔗 link | nosplit | ↑ parent "List of mathematicians"
    - Euclid | 0, 80, 4 | 🔗 link | nosplit | ↑ parent "List of mathematicians"
      - Euclid's Elements | 0, 80, 3 | 🔗 link | nosplit | ↑ parent "Euclid"
        
        Synthetic geometry | 47 | 🔗 link | nosplit | ↑ parent "Euclid's Elements"
        
        Euclid's postulates | 33, 33, 1 | 🔗 link | nosplit | ↑ parent "Euclid's Elements"
        
        Parallel postulate | 🔗 link | nosplit | ↑ parent "Euclid's postulates"
    - Évariste Galois | 🔗 link | nosplit | ↑ parent "List of mathematicians"
    - G. H. Hardy | 0, 116, 1 | 🔗 link | nosplit | ↑ parent "List of mathematicians"
      - A Mathematician's Apology (1940) | 116 | 🔗 link | nosplit | ↑ parent "G. H. Hardy"
    - James Harris Simons | 50 | 🔗 link | nosplit | ↑ parent "List of mathematicians"
    - Joseph Fourier | 🔗 link | nosplit | ↑ parent "List of mathematicians"
    - Paul Erdos | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "List of mathematicians"
      - Erdos number | 🔗 link | nosplit | ↑ parent "Paul Erdos"
    - René Descartes | 🔗 link | nosplit | ↑ parent "List of mathematicians"
- Mathematical notation | 51, 76, 1 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - Mathematical symbol that looks like a Greek letter but isn't | 25 | 🔗 link | nosplit | ↑ parent "Mathematical notation"
- Number theory | 0, 94, 17 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - Arithmetic | 50 | 🔗 link | nosplit | ↑ parent "Number theory"
  - Modular arithmetic | 0, 14, 4 | 🔗 link | nosplit | ↑ parent "Number theory"
    - Modulo operation | 🔗 link | nosplit | ↑ parent "Modular arithmetic"
    - Modular multiplication | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Modular arithmetic"
      - Modular multiplicative inverse | 🔗 link | nosplit | ↑ parent "Modular multiplication"
    - Modular exponentiation | 14 | 🔗 link | nosplit | ↑ parent "Modular arithmetic"
  - Lowest common denominator (LCD) | 🔗 link | nosplit | ↑ parent "Number theory"
  - Prime number | 0, 30, 9 | 🔗 link | nosplit | ↑ parent "Number theory"
    - Goldbach's conjecture | 🔗 link | nosplit | ↑ parent "Prime number"
    - Prime number theorem | 🔗 link | nosplit | ↑ parent "Prime number"
    - Prime power | 16 | 🔗 link | nosplit | ↑ parent "Prime number"
    - Primality test | 🔗 link | nosplit | ↑ parent "Prime number"
    - Greatest common divisor (GCD) | 0, 14, 3 | 🔗 link | nosplit | ↑ parent "Prime number"
      - Coprime | 14 | 🔗 link | nosplit | ↑ parent "Greatest common divisor"
      - Euclidean algorithm | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Greatest common divisor"
        
        Extended Euclidean algorithm | 🔗 link | nosplit | ↑ parent "Euclidean algorithm"
    - Least common multiple (lcm) | 🔗 link | nosplit | ↑ parent "Prime number"
- Numerical analysis | 96, 349, 7 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - Floating-point arithmetic | 0, 47, 2 | 🔗 link | nosplit | ↑ parent "Numerical analysis"
    - Floating-point number | 🔗 link | nosplit | ↑ parent "Floating-point arithmetic"
    - IEEE 754 | 47 | 🔗 link | nosplit | ↑ parent "Floating-point arithmetic"
  - Numerical computing language | 132, 132, 2 | 🔗 link | nosplit | ↑ parent "Numerical analysis"
    - Scilab | 🔗 link | nosplit | ↑ parent "Numerical computing language"
    - MATLAB | 🔗 link | nosplit | ↑ parent "Numerical computing language"
  - Perturbation theory | 74 | 🔗 link | nosplit | ↑ parent "Numerical analysis"
- Polynomial | 0, 614, 20 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - Algebraic equation (Polynomial equation) | 0, 14, 9 | 🔗 link | nosplit | ↑ parent "Polynomial"
    - Named algebraic equation | 0, 0, 6 | 🔗 link | nosplit | ↑ parent "Algebraic equation"
      - Quadratic equation | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Named algebraic equation"
        
        Quadratic formula | 🔗 link | nosplit | ↑ parent "Quadratic equation"
      - Cubic equation | 🔗 link | nosplit | ↑ parent "Named algebraic equation"
      - Quartic equation | 🔗 link | nosplit | ↑ parent "Named algebraic equation"
      - Quintic equation | 0, 0, 1 | 🔗 link | nosplit | ↑ parent "Named algebraic equation"
        
        Abel-Ruffini theorem | 🔗 link | nosplit | ↑ parent "Quintic equation"
    - Algebraic number | 0, 14, 1 | 🔗 link | nosplit | ↑ parent "Algebraic equation"
      - Transcendental number | 14 | 🔗 link | nosplit | ↑ parent "Algebraic number"
  - Diophantine equation | 12, 48, 1 | 🔗 link | nosplit | ↑ parent "Polynomial"
    - Undecidable Diophantine equation problems | 36 | 🔗 link | nosplit | ↑ parent "Diophantine equation"
  - Named small order polynomial | 0, 18, 1 | 🔗 link | nosplit | ↑ parent "Polynomial"
    - Linear polynomial | 18 | 🔗 link | nosplit | ↑ parent "Named small order polynomial"
  - Galois theory | 🔗 link | nosplit | ↑ parent "Polynomial"
  - Irreducible polynomial | 🔗 link | nosplit | ↑ parent "Polynomial"
  - Multivariate polynomial | 60 | 🔗 link | nosplit | ↑ parent "Polynomial"
  - Polynomial over a field ( $F i e l d [X]$ ) | 270, 449, 1 | 🔗 link | nosplit | ↑ parent "Polynomial"
    - Polynomial over a ring | 179 | 🔗 link | nosplit | ↑ parent "Polynomial over a field"
  - Polynomial ring | 25 | 🔗 link | nosplit | ↑ parent "Polynomial"
- Probability | 0, 0, 2 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - Expectation value | 🔗 link | nosplit | ↑ parent "Probability"
  - Standard deviation | 🔗 link | nosplit | ↑ parent "Probability"
- Mathematics bibliography | 37, 248, 5 | 🔗 link | nosplit | ↑ parent "Mathematics"
  - Mathematics website | 0, 11, 1 | 🔗 link | nosplit | ↑ parent "Mathematics bibliography"
    - Theorem of the Day | 11 | 🔗 link | nosplit | ↑ parent "Mathematics website"
  - Mathematics YouTube channel | 0, 200, 2 | 🔗 link | nosplit | ↑ parent "Mathematics bibliography"
    - 3Blue1Brown | 113 | 🔗 link | nosplit | ↑ parent "Mathematics YouTube channel"
    - MathDoctorBob (Robert Donley) | 87 | 🔗 link | nosplit | ↑ parent "Mathematics YouTube channel"

Ancestors

Ciro Santilli's Homepage

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