BookofProofs is a growing library of open books with a mathematical context.However, it is not always possible to write a complete online book from the very beginning to the end. It might happen that some theorems remain unproven, some sections remain without text or exercises remain without solutions.

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Missing Proofs (1)
A proof for this theorem is still missing.

Isomorphism of Rings [171]

Unchained Proofs (0)
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Missing Text (278)
This node has only a title, but no text was provided.

Basic Concepts of Logic [26]Topological Vector Spaces [69]Analytic Number Theory [72]Probability Theory and Statistics [73]Homotopy [83]Theory of Algorithms [84]Elliptic Geometry [86]Optimization Methods [88]Paradigms [89]Prime Number Theorem [91]Randomness and Probability Calculus [93]Languages [94]Correctness [95]First and Second Axiom of Countability [98]Linear Integral Equations [99]Hyperbolic Geometry [102]Inclusion and Exclusion [104]Automata Theory [107]Projective Geometry [110]Proof Theory [113]Galois Theory [114]Functional Analysis [116]Differential Geometry [124]Vector Analysis [128]Continuity [129]Complex Infinite Series [130]Classification of Differential Equations [131]CW Complexes [132]Computational Complexity Theory [133]Tables [135]Genetic Programming [136]Real Infinite Series [142]Differentiability [144]Calculus of Variations [145]Geometric Aspects [146]Methods to Solve Ordinary DE [149]Computability Theory [151]Dynamic Programming [152]Linked Lists [153]Trees [154]Fuzzy Logic [157]Decidability [158]Paths, Cycles and Connectivity [159]Methods to Solve Partial DE [160]Topological Aspects [161]Moebius Transformations [162]Integrability [163]Implicit Functions [164]Types of Real Functions [166]Algebraic Geometry [168]Eigenvalues and Eigenvectors [169]Symmetry Groups [172]Hashing [176]Numerical Algorithms [177]Planar Graphs [178]Prime Number Theorem for Arithmetic Progressions [180]Constructions with Ruler and Compass [193]Criteria for Convergence of Real Series [196]Properties of Real Functions [200]Types of Complex Functions [201]Fredholm Integral Equations [202]Entropy [204]Neural Networks [205]Sets [206]Higher-Order Logics [207]Peano Arithmetic [208]Universal Algebras [210]Principal Axis Transformation [213]Subspaces [214]Taylor Series [220]Banach Spaces and Banach Algebra [221]Fixed Point Theory [223]Properties of Complex Functions [224]Vertex Colourings and Decompositions [226]Greedy Algorithms [228]Sorting [229]Positional Notation Systems [230]Linear Programming [231]Laws of Large Numbers [236]Transitive Hull and Irreducible Kernels [238]Bipartite Graphs [239]Infinite Series Approximations [241]Roman Numbers [242]String Matching [243]Randomized Rounding [245]Volterra Integral Equation [246]Linear 1. Order DE [248]Linear 1. Order DE [249]Laurant Series [250]Paths [253]Accumulation Points [255]Path Integrals [257]Differential Operations on Vector Fields [258]Hilbert Spaces [259]Power Series [260]Jordan Normal Form [262]Categories [264]Continuum Hypothesis [268]Gödel's Incompleteness Theorems [270]Solving Strategies and Sample Solutions to Problems in Set Theory [271]Rotations and Basic Transformations [278]Fourier Series [283]Linear Operators and Linear Functionals [284]Integral Operations on Vector Fields [285]Criteria for Absolute Convergence of Real Series [286]Multiple Riemann Integrals [287]Riemann's Plane and Sphere [289]Homology and Winding Numbers [290]Complex Rational Functions [291]Differentiable Complex Functions [292]Stirling Numbers [293]Touring's Maschine [297]Determinants [298]Solving Strategies and Sample Solutions to Problems in Logic [300]Logarithms [301]Non-linear Operator [303]Extremal Values with Side Conditions [304]Multiple Lebesque Integrals [305]Criteria for Convergent Sequences [307]Inversion [309]Isogonality [310]Homotopy [311]Periodic Complex Functions [313]Isolated Singularities [314]Linear vs. Non-Linear DE [315]Linear 2. Order DE [316]Linear 2. Order DE [317]Liouville-Neumann Series [318]Tychonoff's Theorem [319]Worst Case [320]Simulated Annealing [321]Stacks [322]External Sorting [323]Discrete Distributions [324]Continuous Distributions [325]Chebyshev's Lemma [326]Multidimensional Random Variables [327]Graph Transformations [328]Zeta Functions [329]Analytic Continuation [331]Jordan Measurability [332]Brouwer's Theorem [333]Complex Logarithms [334]Invertible Complex Functions [335]Meromorphic Functions [336]Queues [337]Mixing [338]Matrices [343]Dual Space [344]Solving Strategies and Sample Solutions Related to Arithmetics [345]Trigonometric Functions [346]Lebesque Measure and Lebesque Integral [348]Schauder's Theorem [349]Fixed Points [350]Complex Trigonometric Functions [351]Residue Theorem [353]Order of DE [354]Linear n-th Order DE [355]Abel Integral Equations [356]Average Case [357]Strings [358]Graph Traversing [363]Dirichlet Convolution [365]Sieve Methods [366]Random Sample Models [367]Weak Law of Large Numbers [369]Markov Chains [370]Subalgebras [371]Vectors [372]Some Important Constants [373]Cyclometric Functions [375]Kakutani's Theorem [378]Cross-Ratio [379]Complex Cyclometric Functions [380]Integrable Complex Functions [381]Discrete Fourier Transform [382]Systems of DE [383]Linear Systems of 1. Order DE [384]Uniform Complexity Measure and Bit Complexity [385]Files [386]Data Compression [387]Pseudo-Random Numbers [388]Interpolation [389]Shortest Paths [392]Uniform Distribution [396]Normal Distribution [397]Strong Law of Large Numbers [398]Discrete Time Markov Chains [399]Estimation Theory [400]Cross Product [402]Hyporbolic Functions [406]Complex Hyporbolic Functions [409]Holomorphic Functions [410]Polynomial Time [411]Kernel and Image [413]Inverse Hyperbolic Functions [415]Simple Connectivity [417]Complex Inverse Hyperbolic Functions [418]Indefinite Integral [419]Non-Linear DE [420]NP-Completeness [421]Branch and Bound [422]Multiplication [423]Extrapolation [424]Flows [425]Reduction [426]Logarithmic Normal Distribution [430]Continuous Time Markov Chains [431]Matrices of Linear Maps [433]Mixed Functions [435]Integrable Functions [436]The $C(X)$ Algebra [437]Complex Mixed Functions [438]Path Integrals [439]Criteria for Holomorphic Functions [440]Boundary Value Problems [441]Probabilistic Complexity [442]And / Or Trees [443]Differentiation [445]Matchings [446]Similarity of Graphs [447]Goldbach Conjecture [448]Student Distribution [451]Affine Maps [452]Properties [453]Min-Max and Alpha-Beta [454]Normal Forms [455]Indefinite Integral [456]Gamma Function [457]Harmonic Functions [458]Satisfaction Problem Solving [459]Integration [461]Contraction and Minors [462]Network Design and Routing [463]Hypergeometric Distribution [465]$\chi^2$ Distribution [466]Fisher Distribution [467]Poisson Distribution [468]Infinite Graphs [470]Graph Representations [471]Linear Equation Systems [472]Quadrics [475]Improper Integral [476]Cryptography [477]Elimination [478]Non-Linear Equation Systems [479]Extremal Problems in Graph Theory [480]Riemann-Stieltjes Integral [482]Calendar [483]Combinatorial Algorithms [484]Iterative Methods [485]Orthogonalisation [486]Graph-Theoretic Algorithms [488]Iterative Methods [489]Eigenvalues and Eigenvectors [490]Network Paths [491]Integration of Starting Value Problems (Ordinary DE) [492]Network Flows [493]Error Analysis [494]One-Step Methods [495]Multi-Step Methods [496]Fibonacci Numbers [498]Quantum Computation [622]General Relativity [643] [1016] [1018] [2427] [2788]600 BC [2792]569 BC [3248]547 BC [3249]Graphs [6217]Algebraic Topology [6285]Quantum Field Theory [6302]Classical Physics [6303]Fractional Arithmetic [6630]Closed Formulas for Infinite Real Series [6655]Complex Numbers [6788]

Missing Informal Examples, Explanations, etc. (24)
This node includes an important theoretical result, but no informal examples, applications or explanations have yet been provided.

Nested Closed Subset Theorem [127]Law of Total Probability [449]Bayes' Theorem [464]Every Bounded Real Sequence has a Convergent Subsequence [1152]Simulating LOOP Programs Using WHILE Programs [1199]Intermediate Value Theorem [1259]Completeness Principle For Complex Numbers [1709]Supremum Property, Infimum Property [1756]Indefinite Integral, Antiderivative [1768]Mean Value Theorem For Riemann Integrals [1772]Multinomial Theorem [1822]Theorem of Large Numbers for Relative Frequencies [1838]Characterization of Eulerian Graphs [6381]Heine-Borel Theorem [6596]Continuous Functions Mapping Compact Domains to Real Numbers Take Maximum and Minimum Values on these Domains [6604]Theorem of Bolzano-Weierstrass [6608]Continuous Functions on Compact Domains are Uniformly Continuous [6614]Continuous Real Functions on Closed Intervals are Uniformly Continuous [6616]Reverse Triangle Inequalities [6637]Intermediate Root Value Theorem [6692]Rolle's Theorem [6778]Darboux's Theorem [6779]Fundamental Theorem of Calculus [6807]Integration by Substitution [6813]

Incomplete Biographies of Mathematicians (0)
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Missing Solution (5)
A solution to this problem/exercise is still missing.

Are there infinitely many primorial primes? [511]TSP - The Traveling Salesman Problem [1780]Even Perfect Numbers Problem [8132]Odd Perfect Numbers Problem [8133]Twin Prime Problem [8203]

Hidden (0)
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