قائمة المبرهنات الرياضية

هذه هي قائمة المبرهنات. انظر أيضاً:

قائمة المبرهنات الأساسية

list of lemmas

Summation by parts Abel's lemma
Artin-Rees lemma (commutative algebra)
Borel's lemma (partial differential equations)
Borel-Cantelli lemma (probability theory)
Burnside's lemma
Covering lemma
Dehn's lemma (geometric topology)
Diagonalization lemma
Dickson's lemma (combinatorics)
Euclid's lemma
Fatou's lemma
Subadditive function Fekete's lemma
Fitting lemma
Five lemma
Fixed-point lemma for normal functions
Fodor's lemma
Gauss's lemma
Gödel's diagonal lemma
Grönwall's inequality Grönwall's lemma
Grothendieck lemma (differential forms)
Handshaking lemma
Hartogs' lemma (several complex variables)
Hensel's lemma
Injective module Injective test lemma
Itō's lemma
König's lemma
Lambda lemma
Lebesgue's number lemma (dimension theory)
Lindelöf's lemma
Lindenbaum's lemma
Lovász local lemma
Mautner's lemma (representation theory)
Morse theory Morse lemma (differential topology)
Nakayama lemma
Newman's lemma (term rewriting)
Neyman-Pearson lemma
Nine lemma (homological algebra)
Noether's normalization lemma (commutative algebra)
Ogden's lemma
Piling-up lemma
Poincaré lemma of closed and exact differential forms (differential forms)
Pumping lemma (formal languages) Bar-Hillel lemma
Rasiowa-Sikorski lemma (set theory)
Riemann lemma
Sard's lemma (mathematical analysis, singularity theory)
Schanuel's lemma (projective modules)
Schreier's subgroup lemma
Shephard's lemma
Short five lemma (homological algebra)
Siegel's lemma (Diophantine approximation)
Snake lemma (homological algebra)
Sperner's lemma (combinatorics)
Splitting lemma (homological algebra)
Stein's lemma (probability theory)
Szemerédi regularity lemma (graph theory)
Ultrafilter lemma
Urysohn's lemma (general topology)
Whitehead's lemma (Lie algebras)
Yoneda lemma (category theory)
Zassenhaus lemma (group theory)
Zolotarev's lemma (number theory)
Zorn's lemma (Kuratowski-Zorn lemma)

list of conjectures

Proved (now theorems)

Adams conjecture (J-homomorphism)
Bieberbach conjecture (De Branges' theorem)
Blattner's conjecture (Blattner formula)
Catalan's conjecture (Mihailescu's theorem)
Conway-Norton conjecture (Monstrous moonshine)
Dinitz conjecture (Galvin's theorem)
Dodecahedral conjecture (Hales-McLaughlin theorem)
Epsilon conjecture (Ribet's theorem)
Fermat's Last Theorem
Gradient conjecture (Kurdyka-Mostowski-Parusinski theorem)
Heawood conjecture (Ringel-Youngs' theorem)
Kummer's conjecture on cubic Gauss sums (Kummer sum)
Mahler-Manin conjecture
Manin-Mumford conjecture (Raynaud's theorem)
Milnor conjecture (Voevodsky's theorem)
Mordell conjecture (Faltings' theorem)
Mumford conjecture (Haboush's theorem)
Oppenheim conjecture (Margulis' theorem)
Ramanujan conjecture on the cusp form Δ (proved by the proof of the Weil conjectures)
Segal's Burnside ring conjecture (Carlsson theorem)
Serre's conjecture (Quillen-Suslin theorem)
Seymour's conjecture
Smith conjecture (Gordon's theorem)
Star height problem (Hashiguchi theorem)
Strong perfect graph conjecture (Chudnovsky-Robertson-Seymour-Thomas theorem)
Sullivan conjecture
Tameness conjecture (Agol or Calegari-Gabai theorem)
Taniyama-Shimura conjecture (Shimura–Taniyama theorem)
Wagner's conjecture (Robertson-Seymour theorem)
Weil conjectures (Deligne's theorems)

Disproved

Recent work

Open problems

list of inequalities

This page lists Wikipedia articles about named mathematical inequalities.

Pure mathematics

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Inequalities in probability theory

An inequality on location and scale parameters (of probability distributions)
Azuma's inequality
Boole's inequality
Chebyshev's inequality
Chernoff's inequality
Cramér-Rao inequality
Hoeffding's inequality
le Cam's theorem
Markov's inequality
Vysochanskiï-Petunin inequality

Inequalities particular to physics

Bell's inequality — see Bell's theorem
- Bell's original inequality
Heisenberg's inequality
Rushbrooke inequality
Tsirelson's inequality

list of mathematical proofs

A list of articles with mathematical proofs:

Theorems of which articles are primarily devoted to proving them

Articles devoted to theorems of which a (sketch of a) proof is given

Banach fixed point theorem
Banach–Tarski paradox
Basel problem
Bolzano-Weierstrass theorem
Brouwer fixed point theorem
Buckingham π theorem (proof in progress)
Burnside's lemma
Cantor's theorem
Cantor–Bernstein–Schroeder theorem
Cayley's formula
Cayley's theorem
Clique problem (to do)
Compactness theorem (very compact proof)
Erdős-Ko-Rado theorem
Euler's formula
Euler's four-square identity
Euler's theorem
Five color theorem
Five lemma
Fundamental theorem of arithmetic
Gauss-Markov theorem (brief pointer to proof)
Gödel's incompleteness theorem
- Gödel's first incompleteness theorem
- Gödel's second incompleteness theorem
Goodstein's theorem
Green's theorem (to do)
- Green's theorem when D is a simple region
Heine-Borel theorem
Intermediate value theorem
Itô's lemma
König's lemma
König's theorem (to do)
Lagrange's theorem
Liouville's theorem (brief pointer to proof)
Markov's inequality (proof of a generalization)
Mean value theorem
Multivariate normal distribution (to do)
Holomorphic functions are analytic
Pythagorean theorem
Quadratic equation
Quotient rule
Ramsey's theorem
Rao-Blackwell theorem
Rice's theorem
Rolle's theorem
Splitting lemma
squeeze theorem
Sum rule in differentiation
Sum rule in integration
Sylow theorem
Transcendence of e and π (as corollaries of Lindemann-Weierstrass)
Tychonoff's theorem (to do)
Ultrafilter lemma
Ultraparallel theorem
Urysohn's lemma
Van der Waerden's theorem
Wilson's theorem
Zorn's lemma

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Articles devoted to algorithms in which their correctness is proven

Articles where example statements are proven

Articles which mention dependencies of theorems

Cauchy's integral formula
Cauchy integral theorem
Computational geometry
Fundamental theorem of algebra
Lambda calculus
Invariance of domain
Minkowski inequality
Nash embedding theorem
Open mapping theorem
Product topology
Riemann integral
Time hierarchy theorem
- Deterministic time hierarchy theorem

Articles giving mathematical proofs within a physical model

انظر أيضاً

Most of the results below come from pure mathematics, but some are from theoretical physics, علم الاقتصاد, and other applied fields.

فهرست:	أعلى - 0-9 \| ا \| ب \| ت \| ث \| ج \| ح \| خ \| د \| ذ \| ر \| ز \| س \| ش \| ص \| ض \| ط \| ظ \| ع \| غ \| ف \| ق \| ك \| ل \| م \| ن \| ه \| و \| ي

A

B

Baire category theorem (topology, metric spaces)
Banach-Alaoglu theorem (functional analysis)
Banach fixed point theorem (metric spaces, differential equations)
Banach-Steinhaus theorem (functional analysis)
Barbier's theorem (هندسة رياضية)
Bass's theorem (group theory)
Bayes' theorem (probability)
Beatty's theorem (diophantine approximation)
Beck's monadicity theorem (category theory)
Beck's theorem (incidence geometry)
Bell's theorem (quantum theory - physics)
Bendixson-Dulac theorem (dynamical systems)
Berry-Esséen theorem (probability theory)
Bertrand's ballot theorem (probability theory, combinatorics)
Bertrand's postulate (prime numbers)
Bézout's theorem (algebraic curves)
Binomial theorem (algebra, combinatorics)
Birkhoff's theorem (ergodic theory)
Bohr-Mollerup theorem (gamma function)
Bolyai-Gerwien theorem (هندسة رياضية)
Bolzano's theorem (real analysis, calculus)
Bolzano-Weierstrass theorem (real analysis, calculus)
Boolean prime ideal theorem (mathematical logic)
Borel-Bott-Weil theorem (representation theory)
Bott periodicity theorem (homotopy theory)
Borsuk-Ulam theorem (topology)
Brouwer fixed point theorem (topology)
Brown's representability theorem (homotopy theory)
Bruck-Chowla-Ryser theorem (combinatorics)
Buckingham π theorem (dimensional analysis)

C

Cantor–Bernstein–Schroeder theorem (Set theory, cardinal numbers)
Cantor's theorem (Set theory, Cantor's diagonal argument)
Carathéodory-Jacobi-Lie theorem (symplectic topology)
Carathéodory's theorem (conformal mapping)
Carathéodory's theorem (convex hull)
Carathéodory's theorem (measure theory)
Cartan's theorem (Lie group)
Cartan's theorems A and B (several complex variables)
Cauchy integral theorem (Complex analysis)
Cayley-Hamilton theorem (Linear algebra)
Cayley's theorem (group theory)
Central limit theorem (probability)
Ceva's theorem (هندسة رياضية)
Chebotarev's density theorem (number theory)
Chen's theorem (number theory)
Chern-Gauss-Bonnet theorem (differential geometry)
Chinese remainder theorem (number theory)
Chowla-Mordell theorem (number theory)
Church-Rosser theorem (lambda calculus)
Closed graph theorem (functional analysis)
Cluster decomposition theorem (quantum field theory)
Coase theorem (علم الاقتصاد)
Cochran's theorem (statistics)
Compactness theorem (mathematical logic)
Conservativity theorem (mathematical logic)
Convolution theorem (Fourier transforms)
Cook's theorem (computational complexity theory)
Cox's theorem (probability foundations)
Crystallographic restriction theorem (group theory, crystallography)
Cut-elimination theorem (proof theory)

D

E

F

G

H

H-theorem (thermodynamics)
Haag's theorem (quantum field theory)
Haboush's theorem (algebraic groups, representation theory, invariant theory)
Hadwiger's theorem (هندسة رياضية, measure theory)
Hahn embedding theorem (ordered groups)
Hairy ball theorem (algebraic topology)
Hahn-Banach theorem (functional analysis)
Hales-Jewett theorem (combinatorics)
Ham sandwich theorem (topology)
Heine-Borel theorem (real analysis)
Hellinger-Toeplitz theorem (functional analysis)
Helly's theorem (convex sets)
Herbrand-Ribet theorem (cyclotomic fields)
Hilbert's basis theorem (commutative algebra,invariant theory)
Hilbert's Nullstellensatz (theorem of zeroes) (commutative algebra, algebraic geometry)
Hilbert-Speiser theorem (cyclotomic fields)
Hinge theorem (هندسة رياضية)
Hopf-Rinow theorem (differential geometry)
Hurewicz theorem (algebraic topology)
Hurwitz's automorphisms theorem (algebraic curves)

I

Intermediate value theorem (calculus)
Implicit function theorem (vector calculus)
Infinite monkey theorem (probability)
Inverse function theorem (vector calculus)
Isomorphism theorem (abstract algebra)
Isoperimetric theorem (curves, calculus of variations)

J

Jacobson density theorem (ring theory)
Jordan curve theorem (topology)
Jordan-Hölder theorem (group theory)
Jordan-Schönflies theorem (geometric topology)

K

L

M

Mahler's compactness theorem (geometry of numbers)
Mahler's theorem (p-adic analysis)
Marcinkiewicz theorem (functional analysis)
Marriage theorem (combinatorics)
Master theorem (recurrence relations, asymptotic analysis)
Maschke's theorem (group representations)
Matiyasevich's theorem (mathematical logic)
Max flow min cut theorem (graph theory)
Maximum power theorem (electrical circuits)
Maxwell's theorem (probability theory)
Mean value theorem (calculus)
Menger's theorem (graph theory)
Mercer's theorem (functional analysis)
Mertens' theorems (number theory)
Metrization theorems (topological spaces)
Min-max theorem (functional analysis)
Minimax theorem
Minkowski's theorem (geometry of numbers)
Mitchell's embedding theorem (category theory)
Mittag-Leffler's theorem (complex analysis)
Modigliani-Miller theorem (finance theory)
Mohr-Mascheroni theorem (هندسة رياضية)
Monotone convergence theorem (mathematical analysis)
Mordell-Weil theorem (number theory)
Morera's theorem (complex analysis)
Morley's categoricity theorem (model theory)
Morley's trisector theorem (هندسة رياضية)
Multinomial theorem (algebra, combinatorics)
Myers theorem (differential geometry)
Myhill-Nerode theorem (formal languages)

N

Nagell-Lutz theorem (elliptic curves)
Nash embedding theorem (differential geometry)
Nielsen-Schreier theorem (free groups)
No cloning theorem (quantum computation)
Noether's theorem (Lie groups, calculus of variations, differential invariants, physics)
No-ghost theorem (vertex algebras)
Norton's theorem (electrical networks)
Nyquist-Shannon sampling theorem (information theory)

O

Open mapping theorem (functional analysis)

P

Paley-Wiener theorem (Fourier transforms)
Pappus's centroid theorem (هندسة رياضية)
Parseval's theorem (Fourier analysis)
Pascal's theorem (conics)
Pentagonal number theorem (number theory)
Perfect graph theorem (graph theory)
Peter-Weyl theorem (representation theory)
Picard theorem (complex analysis)
Picard-Lindelöf theorem (ordinary differential equations)
Pick's theorem (هندسة رياضية)
Pitman-Koopman-Darmois theorem (statistics)
Plancherel theorem (Fourier analysis)
Poincaré-Bendixson theorem (dynamical systems)
Poincaré-Birkhoff-Witt theorem (universal enveloping algebras)
Poincaré duality theorem (algebraic topology of manifolds)
Poncelet-Steiner theorem (هندسة رياضية)
Post's theorem (mathematical logic)
Prime number theorem (number theory)
Primitive element theorem (field theory)
Ptolemaios' theorem (هندسة رياضية)
Pythagorean theorem (هندسة رياضية)

R

S

Sahlqvist correspondence theorem (modal logic)
Sarkovskii's theorem (dynamical systems)
Savitch's theorem (computational complexity theory)
Schauder fixed point theorem (functional analysis)
Schreier refinement theorem (group theory)
Schur's lemma (representation theory)
Schur's theorem (Ramsey theory)
Seifert-van Kampen theorem (algebraic topology)
Shannon's theorem (information theory)
Simplicial approximation theorem (algebraic topology)
Skolem-Noether theorem (simple algebras)
Soundness theorem (mathematical logic)
Space hierarchy theorem (computational complexity theory)
Spectral theorem (functional analysis)
Speedup theorem (computational complexity theory)
Sperner's theorem (combinatorics)
Spin-statistics theorem (physics)
Sprague-Grundy theorem (combinatorial game theory)
Squeeze theorem (mathematical analysis)
Stanley's reciprocity theorem (combinatorics)
Stark-Heegner theorem (number theory)
Stokes' theorem (vector calculus, differential topology)
Stolper-Samuelson theorem (علم الاقتصاد)
Stone's representation theorem for Boolean algebras (mathematical logic)
Stone's theorem on one-parameter unitary groups (functional analysis)
Stone-Tukey theorem (topology)
Stone-von Neumann theorem (functional analysis, representation theory of the Heisenberg group, quantum mechanics)
Stone-Weierstrass theorem (functional analysis)
Sturm's theorem (theory of equations)
Swan's theorem (module theory)
Sylow theorem (group theory)
Sylvester's theorem (number theory)
Sylvester-Gallai theorem (plane geometry)
Szemerédi's theorem (combinatorics)
Szemerédi-Trotter theorem (combinatorics)

T

U

V

Van der Waerden's theorem (combinatorics)
Virial theorem (classical mechanics)
Vitali theorem (measure theory)
Vitali-Hahn-Saks theorem (measure theory)
Von Neumann bicommutant theorem (functional analysis)

W

Z

^ Newcomb, S. (1881). "Note on the frequency of use of the different digits in natural numbers". Amer. J. Math. 4: 39–40.
^ Benford, F. (1938). "The law of anomalous numbers". Proc. Amer. Phil. Soc. 78: 551–572.
^ Hill, Theodore P. (1995). "The Significant Digit Phenomenon". Am. Math. Monthly. 102 (4): 322–327. {{cite journal}}: Unknown parameter |month= ignored (help)
^ Bix, Robert (1998). Conics and Cubics. Springer. ISBN 0-387-98401-1.
^ Burnside, William (1897). Theory of groups of finite order. Cambridge University Press.
^ Scott, Charlotte Agnas (1898). "On the Intersection of Plane Curves". Bull. Am. Math. Soc. 4: 260–273. {{cite journal}}: Unknown parameter |month= ignored (help)
^ Deahna, F. (1840). "Über die Bedingungen der Integrabilität". J. Reine Angew. Math. 20. {{cite journal}}: Text "pages-340-350" ignored (help)
^ Frobenius, Georg (1895). "Ūber die Pfaffsche Problem". J. Reine Angew. Math.: 230–315.
^ ^أ ^ب Samelson, Hans (2001). "Differential Forms, the Early days; or the Stories of Deahna's Theorem and of Volterra's Theorem". Am. Math. Monthly. 108 (6): 552–530. {{cite journal}}: Unknown parameter |month= ignored (help)
^ Cajori, Florian (1999). A History of Mathematics. New York: Chelsea. (reprint of fifth edition, 1891).
^ Whitford, Edward Everett (1912). The Pell Equation. New York: E. E. Whitford. This is Whitford's 1912 Ph.D. dissertation, written at Columbia University and published at his own expense in 1912.
^ Poincaré, H. (1886–1887). "Sur les residus des intégrales doubles". Acta Math. 9: 321–380.{{cite journal}}: CS1 maint: date format (link)
^ Redfield, J. H. (1927). "The theory of group related distributions". Amer. J. Math. 49: 433–445.
^ Pólya, G. (1936). "Algebraische Berechnung der Isomeren einiger organischer Verbindungen". Z. für Krystallogr. A. 93: 414.
^ Read, R. C. (1987). "Pólya's Theorem and its Progeny". Mathematics Magazine. 60 (5): 275–282. {{cite journal}}: Unknown parameter |month= ignored (help)

الكلمات الدالة:

علم الاقتصاد

[Newcomb_1881-1] Newcomb, S. (1881). "Note on the frequency of use of the different digits in natural numbers". Amer. J. Math. 4: 39–40.

[Benford_1938-2] Benford, F. (1938). "The law of anomalous numbers". Proc. Amer. Phil. Soc. 78: 551–572.

[Hill_1995-3] Hill, Theodore P. (1995). "The Significant Digit Phenomenon". Am. Math. Monthly. 102 (4): 322–327. {{cite journal}}: Unknown parameter |month= ignored (help)

[Bix_1998-4] Bix, Robert (1998). Conics and Cubics. Springer. ISBN 0-387-98401-1.

[Burnside_1897-5] Burnside, William (1897). Theory of groups of finite order. Cambridge University Press.

[Scott_1898-6] Scott, Charlotte Agnas (1898). "On the Intersection of Plane Curves". Bull. Am. Math. Soc. 4: 260–273. {{cite journal}}: Unknown parameter |month= ignored (help)

[Deahna_1840-7] Deahna, F. (1840). "Über die Bedingungen der Integrabilität". J. Reine Angew. Math. 20. {{cite journal}}: Text "pages-340-350" ignored (help)

[Frobenius_1895-8] Frobenius, Georg (1895). "Ūber die Pfaffsche Problem". J. Reine Angew. Math.: 230–315.

[Samelson_2001-9] أ ^ب Samelson, Hans (2001). "Differential Forms, the Early days; or the Stories of Deahna's Theorem and of Volterra's Theorem". Am. Math. Monthly. 108 (6): 552–530. {{cite journal}}: Unknown parameter |month= ignored (help)

[Cajori_1999-10] Cajori, Florian (1999). A History of Mathematics. New York: Chelsea. (reprint of fifth edition, 1891).

[Whitford_1912-11] Whitford, Edward Everett (1912). The Pell Equation. New York: E. E. Whitford. This is Whitford's 1912 Ph.D. dissertation, written at Columbia University and published at his own expense in 1912.

[Poincare_1886-12] Poincaré, H. (1886–1887). "Sur les residus des intégrales doubles". Acta Math. 9: 321–380.{{cite journal}}: CS1 maint: date format (link)

[Redfield_1927-13] Redfield, J. H. (1927). "The theory of group related distributions". Amer. J. Math. 49: 433–445.

[Pólya_1936-14] Pólya, G. (1936). "Algebraische Berechnung der Isomeren einiger organischer Verbindungen". Z. für Krystallogr. A. 93: 414.

[Read_1987-15] Read, R. C. (1987). "Pólya's Theorem and its Progeny". Mathematics Magazine. 60 (5): 275–282. {{cite journal}}: Unknown parameter |month= ignored (help)

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