List of mathematical proofs
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Template:SHORTDESC: A list of articles with mathematical proofs:
Theorems of which articles are primarily devoted to proving them
[edit | edit source]- Bertrand's postulate and a proof
- Estimation of covariance matrices
- Fermat's little theorem and some proofs
- Gödel's completeness theorem and its original proof
- Mathematical induction and a proof
- Proof that 0.999... equals 1
- Proof that 22/7 exceeds π
- Proof that e is irrational
- Proof that π is irrational
- Proof that the sum of the reciprocals of the primes diverges
Articles devoted to theorems of which a (sketch of a) proof is given
[edit | edit source]- 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
- Kőnig's lemma
- Kőnig's theorem (set theory)
- Kőnig's theorem (graph theory)
- Lagrange's theorem (group theory)
- Lagrange's theorem (number theory)
- Liouville's theorem (complex analysis)
- 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 theorems
- 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
Articles devoted to algorithms in which their correctness is proved
[edit | edit source]- Bellman–Ford algorithm (to do)
- Euclidean algorithm
- Kruskal's algorithm
- Gale–Shapley algorithm
- Prim's algorithm
- Shor's algorithm (incomplete)
Articles where example statements are proved
[edit | edit source]- Basis (linear algebra)
- Burrows–Abadi–Needham logic
- Direct proof
- Generating a vector space
- Linear independence
- Polynomial
- Proof
- Pumping lemma
- Simpson's rule
Other articles containing proofs
[edit | edit source]- Accumulation point
- Addition in N
- associativity of addition in N
- commutativity of addition in N
- uniqueness of addition in N
- Algorithmic information theory
- Boolean ring
- commutativity of a boolean ring
- Boolean satisfiability problem
- NP-completeness of the Boolean satisfiability problem
- Cantor's diagonal argument
- set is smaller than its power set
- uncountability of the real numbers
- Cantor's first uncountability proof
- uncountability of the real numbers
- Combinatorics
- Combinatory logic
- Co-NP
- Coset
- Countable
- countability of a subset of a countable set (to do)
- Angle of parallelism
- Galois group
- Fundamental theorem of Galois theory (to do)
- Gödel number
- Gödel's incompleteness theorem
- Group (mathematics)
- Halting problem
- insolubility of the halting problem
- Harmonic series (mathematics)
- divergence of the (standard) harmonic series
- Highly composite number
- Area of hyperbolic sector, basis of hyperbolic angle
- Infinite series
- convergence of the geometric series with first term 1 and ratio 1/2
- Integer partition
- Irrational number
- irrationality of log23
- irrationality of the square root of 2
- Mathematical induction
- sum identity
- Power rule
- differential of xn
- Product and Quotient Rules
- Derivation of Product and Quotient rules for differentiating.
- Prime number
- Infinitude of the prime numbers
- Primitive recursive function
- Principle of bivalence
- no propositions are neither true nor false in intuitionistic logic
- Recursion
- Relational algebra (to do)
- Solvable group
- Square root of 2
- Tetris
- Algebra of sets
- idempotent laws for set union and intersection
Articles which mention dependencies of theorems
[edit | edit source]- 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 (functional analysis)
- Product topology
- Riemann integral
- Time hierarchy theorem
- Deterministic time hierarchy theorem