* Fundamental theorem of arithmetic

* 1799: Doctoral dissertation on the Fundamental theorem of algebra, with the title: Demonstratio nova theorematis omnem functionem algebraicam rationalem integram unius variabilis in factores reales primi vel secundi gradus resolvi posse (" New proof of the theorem that every integral algebraic function of one variable can be resolved into real factors ( i. e., polynomials ) of the first or second degree ")

Fundamental theorem of arithmetic.

simple: Fundamental theorem of arithmetic

# REDIRECT Fundamental theorem of arithmetic

* Fundamental theorem of analog circuits: a minimum level of power must be dissipated to maintain a level of SNR

This fact has led some to remark that the Fundamental Theorem of Algebra is neither fundamental, nor a theorem of algebra.

# REDIRECT Fundamental theorem on homomorphisms

Interest in prime elements comes from the Fundamental theorem of arithmetic, which asserts that each integer can be written in essentially only one way as 1 or − 1 multiplied by a product of positive prime numbers.

* Fundamental theorem of software engineering

Fundamental theorem of poker

This is the Fundamental theorem of algebra.

* Fundamental theorem of calculus

* Fundamental theorem of arithmetic –

The first Fundamental theorem is a simple consequence

The Second Fundamental theorem says that for every k distinct values a < sub > j </ sub > on the Riemann sphere, we have

This theorem is called the Second Fundamental Theorem of Nevanlinna Theory, and it allows to give an upper bound for the characteristic function in terms of N ( r, a ).

For example, if f is a transcendental entire function, using the Second Fundamental theorem with k = 3 and a < sub > 3 </ sub > = ∞, we obtain that f takes every value infintiely often, with at most two exceptions,

* Fundamental theorem of vector analysis

* Fundamental theorem of arbitrage-free pricing

* Fundamental theorem of vector analysis

By the Fundamental theorem of projective geometry a reciprocity is the composition of an automorphic function of K and a homography.

# REDIRECT Fundamental theorem of asset pricing

See Fundamental theorem of arbitrage-free pricing.

Fundamental groups also appear in algebraic geometry and are the main topic of Alexander Grothendieck's first Séminaire de géométrie algébrique ( SGA1 ).

* Fundamental theorem of Riemannian geometry

* Barbara Fantechi, Lothar Göttsche, Luc Illusie, Steven L. Kleiman, Nitin Nitsure, Angelo Vistoli, Fundamental algebraic geometry.

From the nineteenth century there is not a separate curve theory, but rather the appearance of curves as the one-dimensional aspect of projective geometry, and differential geometry ; and later topology, when for example the Jordan curve theorem was understood to lie quite deep, as well as being required in complex analysis.

The most delicate part of Bézout's theorem and its generalization to the case of k algebraic hypersurfaces in k-dimensional projective space is the procedure of assigning the proper intersection multiplicities.

By Chow's theorem, a projective complex manifold is also a smooth projective algebraic variety, that is, it is the zero set of a collection of homogenous polynomials.

For finite projective spaces of geometric dimension at least three, Wedderburn's theorem implies that the division ring over which the projective space is defined must be a finite field, GF ( q ), whose order ( that is, number of elements ) is q ( a prime power ).

The Desarguesian planes ( those which are isomorphic with a PG ( 2, q )) satisfy Desargues's theorem and are projective planes over finite fields, but there are many non-Desarguesian planes.

The Veblen-Young theorem states in the finite case that every projective space of geometric dimension n ≥ 3 is isomorphic with a PG ( n, q ), the n-dimensional projective space over some finite field GF ( q ).

The first theorem of Wigner is that under these conditions, we can express invariance more conveniently in terms of linear or anti-linear operators ( indeed, unitary or antiunitary operators ); the symmetry operator on the projective space of rays can be lifted to the underlying Hilbert space.

Although that is strictly speaking a question about a real vector bundle ( the " hairs " on a ball are actually copies of the real line ), there are generalizations in which the hairs are complex ( see the example of the complex hairy ball theorem below ), or for 1-dimensional projective spaces over many other fields.

This theorem is extended as a definition of noncommutative projective geometry by Michael Artin and J. J. Zhang, who add also some general ring-theoretic conditions ( e. g. Artin-Schelter regularity ).

Chow's theorem says that a subvariety of the projective space is analytic ( closed in the strong sense ) if and only if it is algebraic ( closed in the Zariski topology ).

* The Kodaira embedding theorem gives a criterion for a kähler manifold to be projective.

One of the fundamental results here is Chow's theorem, which states that every analytic subvariety of a complex projective space is algebraic.

The theorem may be interpreted to saying that a holomorphic function satisfying certain growth condition is necessarily algebraic: " projective " provides this growth condition.

) In particular, Chow's theorem implies that a holomorphic map between projective varieties is algebraic.

In projective geometry, Desargues ' theorem, named in honor of Gérard Desargues ( pronounced day ZARG ), states:

Desargues's theorem is true for the real projective plane, for any projective space defined arithmetically from a field or division ring, for any projective space of dimension unequal to two, and for any projective space in which Pappus's theorem holds.