Algebraic geometry now finds application in statistics, control theory, robotics, error-correcting codes, phylogenetics and geometric modelling.

* Algebraic geometry entry on PlanetMath

Category: Algebraic geometry

* Algebraic geometry

Category: Algebraic geometry

Category: Algebraic geometry

# REDIRECT Algebraic geometry

Category: Algebraic geometry

Category: Algebraic geometry

Meanwhile, in order to make the proof of the Riemann hypothesis for curves over finite fields that he had announced in 1940 work, he had to introduce the notion of an abstract variety and to rewrite the foundations of algebraic geometry to work with varieties without projective embeddings ( see also the history section in the Algebraic Geometry article ).

Algebraic sets and algebraic varieties are the central objects of study in algebraic geometry.

Category: Algebraic geometry

Algebraic geometry is essentially the theory of simultaneous polynomial equations.

Algebraic geometry and algebraic number theory, which provide many natural examples of commutative rings, have driven much of the development of commutative ring theory, which is now, under the name of commutative algebra, a major area of modern mathematics.

where the coefficients are polynomial functions of x. Algebraic functions play an important role in mathematical analysis and algebraic geometry.

* Algebraic variety, the basic object of study in algebraic geometry

Category: Algebraic geometry

Algebraic geometry.

Category: Algebraic geometry

Category: Algebraic geometry

Category: Algebraic geometry

Category: Algebraic geometry

Category: Algebraic geometry

Algebraic notation describes how algebra is written.

The beginning of set theory as a branch of mathematics is often marked by the publication of Cantor's 1874 article, " Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen " (" On a Property of the Collection of All Real Algebraic Numbers ").

* Algebraic chess notation is first recorded.

Algebraic manipulation of the symbols in the equations would provide a fail-safe method of logical deduction: i. e. logic is reduced to a type of algebra.

Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces.

Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group.

Algebraic topology is another domain which prominently associates groups to the objects the theory is interested in.

Algebraic notation ( or AN ) is a method for recording and describing the moves in a game of chess.

Algebraic notation is based on a system developed by Philipp Stamma.

Figurine Algebraic Notation ( or FAN ), as noted earlier, is a widely used variation of algebraic notation which substitutes a piece symbol for the letter representing a piece, for example: in place of Nc6.

Developed in 1959 at the University of Michigan by Bernard Galler, Bruce Arden and Robert M. Graham, MAD is a variant of the International Algebraic Language ( IAL ).

MAD is a variant of the International Algebraic Language ( IAL ).

Algebraic notation is more concise and requires less effort to avoid ambiguity ; however much older literature uses descriptive notation.

* G. 723 is a hybrid speech coder, with high bit rate using Multi-Pulse Maximum Likelihood Quantization ( MP-MLQ ) and low bit rate using Algebraic Code Excited Linear Prediction ( ACELP )

Algebraic number theory is a major branch of number theory which studies algebraic structures related to algebraic integers.

Algebraic enumeration is a subfield of enumeration that deals with finding exact formulas for the number of combinatorial objects of a given type, rather than estimating this number asymptotically.

Just as the subject itself was divided into the study of affine and projective varieties ( see the Algebraic variety definitions ) the Zariski topology is defined slightly differently for these two.

Algebraic sets are sometimes also called algebraic varieties, but normally an algebraic variety is an irreducible algebraic set, i. e. one which is not the union of two other algebraic sets.

This includes move number indicators ( numbers followed by either one or three periods ; one if the next move is White's move, three if the next move is Black's move ) and movetext Standard Algebraic Notation ( SAN ).