Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry.

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

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 expressions may be evaluated and simplified, based on the basic properties of arithmetic operations ( addition, subtraction, multiplication, division and exponentiation ).

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

Algebraic operations on the Cartesian product

He died during an outing at the International Symposium on Algebraic Topology in Uxmal, Mexico after tripping and falling off the top of a Mayan step pyramid.

His work on topology was summed up in his monograph Algebraic Topology ( 1942 ).

* Algebraic semantics is a form of axiomatic semantics based on algebraic laws for describing and reasoning about program semantics in a formal manner ;

The Éléments de géométrie algébrique (" Elements of Algebraic Geometry ") by Alexander Grothendieck ( assisted by Jean Dieudonné ), or EGA for short, is a rigorous treatise, in French, on algebraic geometry that was published ( in eight parts or fascicles ) from 1960 through 1967 by the Institut des Hautes Études Scientifiques.

Algebraic tori form an important class of commutative group schemes, defined either by the property of being locally on S a product of copies of G < sub > m </ sub >, or as groups of multiplicative type associated to finitely generated free abelian groups.

* Egri-Nagy, A .; and Nehaniv, C. L. ( 2005 ), " Algebraic Hierarchical Decomposition of Finite State Automata: Comparison of Implementations for Krohn – Rhodes Theory ", in 9th International Conference on Implementation and Application of Automata ( CIAA 2004 ), Kingston, Canada, July 22 – 24, 2004, Revised Selected Papers, Editors: Domaratzki, M .; Okhotin, A .; Salomaa, K .; et al.

* Krohn, K. R .; and Rhodes, J. L. ( 1962 ), " Algebraic theory of machines ", Proceedings of the Symposium on Mathematical Theory of Automata ( editor: Fox, J.

Algebraic K-groups are used in conjectures on special values of L-functions and the formulation of an non-commutative main conjecture of Iwasawa theory and in construction of higher regulators.

* Page on Algebraic Surfaces started in 2008

* Overview and thoughts on designing Algebraic surfaces

Adaptive Multi-Rate Wideband ( AMR-WB ) is a patented speech coding standard developed based on Adaptive Multi-Rate encoding, using similar methodology as Algebraic Code Excited Linear Prediction ( ACELP ).

Algebraic topology provides the larger context, itself built on topology and abstract algebra, with homotopy groups as a basic example.

The Italian school liked to reduce the geometry on an algebraic surface to that of linear systems cut out by surfaces in three-space ; Zariski wrote his celebrated book Algebraic Surfaces to try to pull together the methods, involving linear systems with fixed base points.

* 1982 Tsit-Yuen Lam for his expository work in his book Algebraic theory of quadratic forms ( 1973 ), and four of his papers: K_0 and K_1-an introduction to algebraic K-theory ( 1975 ), Ten lectures on quadratic forms over fields ( 1977 ), Serre's conjecture ( 1978 ), and The theory of ordered fields ( 1980 ).

** formerly SIAM Journal on Algebraic and Discrete Methods

Her dissertation was on Generalized Algebraic Structures and her advisor was Gerald Sacks.

* Number Theory and Algebraic Geometry -- to Peter Swinnerton-Dyer on his 75th birthday, edited by Miles Reid and Alexei Skorobogatov, LMS Lecture Notes 303, Cambridge University Press, 2004 ISBN 0-521-54518-8

* A. Dold: Lectures on Algebraic Topology, Springer ISBN 3-540-58660-1.

The name " SHEEP " is pun on the Lisp Algebraic Manipulator or LAM on which SHEEP is based.

In 1999 he discovered the Algebraic holography ( also Rehren duality ), a duality in the sense of the Holographic principle, which maps N = 4 superconformal SU ( N ) Yang-Mills theory to an ordinary quantum field theory on AdS < sub > 5 </ sub >.