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

Algebraic operations on the Cartesian product

* Algebraic, the order of entering operations when using a calculator ( contrast reverse Polish notation )

Algebraic topologists work with compactly generated spaces, CW complexes, or spectra.

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 ).

During this period, he wrote Algebraic Surfaces as a summation of the work of the Italian school.

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

* 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 ).

He wrote a retrospective of his work, Tossing Algebraic Flowers Down the Great Divide.

In 1941 a collaboration with Hodge started which lasted some twelve years and included the writing of the huge three-volume work, Method of Algebraic Geometry.

The package was written by Inge Frick, using earlier work by Ian Cohen and Ray d ' Inverno, who had written ALAM-Atlas LISP Algebraic Manipulation in earlier ( designed in 1970 ).

Algebraic rules were given geometric proofs by mathematicians such as Pacioli, Cardan, Tartaglia and Ferrari.

Algebraic structures can also coexist with added structure of a non-algebraic nature, such as a partial order or a topology.

MSRI has also held " double ( or jumbo ) programs " ( such as the Algebraic Geometry program in Spring 2009 ) that consist of a single program of twice the typical size.

Algebraic branch points most commonly arise from functions in which there is an ambiguity in the extraction of a root, such as solving the equation z = w < sup > 2 </ sup > for w as a function of z.

* Algebraic extension, a field extension such that every element is an algebraic element over the base field

Algebraic groups over ( possibly imperfect ) fields k such that the k-unipotent radical is trivial are called pseudo-reductive groups.

For more general asymmetrical cases, more general-oriented reconstruction algorithms such as Algebraic Reconstruction Technique ( ART ), Maximum Likelihood Expectation Maximization ( MLEM ), Filtered Back-Projection ( FBP ) algorithms should be employed.

Algebraic solutions form a subset of closed-form expressions, because the latter permit transcendental functions ( non-algebraic functions ) such as the exponential function, the logarithmic function, and the trigonometric functions and their inverses.

Jonardon Ganeri has observed that this period saw George Boole and Augustus De Morgan make their pioneering applications of algebraic ideas to the formulation of logic ( such as Algebraic logic and Boolean logic ), and suggested that these figures were likely to be aware of these studies in xeno-logic, and further that their acquired awareness of the shortcomings of propositional logic are likely to have stimulated their willingness to look outside the system.

* Algebraic fraction, an indicated division in which the divisor, or both dividend and divisor, are algebraic expressions

Algebraic numbers coloured by degree.

Algebraic numbers are all numbers that can be defined explicitly or implicitly in terms of polynomials, starting from the rational numbers.

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.

* Kevin R. Coombes: Algebraic Geometry: A Total Hypertext Online System.

Algebraic Theory of Lattices.

Algebraic notation describes how algebra is written.

Algebraic graph theory has close links with group theory.

* Algebraic Equations at EqWorld: The World of Mathematical Equations.

* Blahut, Richard E. Algebraic Codes for Data Transmission Cambridge University Press, 2004, ISBN 0-521-55374-1

* Algebraic code-excited linear prediction ( ACELP 4. 7 kbit / s – 24 kbit / s )

* 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.

Non-Abelian Algebraic Topology: filtered spaces, crossed complexes, cubical higher homotopy groupoids ; European Mathematical Society Tracts in Mathematics Vol.

* Allen Hatcher, Algebraic topology.

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.