algebra and algebraic structures
 algebra and algebraic structures

Generalized version of arithmetic that uses variables to stand for unspecified numbers.
Its purpose is to solve algebraic equations or systems of equations. Examples of such solutions are the quadratic formula (for solving a
quadratic equation) and GaussJordan elimination (for solving a
system of equations in
matrix form). In higher mathematics, an "algebra" is a structure consisting of a class of objects and a set of rules (analogous to addition and multiplication) for combining them. Basic and higher algebraic structures share two essential characteristics: (1) calculations involve a finite number of steps and (2) calculations involve abstract symbols (usually letters) representing more general objects (usually numbers). Higher algebra (also known as modern or abstract algebra) includes all of elementary algebra, as well as
group theory, theory of
rings,
field theory, manifolds, and vector spaces.
* * *
Universalium.
2010.
Look at other dictionaries:
Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… … Wikipedia
List of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… … Wikipedia
Comparison of vector algebra and geometric algebra — Vector algebra and geometric algebra are alternative approaches to providing additional algebraic structures on vector spaces, with geometric interpretations, particularly vector fields in multivariable calculus and applications in mathematical… … Wikipedia
algebra — /al jeuh breuh/, n. 1. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. 2. any of… … Universalium
algebraic — algebraically, adv. /al jeuh bray ik/, adj. 1. of, occurring in, or utilizing algebra. 2. Math. of or pertaining to an element that is the root of a polynomial equation with coefficients from some given field. 3. using arbitrary letters or… … Universalium
Algebra — This article is about the branch of mathematics. For other uses, see Algebra (disambiguation). Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from… … Wikipedia
Algebra of systems — (AoS) is an executable systems modeling framework for system synthesis and evaluation [Koo 2007a] . It can be used to automate complex model reasoning tasks for system design projects. AoS provides a formal structure for reasoning about elements… … Wikipedia
Algebraic structure — In algebra, a branch of pure mathematics, an algebraic structure consists of one or more sets closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties. The… … Wikipedia
Algebraic logic — In mathematical logic, algebraic logic formalizes logic using the methods of abstract algebra.Logics as models of algebrasAlgebraic logic treats logics as models (interpretations) of certain algebraic structures, specifically as models of bounded … Wikipedia
algebra, modern — ▪ mathematics Introduction also called abstract algebra branch of mathematics concerned with the general algebraic structure of various sets (such as real numbers (real number), complex numbers (complex number), matrices (matrix), and… … Universalium