Algebra Classification

May 28th, 2015
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Elementary algebra, in which the properties of operations on the real number system are recorded using symbols as "place holders" to denote constants and variables, and the rules governing mathematical expressions and equations involving

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AlgebraClassificationAlgebra may be divided roughly into the following categories:Elementary algebra, in which the properties of operations on thereal number systemare recorded using symbols as "place holders" to denoteconstantsandvariables, and the rules governingmathematical expressionsandequationsinvolving these symbols are studied. This is usually taught at school under the titlealgebra(orintermediate algebraandcollege algebrain subsequent years). University-level courses in group theory may also be calledelementary algebra.Abstract algebra, sometimes also calledmodern algebra, in whichalgebraic structuressuch asgroups,ringsandfieldsareaxiomaticallydefined and investigated.Linear algebra, in which the specific properties ofvector spacesare studied (includingmatrices);Universal algebra, in which properties common to all algebraic structures are studied.Algebraic number theory, in which the properties of numbers are studied through algebraic systems.Number theoryinspired much of the original abstraction in algebra.Algebraic geometryapplies abstract algebra to the problems of geometry.Algebraic combinatoric

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