Assignment : Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers. As a single word without article, "algebra" names a broad part of mathematics. As a single word with article or in plural, "algebra" denote a specific mathematical structure. See algebra (ring theory) and algebra over a field. With a qualifier, there is the same distinction: Without article, it means a part of algebra, like linear algebra, elementary algebra (the symbol-manipulation rules taught in elementary courses of mathematics as part of primary and secondary education), or abstract algebra (the study of the algebraic structures for themselves). With an article, it means an instance of some abstract structure, like a Lie algebra or an associative algebra. Frequently both meanings exist for the same qualifier, like in the sentence: Commutative algebra is the study of commutative rings, that all are commutative algebras over the integers. Sometimes "algebra" is also used to denote the operations and methods related to algebra in the study of a structure that does not belong to algebra. For example algebra of infinite series may denotes the methods for computing with series without using the notions of infinite summation, limits and convergence. The adjective "algebraic" usually means relation to algebra, as in "algebraic structure". For historical reasons, it may also mean relation with the roots of polynomial equations, like in algebraic number, algebraic extension or algebraic expression.
Posted on: Sun, 16 Jun 2013 04:54:46 +0000
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