Algebra

:This article is about the branch of mathematics. For other uses of the term "algebra" from the Greek words gean ebrisko ??? ????? ???? ,= AL-GEBRA (calculations in earth surface) and Arabic AL see algebra (disambiguation).

Classification

Algebra may be roughly divided into the following categories:

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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 these symbols are studied (note that this usually includes the subject matter of courses called intermediate algebra and college algebra);
• abstract algebra, sometimes also called modern algebra, in which algebraic structures such as groups, rings and fields are axiomatically defined and investigated;
• linear algebra, in which the specific properties of vector spaces are studied (including matrices);
• universal algebra, in which properties common to all algebraic structures are studied.

In advanced studies, axiomatic algebraic systems like groups, rings, fields, and algebras over a field are investigated in the presence of a natural geometric structure (a topology) which is compatible with the algebraic structure. The list includes

Related Topics:
Geometric - Topology

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• Normed linear spaces
• Banach spaces
• Hilbert spaces
• Banach algebras
• Normed algebras
• Topological algebras
• Topological groups