ECE - Algebra

ALGEBRA

- is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.

History of algebra

Classification

Algebra may be divided roughly into the following categories:

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. This is usually taught at school under the title algebra (or intermediate algebra and college algebra in subsequent years). University-level courses in group theory may also be called elementary 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.
Algebraic number theory, in which the properties of numbers are studied through algebraic systems. Number theory inspired much of the original abstraction in algebra.
Algebraic geometry applies abstract algebra to the problems of geometry.
Algebraic combinatorics, in which abstract algebraic methods are used to study combinatorial questions.

In some directions of advanced study, axiomatic algebraic systems such as groups, rings, fields, and algebras over a field are investigated in the presence of a geometric structure (a metric or a topology) which is compatible with the algebraic structure. The list includes a number of areas of functional analysis:

Normed linear spaces
Banach spaces
Hilbert spaces
Banach algebras
Normed algebras
Topological algebras
Topological group

Sample Problems:

http://www.themathpage.com/alg/algebra.htm

Interesting Questions, Facts, and Information:

http://www.funtrivia.com/en/SciTech/Algebra-7611.html

SOFTMATH develops Algebrator, the leading math software program available to students, parents, teachers and educational institutions today.

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DOWNLOAD ALGEBRATOR

www.4shared.com/file/0PVqxI0K/Algebrator_v41.html

DEMO

http://www.algebra-helper.com/solving-homework/math-trivia-for-algebra.html

TIMELINE IN ALGEBRA

http://en.wikipedia.org/wiki/Timeline_of_algebra