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Algebra is a branch of mathematics concerned with the study of mathematical symbols and the rules for manipulating these symbols. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra.

Elementary algebra is essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.

Algebra includes General algebraic systems, Field theory and polynomials, Commutative algebra, Linear and multi-linear algebra; matrix theory, Associative rings and algebras, Non-associative rings and algebras, Category theory; homological algebra, K-theory and Group theory. Algebra is also used extensively in -Number theory and Algebraic geometry.

vCalc's Algebra library contains numerous equations from elementary as well as abstract algebra.