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{{collapse top| What is Algebra}}

==What is algebra?==

Algebra is ana expansivecomplex branch of mathematics in which many subjects are vastly different from others. Essentially, algebra is manipulation of symbols based on given properties about them.<ref>I. N. Herstein, ''Topics in Algebra'', "An algebraic system can be described as a set of objects together with some operations for combining them." p. 1, Ginn and Company, 1964</ref> For instance, elementary algebra is about manipulating variables, which are abstractions of numbers in a number system. The variables in the number system are only allowed to have properties that are shared by every number it represents, and vice versa.

The most simple parts of algebra begin with computations similar to those of [[arithmetic]] but with variables that take on the properties of numbers.<ref name=citeboyer /> This allows proofs of properties that are true no matter which numbers are involved. For example, in the [[quadratic equation]]