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{{collapse top| What is Algebra}}

==What is algebra?==

Algebra is a multifaceted branch of mathematics with many parts that are vastly different from others. Essentially, algebra is manipulation of entitiessymbols 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.

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

:<math>ax^2+bx+c=0,</math>

<math>a, b, c</math> can be any numbers whatsoever (except that <math>a</math> cannot be <math>0</math>), and the [[quadratic formula]] can be used to quickly and easily find the values of the unknown quantity <math>x</math> which satisfy the equation, known as finding the solutions of the equation. Historically, the study of algebra starts with the solving of equations such as the [[quadratic equation]] above. The study of these equations lead to more general questions that are considered, such as "does an equation have a solution?", "how many solutions does an equation have?", and "what can be said about the nature of the solutions?". These questions lead to ideas of form, structure and symmetry.<ref>{{cite book |last=Gattengo |first=Caleb |year=2010 |title=The Common Sense of Teaching Mathematics |publisher=Educational Solutions Inc. |isbn=978-0878252206 }}</ref>