My favorite way to define "algebra" to my students is to go back to its etymology, from the Persian textbook "Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqāba

My favorite way to define "algebra" to my students is to go back to its etymology, from the Persian textbook "Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqābala", or "The Compendious Book on Calculation by Completion and Balancing". Specifically (borrowing from Wikipedia): "The al-ğabr (in Arabic script 'الجبر') ("forcing " or "restoring") operation is moving a deficient quantity from one side of the equation to the other side. In an al-Khwarizmi's example (in modern notation), "x^2 = 40x − 4x^2" is transformed by al-ğabr into "5x^2 = 40x"."[1] I'll also tell them that Algebra is solving equations through the use of inverses. I admit that both definitions are reductive but mostly to the point. [1]http://en.wikipedia.org/wiki/Compendious_Book_on_Calculation_by_Completion_and_Balancing http://en.wikipedia.org/wiki/Compendious_Book_on_Calculation...