↑ "algebra". Oxford English Dictionary. Oxford University Press. ↑ 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 ↑ I. N. Herstein, Topics in Algebra, "...it also serves as the unifying thread which interlaces almost all of mathematics." p. 1, Ginn and Company, 1964 1 2 3 (Boyer 1991, "Europe in the Middle Ages" p. 258) "In the arithmetical theorems in Euclid's Elements VII-IX, numbers had been represented by line segments to which letters had been attached, and the geometric proofs in al-Khwarizmi's Algebra made use of lettered diagrams; but all coefficients in the equations used in the Algebra are specific numbers, whether represented by numerals or written out in words. The idea of generality is implied in al-Khwarizmi's exposition, but he had no scheme for expressing algebraically the general propositions that are so readily available in geometry." ↑ T. F. Hoad, ed. (2003). "Algebra". The Concise Oxford Dictionary of English Etymology. Oxford: Oxford University Press. (Subscription required (help)). ↑ Gattengo, Caleb (2010). The Common Sense of Teaching Mathematics. Educational Solutions Inc. ISBN 978-0878252206. ↑ "2010 Mathematics Subject Classification". Retrieved 5 October 2014. ↑ Struik, Dirk J. (1987). A Concise History of Mathematics. New York: Dover Publications. ISBN 0-486-60255-9. ↑ Boyer 1991 ↑ Cajori, Florian (2010). A History of Elementary Mathematics – With Hints on Methods of Teaching. p. 34. ISBN 1-4460-2221-8. ↑ Roshdi Rashed (November 2009). "Al Khwarizmi: The Beginnings of Algebra". Saqi Books. ISBN 0-86356-430-5 ↑ "Diophantus, Father of Algebra". Archived from the original on 27 July 2013. Retrieved 5 October 2014. ↑ "History of Algebra". Retrieved 5 October 2014. ↑ Josef W. Meri (2004). Medieval Islamic Civilization. Psychology Press. p. 31. ISBN 978-0-415-96690-0. Retrieved 25 November 2012. ↑ Boyer, Carl B. (1991). A History of Mathematics (Second ed.). Wiley. pp. 178, 181. ISBN 0-471-54397-7. ↑ Boyer, Carl B. (1991). A History of Mathematics (Second ed.). Wiley. p. 228. ISBN 0-471-54397-7. ↑ (Boyer 1991, "The Arabic Hegemony" p. 229) "It is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the translation above. The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation; the word muqabalah is said to refer to "reduction" or "balancing" – that is, the cancellation of like terms on opposite sides of the equation." ↑ (Boyer 1991, "The Arabic Hegemony" p. 230) "The six cases of equations given above exhaust all possibilities for linear and quadratic equations having positive root. So systematic and exhaustive was al-Khwarizmi's exposition that his readers must have had little difficulty in mastering the solutions." ↑ Gandz and Saloman (1936), The sources of al-Khwarizmi's algebra, Osiris i, p. 263–277: "In a sense, Khwarizmi is more entitled to be called "the father of algebra" than Diophantus because Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers". ↑ Rashed, R.; Armstrong, Angela (1994). The Development of Arabic Mathematics. Springer. pp. 11–2. ISBN 0-7923-2565-6. OCLC 29181926 ↑ Mathematical Masterpieces: Further Chronicles by the Explorers, p. 92 ↑ O'Connor, John J.; Robertson, Edmund F., "Sharaf al-Din al-Muzaffar al-Tusi", MacTutor History of Mathematics archive, University of St Andrews . ↑ Victor J. Katz, Bill Barton; Barton, Bill (October 2007). "Stages in the History of Algebra with Implications for Teaching". Educational Studies in Mathematics. Springer Netherlands. 66 (2): 185–201 . doi:10.1007/s10649-006-9023-7 ↑ (Boyer 1991, "The Arabic Hegemony" p. 239) "Abu'l Wefa was a capable algebraist as well as a trigonometer. ... His successor al-Karkhi evidently used this translation to become an Arabic disciple of Diophantus – but without Diophantine analysis! ... In particular, to al-Karkhi is attributed the first numerical solution of equations of the form ax2n + bxn = c (only equations with positive roots were considered)," ↑ "The Origins of Abstract Algebra". University of Hawaii Mathematics Department. ↑ "The Collected Mathematical Papers".Cambridge University Press. ↑ "Hull's Algebra" (pdf). New York Times. July 16, 1904. Retrieved September 21, 2012. ↑ Quaid, Libby (September 22, 2008). "Kids misplaced in algebra" (Report). Associated Press. Retrieved September 23, 2012. ↑ Hamilton, Reeve (7 September 2012). "THE TEXAS TRIBUNE; U.T.-Arlington Adopts New Way to Tackle Algebra". The New York Times. Retrieved 10 September 2012.