This text offers a special account of Indian work in diophantine equations during the 6th through 12th centuries and Italian work on solutions of cubic and biquadratic equations from the 11th through 16th centuries. The volume traces the historical development of algebra and the theory of equations from ancient times to the beginning of modern algebra, outlining some modern themes such as the fundamental theorem of algebra, Clifford algebras, and quarternions. It is geared toward undergraduates who have no background in calculus. For other wonderful titles written by this author see: ""Euler through Time: A New Look at Old Themes"", ""Supersymmetry for Mathematicians: An Introduction"", ""The Mathematical Legacy of Harish-Chandra: A Celebration of Representation Theory and Harmonic Analysis"", and ""The Selected Works of V.S. Varadarajan"".
Some history of early mathematics: Eucild-Archimedes-Diophantus Pythagoras and the Pythagorean triplets Aryabhata-Brahmagupta-Bhaskara Irrational numbers: construction and approximation Arabic mathematics Beginnings of algebra in Europe The cubic and biquadratic equations Solution of the cubic and biquadratic equations: Solution of the cubic equation Solution of the biquadratic equation Some themes from modern algebra: Numbers, algebra, and the real world Complex numbers Fundamental theorem of algebra Equations of degree greater than four General number systems and the axiomatic treatment of algebra References Chronology Index.