Algebra in Ancient and Modern Times (MATHEMATICAL WORLD)

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.ReadershipUndergraduate mathematics majors, graduate students, research mathematicians and historians interested in the history of mathematics. From the reviews: This is a fine book on two counts. First ... there is the singularly excellent treatment of the solution of biquadratic equations. Second, it paints a strong picture of mathematics as a very long sequence of accomplishments, each building on the ones before, in a way that beginning mathematicians can understand and appreciate it. It paints the picture in a concise and economical style, the style that mathematicians find elegant. I would particularly recommend Algebra in Ancient and Modern Times to strong high school students, to high school algebra teachers, to people who want a history of mathematics with a lot of mathematics in the history, and to anyone who needs to know how to find an analytic solution to a nasty fourth degree polynomial. — MAA Online Varadarajan spins a captivating tale, and the mathematics is first-rate. The book belongs on the shelf of any teacher of algebra ... The great treasure of this book is the discussion of the work of the great Hindu mathematicians Aryabhata (c.476–550), Brahmagupta (c.598–665), and Bhaskara (c.1114–1185). Teachers of mathematics history will be especially interested in Varadarajan's exposition of the remarkable cakravala, an algorithm for solving $X^2 - NY^2= \pm 1$. The book contains many exercises that enhance and supplement the text and that also include historical information. Many of the exercises ask readers to apply the historical techniques. Some of the exercises are quite difficult and will challenge any student. —Mathematics Teacher 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 quaternions. It is geared toward undergraduates who have no background in calculus. V. S. Varadarajan is a professor of mathematics at the University of California, Los Angeles. Presents the basics of modern algebra at a very elementary level that presumes no background in calculus. The author uses a historical approach showing the growth of algebra from its ancient origins (Indian and Italian) to its current state, presenting the material in a way that allows the student to see how the ideas emerged in the attempt to answer specific questions. Outlines some modern themes, such as the fundamental theorem, Clifford algebras, and quarternions. Co-published with the Hindustan Book Agency (New Delhi) and distributed by the American Mathematical Society. Annotation c. by Book News, Inc., Portland, Or. The author uses an historical approach to show the advancement of algebra from its ancient beginnings to its modern usage V.s. Varadarajan. Includes Bibliographical References And Index.