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Algebra in Ancient and Modern Times

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Brand new. We distribute directly for the publisher. 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.This book is copublished with the Hindustan Book Agency (New Delhi) and is distributed worldwide, except in India, Sri Lanka, Bangladesh, Pakistan, and Nepal by the American Mathematical Society. Read more Show Less

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Overview

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.

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Editorial Reviews

Booknews
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.
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Product Details

  • ISBN-13: 9780821809891
  • Publisher: American Mathematical Society
  • Publication date: 4/1/1998
  • Series: Mathematical World Series , #12
  • Edition description: New Edition
  • Pages: 142

Table of Contents

Preface
Some history of early mathematics 1
1 Euclid-Diophantus-Archimedes 3
2 Pythagoras and the Pythagorean triplets 11
3 Aryabhata-Brahmagupta-Bhaskara 17
4 Irrational numbers: construction and approximation 33
5 Arabic mathematics 43
6 Beginnings of algebra in Europe 47
7 The cubic and biquadratic equations 55
Solutions for the cubic and biquadratic equations 63
8 Solution of the cubic equation 65
9 Solution of the biquadratic equation 87
Some themes from modern algebra 93
10 Numbers, algebra, and the physical world 95
11 Complex numbers 97
12 Fundamental theorem of algebra 117
13 Equations of degree greater than four 125
14 General number systems and the axiomatic treatment of algebra 127
References 137
Chronology 139
Index 141
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