Algebra in Ancient and Modern Times

Algebra in Ancient and Modern Times

by V. S. Varadarajan
     
 

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

See more details below

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.

Read More

Product Details

ISBN-13:
9780821809891
Publisher:
American Mathematical Society
Publication date:
04/01/1998
Series:
Mathematical World Series, #12
Edition description:
New Edition
Pages:
142
Product dimensions:
7.09(w) x 10.24(h) x (d)

Related Subjects

Table of Contents

Preface
Some history of early mathematics1
1Euclid-Diophantus-Archimedes3
2Pythagoras and the Pythagorean triplets11
3Aryabhata-Brahmagupta-Bhaskara17
4Irrational numbers: construction and approximation33
5Arabic mathematics43
6Beginnings of algebra in Europe47
7The cubic and biquadratic equations55
Solutions for the cubic and biquadratic equations63
8Solution of the cubic equation65
9Solution of the biquadratic equation87
Some themes from modern algebra93
10Numbers, algebra, and the physical world95
11Complex numbers97
12Fundamental theorem of algebra117
13Equations of degree greater than four125
14General number systems and the axiomatic treatment of algebra127
References137
Chronology139
Index141

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >