Volume: 12; 1998; 142 pp; Softcover
MSC: Primary 01; 12;
Print ISBN: 978-0-8218-0989-1
Product Code: MAWRLD/12
List Price: $33.00
AMS Member Price: $26.40
MAA Member Price: $29.70
Electronic ISBN: 978-1-4704-2478-7
Product Code: MAWRLD/12.E
List Price: $31.00
AMS Member Price: $24.80
MAA Member Price: $27.90
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Supplemental Materials
Algebra in Ancient and Modern Times
Share this pageV. S. Varadarajan
A co-publication of the AMS and Hindustan Book Agency
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.
Readership
Undergraduate mathematics majors, graduate students, research mathematicians and historians interested in the history of mathematics.
Reviews & Endorsements
The book was written for freshmen students who should learn algebra by its history. So the topics mentioned above are treated from a mathematical as well as a historical point of view. The material is presented in a way that students should see how ideas have emerged. In some cases a rough look forward to the modern development is given. Many sections are supplemented by notes and exercises, which contain a lot of mathematics as well as additional historical facts. The book is completed by a very short list of references and an index.
-- Zentralblatt MATH
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
Varadarajan gives us nice treatment of the work of Indian mathematicians on the so-called Pell equation as well as a very detailed yet teachable discussion of the standard story of the solution of cubic and quartic equations by del Ferro, Tartaglia, Cardano, and Ferrari in sixteenth-century Italy.
-- Mathematical Reviews
Table of Contents
Table of Contents
Algebra in Ancient and Modern Times