Algebra in Ancient and Modern Times (Mathematical World) [Paperback]

V. S. Varadarajan (Author)

Book Description

ISBN-10: 082180989X | ISBN-13: 978-0821809891 | Publication Date: April 29, 1998 | Edition: 1

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.

Editorial Reviews

Review

"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

Product Details

• Paperback: 142 pages
• Publisher: American Mathematical Society; 1 edition (April 29, 1998)
• Language: English
• ISBN-10: 082180989X
• ISBN-13: 978-0821809891
• Product Dimensions: 10 x 7 x 0.4 inches
• Shipping Weight: 9.6 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,665,915 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

8 of 8 people found the following review helpful:

5.0 out of 5 stars Algebra in Ancient and Modern Times: A Teacher's Perspectiv, May 1, 2000

By 

gina Bowles (USA) - See all my reviews

This review is from: Algebra in Ancient and Modern Times (Mathematical World) (Paperback)

This book by V.S. Varadarajan gives a broad historical overview of the evolution of algeba as an independent field of mathematics. Varadarajan does an outstanding job of developing complex mathematical concepts in a step-by-step format.

The text begins, naturally, with the early Greek mathematicians and the first few chapters are about Euclid, Archimedes, counting principles of the ancient Egyptians, etc. Although the author does not devote much space to this early history, enough detail is provided to use this book as a reference in a mathematical classroom.

Section one then proceeds to the period of Cardano, Tartalegia, Ferrari and the mathematical competitions that have become so famous. Not only does the author give a standard account of the conflicts that arose over the publication of Cardano's Ars Magna, he also writes tremendous detail on the supporting equations and terms. Terms such as quadratic, multiple roots, polynomial and others are defined for the high school scholar, yet the text does not seem depreciating to students studying higher level college mathematics.

The third and final section of Algebra in Ancient and Modern Times, is devoted to Guass, whose work the author is obviously enthralled with, and other period four mathematicians. This section develops modern group theory, vector analysis and matrix algebra. The detail is again well written and enough historical content is given that, again, this book becomes a historical reference as well.

Overall, I would reccommend this to any teacher. It would be an excellent addition to a classroom bookshelf for students from high school to graduate students in college. There are additional problems and short notes that could be accessed and referenced as well as using the book for a student material.

I reviewed the book originally for a History of Mathematics course at the University of Lousiville and was quite pleased with my selection.

4 of 5 people found the following review helpful:

5.0 out of 5 stars Algebra in Ancient and Modern Times: A Teacher's Perspectiv, May 1, 2000

By 

gina Bowles (USA) - See all my reviews

This review is from: Algebra in Ancient and Modern Times (Mathematical World) (Paperback)

This book by V.S. Varadarajan gives a broad historical overview of the evolution of algeba as an independent field of mathematics. Varadarajan does an outstanding job of developing complex mathematical concepts in a step-by-step format.

The text begins, naturally, with the early Greek mathematicians and the first few chapters are about Euclid, Archimedes, counting principles of the ancient Egyptians, etc. Although the author does not devote much space to this early history, enough detail is provided to use this book as a reference in a mathematical classroom.

Section one then proceeds to the period of Cardano, Tartalegia, Ferrari and the mathematical competitions that have become so famous. Not only does the author give a standard account of the conflicts that arose over the publication of Cardano's Ars Magna, he also writes tremendous detail on the supporting equations and terms. Terms such as quadratic, multiple roots, polynomial and others are defined for the high school scholar, yet the text does not seem depreciating to students studying higher level college mathematics.

The third and final section of Algebra in Ancient and Modern Times, is devoted to Guass, whose work the author is obviously enthralled with, and other period four mathematicians. This section develops modern group theory, vector analysis and matrix algebra. The detail is again well written and enough historical content is given that, again, this book becomes a historical reference as well.

Overall, I would reccommend this to any teacher. It would be an excellent addition to a classroom bookshelf for students from high school to graduate students in college. There are additional problems and short notes that could be accessed and referenced as well as using the book for a student material.

I reviewed the book originally for a History of Mathematics course at the University of Lousiville and was quite pleased with my selection.