**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.

Readership

Undergraduate mathematics majors, graduate students,
research mathematicians and historians interested in the history of
mathematics.