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Overview
How did algebra arise? What are its subject matter and methods? How have they changed in the process of its evolution? Authors I. G. Bashmakova and G. S. Smirnova answer these questions in an authoritative and compelling way in this latest addition to the Dolciani Mathematical Expositions Series.There is hardly a branch of mathematics whose evolution has undergone as many surprising metamorphoses as has algebra, and these metamorphoses are described by the authors with vividness and clarity. The special merit of the book is that it corrects the widespread view that up to the 1830s the mainspring of the development of algebra was the investigation and solution of determinate algebraic equations, and especially their solution by radicals. The authors show that this viewpoint is one-sided and gives a distorted view of the evolution of algebra. Specifically, they show that the role of indeterminate equations in the evolution of algebra was no less important than that of determinate equations.
Synopsis
An examination of the evolution of one of the cornerstones of modern mathematics.
Choice
"The book effectively conveys the piecemeal, often idiosyncratic, way in which algebra evolved, including the changes of emphasis and notation that have aided or impeded progress.... Highly recommended. Upper-division undergraduates through faculty."
Editorials
Charles Ashbacher
"As is so well documented in this book, the concrete applications of geometry was the first of the mathematical arts, closely followed by algebra. While necessary to measure the physical world, geometry as we now know it would have been very limited without the ability to express the ideas in symbols. The authors also convincingly argue that the solving of indeterminate equations was no less significant than the solving of determinate equations in algebra...I found this book captivating as the authors present in great detail how algebra evolved from the first primitive steps to the dynamic and encompassing entity that it is today. Every mathematician should take some time to read this book and appreciate what their predecessors did."—Charles Ashbacher Technologies
Choice
"The book effectively conveys the piecemeal, often idiosyncratic, way in which algebra evolved, including the changes of emphasis and notation that have aided or impeded progress.... Highly recommended. Upper-division undergraduates through faculty."G. L. Alexanderson
"In addition to having one of the most beautiful book covers of this or any year, this book presents the history of algebra with great clarity and elegance-with no small amount of credit to Shenitzer, who provided a smooth and idiomatic translation from the Russian.... The book shows us a splendid panorama of the development of a discipline with a fascinating history stretching over four millennia. It's a winner!"—in MAA Online
Jeanne Ramirez
"It is fascinating to read about the historical context of mathematical developments, the tidbits of personal history about mathematical developments, the tidbits of personal history about mathematicians, the development of algebraic notation, and the mathematical insights that are often overlooked for centuries. The authors investigate the relationship between algebra and geometry throughout history; they give extensive coverage to Diophantus, Gauss, Descartes, Galois, and Euler."—The Mathematics Teacher
Steve Abbott
"The authors clearly aimed all along to appeal to mathematicians. The treatment is genuinely expository and accessible to undergraduates who are studying the corresponding mathematics.... Books like this serve a useful purpose in making it clear that mathematics starts from concrete problems whose generalization reveals the underlying theory only gradually. I gladly recommend The Beginnings and Evolution of Algebra as a companion to undergraduate courses."—Mathematical Gazette