Synopses & Reviews
Tignol is primarily concerned with methodology rather than algebra orhistory, he says. His goal is to convey to undergraduate students and other readers an idea of how mathematics is made. He reviews howthe theory of equations evolved from ancient times to its completion by Galois around 1830. He has incorporated into the second editioninsights he had working on other projects. His topics include quadratic equations, the creation of polynomials, the fundamental theorem of algebra, and Ruffini and Abel on general equations.Annotation ©2016 Ringgold, Inc., Portland, OR (protoview.com)
The book gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel, and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as 'group' and 'field'. A brief discussion of the fundamental theorems of modern Galois theory and complete proofs of the quoted results are provided, and the material is organized in such a way that the more technical details can be skipped by readers who are interested primarily in a broad survey of the theory.In this second edition, the exposition has been improved throughout and the chapter on Galois has been entirely rewritten to better reflect Galois' highly innovative contributions. The text now follows more closely Galois' memoir, resorting as sparsely as possible to anachronistic modern notions such as field extensions. The emerging picture is a surprisingly elementary approach to the solvability of equations by radicals, and yet is unexpectedly close to some of the most recent methods of Galois theory.