Galois’ Theory Of Algebraic Equations (Second Edition): 2nd Edition 2nd Edition by Jean-pierre Tignol (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I’ve read over 40 books on this area of mathematics cover to cover, and Tignol’s stands out as best for several important reasons –- most comprehensive, covering quadratic equations in ancient times contrasted to middle ages, Renaissance, 17th century symbolic algebra all the way through Galois Theory, with appendices on modern ways of seeing Galois’ work.- Cleanest, most focused path through the topic- Clearest exposition, easiest to follow and understand- best use of historical information and placement of that information- math is a relay race, with the baton handed from one creative mind to another; Tignol does the best job of illustrating this handoff. His exposition of contributions by Lagrange and Vandermonde is exemplary and unique

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