Galois Theory

Ian Stewart

288 pages, parution le 15/09/2003 (3^eme édition)

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Résumé

Ian Stewart's Galois Theory has been in print for 30 years. Resoundingly popular, it still serves its purpose exceedingly well. Yet mathematics education has changed considerably since 1973, when theory took precedence over examples, and the time has come to bring this presentation in line with more modern approaches.

To this end, the story now begins with polynomials over the complex numbers, and the central quest is to understand when such polynomials have solutions that can be expressed by radicals. Reorganization of the material places the concrete before the abstract, thus motivating the general theory, but the substance of the book remains the same.

Historical Introduction
Classical Algebra
The Fundamental Theorem of Algebra
Factorization of Polynomials
Field Extensions
Simple Extensions
The Degree of an Extension
Ruler-and-Compass Constructions
The Idea Behind Galois Theory
Normality and Separability
Counting Principles
Field Automorphisms
The Galois Correspondence
A Worked Example
Solubility and Simplicity
Solution by Radicals
Abstract Rings and Fields
Abstract Field Extensions
The General Polynomial
Regular Polygons
Finite Fields
Circle Division
Calculating Galois Groups
Algebraically Closed Fields
Transcendental Numbers
References
Index

L'auteur - Ian Stewart

Ian Stewart, professeur émérite de mathématiques à l'université de Warwick (Grande-Bretagne), prix Faraday 2001 de la Royal Society, a publié plus de quatre-vingts livres, dont de nombreux best-sellers. Sont disponibles dans la collection Champs : Dieu joue-t-il aux dés ?, La Chasse aux trésors mathématiques, 17 équations qui ont changé le monde.

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Ian Stewart
Parution	15/09/2003
Édition	3^eme édition
Nb. de pages	288
Format	15 x 23,5
Couverture	Broché
Poids	465g
Intérieur	Noir et Blanc
EAN13	9781584883937
ISBN13	978-1-58488-393-7