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A Classical Introduction to Galois Theory

Name: A Classical Introduction to Galois Theory
Author: Stephen C. Newman

Auteur: Stephen C. Newman

Taal: Engels

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Uitgever: John Wiley & Sons Inc

Auteur: Stephen C. Newman

Engels
Hardcover
9781118091395
26 juli 2012
296 pagina's

Alle productspecificaties

Samenvatting

With a focus on one central theme (the Impossibility Theorem) throughout, this highly accessible introduction to Galois theory presents a classical treatment of the topic and poses questions related to the solvability of polynomial equations by radicals. Modern points of view are also discussed in contrast to the historical development and context.

Explore the foundations and modern applications of Galois theory

Galois theory is widely regarded as one of the most elegant areas of mathematics. A Classical Introduction to Galois Theory develops the topic from a historical perspective, with an emphasis on the solvability of polynomials by radicals. The book provides a gradual transition from the computational methods typical of early literature on the subject to the more abstract approach that characterizes most contemporary expositions.

The author provides an easily-accessible presentation of fundamental notions such as roots of unity, minimal polynomials, primitive elements, radical extensions, fixed fields, groups of automorphisms, and solvable series. As a result, their role in modern treatments of Galois theory is clearly illuminated for readers. Classical theorems by Abel, Galois, Gauss, Kronecker, Lagrange, and Ruffini are presented, and the power of Galois theory as both a theoretical and computational tool is illustrated through:

A study of the solvability of polynomials of prime degree
Development of the theory of periods of roots of unity
Derivation of the classical formulas for solving general quadratic, cubic, and quartic polynomials by radicals

Throughout the book, key theorems are proved in two ways, once using a classical approach and then again utilizing modern methods. Numerous worked examples showcase the discussed techniques, and background material on groups and fields is provided, supplying readers with a self-contained discussion of the topic.

A Classical Introduction to Galois Theory is an excellent resource for courses on abstract algebra at the upper-undergraduate level. The book is also appealing to anyone interested in understanding the origins of Galois theory, why it was created, and how it has evolved into the discipline it is today.

Productspecificaties

Inhoud

Taal: en
Bindwijze: Hardcover
Oorspronkelijke releasedatum: 26 juli 2012
Aantal pagina's: 296
Illustraties: Nee

Betrokkenen

Hoofdauteur: Stephen C. Newman
Hoofduitgeverij: John Wiley & Sons Inc

Overige kenmerken

Extra groot lettertype: Nee
Product breedte: 163 mm
Product hoogte: 25 mm
Product lengte: 243 mm
Studieboek: Ja
Verpakking breedte: 244 mm
Verpakking hoogte: 29 mm
Verpakking lengte: 244 mm
Verpakkingsgewicht: 582 g

EAN

EAN: 9781118091395

Je vindt dit artikel in

Categorieën: Wetenschap & Natuur

Wiskunde

Algebra

Boeken
Taal: Engels
Beschikbaarheid: Leverbaar
Boek, ebook of luisterboek?: Boek
Studieboek of algemeen: Algemene boeken

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