Galois theory [ Livre] / David A., Cox

Auteur principal: Cox, David A., 1948-....Langue: Anglais ; de l'oeuvre originale, Anglais.Mention d'édition: Second editionPublication : Hoboken (N.J.) : Wiley, 2012Description : 1 vol. (XXVIII-570 p.) ; 25 cmISBN: 9781118072059.Collection: Pure and applied mathematicsClassification: 512.1 Algèbre, théorie des corpsRésumé: Galois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel’s theory of Abelian equations, casus irreducibili, and the Galois theory of origami. In addition, this book features detailed treatments of several topics not covered in standard texts on Galois theory, including: The contributions of Lagrange, Galois, and Kronecker How to compute Galois groups Galois's results about irreducible polynomials of prime or prime-squared degree Abel's theorem about geometric constructions on the lemniscates Galois groups of quartic polynomials in all characteristics Throughout the book, intriguing Mathematical Notes and Historical Notes sections clarify the discussed ideas and the historical context; numerous exercises and examples use Maple and Mathematica to showcase the computations related to Galois theory; and extensive references have been added to provide readers with additional resources for further study. Galois Theory, Second Edition is an excellent book for courses on abstract algebra at the upper-undergraduate and graduate levels. The book also serves as an interesting reference for anyone with a general interest in Galois theory and its contributions to the field of mathematics..Sujet - Nom commun: Galois, Théorie de
Current location Call number Status Notes Date due Barcode
ENS Rennes - Bibliothèque
Mathématiques
512.1 COX (Browse shelf) Available 512.1 Algèbre, théorie des corps 039955

Galois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel’s theory of Abelian equations, casus irreducibili, and the Galois theory of origami.

In addition, this book features detailed treatments of several topics not covered in standard texts on Galois theory, including:

The contributions of Lagrange, Galois, and Kronecker
How to compute Galois groups
Galois's results about irreducible polynomials of prime or prime-squared degree
Abel's theorem about geometric constructions on the lemniscates
Galois groups of quartic polynomials in all characteristics

Throughout the book, intriguing Mathematical Notes and Historical Notes sections clarify the discussed ideas and the historical context; numerous exercises and examples use Maple and Mathematica to showcase the computations related to Galois theory; and extensive references have been added to provide readers with additional resources for further study.

Galois Theory, Second Edition is an excellent book for courses on abstract algebra at the upper-undergraduate and graduate levels. The book also serves as an interesting reference for anyone with a general interest in Galois theory and its contributions to the field of mathematics.

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