Galois Theory (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts Book 106) 2nd Edition by David A. Cox (PDF)

Description

Praise for the First Edition”. . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!” —Monatshefte fur MathematikGalois 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 KroneckerHow to compute Galois groupsGalois’s results about irreducible polynomials of prime or prime-squared degreeAbel’s theorem about geometric constructions on the lemniscatesGalois groups of quartic polynomials in all characteristicsThroughout 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.

User’s Reviews

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

⭐This book is very frustrating. One really wants to like it, but it covers the same material as van der Waerden’s Algebra (the part on Galois Theory, that is), but does it in a far more muddled way. Now, the classic book on Galois Theory these days is Artin’s little book (and van der Waerden’s treatment is generally also attributed to Artin), but Artin is really too abstract, and not really suitable as an introduction, in my opinion. The one advantage of Cox is the wealth of exercises – if not for this, the book would get one star less.

⭐Cox relies heavily on the intuition of the reader to pick up on what he means by a Galois group. Takes him 7 chapters into the book to actually use the term “Galois.” Most of his examples are “historical,” which here translates as “messy and abstruse.” As someone who was assigned to teach a class with this book, I found it to be a massively frustrating book. I research algebra for a living at the university level, and this book is marginal at best. Dummit and Foote shred this book in terms of quality and understandability. I feel that Cox at times tries to find the worst possible way to notate something using a combination of unconventional symbols and steady streams of Greek. Most of his theorems are useless to students trying to accomplish his exercises I have found.

⭐Galois theory is very instructive book, why It chose and I like it because the study of the Galois group is very rigourous why i would recommend this book.

⭐ouvrage complet joignant exposé moderne et cheminement historique avec exercices nombreux et incluant des info pour traitement “maple” d’exemples de calcul!Doit figurer dans toute bibli d’un honnete mathematicien

⭐

⭐Il y a tous ce qu’il faut savoir sur la théorie de Galois. Un livre très agréable à lire.Une référence dans la théorie de Galois.

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