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„There is barely a better introduction to the subject, in all its theoretical and practical aspects, than the book under review.“ (Zentralblatt MATH, 1 December 2012)
"the great merit of this book (one of many expositions of the subject) is that everything is taken at a slow pace, with many examples to illustrate every idea. You get the (probably true) impression that the author loves this material, has taught it to undergraduates at Amherst College many times, has learned by experience the ideas which students find difficult, and has then taken great trouble to dissect these ideas and to pick out exactly the right examples and exercises to make them part of the reader's mental equipment." (The Mathematical Gazette 2016)
Galois Theory
von David A. CoxPraise for the First Edition
„. . . will certainly fascinate anyone interested in abstractalgebra: a remarkable book!“
--Monatshefte fur Mathematik
Galois theory is one of the most established topics inmathematics, with historical roots that led to the development ofmany central concepts in modern algebra, including groups andfields. Covering classic applications of the theory, such assolvability by radicals, geometric constructions, and finitefields, Galois Theory, Second Edition delves into noveltopics like Abel's theory of Abelian equations, casusirreducibili, and the Galois theory of origami.
In addition, this book features detailed treatments of severaltopics 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 primeor prime-squared degree
* Abel's theorem about geometric constructions on thelemniscates
* Galois groups of quartic polynomials in allcharacteristics
Throughout the book, intriguing Mathematical Notes andHistorical Notes sections clarify the discussed ideas andthe historical context; numerous exercises and examples use Mapleand Mathematica to showcase the computations related to Galoistheory; and extensive references have been added to provide readerswith additional resources for further study.
Galois Theory, Second Edition is an excellent book forcourses on abstract algebra at the upper-undergraduate and graduatelevels. The book also serves as an interesting reference for anyonewith a general interest in Galois theory and its contributions tothe field of mathematics.
„. . . will certainly fascinate anyone interested in abstractalgebra: a remarkable book!“
--Monatshefte fur Mathematik
Galois theory is one of the most established topics inmathematics, with historical roots that led to the development ofmany central concepts in modern algebra, including groups andfields. Covering classic applications of the theory, such assolvability by radicals, geometric constructions, and finitefields, Galois Theory, Second Edition delves into noveltopics like Abel's theory of Abelian equations, casusirreducibili, and the Galois theory of origami.
In addition, this book features detailed treatments of severaltopics 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 primeor prime-squared degree
* Abel's theorem about geometric constructions on thelemniscates
* Galois groups of quartic polynomials in allcharacteristics
Throughout the book, intriguing Mathematical Notes andHistorical Notes sections clarify the discussed ideas andthe historical context; numerous exercises and examples use Mapleand Mathematica to showcase the computations related to Galoistheory; and extensive references have been added to provide readerswith additional resources for further study.
Galois Theory, Second Edition is an excellent book forcourses on abstract algebra at the upper-undergraduate and graduatelevels. The book also serves as an interesting reference for anyonewith a general interest in Galois theory and its contributions tothe field of mathematics.
