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Classical Introduction to Galois Theory

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ISBN-10: 1118091396

ISBN-13: 9781118091395

Edition: 2012

Authors: Stephen C. Newman

List price: $85.95
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Description:

This book provides an introduction to Galois theory and focuses on one central theme - the solvability of polynomials by radicals.  Both classical and modern approaches to the subject are described in turn in order to have the former (which is relatively concrete and computational) provide motivation for the latter (which can be quite abstract).  The theme of the book is historically the reason that Galois theory was created, and it continues to provide a platform for exploring both classical and modern concepts.  This book examines a number of problems arising in the area of classical mathematics, and a fundamental question to be considered is: For a given polynomial equation (over a given…    
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Book details

List price: $85.95
Copyright year: 2012
Publisher: John Wiley & Sons Canada, Limited
Publication date: 7/17/2012
Binding: Hardcover
Pages: 296
Size: 6.50" wide x 9.50" long x 1.00" tall
Weight: 1.342
Language: English

Preface
Classical Formulas
Quadratic Polynomials
Cubic Polynomials
Quartic Polynomials
Polynomials and Field Theory
Divisibility
Algebraic Extensions
Degree of Extensions
Derivatives
Primitive Element Theorem
Isomorphism Extension Theorem and Splitting Fields
Fundamental Theorem on Symmetric Polynomials and Discriminants
Fundamental Theorem on Symmetric Polynomials
Fundamental Theorem on Symmetric Rational Functions
Some Identities Based on Elementary Symmetric Polynomials
Discriminants
Discriminants and Subfields of the Real Numbers
Irreducibility and Factorization
Irreducibility Over the Rational Numbers
Irreducibility and Splitting Fields
Factorization and Adjunction
Roots of Unity and Cyclotomic Polynomials
Roots of Unity
Cyclotomic Polynomials
Radical Extensions and Solvability by Radicals
Basic Results on Radical Extensions
Gauss's Theorem on Cyclotomic Polynomials
Abel's Theorem on Radical Extensions
Polynomials of Prime Degree
General Polynomials and the Beginnings of Galois Theory
General Polynomials
The Beginnings of Galois Theory
Classical Galois Theory According to Galois
Modern Galois Theory
Galois Theory and Finite Extensions
Galois Theory and Splitting Fields
Cyclic Extensions and Cyclotomic Fields
Cyclic Extensions
Cyclotomic Fields
Galois's Criterion for Solvability of Polynomials by Radicals
Polynomials of Prime Degree
Periods of Roots of Unity
Denesting Radicals
Classical Formulas Revisited
General Quadratic Polynomial
General Cubic Polynomial
General Quartic Polynomial
Cosets and Group Actions
Cyclic Groups
Solvable Groups
Permutation Groups
Finite Fields and Number Theory
Further Reading
References
Index