Classical Introduction to Galois Theory

Name: Classical Introduction to Galois Theory
Price: 71.54 USD
Availability: InStock
ISBN: 9781118091395

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…

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