Galois Theory

ISBN-10: 1118072057
ISBN-13: 9781118072059
Edition: 2nd 2012
Authors: David A. Cox
List price: $111.95
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Description: This book brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike. The Second Edition features new exercises and an updated bibliography. A new discussion provides a different  More...

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Book details

List price: $111.95
Edition: 2nd
Copyright year: 2012
Publisher: John Wiley & Sons, Incorporated
Publication date: 3/6/2012
Binding: Hardcover
Pages: 602
Size: 6.25" wide x 9.25" long x 1.25" tall
Weight: 2.2

This book brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike. The Second Edition features new exercises and an updated bibliography. A new discussion provides a different method for computing the Galois group of a quartic polynomial. Chapter coverage includes: cubic equations; symmetric polynomials; roots of polynomials; extension fields; normal and separable extensions; the Galois group; the Galois correspondence; solvability by radical; cyclotomic extensions; geometric constructions; finite field; computing Galois groups; solvable permutation groups; the Lemniscate; and an introduction to abstract algebra.

Preface to the First Edition
Preface to the Second Edition
Notation
Basic Notation
Chapter-by-Chapter Notation
Polynomials
Cubic Equations
Cardan's Formulas
Permutations of the Roots
Cubic Equations over the Real Numbers
Symmetric Polynomials
Polynomials of Several Variables
Symmetric Polynomials
Computing with Symmetric Polynomials (Optional)
The Discriminant
Roots of Polynomials
The Existence of Roots
The Fundamental Theorem of Algebra
Fields
Extension Fields
Elements of Extension Fields
Irreducible Polynomials
The Degree of an Extension
Algebraic Extensions
Normal and Separable Extensions
Splitting Fields
Normal Extensions
Separable Extensions
Theorem of the Primitive Element
The Galois Group
Definition of the Galois Group
Galois Groups of Splitting Fields
Permutations of the Roots
Examples of Galois Groups
Abelian Equations (Optional)
The Galois Correspondence
Galois Extensions
Normal Subgroups and Normal Extensions
The Fundamental Theorem of Galois Theory
First Applications
Automorphisms and Geometry (Optional)
Applications
Solvability by Radicals
Solvable Groups
Radical and Solvable Extensions
Solvable Extensions and Solvable Groups
Simple Groups
Solving Polynomials by Radicals
The Casus Irreducbilis (Optional)
Cyclotomic Extensions
Cyclotomic Polynomials
Gauss and Roots of Unity (Optional)
Geometric Constructions
Constructible Numbers
Regular Polygons and Roots of Unity
Origami (Optional)
Finite Fields
The Structure of Finite Fields
Irreducible Polynomials over Finite Fields (Optional)
Further Topics
Lagrange, Galois, and Kronecker
Lagrange
Galois
Kronecker
Computing Galois Groups
Quartic Polynomials
Quintic Polynomials
Resolvents
Other Methods
Solvable Permutation Groups
Polynomials of Prime Degree
Imprimitive Polynomials of Prime-Squared Degree
Primitive Permutation Groups
Primitive Polynomials of Prime-Squared Degree
The Lemniscate
Division Points and Arc Length
The Lemniscatic Function
The Complex Lemniscatic Function
Complex Multiplication
Abel's Theorem
Abstract Algebra
Basic Algebra
Complex Numbers
Polynomials with Rational Coefficients
Group Actions
More Algebra
Index

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