Book:Ian Stewart/Galois Theory/Third Edition

Subject Matter

 * Galois Theory

Contents

 * Preface to the First Edition
 * Preface to the Second Edition
 * Preface to the Third Edition
 * Illustration Acknowledgments
 * Historical Introduction


 * 1 Classical Algebra
 * 2 The Fundamental Theorem of Algebra
 * 3 Factorization of Polynomials
 * 4 Field Extensions
 * 5 Simple Extensions
 * 6 The Degree of an Extension
 * 7 Ruler-and-Compass Constructions
 * 8 The Idea Behind Galois Theory
 * 9 Normality and Separability
 * 10 Counting Principles
 * 11 Field Automorphisms
 * 12 The Galois Correspondence
 * 13 A Worked Example
 * 14 Solubility and Simplicity
 * 15 Solution by Radicals
 * 16 Abstract Rings and Fields
 * 17 Abstract Field Extensions
 * 18 The General Polynomial
 * 19 Regular Polygons
 * 20 Finite Fields
 * 21 Circle Division
 * 22 Calculating Galois Groups
 * 23 Algebraically Closed Fields
 * 24 Transcendental Numbers


 * References
 * Index