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