Galois theory, (3^rd Ed.)

This book provides a rigorous yet accessible treatment, motivated by discussion and examples. It retains the features that made the previous editions popular: mathematically rigorous treatment, lively, highly readable style, and entertaining historical notes. Develops the entire theory over the complex numbers before moving to the general theory. Offers a historical perspective, including a short biography of Évariste Galois, photographs of his original manuscripts, and other illustrations, and includes over 200 exercises and provides a solutions manual with qualifying course adoptions.

Historical Introduction Classical Algebra The Fundamental Theorem of Algebra Factorization of Polynomials Field Extensions Simple Extensions The Degree of an Extension Ruler-and-Compass Constructions The Idea Behind Galois Theory Normality and Separability Counting Principles Field Automorphisms The Galois Correspondence A Worked Example Solubility and Simplicity Solution by Radicals Abstract Rings and Fields Abstract Field Extensions The General Polynomial Regular Polygons Finite Fields Circle Division Calculating Galois Groups Algebraically Closed Fields Transcendental Numbers References Index