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More About This Textbook
Overview
Ian Stewart's Galois Theory has been in print for 30 years. Resoundingly popular, it still serves its purpose exceedingly well. Yet mathematics education has changed considerably since 1973, when theory took precedence over examples, and the time has come to bring this presentation in line with more modern approaches.
To this end, the story now begins with polynomials over the complex numbers, and the central quest is to understand when such polynomials have solutions that can be expressed by radicals. Reorganization of the material places the concrete before the abstract, thus motivating the general theory, but the substance of the book remains the same.
Editorial Reviews
Booknews
Beautifully produced text for advanced undergraduates, in which a master expositor takes obvious delight in introducing young mathematicians to the classical aspects of one of the glories of their field. Expanded revision of the edition of 1973. Keeps in nice focus the motivating historical roots of the theory, and treats explicitly its relation to some classic ruler-and-compass construction problems. Nineteen brief chapters, many exercises, with selected solutions and references. A slim treasure. Paper edition unseen, $22.50. NW Annotation c. Book News, Inc., Portland, OR booknews.comProduct Details
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Table of Contents
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