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This bestseller continues to deliver a rigorous yet engaging treatment of the subject while keeping pace with current educational requirements. This fourth edition replaces the topological proof of the fundamental theorem of algebra with a simple and plausible result from point-set topology. It revises the chapter on ruler-and-compass constructions and includes a new section on constructions using an angle-trisector. In addition, a new chapter takes a retrospective look at what Galois actually did compared to what many assume he did.

Galois Theory

Classical Algebra. The Fundamental Theorem of Algebra. Factorisation 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 Equation. Finite Fields. Regular Polygons. Circle Division. Calculating Galois Groups. Algebraically Closed Fields. Transcendental Numbers. What Did Galois Do or Know? References. Index.