Galois theory
著者
書誌事項
Galois theory
CRC Press, Taylor & Francis Group, c2015
4th ed
- : pbk
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注記
References: p. 309-314
Includes indexes
内容説明・目次
内容説明
Since 1973, Galois Theory has been educating undergraduate students on Galois groups and classical Galois theory. In Galois Theory, Fourth Edition, mathematician and popular science author Ian Stewart updates this well-established textbook for today's algebra students.
New to the Fourth Edition
The replacement of the topological proof of the fundamental theorem of algebra with a simple and plausible result from point-set topology and estimates that will be familiar to anyone who has taken a first course in analysis
Revised chapter on ruler-and-compass constructions that results in a more elegant theory and simpler proofs
A section on constructions using an angle-trisector since it is an intriguing and direct application of the methods developed
A new chapter that takes a retrospective look at what Galois actually did compared to what many assume he did
Updated references
This bestseller continues to deliver a rigorous yet engaging treatment of the subject while keeping pace with current educational requirements. More than 200 exercises and a wealth of historical notes augment the proofs, formulas, and theorems.
目次
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.
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