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.
Rezensionen / Stimmen
"... this book remains a highly recommended introduction to Galois theory along the more classical lines. It contains many exercises and a wealth of examples, including a pretty application of finite fields to the game solitaire. ... provides readers with insight and historical perspective; it is written for readers who would like to understand this central part of basic algebra rather than for those whose only aim is collecting credit points."
-Zentralblatt MATH 1322
Praise for the Third Edition:"This edition preserves and even extends one of the most popular features of the original edition: the historical introduction and the story of the fatal duel of Evariste Galois. ... These historical notes should be of interest to students as well as mathematicians in general. ... after more than 30 years, Ian Stewart's Galois Theory remains a valuable textbook for algebra undergraduate students."
-Zentralblatt MATH, 1049
"The penultimate chapter is about algebraically closed fields and the last chapter, on transcendental numbers, contains 'what-every-mathematician-should-see-at-least-once,' the proof of transcendence of pi. ... The book is designed for second- and third-year undergraduate courses. I will certainly use it."
-EMS Newsletter
Auflage
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Illustrationen
29 s/w Abbildungen, 2 s/w Tabellen
2 Tables, black and white; 29 Illustrations, black and white
Maße
Höhe: 234 mm
Breite: 156 mm
Gewicht
ISBN-13
978-1-4822-4582-0 (9781482245820)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Ian Stewart is an emeritus professor of mathematics at the University of Warwick and a fellow of the Royal Society. Dr. Stewart has been a recipient of many honors, including the Royal Society's Faraday Medal, the IMA Gold Medal, the AAAS Public Understanding of Science and Technology Award, and the LMS/IMA Zeeman Medal. He has published more than 180 scientific papers and numerous books, including several bestsellers co-authored with Terry Pratchett and Jack Cohen that combine fantasy with nonfiction.
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.
