Galois Theory, Third Edition

Ian Stewart (Autor)

Buch | Softcover

328 Seiten

2003 | 3rd New edition
Chapman & Hall/CRC (Verlag)
978-1-58488-393-7 (ISBN)

Infos

An introduction to the intriguing concepts of abstract algebra and Galois Theory.

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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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 28.7.2003
• Zusatzinfo: 13 Halftones, black and white; 40 Illustrations, black and white
• Sprache: englisch
• Maße: 156 x 234 mm
• Gewicht: 476 g
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Sozialwissenschaften ► Pädagogik
• ISBN-10: 1-58488-393-6 / 1584883936
• ISBN-13: 978-1-58488-393-7 / 9781584883937
• Zustand: Neuware