『明解ガロア理論』（原書） Galois Theory (Chapman Hall/crc Mathematics) （3TH）

Stewart, Ian

Chapman & Hall（2003/07発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 328 p.
• 言語 ENG
• 商品コード 9781584883937
• DDC分類 512.3

基本説明

邦訳：2008年。講談社。
Provides key examples and uses them to motivate the abstractions.

Full Description

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.

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