伽罗瓦理论
微分伽罗瓦理论
域代数上的
指南针
伽罗瓦理论的基本定理
数学
伽罗瓦集团
一般多项式
多项式的
嵌入问题
方程理论
代数理论
基础理论
抽象代数
代数数
纯数学
计算机科学
数学分析
微分方程
地图学
常微分方程
微分代数方程
程序设计语言
地理
标识
DOI:10.1017/9781108979184
摘要
Galois Theory, the theory of polynomial equations and their solutions, is one of the most fascinating and beautiful subjects of pure mathematics. Using group theory and field theory, it provides a complete answer to the problem of the solubility of polynomial equations by radicals: that is, determining when and how a polynomial equation can be solved by repeatedly extracting roots using elementary algebraic operations. This textbook contains a fully detailed account of Galois Theory and the algebra that it needs and is suitable both for those following a course of lectures and the independent reader (who is assumed to have no previous knowledge of Galois Theory). The second edition has been significantly revised and re-ordered; the first part develops the basic algebra that is needed, and the second a comprehensive account of Galois Theory. There are applications to ruler-and- compass constructions, and to the solution of classical mathematical problems of ancient times. There are new exercises throughout, and carefully-selected examples will help the reader develop a clear understanding of the mathematical theory.
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