域论及其经典问题（Field Theory and Its Classical Problems）（影印版）

样章

作者：

Charles Robert Hadlock

定价：

135.00 元

版面字数：

340.00千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2026-01-09

ISBN：

978-7-04-065926-9

物料号：

65926-00

出版时间：

2026-03-27

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

代数学

暂无

前辅文
INTRODUCTION
CHAPTER1 - THE THREE GREEK PROBLEMS
- 1.1 Constructible Lengths
- 1.2 Doubling the Cube
- 1.3 Trisecting the Angle
- 1.4 Squaring the Circle
- 1.5 Polynomials and Their Roots
- 1.6 Symmetric Functions
- 1.7 The Transcendence of π
- References and Notes
CHAPTER 2 - FIELD EXTENSIONS
- 2.1 Arithmetic of Polynomials
- 2.2 Simple, Multiple, and Finite Extensions
- 2.3 Geometric Constructions Revisited
- 2.4 Roots of Complex Numbers
- 2.5 Constructibility of Regular Polygons I
- 2.6 Congruences
- 2.7 Constructibility of Regular Polygons II
- References and Notes
CHAPTER 3 - SOLUTION BY RADICALS
- 3.1 Statement of the Problem
- 3.2 Automorphisms and Groups
- 3.3 The Group of an Extension
- 3.4 Two Fundamental Theorems
- 3.5 Galois' Theorem
- 3.6 Abel's Theorem
- 3.7 Some Solvable Equations
- References and Notes
CHAPTER 4 - POLYNOMIALS WITH SYMMETRIC GROUPS
- 4.1 Background Information
- 4.2 Hilbert's Irreducibility Theorem
- 4.3 Existence of Polynomials over Q with Group Sn
- References and Notes
SOLUTIONS TO THE PROBLEMS
INDEX