域论及其经典问题（影印版）
定价：￥135.00
作者： Charles Robert Hadlock
出版社：高等教育出版社
- 高等教育出版社
- 9787040659269
- 1版
- 64270738-4
- 特殊
- 340
- 理学
- 数学类
- 数学类
- 本科 研究生及以上
目录
目录
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
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
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
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
