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抽象代数 英文【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

抽象代数 英文
  • Deborah C. Arangno 著
  • 出版社: 北京:高等教育出版社;麦格劳-希尔国际出版公司
  • ISBN:7040087553
  • 出版时间:2000
  • 标注页数:228页
  • 文件大小:11MB
  • 文件页数:240页
  • 主题词:

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图书目录

CHAPTER1 RUDIMENTS1

1.1 Sets1

Classical Problems:Sets7

Supplemental Exercises:Sets9

1.2 Mappings9

INTRODUCTION11

Classical Problems:Mappings15

Supplemental Exercises:Mappings18

1.3 Relations and Operations19

Classical Problems:Relations and Operations24

Supplemental Exercises:Relations and Operations28

1.4 Number Systems29

1.4.1 The Natural Numbers29

1.4.2 The Integers31

1.4.3 The Rational Numbers36

1.4.4 The Reals37

1.4.5 The Complex Numbers38

Classical Problems:Number Systems39

Supplemental Exercises:Number Systems49

CHAPTER2 GROUPS51

2.1 Introduction to Groups51

Classical Problems:Groups and Subgroups57

2.2 Working With Groups63

Classical Problems:Working With Groups69

2.3 More on Group Structure79

Classical Problems:More on Group Structure81

2.4 Supplemental Exercises:Groups90

CHAPTER 3 PINGS93

3.1 Basic Ring Structure93

Classical Problems:Basic Ring Structure96

3.2 Ring Substructures102

Classical Problems:Ring Substructures104

3.3 Specialized Rings110

Classical Problems:Specialized Rings113

3.4 Working With Rings120

Classical Problems:Working With Rings122

3.5 Notes on Rings128

3.6 Supplemental Exercises:Rings129

CHAPTER 4 R-MODULES131

4.1 Introduction to R-Modules131

4.2 Notes on Modules135

4.3 Classical Problems: R-Modules140

4.4 Supplemental Exercises:R-Modules144

CHAPTER 5 VECTOR SPACES145

5.1 Introduction to Vector Spaces145

5.2 Nots on Vector Spaces151

5.3 Classical Problems:Vector Spaces152

5.4 Supplemental Exercises:Vector Spaces158

CHAPTER 6 INTRODUCTION TO MATRICES159

6.1 Basic Linear Algebra159

6.1.1 Basic Structures159

6.1.2 Notes:Basic Linear Algebra167

Classical Problems:Matrices169

6.2.1 Introduction176

6.2 Matrices in Solving Systems of Equations176

6.2.2 Examples180

Classical Problems:Applying Matrices in Solving Systems of Equations181

6.3 Supplemental Exercises:Matrices186

CHAPTER 7 POLYNOMIALS188

7.1 Definitions188

7.2 Background and Notes:Polynomials192

7.3 Classical Problems:Polynomials193

7.4 Supplemental Exercises:Polynomials196

8.1 Definitions198

CHAPTER 8 INTRODUCTION TO GALOIS THEORY198

8.2 Theorems202

8.3 Background and Notes:Galois Theory203

8.4 Classical Problems:Extension Fields206

8.5 Supplemental Exercises:Galois Theory209

GLOSSARY215

BIOGRAPHICAL SKETCHES217

BIBLIOGRAPHY221

INDEX223

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