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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】
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- 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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