图书介绍
抽象代数 英文pdf电子书版本下载
- 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 RUDIMENTS 1
1.1 Sets 1
Classical Problems:Sets 7
Supplemental Exercises:Sets 9
1.2 Mappings 9
INTRODUCTION 11
Classical Problems:Mappings 15
Supplemental Exercises:Mappings 18
1.3 Relations and Operations 19
Classical Problems:Relations and Operations 24
Supplemental Exercises:Relations and Operations 28
1.4 Number Systems 29
1.4.1 The Natural Numbers 29
1.4.2 The Integers 31
1.4.3 The Rational Numbers 36
1.4.4 The Reals 37
1.4.5 The Complex Numbers 38
Classical Problems:Number Systems 39
Supplemental Exercises:Number Systems 49
CHAPTER2 GROUPS 51
2.1 Introduction to Groups 51
Classical Problems:Groups and Subgroups 57
2.2 Working With Groups 63
Classical Problems:Working With Groups 69
2.3 More on Group Structure 79
Classical Problems:More on Group Structure 81
2.4 Supplemental Exercises:Groups 90
CHAPTER 3 PINGS 93
3.1 Basic Ring Structure 93
Classical Problems:Basic Ring Structure 96
3.2 Ring Substructures 102
Classical Problems:Ring Substructures 104
3.3 Specialized Rings 110
Classical Problems:Specialized Rings 113
3.4 Working With Rings 120
Classical Problems:Working With Rings 122
3.5 Notes on Rings 128
3.6 Supplemental Exercises:Rings 129
CHAPTER 4 R-MODULES 131
4.1 Introduction to R-Modules 131
4.2 Notes on Modules 135
4.3 Classical Problems: R-Modules 140
4.4 Supplemental Exercises:R-Modules 144
CHAPTER 5 VECTOR SPACES 145
5.1 Introduction to Vector Spaces 145
5.2 Nots on Vector Spaces 151
5.3 Classical Problems:Vector Spaces 152
5.4 Supplemental Exercises:Vector Spaces 158
CHAPTER 6 INTRODUCTION TO MATRICES 159
6.1 Basic Linear Algebra 159
6.1.1 Basic Structures 159
6.1.2 Notes:Basic Linear Algebra 167
Classical Problems:Matrices 169
6.2.1 Introduction 176
6.2 Matrices in Solving Systems of Equations 176
6.2.2 Examples 180
Classical Problems:Applying Matrices in Solving Systems of Equations 181
6.3 Supplemental Exercises:Matrices 186
CHAPTER 7 POLYNOMIALS 188
7.1 Definitions 188
7.2 Background and Notes:Polynomials 192
7.3 Classical Problems:Polynomials 193
7.4 Supplemental Exercises:Polynomials 196
8.1 Definitions 198
CHAPTER 8 INTRODUCTION TO GALOIS THEORY 198
8.2 Theorems 202
8.3 Background and Notes:Galois Theory 203
8.4 Classical Problems:Extension Fields 206
8.5 Supplemental Exercises:Galois Theory 209
GLOSSARY 215
BIOGRAPHICAL SKETCHES 217
BIBLIOGRAPHY 221
INDEX 223