抽象代數(shù)

INTRODUCTION
CHAPTER 1
RUDIMENTS
1.1 Sets
Classical Problems: Sets
Supplemental Exercises: Sets
1.2 Mappings
Classical Problems: Mappings
Supplemental Exercises: Mappings
1.3 Relations and Operations
Classical Problems: Relations and Operations
Supplemental Exercises: Relations and Operations
1.4 Number Systems
1.4.1 The Natural Numbers
1.4.2 The Integers
1.4.3 The Rational Numbers
1.4.4 The Reals
1.4.5 The Complex Numbers
Classical Problems: Number Systems
Supplemental Exercises: Number Systems
CHAPTER 2
GROUPS
2.1 Introduction to Groups
Classical Problems: Groups and Subgroups
2.2 Working With Groups
Classical Problems: Working With Groups
2.3 More on Group Structure
Classical Problems: More on Group Structure
2.4 Supplemental Exercises: Groups
CHAPTER 3
RINGS
3.1 Basic Ring Structure
Classical Problems: Basic Ring Structure
3.2 Ring Substructures
Classical Problems: Ring Substructures
3.3 Specialized Rings
Classical Problems: Specialized Rings
3.4 Working With Rings
Classical Problems: Working With Rings
3.5 Notes on Rings
3.6 Supplemental Exercises: Rings
CHAPTER 4
R-MODULES
4.1 Introduction to R-Modules
4.2 Notes on Modules
4.3 Classical Problems: R-Modules
4.4 Supplemental Exercises: R-Modules
CHAPTER 5
VECTOR SPACES
5.1 Introduction to Vector Spaces
5.2 Notes on Vector Spaces
5.3 Classical Problems: Vector Spaces
5.4 Supplemental Exercises: Vector Spaces
CHAPTER 6
INTRODUCTION TO MATRICES
6.1 Basic Linear Algebra
6.1.1 Basic Structures
6.1.2 Notes: Basic Linear Algebra
Classical Problems: Matrices
6.2 Matrices in Solving Systems of Equations
6.2.1 Introduction
6.2.2 Examples
Classical Problems: Applying Matrices in Solving Systems of Equations
6.3 Supplemental Exercises: Matrices
CHAPTER 7
POLYNOMIALS
7.1 Definitions
7.2 Background and Notes: Polynomials
7.3 Classical Problems: Polynomials
7.4 Supplemental Exercises: Polynomials
CHAPTER 8
INTRODUCTION TO GALOIS THEORY
8.1 Definitions
8.2 Theorems
8.3 Background and Notes: Galois Theory
8.4 Classical Problems: Extension Fields
8.5 Supplemental Exercises: Galois Theory
GLOSSARY
BIOGRAPHICAL SKETCHES