PREFACE
CHAPTER 1 SETS
1．1 Operations on Sets
Exercise Set 1．1
1．2 Set Mappings
Exercise Set 1．2
1．3 Products of Mappings
Exercise Set 1．3
1．4 Some Properties of Integers
Exercise Set 1．4
CHAPTER 2 MATRICES AND DETERMINANTS
2．1 Operations on Matrices
Exercise Set 2．1
2．2 Permutations of Finite Sets
Exercise Set 2．2
2．3 Determinants of Matrices
Exercise Set 2．3
2．4 Computing Determinants
Exercise Set 2．4
2．5 Properties of the Product of Matrices
Exercise Set 2．5
CHAPTER 3 FIELDS
3．1 Binary Algebraic Operations
Exercise Set 3．1
3．2 Basic Properties of Fields
Exercise Set 3．2
3．3 The Field of Complex Numbers
Exercise Set 3．3
CHAPTER 4 VECTOR SPACES
4．1 Vector Spaces
Exercise Set 4．1
4．2 Dimension
Exercise Set 4．2
4．3 The Rank of a Matrix
Exercise Set 4．3
4．4 Quotient Spaces
Exercise Set 4．4
CHAPTER 5 LINEAR MAPPINGS
5．1 Linear Mappings
Exercise Set 5．1
5．2 Matrices of Linear Mappings
Exercise Set 5．2
5．3 Systems of Linear Equations
Exercise Set 5．3
5，4 Eigenvectors and Eigenvalues
Exercise Set 5．4
CHAPTER 6 BILINEAR FORMS
6．1 Bilinear Forms
Exercise Set 6．1
6．2 Classical Forms
Exercise Set 6，2
6．3 Symmetric Forms over R
Exercise Set 6，3
6．4 Euclidean Spaces
Exercise Set 6．4
CHAPTER 7 RINGS
7．1 Rings， Subrings， and Examples
Exercise Set 7．1
7．2 Equivalence Relations
Exercise Set 7．2
7．3 Ideals and Quotient Rings
Exercise Set 7．3
7．4 Homomorphisms of Rings
Exercise Set 7．4
7．5 Rings of Polynomials and Formal Power Series
Exercise Set 7．5
7．6 Rings of Multivariable Polynomials
Exercise Set 7．6
CHAPTER 8 GROUPS
8．1 Groups and Subgroups
Exercise Set 8．1
8．2 Examples of Groups and Subgroups
Exercise Set 8．2
8．3 Cosets
Exercise Set 8．3
8．4 Normal Subgroups and Factor Groups
Exercise Set 8．4
8．5 Homomorphisms of Groups
Exercise Set 8．5
CHAPTER 9 ARITHMETIC PROPERTIES OF RINGS
9．1 Extending Arithmetic to Commutative Rings
Exercise Set 9．1
9．2 Euclidean Rings
Exercise Set 9．2
9．3 Irreducible Polynomials
Exercise Set 9．3
9．4 Arithmetic Functions
Exercise Set 9．4
9．5 Congruences
Exercise Set 9．5
CHAPTER 10 THE REAL NUMBER SYSTEM
10．1 The Natural Numbers
10．2 The Integers
10．3 The Rationals
10．4 The Real Numbers
ANSWERS TO SELECTED EXERCISES
INDEX
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