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ALGEBRA AND NUMBER THEORY An Integrated Approach ebook 电子书代购

ALGEBRA AND NUMBER THEORY An Integrated Approach ebook 电子书代购

ALGEBRA AND NUMBER
THEORY
An Integrated Approach
MARTYN R. DIXON
Department of Mathematics
University of Alabama
LEONID A. KURDACHENKO
Department of Algebra
School of Mathematics and Mechanics
National University of Dnepropetrovsk
IGOR VA. SUBBOTIN
Department of Mathematics and Natural Sciences
National University
~

CONTENTS
PREFACE ix
CHAPTER 1 SETS 1
1.1 Operations on Sets I
Exercise Set 1.1 I 6
1.2 Set Mappings I 8
Exercise Set 1.2 I 19
1.3 Products of Mappings I 20
Exercise Set 1.3 I 26
1.4 Some Properties of Integers I 28
Exercise Set 1.4 I 39
CHAPTER 2 MATRICES AND DETERMINANTS 41
2.1 Operations on Matrices I 41
Exercise Set 2.1 I 52
2.2 Permutations of Finite Sets I 54
Exercise Set 2.2 I 64
2.3 Determinants of Matrices I 66
Exercise Set 2.3 I 77
2.4 Computing Determinants I 79
Exercise Set 2.4 I 91
v

CONTENTS
2.5 Properties of the Product of Matrices I 93
Exercise Set 2.5 I 103
CHAPTER 3 FIELDS
CHAPTER4
CHAPTER 5
3.1 Binary Algebraic Operations I 105
Exercise Set 3 .1 I 118
3.2 Basic Properties of Fields I 119
Exercise Set 3.2 I 129
3.3 The Field of Complex Numbers I 130
Exercise Set 3.3 I 144
VECTOR SPACES
4.1 Vector Spaces I 146
Exercise Set 4.1 I 158
4.2 Dimension I 159
Exercise Set 4.2 I 172
4.3 The Rank of a Matrix I
Exercise Set 4.3 I 181
4.4 Quotient Spaces I 182
Exercise Set 4.4 I 186
LINEAR MAPPINGS
5.1 Linear Mappings I 187
Exercise Set 5 .1 I 199
174
5.2 Matrices of Linear Mappings I 200
Exercise Set 5.2 I 207
5.3 Systems of Linear Equations I 209
Exercise Set 5.3 I 215
5.4 Eigenvectors and Eigenvalues I 217
Exercise Set 5.4 I 223
CHAPTER 6 BILINEAR FORMS
6.1 Bilinear Forms I 226
Exercise Set 6.1 I 234
6.2 Classical Forms I 235
Exercise Set 6.2 I 247
6.3 Symmetric Forms over ffi. I 250
Exercise Set 6.3 I 257
6.4 Euclidean Spaces I 259
Exercise Set 6.4 I 269
CHAPTER 7 RINGS 272

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