## 手植记：旅行找食材，原生本初心

 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 v分雅 联系QQ：526781618 淘宝旺旺：跟朝流走 有需要的欢迎联系！专业代购电子书 ebook 英文电子书代购