抽象代数:群、环与域的应用导论:第二版:英文

Preface to the Second Edition Preface to the First Edition List of Figures List of Tables 1.Logic and Proofs 1.1 Introduction 1.2 Statements, Connectives and Truth Tables 1.3 Relations between Statements 1.4 Quantifiers 1.5 Methods of Proof 1.6 Exercises 2.Set Theory 2.1 Initial Concepts 2.2 Relations between Sets 2.3 Operations Defined on Sets--or New Sets from Old 2.4 Exercises 3.Cartesian Products, Relations, Maps and Binary Operations 3.1 Introduction 3.2 Cartesian Product 3.3 Maps 3.4 Binary Operations 3.5 Exercises 4.The Integers 4.1 Introduction 4.2 Elementary Properties 4.3 Divisibility 4.4 The Fundamental Theorem of Arithmetic 4.5 Congruence Modulo n and the Algebraic System (Zn,+,) 4.6 Linear Congruences in Z and Linear Equations in Zn 4.7 Exercises 5.Groups 5.1 Introduction 5.2 Definitions and Elementary Properties 5.3 Alternative Axioms for Groups 5.4 Subgroups 5.5 Cyclic Groups 5.6 Exercises 6.Further Properties of Groups 6.1 Introduction 6.2 Cosets 6.3 Isomorphisms and Homomorphisms 6.4 Normal Subgroups and Factor Groups 6.5 Direct Product of Groups 6.6 Exercises 7.The Symmetric Groups 7.1 Introduction 7.2 The Cayley Representation Theorem 7.3 Permutations as Products of Disjoint Cycles 7.4 Even and Odd Permutations 7.5 The Simplicity of An