离散数学概要(第3版)(英文版)

《离散数学概要》是一部教材，初版于2008年， 这是第3版。主要面向计算机和数学等相关专业本科生 ，学时一个学期。本书旨在指导学生深入理解建立在 数学复杂性之上的离散数学的基本理论，内容涉及逻 辑思维，关系思维，递归式思维，数量思维和分析思 维等5部分内容。为便于读者快速了解全书内容，该书 开头首先引入核心和辅助内容树图，算法理论出现在 书的后半部分。书中有大量应用实例，最后一章介绍 离散数学在生物、社会学、语言学、经济学等领域的 应用。

Preface How to Use This Book Chapter 1 Logical Thinking 1.1 Formal Logic 1.1.1 Inquiry Problems 1.1.2 Connectives and Propositions 1.1.3 Truth Tables 1.1.4 Logical Equivalences Exercises 1.1 1.2 Propositional Logic 1.2.1 Tautologies and Contradictions 1.2.2 Derivation Rules 1.2.3 Proof Sequences 1.2.4 Forward-Backward Exercises 1.2 1.3 Predicate Logic 1.3.1 Predicates 1.3.2 Quantifiers 1.3.3 Translation 1.3.4 Negation 1.3.5 Two Common Constructions Exercises 1.3 1.4 Logic in Mathematics 1.4.1 The Role of Definitions in Mathematics 1.4.2 Other Types of Mathematical Statements 1.4.3 Counterexamples 1.4.4 Axiomatic Systems Exercises 1.4 1.5 Methods of Proof 1.5.1 Direct Proofs 1.5.2 Proof by Contraposition 1.5.3 Proof by Contradiction Exercises 1.5 Chapter 2 Relational Thinking 2.1 Graphs 2.1.1 Edges and Vertices 2.1.2 Terminology 2.1.3 Modeling Relationships with Graphs Exercises 2.1 2.2 Sets 2.2.1 Membership and Containment 2.2.2 New Sets from Old 2.2.3 Identities Exercises 2.2 2.3 Functions 2.3.1 Definition and Examples 2.3.2 One-to-One and Onto Functions 2.3.3 New Functions from Old Exercises 2.3 2.4 Relations and Equivalences