本书是经典的离散数学教材,被全球数百所大学广为采用。英文精编版为满足本科教学需求而缩减了篇幅,保留的主要内容包括:逻辑和证明,集合、函数、序列、求和与矩阵,计数,关系,图,树,布尔代数。全书取材广泛,除包括定义、定理的严格陈述外,还配备大量的例题、图表、应用实例和练习。第8版做了与时俱进的更新,成为更加实用的教学工具。本书可作为高等院校数学、计算机科学和计算机工程等专业的教材,也可作为科技领域从业人员的参考书。

The Adapter's Words Preface Online Resources To the Student About the Author List of Symbols 1 The Foundations: Logic and Proofs1 1.1 Propositional Logic1 1.2 Applications of Propositional Logic15 1.3 Propositional Equivalences22 1.4 Predicates and Quantifiers34 1.5 Nested Quantifiers51 1.6 Rules of Inference62 1.7 Introduction to Proofs72 1.8 Proof Methods and Strategy84 End-of-ChapterMaterial (Online) 2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices101 2.1 Sets101 2.2 Set Operations111 2.3 Functions124 2.4 Sequences and Summations140 2.5 Cardinality of Sets153 2.6 Matrices161 End-of-ChapterMaterial (Online) 3 Counting169 3.1 The Basics of Counting169 3.2 The Pigeonhole Principle182 3.3 Permutations and Combinations189 3.4 Binomial Coefficients and Identities197 3.5 Generalized Permutations and Combinations204 3.6 Generating Permutations and Combinations215 End-of-ChapterMaterial (Online) 4 Advanced Counting Techniques221 4.1 Applications of Recurrence Relations221 4.2 Solving Linear Recurrence Relations232 4.3 Divide-and-Conquer Algorithms and Recurrence Relations244 4.4 Generating Functions253 4.5 Inclusion朎xclusion268 4.6 Applications of Inclusion朎xclusion273 End-of-ChapterMaterial (Online) 5 Relations281 5.1 Relations and Their Properties281 5.2 n-ary Relations and Their Applications292 5.3 Representing Relations302 5.4 Closures of Relations308 5.5 Equivalence Relations317 5.6 Partial Orderings327 End-of-ChapterMaterial (Online) 6 Graphs343 6.1 Graphs and Graph Models343 6.2 Graph Terminology and Special Types of Graphs354 6.3 Representing Graphs and Graph Isomorphism371 6.4 Connectivity380 6.5 Euler and Hamilton Paths393 6.6 Shortest-Path Problems405 6.7 Planar Graphs415 6.8 Graph Coloring423 End-of-ChapterMaterial (Online) 7 Trees431 7.1 Introduction to Trees431 7.2 Applications of Trees442 7.3 Tree Traversal456 7.4 Spanning Trees468 7.5 Minimum Spanning Trees481 End-of-ChapterMaterial (Online) 8 Boolean Algebra487 8.1 Boolean Functions487 8.2 Representing Boolean Functions494 8.3 Logic Gates497 8.4 Minimization of Circuits503 End-of-ChapterMaterial (Online) Suggested Readings (Online) Answers to Odd-Numbered Exercises (Online)