离散数学及其应用（英文精编版·第7版）

作者: 陈琼译

出版社: 机械工业出版社

出版时间: 2017-02

版次: 1

ISBN: 9787111555360

定价: 79.00

装帧: 平装

开本: 16开

纸张: 胶版纸

页数: 537页

丛书: 经典原版书库

分类: 计算机与互联网

36人买过

　　本书是经典的离散数学教材，为全球多所大学广为采用。本书全面而系统地介绍了离散数学的理论和方法，内容涉及逻辑和证明，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，还配备大量的实例和图表说明、各种练习和题目。第7版在前六版的基础上做了大量的改进，使其成为更有效的教学工具。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或参考书。

　　Kenneth H. Rosen，1972年获密歇根大学数学学士学位，1976年获麻省理工学院数学博士学位，1982年加入贝尔实验室，现为AT&T实验室特别成员，国际知名的计算机数学专家，除本书外，还著有《初等数论及其应用》等书。

‍‍
The Adapter 's Words
Preface　
About the Author
The Companion Website　
To the Student　
List of Symbols　
1 The Foundations: Logic and Proofs.
1.1 Propositional Logic
1.2 Applications of Propositional Logic
1.3 Propositional Equivalences.
1.4 Predicates and Quantifiers
1.5 Nested Quantifiers.
1.6 Rules of Inference.
1.7 Introduction to Proofs
1.8 Proof Methods and Strategy.
End-of-Chapter Material.
2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices
2.1 Sets..
2.2 Set Operations
2.3 Functions
2.4 Sequences and Summations.
2.5 Cardinality of Sets
2.6 Matrices
End-of-Chapter Material
3 Counting
3.1 The Basics of Counting
3.2 The Pigeonhole Principle.
3.3 Permutations and Combinations.
3.4 Binomial Coefficients and Identities
3.5 Generalized Permutations and Combinations.
3.6 Generating ermutations and Combinations
End-of-Chapter Material
4 Advanced Counting Techniques
4.1 Applications of Recurrence Relations
4.2 Solving Linear Recurrence Relations
4.3 Divide-and-Conquer Algorithms and Recurrence Relations
4.4 Generating Functions
4.5 Inclusion xclusion.
4.6 Applications of Inclusion xclusion
End-of-Chapter Material..
5 Relations.
5.1 Relations and Their Properties
5.2 n-ary Relations and Their Applications
5.3 Representing Relations.
5.4 Closures of Relations
5.5 Equivalence Relations.
5.6 Partial Orderings.
End-of-Chapter Material.
6 Graphs.
6.1 Graphs and Graph Models.
6.2 Graph Terminology and Special Types of Graphs
6.3 Representing Graphs and Graph Isomorphism.
6.4 Connectivity.
6.5 Euler and Hamilton Paths.
6.6 Shortest-Path Problems.
6.7 Planar Graphs.
6.8 Graph Coloring.
End-of-Chapter Material
7 Trees
7.1 Introduction to Trees.
7.2 Applications of Trees.
7.3 Tree Traversal.
7.4 Spanning Trees
7.5 Minimum Spanning Trees
End-of-Chapter Material.
8 Boolean Algebra
8.1 Boolean Functions
8.2 Representing Boolean Functions
8.3 Logic Gates
8.4 Minimization of Circuits
End-of-Chapter Material..
Suggested Readings
Answers to Exercises
内容简介:
　　本书是经典的离散数学教材，为全球多所大学广为采用。本书全面而系统地介绍了离散数学的理论和方法，内容涉及逻辑和证明，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，还配备大量的实例和图表说明、各种练习和题目。第7版在前六版的基础上做了大量的改进，使其成为更有效的教学工具。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或参考书。
作者简介:
　　Kenneth H. Rosen，1972年获密歇根大学数学学士学位，1976年获麻省理工学院数学博士学位，1982年加入贝尔实验室，现为AT&T实验室特别成员，国际知名的计算机数学专家，除本书外，还著有《初等数论及其应用》等书。
目录:
‍‍
The Adapter 's Words
Preface　
About the Author
The Companion Website　
To the Student　
List of Symbols　
1 The Foundations: Logic and Proofs.
1.1 Propositional Logic
1.2 Applications of Propositional Logic
1.3 Propositional Equivalences.
1.4 Predicates and Quantifiers
1.5 Nested Quantifiers.
1.6 Rules of Inference.
1.7 Introduction to Proofs
1.8 Proof Methods and Strategy.
End-of-Chapter Material.
2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices
2.1 Sets..
2.2 Set Operations
2.3 Functions
2.4 Sequences and Summations.
2.5 Cardinality of Sets
2.6 Matrices
End-of-Chapter Material
3 Counting
3.1 The Basics of Counting
3.2 The Pigeonhole Principle.
3.3 Permutations and Combinations.
3.4 Binomial Coefficients and Identities
3.5 Generalized Permutations and Combinations.
3.6 Generating ermutations and Combinations
End-of-Chapter Material
4 Advanced Counting Techniques
4.1 Applications of Recurrence Relations
4.2 Solving Linear Recurrence Relations
4.3 Divide-and-Conquer Algorithms and Recurrence Relations
4.4 Generating Functions
4.5 Inclusion xclusion.
4.6 Applications of Inclusion xclusion
End-of-Chapter Material..
5 Relations.
5.1 Relations and Their Properties
5.2 n-ary Relations and Their Applications
5.3 Representing Relations.
5.4 Closures of Relations
5.5 Equivalence Relations.
5.6 Partial Orderings.
End-of-Chapter Material.
6 Graphs.
6.1 Graphs and Graph Models.
6.2 Graph Terminology and Special Types of Graphs
6.3 Representing Graphs and Graph Isomorphism.
6.4 Connectivity.
6.5 Euler and Hamilton Paths.
6.6 Shortest-Path Problems.
6.7 Planar Graphs.
6.8 Graph Coloring.
End-of-Chapter Material
7 Trees
7.1 Introduction to Trees.
7.2 Applications of Trees.
7.3 Tree Traversal.
7.4 Spanning Trees
7.5 Minimum Spanning Trees
End-of-Chapter Material.
8 Boolean Algebra
8.1 Boolean Functions
8.2 Representing Boolean Functions
8.3 Logic Gates
8.4 Minimization of Circuits
End-of-Chapter Material..
Suggested Readings
Answers to Exercises