书籍详情
离散数学及其应用（英文版·第6版）
作者：（美）罗森
出版社：机械工业出版社
出版时间：2008-01-01
ISBN：9787111239352
定价：¥89.00
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内容简介
《离散数学及其应用（英文版）（第6版）》是介绍离散数学理论和方法的经典教材，已经成为采用率最高的离散数学教材，仅在美国就被600多所高校用作教材，获得了极大的成功。中文版也已被国内大学广泛采用为教材。第6版在前五版的基础上做了大量的改进，使其成为更有效的教学工具。《离散数学及其应用（英文版）（第6版）》可作为1至2个学期的离散数学课入门教材。
作者简介
罗森（Rosen K.H.），美国，密歇根大学数学学士，麻省理工学院数学博士。曾就职于科罗拉多大学、俄亥俄州立大学、缅因大学，后加盟贝尔实验室，现为AT＆T实验室特别成员。除本书外，他还著有《初等数论及其应用》等书，并担任CRC离散数学丛书的主编。
目录
Preface
About the Author
To the Student
LIST OF SYMBOLS
1 The Foundations： Logic and Proofs
1.1 Propositional Logic
1.2 Propositional Equivalences
1.3 Predicates and Quantifiers
1.4 Nested Quantifiers
1.5 Rules oflnference
1.6 Introduction to Proofs
1.7 Proof Methods and Strategy End-of-Chapter Material
2 Basic Structures： Sets， Functions， Sequences， and Sums
2.1 Sets
2.2 Set Operations
2.3 Functions
2.4 Sequences and Summations End-of-Chapter Material
3 The Fundamentals： Algorithms， the Integers， and Matrices
3.1 Algorithms
3.2 The Growth of Functions
3.3 Complexity of Algorithms
3.4 The Integers and Division
3.5 Primes and Greatest Common Divisors
3.6 Integers and Algorithms
3.7 Applications of Number Theory
3.8 Matrices End-of-Chapter Material
4 Induction and Recursion
4.1 Mathematical Induction
4.2 Strong Induction and Well-Ordering
4.3 Recursive Definitions and Structural Induction
4.4 Recursive Algorithms
4.5 Program Correctness End-of-Chapter Material
5 Counting
5.1 The Basics of Counting
5.2 The Pigeonhole Principle
5.3 Permutations and Combinations
5.4 Binomial Coefficients
5.5 Generalized Permutations and Combinations
5.6 Generating Permutations and Combinations End-of-Chapter Material
6 Discrete Probability
6.1 An Introduction to Discrete Probability
6.2 Probability Theory
6.3 Bayes Theorem
6.4 Expected Value and Variance End-of-Chapter Material
7 Advanced Counting Techniques
7.1 Recurrence Relations
7.2 Solving Linear Recurrence Relations
7.3 Divide-and-Conquer Algorithms and Recurrence Relations
7.4 Generating Functions
7.5 Inclusion-Exclusion
7.6 Applications of Inclusion-Exclusion End-of-Chapter Material
8 Relations
8.1 Relations and Their Properties
8.2 n-ary Relations and Their Applications
8.3 Representing Relations
8.4 Closures of Relations
8.5 Equivalence Relations
8.6 Partial Orderings End-of-Chapter Material
9 Graphs
9.1 Graphs and Graph Models
9.2 Graph Terminology and Special Types of Graphs
9.3 Representing Graphs and Graph Isomorphism
9.4 Connectivity
9.5 Euler and Hamilton Paths
9.6 Shortest-Path Problems
9.7 Planar Graphs
9.8 Graph Coloring End-of-Chapter Material
10 Trees
11 Boolean Algebra
12 Modeling Computation
Appendixes
Suggested Readings B-1
Answers to Odd-Numbered Exercises @ S-1
Index of Biographies I-1
Index I-2
About the Author
To the Student
LIST OF SYMBOLS
1 The Foundations： Logic and Proofs
1.1 Propositional Logic
1.2 Propositional Equivalences
1.3 Predicates and Quantifiers
1.4 Nested Quantifiers
1.5 Rules oflnference
1.6 Introduction to Proofs
1.7 Proof Methods and Strategy End-of-Chapter Material
2 Basic Structures： Sets， Functions， Sequences， and Sums
2.1 Sets
2.2 Set Operations
2.3 Functions
2.4 Sequences and Summations End-of-Chapter Material
3 The Fundamentals： Algorithms， the Integers， and Matrices
3.1 Algorithms
3.2 The Growth of Functions
3.3 Complexity of Algorithms
3.4 The Integers and Division
3.5 Primes and Greatest Common Divisors
3.6 Integers and Algorithms
3.7 Applications of Number Theory
3.8 Matrices End-of-Chapter Material
4 Induction and Recursion
4.1 Mathematical Induction
4.2 Strong Induction and Well-Ordering
4.3 Recursive Definitions and Structural Induction
4.4 Recursive Algorithms
4.5 Program Correctness End-of-Chapter Material
5 Counting
5.1 The Basics of Counting
5.2 The Pigeonhole Principle
5.3 Permutations and Combinations
5.4 Binomial Coefficients
5.5 Generalized Permutations and Combinations
5.6 Generating Permutations and Combinations End-of-Chapter Material
6 Discrete Probability
6.1 An Introduction to Discrete Probability
6.2 Probability Theory
6.3 Bayes Theorem
6.4 Expected Value and Variance End-of-Chapter Material
7 Advanced Counting Techniques
7.1 Recurrence Relations
7.2 Solving Linear Recurrence Relations
7.3 Divide-and-Conquer Algorithms and Recurrence Relations
7.4 Generating Functions
7.5 Inclusion-Exclusion
7.6 Applications of Inclusion-Exclusion End-of-Chapter Material
8 Relations
8.1 Relations and Their Properties
8.2 n-ary Relations and Their Applications
8.3 Representing Relations
8.4 Closures of Relations
8.5 Equivalence Relations
8.6 Partial Orderings End-of-Chapter Material
9 Graphs
9.1 Graphs and Graph Models
9.2 Graph Terminology and Special Types of Graphs
9.3 Representing Graphs and Graph Isomorphism
9.4 Connectivity
9.5 Euler and Hamilton Paths
9.6 Shortest-Path Problems
9.7 Planar Graphs
9.8 Graph Coloring End-of-Chapter Material
10 Trees
11 Boolean Algebra
12 Modeling Computation
Appendixes
Suggested Readings B-1
Answers to Odd-Numbered Exercises @ S-1
Index of Biographies I-1
Index I-2
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