离散数学及其应用(英文版原书第8版)/经典原版书库 9787111645306
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作者(美)肯尼思·H.罗森|责编:曲熠
出版社机械工业
ISBN9787111645306
出版时间2020-01
装帧平装
开本其他
定价139元
货号30813921
上书时间2024-03-03
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目录
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 Algorithms
3.1 Algorithms
3.2 The Growth of Functions
3.3 Complexity of Algorithms
End-of-Chapter Material
4 Number Theory and Cryptography
4.1 Divisibility and Modular Arithmetic
4.2 Integer Representations and Algorithms
4.3 Primes and Greatest Common Divisors
4.4 Solving Congruences
4.5 Applications of Congruences
4.6 Cryptography
End-of-Chapter Material
5 Induction and Recursion
5.1 Mathematical Induction
5.2 Strong Induction and Well-Ordering
5.3 Recursive Definitions and Structural Induction
5.4 Recursive Algorithms
5.5 Program Correctness
End-of-Chapter Material
6 Counting
6.1 The Basics of Counting
6.2 The Pigeonhole Principle
6.3 Permutations and Combinations
6.4 Binomial Coefficients and Identifies
6.5 Generalized Permutations and Combinations
6.6 Generating Permutations and Combinations
End-of-Chapter Material
7 Discrete Probability
7.1 An Introduction to Discrete Probability
7.2 Probability Theory
7.3 Bayes' Theorem
7.4 Expected Value and Variance
End-of-Chapter Material
8 Advanced Counting Techniques
8.1 Applications of Recurrence Relations
8.2 Solving Linear Recurrence Relations
8.3 Divide-and-Conquer Algorithms and Recurrence Relations
8.4 Generating Functions
8.5 Inclusion-Exclusion
8.6 Applications of Inclusion-Exclusion
End-of-Chapter Material
9 Relations
9.1 Relations and Their Properties
9.2 n-ary Relations and Their Applications
9.3 Representing Relations
9.4 Closures of Relations
9.5 Equivalence Relations
9.6 Partial Orderings
End-of-Chapter Material
10 Graphs
10.1 Graphs and Graph Models
10.2 Graph Terminology and Special Types of Graphs
10.3 Representing Graphs and Graph Isomorphism
10.4 Connectivity
10.5 Euler and Hamilton Paths
10.6 Shortest-Path Problems
10.7 Planar Graphs
10.8 Graph Coloring
End-of-Chapter Material
11 Trees
11.1 Introduction to Trees
11.2 Applications of Trees
11.3 Tree Traversal
11.4 Spanning Trees
11.5 Minimum Spanning Trees
End-of-Chapter Material
12 Boolean Algebra
12.1 Boolean Functions
12.2 Representing Boolean Functions
12.3 Logic Gates
12.4 Minimization of Circuits
End-of-Chapter Material
13 Modeling Computation
13.1 Languages and Grammars
13.2 Finite-State Machines with Output
13.3 Finite-State Machines with No Output
13.4 Language Recognition
13.5 Turing Machines
End-of-Chapter Material
Appendices
1 Axioms for the Real Numbers and the Positive Integers
2 Exponential and Logarithmic Functions
3 Pseudocode
Suggested Readings B-1
Answers to Odd-Numbered Exercises S-1
Index of Biographies I-1
Index I-2
内容摘要
本书是介绍离散数学理论和方法的经典教材，被全球数百所高校采用，获得了极大的成功。第8版做了与时俱进的更新，添加了多重集、字符串匹配算法、
同态加密、数据挖掘中的关联规则、语义网络等内容，同时更新了配套教辅资源，成为更加实用的教学工具。本书可作为1～2个学期的离散数学课程教材，适
用于数学、计算机科学、计算机工程、信息技术等专业的学生。
本书特色：例题：共800多道例题，用于阐明概念、建立不同主题之间的关联以及介绍实际应用。
应用：涉及的领域包括计算机科学、数据网络、
心理学、化学、工程学、语言学、生物学、商业和因特网等，展示了离散数学的实用性。
算法：每一章都介绍了一些关键算法，提供伪代码，并简要分析其计算复杂度。
历史资料：给出了89位数学家和计算机科学家的简短传记，帮助读者了解不同技术的历史背景和发展轨迹。
练习、复习题和补充练习：共有4200多道难度各异的练习题，可以满足不同层次学生的需求。此外，还有一些研究性题目，帮助学生通过计算来探索新知识和新想法。
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