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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

前言/序言

　　PrefaceIn writing this book, I was guided by my long-standing experience and interest in teaching discrete mathematics. For the student, my purpose was to present material in a precise, readable manner, with the concepts and techniques of discrete mathematics clearly presented and demonstrated. My goal was to show the relevance and practicality of discrete mathematics to students, who are often skeptical. I wanted to give students studying computer science all of the mathematical foundations they need for their future studies. I wanted to give mathematics students an understanding of important mathematical concepts together with a sense of why these concepts are important for applications. And most importantly, I wanted to accomplish these goals without watering down the material.For the instructor, my purpose was to design a flexible, comprehensive teaching tool using proven pedagogical techniques in mathematics. I wanted to provide instructors with a package of materials that they could use to teach discrete mathematics effectively and efficiently in the most appropriate manner for their particular set of students. I hope that I have achieved these goals.I have been extremely gratified by the tremendous success of this text. The many improvements in the seventh edition have been made possible by the feedback and suggestions of a large number of instructors and students at many of the more than 600 North American schools, and at any many universities in parts of the world, where this book has been successfully used.This text is designed for a one-or two-term introductory discrete mathematics course taken by students in a wide variety of majors, including mathematics, computer science, and engineering. College algebra is the only explicit prerequisite, although a certain degree of mathematical maturity is needed to study discrete mathematics in a meaningful way. This book has been designed to meet the needs of almost all types of introductory discrete mathematics courses. It is highly flexible and extremely comprehensive. The book is designed not only to be a successful textbook, but also to serve as valuable resource students can consult throughout their studies and professional life.Goals of a Discrete Mathematics CourseA discrete mathematics course has more than one purpose. Students should learn a particular set of mathematical facts and how to apply them; more importantly, such a course should teach students how to think logically and mathematically. To achieve these goals, this text stresses mathematical reasoning and the different ways problems are solved. Five important themes are interwoven in this text: mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and applications and modeling. A successful discrete mathematics course should carefully blend and balance all five themes.1. Mathematical Reasoning: Students must understand mathematical reasoning in order to read, comprehend, and construct mathematical arguments. This text starts with a discussion of mathematical logic, which serves as the foundation for the subsequent discussions of methods of proof. Both the science and the art of constructing proofs are addressed. The technique of mathematical induction is stressed through many different types of examples of such proofs and a careful explanation of why mathematical induction is a valid proof technique.2. Combinatorial Analysis: An important problem-solving skill is the ability to count or enumerate objects. The discussion of enumeration in this book begins with the basic techniques of counting. The stress is on performing combinatorial analysis to solve counting problems and analyz ealgorithms, not on applying formulae.3. Discrete Structures: A course in discrete mathematics should teach students how to work with discrete structures, which are the abstract mathematical structures used to represent discrete objects and relationships between these objects. These discrete structures include sets, permutations, relations, graphs, trees, and finite-state machines.4. Algor

离散数学及其应用（英文精编版·第7版） 电子书 下载 mobi epub pdf txt

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