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### 基本信息

- 原书名：Discrete Mathematics and Its Applications
- 原出版社： McGraw-Hill

- 作者：
**（美）Kenneth H.Rosen** - 丛书名：
**经典原版书库** - 出版社：机械工业出版社
- ISBN：
**9787111115038** - 上架时间：2003-3-25
- 出版日期：2003 年3月
- 开本：16开
- 页码：787
- 版次：1-1
- 所属分类：数学 > 代数，数论及组合理论 > 离散数学

教材 > 研究生/本科/专科教材 > 理学 > 数学

### 内容简介

数学书籍

[font color="#CC0000">本书第4版是全球500多所大学的指定教材，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5版在前四版的基础上做了大量的改进，使其成为更有效的教学工具。[/font>

本书可作为1至2个学期的离散数学课入门教材，适用于数、计算机科学、工程等专业的学生。

[font color="#CC0000">第5版的特点[/font>

[font color="#000000" size="2">◆[/font>易入门：实践证明本书对初学者来说易读易懂

[font size="2">◆[/font>灵活：本教材为灵活使用做了精心设计，各章对其前面内容的依赖降到最小

[font size="2">◆[/font>广泛的课堂实践：本书已在500多所学校得到了多年检验

[font size="2">◆[/font>实例：书中有700多个实例，用于阐明要领联系不同内容，并引入各种应用

[font size="2">◆[/font>应用：本书涉及的应用领域很广，包括计算机科学、数据网络、心理学、化学、 工程、语言学、生物学、商业和互联网

[font size="2">◆[/font>历史资料：本书以脚注的形式给出了60多位数学和计算机科学家的传记，并配有照片

[font size="2">◆[/font>关键术语和结论：每一章后面都列出了本章的关键术语和结论

[font size="2">◆[/font>练习、复习题、补充练习：正文中有3500多道练习，每章最后都有一组复习题才一组丰富而多样的补充练习

[font size="2">◆[/font>计算机课题：每一章后面还有一组计算机课题，把学生已经学到的计算和离散数学的内容结合在一起

[font color="#CC0000">相关链接[/font>

《离散数学及其应用（原书第4版）》[/a>

《离散数学及其应用（英文版，第4版)》[/a>

### 作译者

Dr.Rosen has published numerous articles in professional journals in the areas of number theory and mathematical modeling. He is the author of the textbooks Elementary Number Theory and Its Applications, currently in its fourth edition, published by Addison-Wesley, and Discrete Mathematics and Its Applicattons, in its fifth edition, published by McGraw-Hill. Both books have been used extensively at hundreds of universities. He is coauthor of UNIX: The Complete Reference, UNIX System V Release 4: An Introduction, and Best UNIX Tips Ever,published by Osborne McGraw-Hill. These books have sold more than l00,000 copies, with translations into Chinese, German, Spanish, and Italian. Ken is also the editor of the Handbook Of Discrete and Combinatorial Mathematics, published in 2000 by CRC Press, and he is the advisory editor of the CRC series of books in discrete mathematics. Ken is also interested in integrating mathematical software into the educational and professional environments and has worked on projects with Watrloo MAPLE software in both these areas.

At Bell Laboratories, and now AT&T Laboratories, Dr.Rosen has worked on a wide range of projects, including operations research studies and product line planning for computers and data communications equipment. He has helped plan AT&T's future products and services in the area of multimedia, including video communications, speech recognition and synthesis,and image networking. He has evaluated new technology for use by AT&T He has also invented many new services, and holds or has submitted more than 65 patents. One of his more interesting projects involved helping evaluate technology for the AT&T attraction at EPCOT Center.

### 前言

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 fifth edition have been made possible by the feedback and suggestions of a large number of instructors and students at many of the more than 500 schools where this book has been successfully used. There are many enhancements in this edition. The ancillary package has been enriched, and a companion website provides helpful material,making it easier for students and instructors to achieve their goals.

This text is designed for a one-or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including mathematics, computer science, and engineering. College algebra is the only explicit prerequisite.

Goals of a Discrete Mathematics Course

A 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 mathematically To achieve these goals, this text stresses mathematical reasoning and the different ways problems are solved. Five impor tant 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 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, 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. Algorithmic Thinking: Certain classes of problems are solved by the specification of an algorithm. After an algorithm has been described, a computer program can be constructed implementing it. The mathematical portions of this activity, which include the specification of the algorithm, the verification that it works properly, and the analysis of the computer memory and time required to perform it, are all covered in this text. Algorithms are described using both English and an easily understood form of pseudocode.

5. Applications and Modeling: Discrete mathematics has applications to almost every conceivable area of study There are many applications to computer science and data networking in this text, as well as applications to such diverse areas as chemistry botany, zoology, linguistics, geography business, and the Internet. These applications are natural and important uses of discrete mathematics and are not contrived. Modeling with discrete mathematics is an extremely important problem-solving skill, which students have the opportunity to develop by constructing their own models in some of the exercises.

Changes in the Fifth Edition

The fourth edition of this book has been used successfully at over 500 schools in the United States, dozens of Canadian universities, and at universities throughout Europe, Asia, and Oceania. Although the fourth edition has been an extremely effective text, many instructors, including longtime users, have requested changes designed to make this book more effective. I have devoted a significant amount of time and energy to satisfy these requests.

The result is a fifth edition that offers both instructors and students much more than the fourth edition did. Most significantly an improved organization of topics has been implemented in this fifth edition, making the book a more effective teaching tool.Substantial enhancements to the material devoted to logic, method of proof, and proof strategies are designed to help students master matheinatical reasoning. Additional explanations and examples have been added to clarify material.where students often have difficulty New exercises, both routine and challenging, have been inserted into the exer cise sets. Highly relevant applications. including many related to the Web and computer science, have been added. The companion website has benefited from extensive development activity and now provides tools students can use to master key concepts and explore the world of discrete mathematics.

Special Features

ACCESSIBILITY This text has proven to be easily read and understood by beginning students. There are no mathematical prerequisites beyond college algebra for almost all of this text. The few places in the book where calculus is referred to are explicitly noted. Most students should easily understand the pseudocode used in the text to express algorithms, regardless of whether they have formally studied programming languages. There is no formal computer science prerequisite.

Each chapter begins at an easily understood and accessible level. Once basic mathematical concepts have been carefully developed, more difficult material and applications to other areas of study are presented.

FLEXIBILITY This text has been carefully designed for flexible use. The dependence of chapters on previous material has been minimized. Each chapter is divided into sections of approximately the same length, and each section is divided into subsections that form natural blocks of material for teaching. Instructors can easily pace their lectures using these blocks.

WRITING STYLE The writing style in this book is direct and pragmatic. Precise mathematical language is used without excessive formalism and abstraction. Care has been taken to balance the mix of notation and words in mathematical statements.

EXTENSIVE CLASSROOM USE This book has been used at over 500 schools,and more than 400 have dsed it more than once. The feedback from instructors and students at many of the schools has helped make this fifth edition an even more successful teaching tool than previous editions.