離散數(shù)學及其應用

前言

PurposeThe original of Discrete Mathematics and its Applications is intended for one-term or two-termintroductory courses of Discrete Mathematics taken by students from wide variety of majors ,including computer science, mathematics, engineering and etc. It's an excellent textbook writtenby Prof. Kenneth H. Rosen and has been widely used in over 600 institutions around the world.The sixth edition gives a focused introduction to the primary themes of the Discrete Mathe-matics course and demonstrates the relevance and practicality of Discrete Mathematics to a widevariety of real-world applications. All the topics, examples, references and exercises are quitehelpful to the students.In recent years, bilingual teaching has been encouraged in universities and colleges in China.More and more Chinese instructors and students are getting interested in this book. However, asa textbook, over 800 original pages make Chinese students find it difficult to read. In order tointroduce this book to more Chinese college students, we tried to maintain the author's writingstyle and omitted some contents to adapt for the Chinese students' English reading ability. Thecompressed version fits into the syllabus of undergraduate course, and reduce students' readingburden as well.What is CompressedSince some contents in the original are taught in some other courses, such as Number theory,Discrete Probability, Induction and Recursion, Boolean Algebra and Finite-state Machine, weremoved them which were in the original book as Chapter 3, Chapter 4, Chapter 6, Chapter11 and Chapter 12. As a resuR, Logic and Proofs, Sets, Functions, Relations, Graphs, Trees,Counting and Advanced Counting Techniques are reserved in the compressed version.There are over 3800 exercises in the original textbook, posing various types of questions. Some of them are designed for basic skill development, some are in intermediate level and some are more difficult and challenging. In order to keep the original feature of the book, we removed the even-number questions of the remained Chapters, so that the questions with different difficul-ties are reserved. The historical information for the background of many topics is also removed,so as to reduce the reading burden of students.Some concepts are given in the exercises. It is difficult for students to comprehend becauseof the simplicity of the descriptions, such as the concepts about the Normal and Canonical formsfor a proposition. So we have added the detail description about them in Chapter 1.

內(nèi)容概要

《離散數(shù)學及其應用》一書是介紹離散數(shù)學理論和方法的經(jīng)典教材，已經(jīng)成為采用率最高的離散數(shù)學教材，僅在美國就被600多所高校用作教材。并獲得了極大的成功。第6版在前5版的基礎(chǔ)上做了大量的改進，使其成為更有效的教學工具。    本書基于該書第6版進行改編。保留了國內(nèi)離散數(shù)學課程涉及的基本內(nèi)容。更加適合作為國內(nèi)高校計算機及相關(guān)專業(yè)本科生的離散數(shù)學課程教材。本書的具體改編情況如下：    補充了第1章中的基礎(chǔ)內(nèi)容，詳細描述了范式和標準型。    刪去了在其他課程中講授的內(nèi)容。如數(shù)論、離散概率、歸納和遞歸等。    對于保留章節(jié)，刪去了編號為偶數(shù)的練習題。      刪去了相關(guān)的歷史資料。

作者簡介

作者：（美國）羅森（Kenneth H.Rosen）Kenneth H.Rosen密歇根大學數(shù)學學士。麻省理工學院數(shù)學博士。曾就職于科羅拉多大學、俄亥俄州立大學、緬因大學，后加盟貝爾實驗室，現(xiàn)為AT&T實驗室特別成員。除本書外。他還著有《初等數(shù)論及其應用》等書，并擔任CRC離散數(shù)學叢書的主編。

書籍目錄

Adapter's ForwordPrefaceTo the StudentLIST OF SYMBOLSChapter 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 of Inference  1.6  Introduction to Proofs  1.7  Proof Methods and Strategy  End-of-Chapter MaterialChapter 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 MaterialChapter3  Counting  3.1  The Basics of Counting  3.2  The Pigeonhole Principle  3.3  Permutations and Combinations  3.4  Binomial Coefficients  3.5  Generalized Permutations and Combinations  3.6  Generating Permutations and Combinations  End-of-Chapter MaterialChapter 4  Advanced Counting Techniques  4.1  Recurrence Relations  4.2  Solving Linear Recurrence Relations  4.3  Divide-and-Conquer Algorithms and Recurrence Relations  4.4  Generating Functions  4.5  Inclusion-Exclusion  4.6  Applications of Inclusion-Exclusion  End-of-Chapter MaterialChapter 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 MaterialChapter 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 MaterialChapter 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 MaterialAnswers to Exercises

章節(jié)摘錄

插圖：25. Are these system specifications consistent？ "The system is in multiuser state if and only if it is operating normally. If the system is operating normally, the kernel is functioning. The kernel is not functioning or the system is in interrupt mode. If the system is not in multiuser state, then it is in interrupt mode. The system is not in interrupt mode."26. Are these system specifications consistent？ "The router can send packets to the edge system only if it supports the new address space. For the router to support the new address space it is necessary that the latest software release be installed. The router can send packets to the edge system if the latest software release is installed, The router does not support the new address space."27. What Boolean search would you use to look for Web pages about beaches in New Jersey？ What if you wanted to find Web pages about beaches on the isle of Jersey （in the English Channel）？ Exercises 28-29 relate to inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, A and B. Determine, if possible, what A and B are if they address you in the ways described. If you cannot determine what these two people are, can you draw any conclusions？28. A says "At least one of us is a knave" and B says nothing.29. A says "We are both knaves" and B says nothing. Exercises 30-32 are puzzles that can be solved by translating statements into logical expressions and reasoning from these expressions using truth tables.30. Steve would like to determine the relative salaries of three coworkers using two facts. First, he knows that if Fred is not the highest paid of the three, then Janice is. Second, he knows that if Janice is not the lowest paid, then Maggie is paid the most. Is it possible to determine the relative salaries of Fred, Maggie, and Janice from what Steve knows？ If so, who is paid the most and who the least？ Explain your reasoning.

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