离散数学和组合数学

出版时间：2005-7  出版社：高等教育出版社  作者：JamesA.Anderso  页数：608  
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前言

As in the first edition, the purpose of this book is to present an extensive range anddepth of topics in discrete mathematics and also work in a theme on how to do proofs.Proofs are introduced in the first chapter and continue throughout the book. Moststudents taking discrete mathematics are mathematics and computer science majors.Although the necessity of learning to do proofs is obvious for mathematics majors, itis also critical for computer science students to think logically. Essentially, a logicalbug-free computer program is equivalent to a logical proof, Also, it is assumed in thisbook that it is easier to use （or at least not misuse） an application if one understandswhy it works. With few exceptions, the book is self-contained. Concepts are developedmathematically before they are seen in an applied context.Additions and alterations in the second edition:More coverage of proofs, especially in Chapter l.   Added computer science applications, such as a greedy algorithm for coloring the nodes of a graph, a recursive algorithm for counting the number of nodes on a binary search tree, or an efficient algorithm for computing ab modn for very largevalues of a, b, and n.An extensive increase in the number of problems in the first seven chapters.More problems are included that involve proofs.Additional material is included on matrices.True-False questions at the end of each chapter.Summary questions at the end of each chapter.Functions and sequences are introduced earlier （in Chapter 2）.Calculus is not required for any of the material in this book. College algebra isadequate for the basic chapters. However, although this book is self-contained, some ofthe remaining chapters require more mathematical maturity than do the basic chapters,so calculus is recommended more for giving maturity, than for any direct uses.This book is intended for either a one- or two-term course in discrete mathematics.The first eight chapters of this book provide a foundation in discrete mathematicsand would be appropriate for a first-level course for freshmen or sophomores. Thesechapters are essentially independent, so that the instructor can pick the material he/shewishes to cover. The remainder of the book contains appropriate material for a secofidcourse in discrete mathematics. These chapters expand concepts introduced earlier andintroduce numerous advanced topics. Topics are explored from different points of viewto show how they may be used in different settings. The range of topics include:Logic-Including truth tables, propositional logic, predicate calculus, circuits, induction, and proofs. Set Theory-Including cardinality of sets, relations, partially ordered sets, congruence relations, graphs, directed graphs, and functions.Algorithms-Including complexity of algorithms, search and sort algorithms, theEuclidean algorithm, Huffman's algorithm, Prim's algorithms, Warshall's algorithm, the Ford-Fulkerson algorithm, the Floyd-Warshall algorithm, and Dijkstra'salgorithms.

内容概要

　　用计算机编程解题的核心问题是算法，而组合数学是算法的主要内容。组合数学对于参加信息学奥林匹克活动的青少年而言，是一门提高思维能力、分析与判断能力．以及自我构造算法的重要课程。《离散数学和组合数学》力求将分析问题与自己上机编程结合起来，这样做可以化难为易。书上不但讲了组合数学的原理、概念和分析问题的思路，还讲了如何编程，并给出了参考程序，这对自学《离散数学和组合数学》极为有利。《离散数学和组合数学》是参加信息学奥林匹克竞赛学生的必读书，同时对于一些理工科的大学生也可用作学习编程解题的参考资料。

作者简介

作者：（美国）安德森（James A Anderson）  改编：俞正光 陆玫

书籍目录

序言1　真值表、逻辑和证明　1.1　语句和连接词　1.2　条件语句　1.3　等价语句　1.4　公理系统：论证和证明　1.5　命题逻辑的完备性2　集合论　2.1　集合导引　2.2　集合运算　2.3　Venn图　2.4　布尔代数　2.5　关系　2.6　偏序集　2.7　等价关系　2.8　函数3　逻辑、整数集和证明　3.1　谓词演算　3.2　证明的概念与整数集的结构　3.3　素数　3.4　同余关系4　函数　4.1　特殊函数　4.2　基数　4.3　基数的继续讨论5　算法　5.1　“for”过程与矩阵算法　5.2　递归函数与算法　5.3　算法复杂性6　图、有向图和树　6.1　图　6.2　有向图　6.3　树　6.4　欧拉路和欧拉回路　6.5　关联矩阵和邻接矩阵7　计数　7.1　基本计数原理　7.2　包含排斥原理　7.3　排列与组合　7.4　生成排列与组合　7.5　广义排列与组合　7.6　有重复的排列与组合　7.7　鸽巢原理8　代数结构　8.1　偏序集的进一步讨论　8.2　半群和半格　8.3　格　8.4　群　8.5　群和群同态9　递归的进一步讨论　9.1　齐次线性递归关系　9.2　非齐次线性递归关系　9.3　有限差分　9.4　阶乘多项式　9.5　差分的和10　计数的进一步讨论　10.1　占有问题　10.2　Catalan数　10.3　广义包含排斥与重排　10.4　Rook多项式和禁用位置11　生成函数　11.1　定义生成函数　11.2　生成函数与递归关系　11.3　生成函数与计数　11.4　划分　11.5　指数生成函数12　图论的进一步讨论　12.1　图的代数性质　12.2　平面图　12.3　着色图　12.4　哈密顿路和哈密顿圈　12.5　加权图和最短路算法13　树　13.1　树的性质　13.2　分搜索树　13.3　加权树　13.4　遍历二分树　13.5　生成树　13.6　极小生成树14　网络　14.1　网络和流　14.2　配　14.3　佩特里网15　染色的枚举　15.1　伯恩赛德定理　15.2　波利亚定理16　环、整环和域　16.1　环和整环　16.2　整环　16.3　多项式　16.4　代数和多项式参考文献部分习题答案中英文词汇表

章节摘录

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用户评论 (总计3条)

•   书的质量没问题，而且比较便宜 ，还不错，以后就再网上买书了
•   发货很快...包装不错 很满意
•   我的英文虽然很牛,但是毕竟还是要费点精力才能读下去的.可惜.