离散数学

出版时间：2005-7  出版社：高等教育出版社  作者：多塞  页数：462  字数：550000  

前言

　　Today art increasing proportion of the applications of mathematics involves discrete rather than continuous models．The main reason for this trend is the integration of the computer into more and more of modem society．This book iS intended for a one-semester introductory course in discrete mathematics． Prerequisites Even though a course taught from this book requires few formal mathematical prerequisites，students are assumed to have the mathematical matu- rity ordinarily obtained by taking at least two years of high school mathematics， including problem-solving and algorithmic skills，and the ability to think abstractly． Approach This book has a strong algorithmic emphasis that serves to unify the material．Algorithms are presented in English SO that knowledge of a particular programming language IS not required. Choice of Topics The choice of topics is based upon the recommendations of Var- iOUS professional organizations．including those of the MAAS Panel on Discrete Mathematics in the First Two YearS，the NCTM’S Princ咖les and Standards for School Mathematics．and the CBMS’S recommendations for the mathematical ed- ucation of teachers． Ftexibility　A、though designed for a one．semester course、the book containS more material than Can be covered in either one semester or two quarters．Consequently, instructors will have considerable freedom to choose topics tailored to the particu- lar needs and interests of their students．Users of previous editions have reported　considerable success in courses ranging from freshman．1evel courses for computer　science students to upper-level courses for mathematics majors．The present edition　continues to allow instructors the flexibility to devise a course that iS appropriate for　a variety of different types of students．

内容概要

为适应当前我国高校各类创新人才培养的需要，大力推进教育部倡导的双语教学，配合教育部实施的“高等学校教学质量与教学改革工程”和“精品课程”建设的需要，我社开始有计划、大规模地开展了海外优秀理科系列教材的影印及改编工作。海外优秀教材在立体化配套、多种教学资源的整合以及为课程提供整体教学解决方案等方面对我们有不少可资借鉴之处。但一个不容忽视的问题是，外版教材与我国现行的教学内容、教学体系、教学模式和习惯等存在着巨大的差异。譬如，重点课程的原版教材通常很厚，内容很多，容量是国内自编教材的好几倍，国外的情况是，老师未必会都讲，剩下大量的内容留给学生自学；而国内的情况则不尽相同。受国内教学学时所限，完全照搬是不合时宜的。教材的国际化必须与本民族的文化教育传统相融合，在原有的基础上吸收国外优秀教材的长处，这使得我们需要对外文原版教材进行适当的改编。改编不是简单地使内容增删，而是结合国内教学特点，引进国外先进的教学思想，在教学内容和方式上更中国化，使之更符合国内的课程设置及教学环境。

书籍目录

序言致读者1　组合问题与方法人门  1.1　完成作业的时间  1.2　匹配问题  1.3　背包问题  1.4　算法及其效率　历史注记　补充习题　计算机作业　进一步读物2　集合、关系与函数  2.1　集合运算  2.2　等价关系  2.3　同余  2.4　函数  2.5　数学归纳法  2.6　应用　历史注记　补充习题　计算机作业　进一步读物3　图论　  3.1　图及其表示  3.2　路和圈  3.3　最短路和距离  3.4　图的着色  3.5　有向图和多重图　历史注记　补充习题　计算机作业　进一步读物4　树  4.1　树的性质  4.2　生成树  4.3　深度优先搜索  4.4　有根树  4.5　二分树及遍历  4.6　最优二分树及二分搜索树　历史注记　补充习题　计算机作业　进一步读物5　计数方法　  5.1　帕斯卡三角形与二项式定理  5.2　三个基本原理  5.3　排列与组合  5.4　排列及有重复排列　历史注记　补充习题　计算机作业　进一步读物6　递推关系与生成函数  6.1　递推关系  6.2　迭代法  6.3　常系数线性差分方程  6.4　用生成函数计数……7　组合同路与有限状态机附录A　逻辑与证明简介附录B　本书的算法参考文献部分习题答案中英文词汇表