離散數(shù)學(xué)

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．a(chǎn)nd 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．

內(nèi)容概要

為適應(yīng)當(dāng)前我國高校各類創(chuàng)新人才培養(yǎng)的需要，大力推進(jìn)教育部倡導(dǎo)的雙語教學(xué)，配合教育部實(shí)施的“高等學(xué)校教學(xué)質(zhì)量與教學(xué)改革工程”和“精品課程”建設(shè)的需要，我社開始有計(jì)劃、大規(guī)模地開展了海外優(yōu)秀理科系列教材的影印及改編工作。海外優(yōu)秀教材在立體化配套、多種教學(xué)資源的整合以及為課程提供整體教學(xué)解決方案等方面對(duì)我們有不少可資借鑒之處。但一個(gè)不容忽視的問題是，外版教材與我國現(xiàn)行的教學(xué)內(nèi)容、教學(xué)體系、教學(xué)模式和習(xí)慣等存在著巨大的差異。譬如，重點(diǎn)課程的原版教材通常很厚，內(nèi)容很多，容量是國內(nèi)自編教材的好幾倍，國外的情況是，老師未必會(huì)都講，剩下大量的內(nèi)容留給學(xué)生自學(xué)；而國內(nèi)的情況則不盡相同。受國內(nèi)教學(xué)學(xué)時(shí)所限，完全照搬是不合時(shí)宜的。教材的國際化必須與本民族的文化教育傳統(tǒng)相融合，在原有的基礎(chǔ)上吸收國外優(yōu)秀教材的長處，這使得我們需要對(duì)外文原版教材進(jìn)行適當(dāng)?shù)母木?。改編不是?jiǎn)單地使內(nèi)容增刪，而是結(jié)合國內(nèi)教學(xué)特點(diǎn)，引進(jìn)國外先進(jìn)的教學(xué)思想，在教學(xué)內(nèi)容和方式上更中國化，使之更符合國內(nèi)的課程設(shè)置及教學(xué)環(huán)境。

書籍目錄

序言致讀者1　組合問題與方法人門  1.1　完成作業(yè)的時(shí)間  1.2　匹配問題  1.3　背包問題  1.4　算法及其效率　歷史注記　補(bǔ)充習(xí)題　計(jì)算機(jī)作業(yè)　進(jìn)一步讀物2　集合、關(guān)系與函數(shù)  2.1　集合運(yùn)算  2.2　等價(jià)關(guān)系  2.3　同余  2.4　函數(shù)  2.5　數(shù)學(xué)歸納法  2.6　應(yīng)用　歷史注記　補(bǔ)充習(xí)題　計(jì)算機(jī)作業(yè)　進(jìn)一步讀物3　圖論　  3.1　圖及其表示  3.2　路和圈  3.3　最短路和距離  3.4　圖的著色  3.5　有向圖和多重圖　歷史注記　補(bǔ)充習(xí)題　計(jì)算機(jī)作業(yè)　進(jìn)一步讀物4　樹  4.1　樹的性質(zhì)  4.2　生成樹  4.3　深度優(yōu)先搜索  4.4　有根樹  4.5　二分樹及遍歷  4.6　最優(yōu)二分樹及二分搜索樹　歷史注記　補(bǔ)充習(xí)題　計(jì)算機(jī)作業(yè)　進(jìn)一步讀物5　計(jì)數(shù)方法　  5.1　帕斯卡三角形與二項(xiàng)式定理  5.2　三個(gè)基本原理  5.3　排列與組合  5.4　排列及有重復(fù)排列　歷史注記　補(bǔ)充習(xí)題　計(jì)算機(jī)作業(yè)　進(jìn)一步讀物6　遞推關(guān)系與生成函數(shù)  6.1　遞推關(guān)系  6.2　迭代法  6.3　常系數(shù)線性差分方程  6.4　用生成函數(shù)計(jì)數(shù)……7　組合同路與有限狀態(tài)機(jī)附錄A　邏輯與證明簡(jiǎn)介附錄B　本書的算法參考文獻(xiàn)部分習(xí)題答案中英文詞匯表

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