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计算机科学丛书：组合数学（原书第5版）

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计算机科学丛书：组合数学（原书第5版）

Name: 计算机科学丛书：组合数学（原书第5版）
Brand: Jingdong book
SKU: 3118034361
Price: 34.86 USD
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本书是系统阐述组合数学基础、理论、方法和实例的优秀教材，出版三十多年来多次改版，被MIT、哥伦比亚大学、UIUC、威斯康星大学等众多国外高校采用，对国内外组合数学教学产生了较大影响，也是相关学科的主要参考文献之一。
本书侧重于组合数学的概念和思想，包括鸽巢原理、计数技术、排列与组合、Polya计数法、二项式系数、容斥原理、生成函数和递推关系以及组合结构（匹配、试验设计、图）等，深入浅出地表达了作者对该领域全面和深刻的理解。
自2004年出版第4版以来，作者又对本书进行了全面的修订和更新，第5版增加了有限概率、相异代表系、匹配数等内容。

Content Description

《计算机科学丛书：组合数学（原书第5版）》系统地阐述组合数学基础、理论和方法，侧重于组合数学的概念和思想，论述了鸽巢原理、排列与组合、二项式系数、容斥原理及应用、递推关系和生成函数、特殊计数序列、二分图中的匹配、组合设计、图论、有向图及网络、Polya计数法等。此外，各章均包含大量练习题，并在书末给出了参考答案与提示。
《计算机科学丛书：组合数学（原书第5版）》适合作为高等院校相关专业组合数学课程的教材。

Author Description

Richard A.Brualdi美国威斯康星大学麦迪逊分校数学系教授（现已退休），曾任系主任多年。他的研究方向包括组合数学、图论、线性代数和矩阵理论、编码理论等。Brualdi教授的学术活动非常丰富，担任过多种学术期刊的主编。2000年由于在组合数学研究中所做出的杰出终身成就而获得组合数学及其应用学会颁发的欧拉奖章。

Catalogue

出版者的话
译者序
前言
第1章什么是组合数学
1.1 例子：棋盘的完美覆盖
1.2 例子：幻方
1.3 例子：四色问题
1.4 例子：36军官问题
1.5 例子：最短路径问题
1.6 例子：相互重叠的圆
1.7 例子：Nim游戏
1.8 练习题

第2章排列与组合
2.1 四个基本的计数原理
2.2 集合的排列
2.3 集合的组合（子集）
2.4 多重集合的排列
2.5 多重集合的组合
2.6 有限概率
2.7 练习题

第3章鸽巢原理
3.1 鸽巢原理：简单形式
3.2 鸽巢原理：加强版
3.3 Ramsey定理
3.4 练习题

第4章生成排列和组合
4.1 生成排列
4.2 排列中的逆序
4.3 生成组合
4.4 生成r子集
4.5 偏序和等价关系
4.6 练习题

第5章二项式系数
5.1 帕斯卡三角形
5.2 二项式定理
5.3 二项式系数的单峰性
5.4 多项式定理
5.5 牛顿二项式定理
5.6 再论偏序集
5.7 练习题

第6章容斥原理及应用
6.1 容斥原理
6.2 带重复的组合
6.3 错位排列
6.4 带有禁止位置的排列
6.5 另一个禁止位置问题
6.6 莫比乌斯反演
6.7 练习题

第7章递推关系和生成函数
7.1 若干数列
7.2 生成函数
7.3 指数生成函数
7.4 求解线性齐次递推关系
7.5 非齐次递推关系
7.6 一个几何例子
7.7 练习题

第8章特殊计数序列
8.1 Catalan数
8.2 差分序列和Stirling数
8.3 分拆数
8.4 一个几何问题
8.5 格路径和Schroder数
8.6 练习题

第9章相异代表系
9.1 问题表述
9.2 SDR的存在性
9.3 稳定婚姻
9.4 练习题

第10章组合设计
10.1 模运算
10.2 区组设计
10.3 Steiner三元系
10.4 拉丁方
10.5 练习题

第11章图论导引
11.1 基本性质
11.2 欧拉迹
11.3 哈密顿路径和哈密顿圈
11.4 二分多重图
11.5 树
11.6 Shannon开关游戏
11.7 再论树
11.8 练习题

第12章再论图论
12.1 色数
12.2 平面和平面图
12.3 五色定理
12.4 独立数和团数
12.5 匹配数
12.6 连通性
12.7 练习题

第13章有向图和网络
13.1 有向图
13.2 网络
13.3 回顾二分图匹配
13.4 练习题

第14章 Polya计数
14.1 置换群与对称群
14.2 Burnside定理
14.3 Polya计数公式
14.4 练习题
练习题答案与提示
参考文献
索引

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