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离散数学(计数)要点讲解.ppt167页
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* 元素i不在自己原来位置上的排列数 * m个元素在自己原来位置上的排列数. * 每个元素都不在原来位置的排列数为 * Exam1:数1，2，…，9的全排列中，求 偶数在原来位置上，其余都不在原来位 置的错排数目。 solu：实际上是1，3，5，7，9五个数 的错排问题，总数为： * Exam2: 在8个字母A,B,C,D,E,F,G,H的全 排列中,求使A,C,E,G四个字母不在原来 上的错排数目。 8个字母的全排列中，令 分别表示A,C,E,G在原来位置上的排列，则错排数为： * * Exam3:求8个字母A,B,C,D,E,F,G,H的全排列中只有4个不在原来位置的排列 数。 solu：8个字母中只有4个不在原来位置 上，其余4个字母保持不动，相当于4个 元素的错排，其数目为 * 故8个字母的全排列中有4个不在原来位置上的排列数应为：C 8,4 ?D4
C 8,4 ?9 630 分类加法计数原理、分步乘法计数原理 * 分类加法计数原理、分步乘法计数原理 * 分类加法计数原理、分步乘法计数原理 * 分类加法计数原理、分步乘法计数原理 * The pigeonhole principle dirichlet drawer principle 鸽巢原理（狄里克雷抽屉 chōu ti?，狄利克雷）德国数学家。 对数论、数学分析和数学物理有突出贡献，是解析数论的创始人之一。 * * * Ramsey
是英国数理逻辑学家,他把抽屉原理加以推广，
* * 杨辉，中国南宋时期杰出的数学家和数学教育家。在13世纪中叶活动于苏杭一带，其著作甚多。 他著名的数学书共五种二十一卷。著有《详解九章算法》十二卷（1261年）、《日用算法》二卷（1262年）、《乘除通变本末》三卷（1274年）、《田亩比类乘除算法》二卷（1275年）、《续古摘奇算法》二卷（1275年）。 他在《续古摘奇算法》中介绍了各种形式的"纵横图"及有关的构造方法，同时"垛积术"是杨辉继沈括"隙积术"后，关于高阶
正在加载中，请稍后...Logic and Proofs (1/5)
1.1 Proposition Logic
1.2 Proposition Equivalences
1.3 Predicates and Quantifiers
1.4 Nested Quantifiers
Logic and Proofs (2/5)
1.1 Proposition Logic
1.2 Proposition Equivalences
1.3 Predicates and Quantifiers
1.4 Nested Quantifiers
Logic and Proofs (3/5)
1.1 Proposition Logic
1.2 Proposition Equivalences
1.3 Predicates and Quantifiers
1.4 Nested Quantifiers
Logic and Proofs (4/5)
1.5 Rules of Inference
1.6 Introduction to Proofs
Logic and Proofs (5/5)
1.7 Proof Methods and Strategy
Sets, Functions, Sequences, and Sums (1/3)
Preliminary Test #1
2.1 Sets　
Sets, Functions, Sequences, and Sums (2/3)
2.2 Set Operations
2.3 Functions
2.4 Sequences and Summations
Sets, Functions, Sequences, and Sums (3/3)
2.2 Set Operations
2.3 Functions
2.4 Sequences and Summations
Algorithms and the Integers (1/4)
3.4 The Integers and Division
3.5 Primes and Greatest Common Divisors
3.6 Integers and Algorithms
Algorithms and the Integers (2/4)
3.4 The Integers and Division
3.5 Primes and Greatest Common Divisors
3.6 Integers and Algorithms
Algorithms and the Integers (3/4)
3.4 The Integers and Division
3.5 Primes and Greatest Common Divisors
3.6 Integers and Algorithms
Algorithms and the Integers (4/4)
3.7 Applications of Number Theory
Induction and Recur (1/4)
4.1 Mathematical Induction
4.2 Strong Induction and Well-Ordering
Induction and Recur (2/4)
4.1 Mathematical Induction
4.2 Strong Induction and Well-Ordering
Induction and Recur (3/4)
4.3 Recursive Definitions and Structural Induction
4.4 Recursive Algorithms
Induction and Recur (4/4)
4.3 Recursive Definitions and Structural Induction
4.4 Recursive Algorithms
Counting (1/2)
5.1 The Basics of Counting
Counting (2/2)
5.2 The Pigeonhole Principle
5.3 Permutations and Combinations
5.4 Binomial Coefficients
5.5 Generalized Permutations and Combinations　
Advanced Counting Techniques (1/4)
7.1 Recurrence Relations
7.2 Solving Linear Recurrence Relations
Advanced Counting Techniques (2/4)
7.4 Generating Functions
Example 1-3
7.5 Inclusion-Exclusion
7.6 Applications of Inclusion-Exclusion
8.1 Relations and Their Properties
8.2 n-ary Relations and Their Applications
Advanced Counting Techniques (3/4)
7.4 Generating Functions
Example 1-3
7.5 Inclusion-Exclusion
7.6 Applications of Inclusion-Exclusion
8.1 Relations and Their Properties
8.2 n-ary Relations and Their Applications
Advanced Counting Techniques (4/4)
7.4 Generating Functions
Example 1-3
7.5 Inclusion-Exclusion
7.6 Applications of Inclusion-Exclusion
Relations (1/4)
8.1 Relations and Their Properties
8.2 n-ary Relations and Their Applications
Relations (2/4)
8.3 Representing Relations
8.4 Closures of Relations
8.5 Equivalence Relations
Relations (3/4)
8.3 Representing Relations
8.4 Closures of Relations
8.5 Equivalence Relations
Relations (4/4)
8.6 Partial Orderings
Graphs(1/3)
9.1 Graphs and Graph Models
9.2 Graph Terminology and Special Types of Graphs
Graphs (2/3)
9.3 Representing Graphs and Graph Isomorphism
9.4 Connectivity
Graphs (3/3)
9.5 Euler and Hamilton Paths
9.6 Shortest-Path Problems
請提供任何對，作為後續改進之參考。浙江大学离散数学2015期末考试题(英文班)_百度文库
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