離散數學 Discrete Mathematics – 99學年度 | 資訊工程學系易志偉老師

Discrete Mathematics - 99 Academic Year

離散數學 - 99學年度

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課程影音
課程綱要
課程行事曆

1. To demonstrate to students how mathematics can be applied to solve nontrivial real-life problems

2. To gain more experience with mathematical thinking, arguments and proof techniques, which are essential in reasoning about computation

3. To learn about a number of different discrete structures (e.g., sets, relations, graphs, trees, etc.) that provide the mathematical formalizations for many computational problems

4. To hope that students will not only learn some powerful mathematical tools but also develop their ability to perceive, to formulate, and to solve mathematical problems

5. To provide a gateway to more advanced courses in any computer science courses, including data structures, algorithm, database automata theory, computer security, etc.

課程用書：

Kenneth H. Rosen, Discrete Mathematics and Its Applications, 6th ed., McGraw-Hill Inc.

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授課教師	資訊工程學系易志偉老師
課程學分	3學分
授課年度	99學年度
授課對象	大學部
預備知識	無
課程提供	課程影音課程綱要課程行事曆

每頁顯示個資料列

搜尋:

週次	課程內容	課程影音	課程下載
第一週	Logic and Proofs (1/5) 1.1 Proposition Logic 1.2 Proposition Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers	線上觀看	MP4下載
第一週	Logic and Proofs (2/5) 1.1 Proposition Logic 1.2 Proposition Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers	線上觀看	MP4下載
第二週	Logic and Proofs (3/5) 1.1 Proposition Logic 1.2 Proposition Equivalences 1.3 Predicates and Quantifiers 1.4 Nested Quantifiers	線上觀看	MP4下載
第二週	Logic and Proofs (4/5) 1.5 Rules of Inference 1.6 Introduction to Proofs	線上觀看	MP4下載
第三週	Logic and Proofs (5/5) 1.7 Proof Methods and Strategy Sets, Functions, Sequences, and Sums (1/3) Preliminary Test #1 2.1 Sets	線上觀看	MP4下載
第四週	Sets, Functions, Sequences, and Sums (2/3) 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations	線上觀看	MP4下載
第四週	Sets, Functions, Sequences, and Sums (3/3) 2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations	線上觀看	MP4下載
第五週	Algorithms and the Integers (1/4) 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms	線上觀看	MP4下載
第五週	Algorithms and the Integers (2/4) 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms	線上觀看	MP4下載
第五週	Algorithms and the Integers (3/4) 3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms	線上觀看	MP4下載
第七週	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	線上觀看	MP4下載
第七週	Induction and Recur (2/4) 4.1 Mathematical Induction 4.2 Strong Induction and Well-Ordering	線上觀看	MP4下載
第八週	Induction and Recur (3/4) 4.3 Recursive Definitions and Structural Induction 4.4 Recursive Algorithms	線上觀看	MP4下載
第八週	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	線上觀看	MP4下載
第九週	Counting (2/2) 5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.4 Binomial Coefficients 5.5 Generalized Permutations and Combinations	線上觀看	MP4下載
第十一週	Advanced Counting Techniques (1/4) 7.1 Recurrence Relations 7.2 Solving Linear Recurrence Relations	線上觀看	MP4下載
第十二週	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	線上觀看	MP4下載
第十二週	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	線上觀看	MP4下載
第十二週	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	線上觀看	MP4下載
第十四週	Relations (2/4) 8.3 Representing Relations 8.4 Closures of Relations 8.5 Equivalence Relations	線上觀看	MP4下載
第十四週	Relations (3/4) 8.3 Representing Relations 8.4 Closures of Relations 8.5 Equivalence Relations	線上觀看	MP4下載
第十五週	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	線上觀看	MP4下載
第十六週	Graphs (2/3) 9.3 Representing Graphs and Graph Isomorphism 9.4 Connectivity	線上觀看	MP4下載
第十七週	Graphs (3/3) 9.5 Euler and Hamilton Paths 9.6 Shortest-Path Problems	線上觀看	MP4下載

目前顯示第 1 至第 24 個資料列，總計 24 個資料列

課程目標

1. To demonstrate to students how mathematics can be applied to solve nontrivial real-life problems

2. To gain more experience with mathematical thinking, arguments and proof techniques, which are essential in reasoning about computation

3. To learn about a number of different discrete structures (e.g., sets, relations, graphs, trees, etc.) that provide the mathematical formalizations for many computational problems

4. To hope that students will not only learn some powerful mathematical tools but also develop their ability to perceive, to formulate, and to solve mathematical problems

5. To provide a gateway to more advanced courses in any computer science courses, including data structures, algorithm, database automata theory, computer security, etc.

課程書目

Kenneth H. Rosen, Discrete Mathematics and Its Applications, 6th ed., McGraw-Hill Inc.

評分標準

項目	百分比
2 Preliminary Test	20%
2 Midterm	40%
1 Final	35%
Homework, Quizzes and others	10%

本課程行事曆提供課程進度與考試資訊參考。

學期週次	上課日期	參考課程進度
第一週	2011/02/22 & 02/25	1.1 Proposition Logic 1.2 Proposition Equivalences 1.3 Predicates and Quantifiers
第二週	2011/03/01 & 03/04	1.4 Nested Quantifiers 1.5 Rules of Inference 1.6 Introduction to Proofs
第三週	2011/03/08 & 03/11	1.7 Proof Methods and Strategy Preliminary Test #1 2.1 Sets
第四週	2011/03/15 & 03/18	2.2 Set Operations 2.3 Functions 2.4 Sequences and Summations
第五週	2011/03/22 & 03/25	3.4 The Integers and Division 3.5 Primes and Greatest Common Divisors 3.6 Integers and Algorithms
第六週	2011/03/29 & 04/01	Preliminary Test #2 Break
第七週	2011/04/05 & 04/08	3.7 Applications of Number Theory 4.1 Mathematical Induction 4.2 Strong Induction and Well-Ordering
第八週	2011/04/12 & 04/15	4.3 Recursive Definitions and Structural Induction 4.4 Recursive Algorithms 5.1 The Basics of Counting 4.4 Recursive Algorithms
第九週	2011/04/19 & 04/22	5.2 The Pigeonhole Principle 5.3 Permutations and Combinations 5.4 Binomial Coefficients
第十週	2011/04/26 & 04/29	5.5 Generalized Permutations and Combinations Midterm #1 Ch 3.3~3.7 & Ch.4.1~4.4
第十一週	2011/05/03 & 05/06	5.6 Generating Permutations and Combinations 7.1 Recurrence Relations 7.2 Solving Linear Recurrence Relations
第十二週	2011/05/10 & 05/13	7.3 Divide-and-Conquer Algorithms and Recurrence Relations 7.4 Generating Functions 7.5 Inclusion-Exclusion 7.6 Applications of Inclusion-Exclusion
第十三週	2011/05/17 & 05/20	8.1 Relations and Their Properties Midterm #2: Chapter 5,7 (not including 7.3)
第十四週	2011/05/24 & 05/27	8.3 Representing Relations 8.4 Closures of Relations 8.5 Equivalence Relations
第十五週	2011/05/31 & 06/03	8.6 Partial Orderings 9.1 Graphs and Graph Models 9.2 Graph Terminology and Special Types of Graphs
第十六週	2011/06/07 & 06/10	9.3 Representing Graphs and Graph Isomorphism 9.4 Connectivity 9.5 Euler and Hamilton Paths 9.6 Shortest-Path Problems
第十七週	2011/06/14 & 06/17	10.1 Introduction to Trees 10.3 Tree Traversal 10.5 Minimum Spanning Trees
第十八週	2011/06/21 & 06/24	Break Final Exam Chapter 8,9,10