Copyright 2023 - All Right Reserved
Discrete Mathematics - 99 Academic Year

離散數學 - 99學年度

本課程是由 國立陽明交通大學資訊工程學系 提供。

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.

為求學習成效完美，請購買課本！

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  

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

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 Test20%
2 Midterm40%
1 Final35%
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
課程專區
©2024- NYCU OCW