離散數學
Discrete Mathematics
| 節 | 週一 | 週四 |
|---|---|---|
3 10:10–11:00 | 離散數學 EC015（光復） 2 節連堂 | |
4 11:10–12:00 | ||
7 15:30–16:20 | 離散數學 EC015（光復） |
* 根據陽明交大上課時間表所列
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.
basic high school mathematics
無備註
http://www.cis.nctu.edu.tw/~wuuyang/Lecture/lecture.DiscMath.html.
作業部份： 5 homeworks. 考試部份： 1 midterm exam and 1 final exam. 評量部份： (tentative) There will be two exams (40% each) and many short homeworks (15%). Classroom discussion counts as 5% toward the final score.
Chap1: Logic and Proofs
Proposition Logic Proposition Equivalences Predicates and Quantifiers Nested Quantifiers Rules of Inference Introduction to Proofs Proof Methods and Strategy
- 講授：
- 6
Chap 2: Sets, Functions, Sequences, and Sums
Sets Set Operations Functions Sequences and Summations
- 講授：
- 9
Chap 3: Algorithms and the Integers
The Integers and Division Primes and Greatest Common Divisors Integers and Algorithms Applications of Number Theory
- 講授：
- 9
Chap 4: Induction and Recursion
Mathematical Induction Strong Induction and Well-Ordering Recursive Definitions and Structural Induction Recursive Algorithms
- 講授：
- 6
Chap 5: Counting
The Basics of Counting The Pigeonhole Principle Permutations and Combinations Binomial Coefficients Generalized Permutations and Combinations Generating Permutations and Combinations
- 講授：
- 9
Chap 7: Advanced Counting Techniques
Recurrence Relations Solving Linear Recurrence Relations Divide-and-Conquer Algorithms and Recurrence Relations Generating Functions Inclusion-Exclusion Applications of Inclusion-Exclusion
- 講授：
- 9
Chap 8: Relations
Relations and Their Properties n-ary Relations and Their Applications Representing Relations Closures of Relations Equivalence Relations Partial Orderings
- 講授：
- 6
| 週次 | 主題 |
|---|---|
| 第 1 週 | 1.1 Proposition Logic1.2 Proposition Equivalences1.3 Predicates and Quantifiers 2026-02-23(一),2026-02-26(四) |
| 第 2 週 | 1.4 Nested Quantifiers1.5 Rules of Inference1.6 Introduction to Proofs 2026-03-02(一),2026-03-05(四) |
| 第 3 週 | 1.7 Proof Methods and Strategy2.1 Sets2.2 Set Operations 2026-03-09(一),2026-03-12(四) |
| 第 4 週 | 2.3 Functions2.4 Sequences and Summations3.4 The Integers and Division 2026-03-16(一),2026-03-19(四) |
| 第 5 週 | 3.5 Primes and Greatest Common Divisors3.6 Integers and Algorithms 2026-03-23(一),2026-03-26(四) |
| 第 6 週 | 3.7 Applications of Number Theory4.1 Mathematical Induction4.2 Strong Induction and Well-Ordering 2026-03-30(一),2026-04-02(四) |
| 第 7 週 | 4.3 Recursive Definitions and Structural Induction4.4 Recursive Algorithms 2026-04-06(一),2026-04-09(四) |
| 第 8 週 | 5.1 The Basics of Counting5.2 The Pigeonhole Principle5.3 Permutations and Combinations5.4 Binomial Coefficients 2026-04-13(一),2026-04-16(四) |
| 第 9 週 | Midterm exam 2026-04-20(一),2026-04-23(四) |
| 第 10 週 | 5.5 Generalized Permutations and Combinations 2026-04-27(一),2026-04-30(四) |
| 第 11 週 | 5.6 Generating Permutations and Combinations7.1 Recurrence Relations 2026-05-04(一),2026-05-07(四) |
| 第 12 週 | 7.2 Solving Linear Recurrence Relations 2026-05-11(一),2026-05-14(四) |
| 第 13 週 | 7.3 Divide-and-Conquer Algorithms and Recurrence Relations 2026-05-18(一),2026-05-21(四) |
| 第 14 週 | 7.3 Divide-and-Conquer Algorithms and Recurrence Relations7.4 Generating Functions 2026-05-25(一),2026-05-28(四) |
| 第 15 週 | 7.6 Applications of Inclusion-Exclusion 2026-06-01(一),2026-06-04(四) |
| 第 16 週 | 9.6 Shortest-Path Problems10.1 Introduction to Trees10.2 Applications of Trees 2026-06-08(一),2026-06-11(四) |
| 第 17 週 | 8.1 Relations and Their Properties8.2 n-ary Relations and Their Applications8.3 Representing Relations 2026-06-15(一),2026-06-18(四) |
| 第 18 週 | Final Exam 2026-06-22(一),2026-06-25(四) |
Kenneth H. Rosen, Discrete Mathematics and Its Applications, 8th ed., 2018, McGraw-Hill Inc.
- 地點
- EC 332B (my office).
- 時間
- 2CD
- 聯絡方式
- office phone: 03-5712121 ext 56614. email: wuuyang@cs.nctu.edu.tw.