離散數學
Discrete Mathematics
| 節 | 週一 |
|---|---|
3 10:10–11:00 | 離散數學 EC015 2 節連堂 |
4 11:10–12:00 |
* 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
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
- Chap 2: Sets, Functions, Sequences, and Sums
- Chap 3: Algorithms and the Integers
- Chap 4: Induction and Recursion
- Chap 5: Counting
- Chap 7: Advanced Counting Techniques
- Chap 8: Relations
| 週次 | 主題 |
|---|---|
| 第 1 週 | 1.1 Proposition Logic1.2 Proposition Equivalences1.3 Predicates and Quantifiers |
| 第 2 週 | 1.4 Nested Quantifiers1.5 Rules of Inference1.6 Introduction to Proofs |
| 第 3 週 | 1.7 Proof Methods and Strategy2.1 Sets2.2 Set Operations |
| 第 4 週 | 2.3 Functions2.4 Sequences and Summations3.4 The Integers and Division |
| 第 5 週 | 3.5 Primes and Greatest Common Divisors3.6 Integers and Algorithms |
| 第 6 週 | 3.7 Applications of Number Theory4.1 Mathematical Induction4.2 Strong Induction and Well-Ordering |
| 第 7 週 | 4.3 Recursive Definitions and Structural Induction4.4 Recursive Algorithms |
| 第 8 週 | 5.1 The Basics of Counting5.2 The Pigeonhole Principle5.3 Permutations and Combinations5.4 Binomial Coefficients |
| 第 9 週 | Midterm exam |
| 第 10 週 | 5.5 Generalized Permutations and Combinations |
| 第 11 週 | 5.6 Generating Permutations and Combinations7.1 Recurrence Relations |
| 第 12 週 | 7.2 Solving Linear Recurrence Relations |
| 第 13 週 | 7.3 Divide-and-Conquer Algorithms and Recurrence Relations |
| 第 14 週 | 7.3 Divide-and-Conquer Algorithms and Recurrence Relations7.4 Generating Functions |
| 第 15 週 | 7.6 Applications of Inclusion-Exclusion |
| 第 16 週 | 9.6 Shortest-Path Problems10.1 Introduction to Trees10.2 Applications of Trees |
| 第 17 週 | 8.1 Relations and Their Properties8.2 n-ary Relations and Their Applications8.3 Representing Relations |
| 第 18 週 | Final Exam |
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.