離散數學
Discrete Mathematics
學期
110-2
學分
3
學分
當期課號
1179
永久課號
DCP2353
開課單位
資訊學院共同課程
授課教師
紀虹名
校區
光復
類別
必修
上課時間表
| 節 | 週五 |
|---|---|
3 10:10–11:00 | 離散數學 EC022 2 節連堂 |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
概述
This course will teach students to think logically and mathematically, including logic and proofs, sets and matrices, algorithms, number theory, recursion, counting, discrete probability, relations, and graphs. Students learn this mathematical reasoning and how to apply them. Based on this course, students can learn more advanced courses in the future, such as computer architecture, data structures, and artificial intelligence.
先修科目
None
評分方式
Two homework, each 10% Midterm examination, 40% Final examination, 40%
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | Proposition Logic Propositional Equivalences Predicates and Quantifiers |
| 第 2 週 | Nested Quantifiers Rules of Inference Introduction to Proofs |
| 第 3 週 | Proof Methods and Strategy Sets Set Operations |
| 第 4 週 | Functions Sequences and Summations |
| 第 5 週 | Algorithms Integer Representations and Algorithms Primes and Greatest Common Divisors |
| 第 6 週 | Mathematical Induction Strong Induction and Well-Ordering |
| 第 7 週 | Recursive Definitions and Structural Induction Recursive Algorithms |
| 第 8 週 | Midterm Exam |
| 第 9 週 | The Basics of Counting The Pigeonhole Principle Permutations and Combinations |
| 第 10 週 | Binomial Coefficients and Identities Generalized Permutations and Combinations Generating Permutations and Combinations |
| 第 11 週 | Applications of Recurrence Relations Solving Linear Recurrence Relations |
| 第 12 週 | Divide-and-Conquer Algorithms and Recurrence Relations Generating Functions Inclusion-Exclusion Applications of Inclusion-Exclusion |
| 第 13 週 | Relations and Their Properties n-ary Relations and Their Applications |
| 第 14 週 | Representing Relations Closures of Relations Equivalence Relations |
| 第 15 週 | Partial Orderings Graphs and Graph Models Graph Terminology and Special Types of Graphs |
| 第 16 週 | Representing Graphs and Graph Isomorphism Connectivity |
| 第 17 週 | Euler and Hamilton Paths Shortest-Path Problems |
| 第 18 週 | Final Exam |
教科書
K. H. Rosen, "Discrete Mathematics and Its Applications," 8th edition, 2019.
Office Hours
- 地點
- EE235A
- 時間
- d00022@nycu.edu.tw