離散數學
Discrete Mathematics
| 節 | 週三 |
|---|---|
2 09:00–09:50 | 離散數學 ED220 3 節連堂 |
3 10:10–11:00 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
Course Description: This course provides a comprehensive introduction to Discrete Mathematics, the fundamental language of Computer Science and Information Engineering. Unlike Calculus, which deals with continuous data, Discrete Mathematics focuses on distinct, separable structures. The curriculum guides students through logic and proofs, induction, number theory, relations, graph theory, counting techniques, and finite automata. Students will learn to model real-world challenges using discrete mathematical structures and apply rigorous reasoning to solve computational problems. Course Objectives: 1. Logical Rigor: To master logical reasoning and various proof techniques, including mathematical induction, as a basis for algorithmic thinking. 2. Structural Modeling: To understand and apply fundamental discrete structures such as sets, functions, and relations. 3. Number Theory: To explore the properties of integers and modular arithmetic, especially their applications in cryptography and network security. 4. Graph Theory: To analyze networks and trees, applying them to solve optimization and connectivity problems. 5. Combinatorics: To develop systematic counting skills for analyzing complexity and probability in discrete systems. 6. Theory of Computation: To introduce the basics of automata theory and deterministic finite state machines.
High School Mathematics: Algebra and basic sequences. Strong logical reasoning skills. Basic programming knowledge is helpful but not required.
* 4 Individual Assignments (40%) * Midterm Exam (25%) * Final Exam (35%)
| 週次 | 主題 |
|---|---|
| 第 1 週 | Fundamentals of Discrete Mathematics |
| 第 2 週 | Logic and Proof (I): Language for Proofs [A1 Release] |
| 第 3 週 | Logic and Proof (II): Proof Techniques |
| 第 4 週 | Logic and Proof (III): Quantifiers |
| 第 5 週 | Number Theory (I) [A2 Release] |
| 第 6 週 | Number Theory (II) |
| 第 7 週 | Basic Structures |
| 第 8 週 | Midterm Exam |
| 第 9 週 | Graph Theory (I) [A3 Release] |
| 第 10 週 | Graph Theory (II) |
| 第 11 週 | Graph Theory (III) |
| 第 12 週 | Counting Theory (I) [A4 Release] |
| 第 13 週 | Counting Theory (II) |
| 第 14 週 | Counting Theory (III) |
| 第 15 週 | Automaton |
| 第 16 週 | Final Exam |
Eric Lehman, F. Thomson Leighton, and Albert R. Meyer. Mathematics for Computer Science.
- 地點
- ED220[GF]
- 時間
- W234