離散數學
Discrete Mathematics
| 節 | 週一 |
|---|---|
7 15:30–16:20 | 離散數學 MB312 3 節連堂 |
8 16:30–17:20 | |
9 17:30–18:20 |
* 根據陽明交大上課時間表所列
This course intends to cover four basic areas in the study of computer science: discrete methods, combinatorics, graph theory and finite algebraic structures. We will (1) introduce the topics and techniques of discrete mathematics and combinatorial reasoning; (2) develop the mathematical maturity of the students through the study of an area that is so different from the traditional coverage in calculus and differential equations, and (3) present an adequate survey of topics for the computer science students who will be taking more advanced courses.
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Course Web: https://sites.google.com/view/sjdmath/home?authuser=0
In-class Participation and Homework Assignments: 35% Midterm Exam.: 35% Group Presentation: 35%
- Ch. 1: Basic Principles of Counting
- Ch. 3: Set Theory
- Ch. 4: Properties of Integers
- Ch. 5: Relations and Functions
- Ch. 9: Generating Functions
- Midterm
- Ch. 7: Relations: Second Round
- Ch. 8: The Principle of Inclusion and Exclusion
- Ch. 11: An Introduction to Graph Theory
- Ch. 12: Trees
- Ch. 13: Optimization and Matching
- Ch. 16: Coding Theory
- Ch. 16: Coding Theory
| 週次 | 主題 |
|---|---|
| 第 1 週 | Rules of Sum and Product, Permutations, Combinations |
| 第 2 週 | Combinations, Combinations with Repetition |
| 第 3 週 | Catalan Numbers, Set and Subsets |
| 第 4 週 | Set Operations, Laws of Set Theory, Counting and Venn Diagrams |
| 第 5 週 | Well-Ordering Principle: Mathematical Induction, Recursive Definitions |
| 第 6 週 | Cartesian Products and Relations, Plain, One-to-One and Onto Functions |
| 第 7 週 | Pigeonhole Principle, Composition and Inverse, Computational Complexity |
| 第 8 週 | Generating Functions |
| 第 9 週 | Partitions of Integers, The Exponential Generating Function |
| 第 10 週 | Midterm Exam. |
| 第 11 週 | Properties of Relations, Computer Recognition: 0-1 Matrices and Directed Graphs |
| 第 12 週 | Equivalence Relations and Partitions, Principle of Inclusion and Exclusion |
| 第 13 週 | Subgraphs, Complements, and Graph Isomorphism, Graph Isomorphism, |
| 第 14 週 | Planar Graphs, Hamilton Paths and Cycles; Graph Coloring, Euler Trails and Circuits |
| 第 15 週 | Definition and Examples of Trees, Trees and Sorting, Weighted Trees and Prefix Codes, Dijkstra's Shortest-Path Algorithm |
| 第 16 週 | Trees and Sorting, Weighted Trees and Prefix Codes, Dijkstra’s Shortest-Path Algorithm |
| 第 17 週 | Minimal Spanning Trees: Algorithms of Kruskal and Prim, RSA Cryptosystem |
| 第 18 週 | Elements of Coding Theory, Hamming Metric, Parity-Check and Generator Matrices |
R.P. Grimaldi, Discrete and Combinatorial Mathematics, 5th ED., Addison-Wesley, 2003, Reading, Massachusetts. 新月圖書代理
- 地點
- MB311
- 時間
- 1 GHI
- 聯絡方式
- sjshyu@gmail.com