離散數學
Discrete Mathematics
| 節 | 週一 |
|---|---|
8 16:30–17:20 | 離散數學 MB311 |
A 18:30–19:20 | 離散數學 MB311 2 節連堂 |
B 19:30–20:20 |
* 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 shall (1) introduce the fundamentals and techniques of discrete mathematics and combinatorial reasoning that are so different from the traditional coverage in calculus and differential equations; (2) develop the mathematical maturity of the students by bridging the real world problems and the combinatorial implications, and (3) present adequate modern research topic/open problems and encourage master students to explore and investigate.
無
Course site: https://sites.google.com/view/sjdmath
1學期作業 平時作業、程式作業若干次 2.考試狀況 小考、期中考 3.評量方法 平時作業、小考與上課參與:35%、期中考:35%、分組報告: 30%
- Ch. 1: Basic Principles of Counting
- Ch. 3: Set Theory
- Ch. 4: Properties of Integers
- Ch. 5: Relations and Functions
- Ch. 7: Relations: Second Round
- Ch. 8: The Principle of Inclusion and Exclusion
- Ch. 9: Generating Functions
- Ch. 11: An Introduction to Graph Theory
- Ch. 13: Optimization and Matching
- Ch. 14: Ring and Modular Arithmetic
- Ch 17: Finite Fields and Combinatorial Designs
| 週次 | 主題 |
|---|---|
| 第 1 週 | Rules of Sum and Product, Permutations, Combinations |
| 第 2 週 | Combinations, Combinations with Repetition, Binomial theorem |
| 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 | Properties of Relations, Computer Recognition: 0-1 Matrices and Directed Graphs |
| 第 11 週 | Midterm Exam. |
| 第 12 週 | Equivalence Relations and Partitions, Principle of Inclusion and Exclusion |
| 第 13 週 | Subgraphs, Complements, and Graph Isomorphism, Graph Isomorphism, Planar Graphs, Hamilton Paths and Cycles; Graph Coloring, Euler Trails and Circuits |
| 第 14 週 | Definition and Examples of Trees, Trees and Sorting, Weighted Trees and Prefix Codes, Dijkstra's Shortest-Path Algorithm |
| 第 15 週 | Minimal Spanning Trees: Algorithms of Kruskal and Prim |
| 第 16 週 | Rings, Modular arithmetic, Boolean algebra |
| 第 17 週 | Group, Polynomial rings, Hamming matrices |
| 第 18 週 | Irreducible Polynomials, Finite Fields, Latin squares |
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
- Monday EFG
- 聯絡方式
- sjshyu@gmail.com