國立清華大學電機工程學系 特聘教授
美國加州理工學院 博士
| 【經歷】 | 國立清華大學81、90、96校傑出教學獎 |
| 【網站】 | |
| 【授課】 | 通訊系統、錯誤更正碼、線性代數、離散數學 |
| 【專長】 | 數位通訊、錯誤更正碼、訊息理論、無線網路 |
授課老師
課程試聽
趙啟超 教授
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課程大綱
This course gives an introduction to the essentials of discrete and combinatorial mathematics.
【先修課程】
Prerequisites
| ♠ | High-school mathematics, Calculus (preferred). |
【課程說明】
Course Description
| ♠ | This course gives an introduction to the essentials of discrete and |
| combinatorial mathematics. |
【指定用書】
Textbook
| ♠ | R. P. Grimaldi, Discrete and Combinatorial Mathematics: |
| An Applied Introduction, 5th ed. Boston: Pearson Addison Wesley, | |
| 2004. |
【參考書籍】
References
【課程內容】
Course Contents
| Fundamentals | |
| ♠ Logic | |
| ♠ Set theory | |
| ♠ Mathematical induction | |
| ♠ Functions: definitions, pigeonhole principle | |
| ♠ Relations: definitions and properties, equivalence | |
| relations, partial orders | |
| Enumeration | |
| ♠ Principles of counting | |
| ♠ Principle of inclusion and exclusion | |
| ♠ Recurrence relations: homogeneous recurrence relations, | |
| nonhomogeneous recurrence relations | |
| ♠ Generating functions: generating functions for solving recurrence relations, generating functions for | |
| partitions of integers | |
| ♠ Complexity of algorithms | |
| Graph Theory | |
| ♠ Introduction: definitions and properties, graph isomorphism, | |
| Euler trails and circuits, planar graphs | |
| ♠ Trees: definitions and properties, rooted trees, | |
| spanning trees, trees and sorting | |
| ♠ Optimization and matching: shortest-path problem, | |
| minimal spanning trees, matching problem, | |
| maximum flow problem | |
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- 離散數學(Discrete Mathematics)
- 組合數學(combinatorial mathematics)
- 計數(enumeration)
- 圖論(graph theory)
