本課程由清大電機系趙啟超教授授課，嚴謹解析離散數學基礎、組合計數與圖論優化等核心內容。這門硬核課程旨在建立紮實的演算法與邏輯思維根基，為資訊工程領域的基礎必修。
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. | |
| ♠ | 想要紮實邏輯卻怕枯燥？跟著清大電機廣受學生推崇的趙啟超教授準沒錯！ |
| 趙老師將以其招牌的嚴謹解析，帶你從離散數學基礎一路過關斬將，直取組合計數與圖論優化核心。 這門資訊工程必修的「硬核」課程，在趙老師的帶領下，將成為你建立演算法思維最過癮的邏輯重訓營！ |
指定用書
Textbook
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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