Introduction to combinatorics – 109 Academic Year
This course is provided by the NYCU Department of Applied Mathematics .
This is an introductory course of Combinatorics. Based on the courses we have in this department for the first semester, we shall focus on the introduction of the following topics: combinatorial optimization, enumerative combinatorics and additive combinatorics.
Textbook：
Lecture Notes by Hung-Lin Fu.
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| Instructor(s) | Department of Applied Mathematics Prof. Hung-Lin Fu |
|---|---|
| Course Credits | 3 Credits |
| Academic Year | 109 Academic Year |
| Level | Master student |
| Prior Knowledge | Linear Algebra, Discrete Mathematics |
| Related Resources | Course Video Course Syllabus Course Handout |
| Week | Course Content | Course Video | Course Download |
|---|---|---|---|
| Introduction to Combinatorics | Watch Online | MP4 Download | |
| Subgraphs in Simple Graphs 1 | Watch Online | MP4 Download | |
| Subgraphs in Simple Graphs 2 | Watch Online | MP4 Download | |
| Eulerian Circuits and Hamilton Cycles 1 | Watch Online | MP4 Download | |
| Eulerian Circuits and Hamilton Cycles 2 | Watch Online | MP4 Download | |
| Connectivity | Watch Online | MP4 Download | |
| Topological Graph Theory | Watch Online | MP4 Download | |
| Vertex Coloring | Watch Online | MP4 Download | |
| Ramsey Theory 1 | Watch Online | MP4 Download | |
| Ramsey Theory 2 | Watch Online | MP4 Download | |
| Edge-coloring | Watch Online | MP4 Download | |
| Extremal Set Theory | Watch Online | MP4 Download | |
| Block Design 1 | Watch Online | MP4 Download | |
| Block Design 2 | Watch Online | MP4 Download | |
| Latin Square 1 | Watch Online | MP4 Download | |
| Latin Square 2 | Watch Online | MP4 Download | |
| Latin Square 3 | Watch Online | MP4 Download | |
| Latin Square 4 | Watch Online | MP4 Download | |
| Principle of Counting 1 | Watch Online | MP4 Download | |
| Principle of Counting 2 & Generating Function 1 | Watch Online | MP4 Download | |
| Generating Function 2 | Watch Online | MP4 Download | |
| Sum set in Additive Combinatorics 1 | Watch Online | MP4 Download | |
| Sum set in Additive Combinatorics 2 | Watch Online | MP4 Download | |
| Sum set in Additive Combinatorics 3 | Watch Online | MP4 Download | |
| Probabilistic Method (Graphs) | Watch Online | MP4 Download | |
| Random Graphs | Watch Online | MP4 Download | |
| Combinatorial Optimization 1 | Watch Online | MP4 Download | |
| Combinatorial Optimization 2 | Watch Online | MP4 Download | |
| Application of max-flow min-cut theorem | Watch Online | MP4 Download |
課程目標
This is an introductory course of Combinatorics. Based on the courses we have in this department for the first semester, we shall focus on the introduction of the following topics: combinatorial optimization, enumerative combinatorics and additive combinatorics.
課程章節
| 單元主題 |
| 組合學導論簡介 |
| 簡單圖中的子圖 1 |
| 簡單圖中的子圖 2 |
| 歐拉迴路和漢米爾頓圈 1 |
| 歐拉迴路和漢米爾頓圈 2 |
| 連通度 |
| 拓撲圖論 |
| 點著色 |
| 拉姆齊定理 1 |
| 拉姆齊定理 2 |
| 邊著色 |
| 極集合論 |
| 區組設計 1 |
| 區組設計 2 |
| 拉丁方陣 1 |
| 拉丁方陣 2 |
| 拉丁方陣 3 |
| 拉丁方陣 4 |
| 反證歐拉猜想 |
| 計數原理1 |
| 計數原理 2 &生成函數 1 |
| 生成函數 2 |
| 加法組合學 1 |
| 加法組合學 2 |
| 加法組合學 3 |
| 在圖論上的機率方法 |
| 隨機圖 |
| 組合最優化 1 |
| 組合最優化 2 |
| 最大流最小割定理的應用 |
課程書目
Lecture Notes by Hung-Lin Fu.
課程講義 Course Handout
| 章節 | 下載連結 |
| Introductory Combinatorics | |
| Combinatorics, L00 | |
| Combinatorics, L01 | |
| Combinatorics, L02 | |
| Combinatorics, L03 | |
| Combinatorics, L04 | |
| Combinatorics, L05 | |
| Combinatorics, L06 | |
| Combinatorics, L07 | |
| Combinatorics, L08 | |
| Combinatorics, L09 | |
| Combinatorics, L10 | |
| Combinatorics, L11 | |
| Combinatorics, L12 | |
| Combinatorics, L13 | |
| Combinatorics, L14 | |
| Combinatorics, L15 | |
| Combinatorics, L16 |
COURSE
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