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.
For perfect learning results, please buy textbooks!
| 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 |
|---|---|---|
| Introduction to Combinatorics | Watch Online | |
| Subgraphs in Simple Graphs 1 | Watch Online | |
| Subgraphs in Simple Graphs 2 | Watch Online | |
| Eulerian Circuits and Hamilton Cycles 1 | Watch Online | |
| Eulerian Circuits and Hamilton Cycles 2 | Watch Online | |
| Connectivity | Watch Online | |
| Topological Graph Theory | Watch Online | |
| Vertex Coloring | Watch Online | |
| Ramsey Theory 1 | Watch Online | |
| Ramsey Theory 2 | Watch Online | |
| Edge-coloring | Watch Online | |
| Extremal Set Theory | Watch Online | |
| Block Design 1 | Watch Online | |
| Block Design 2 | Watch Online | |
| Latin Square 1 | Watch Online | |
| Latin Square 2 | Watch Online | |
| Latin Square 3 | Watch Online | |
| Latin Square 4 | Watch Online | |
| Principle of Counting 1 | Watch Online | |
| Principle of Counting 2 & Generating Function 1 | Watch Online | |
| Generating Function 2 | Watch Online | |
| Sum set in Additive Combinatorics 1 | Watch Online | |
| Sum set in Additive Combinatorics 2 | Watch Online | |
| Sum set in Additive Combinatorics 3 | Watch Online | |
| Probabilistic Method (Graphs) | Watch Online | |
| Random Graphs | Watch Online | |
| Combinatorial Optimization 1 | Watch Online | |
| Combinatorial Optimization 2 | Watch Online | |
| Application of max-flow min-cut theorem | Watch Online |
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
Menu
