NCHU Course Outline
Course Name (中) 離散數學專題(一)(5160)
(Eng.) Special Topics in Discrete Mathematics (I)
Offering Dept Department of Applied Mathematics
Course Type Elective Credits 3 Teacher LI WEI TIAN
Department Department of Applied Mathematics (Data Science and Computing Program) / Undergraduate Language Chinese Semester 2025-FALL
Course Description 本課程將介紹離散數學中的極值組合學問題。極值組合學要探討的是有限集合的子集合族所構成的結構，而與集合本身所含的元素的性質無關，一般來說，以{1,2,...,n}做為討論的對象即可。一些經典問題如下：
(1)在集合{1,2,3,...,7}中取出子集合{1,2,4},{1,2,6},{1,3,5},{2,5,6},{4,5,6}，{4,6,7}這些子集合間有甚麼特別的性質?
(2)觀察子集合{1,2},{2,3},{3,7},{1,3,4}{2,5,6},{5,6,7}，它們之間有什麼關聯?
課程中，我們將討論上述類型的集合族問題，學習如何用組合計數方法來解決這些問題。
Prerequisites
Relevance of Course Objectives and Core Learning Outcomes(%) Teaching and Assessment Methods for Course Objectives
Course Objectives Competency Indicators Ratio(%) Teaching Methods Assessment Methods
瞭解以下定理的內涵並且能證明
1. Sperner's Theorem
2. Erdos-Ko-Rado Theorem
3. Kruskal Katona Theorem
4. Hilton-Milner Theorem
5. Oddtown Theorem
6. Turan's Theorem
1.Basic Knowledge in Mathematical Sciences
2.Professional Knowledge in Mathematical Analysis
40
60
topic Discussion / Production
Exercises
Discussion
Lecturing
Attendance
Oral Presentation
Assignment
Course Content and Homework/Schedule/Tests Schedule
Week Course Content
Week 1 Introduction to set systems
Week 2 Sperner’s Theorem (I)
Week 3 Sperner’s Theorem (II)
Week 4 Erdos-Ko-Rado Theorem (I)
Week 5 Erdos-Ko-Rado Theorem (II)
Week 6 Kurskal-Katona Theorem (I)
Week 7 Kurskal-Katona Theorem (II)
Week 8 Hilton-Milner theorem
Week 9 Turan’s Theorem (I)
Week 10 Turan’s Theorem (II)
Week 11 Oddtown Theorem (I)
Week 12 Oddtown Theorem (II)
Week 13 專題報告
Week 14 專題報告
Week 15 專題報告
Week 16 專題報告
self-directed
learning		    03.Preparing presentations or reports related to industry and academia.
由同學尋找與課程相關之研究論文，閱讀整理後進行報告
Evaluation
課堂出席50%
作業成績25%
專題報告25%
Textbook & other References
Extremal Problems for Finite Sets/Peter Frankl and Norihide Tokushige/American Mathematical Society (ISBN 9-781470-440398)
Combinatorics of Finite Sets/Ian Anderson/Dover (ISBN 0-486-42257-7)
Teaching Aids & Teacher's Website

Office Hours
Monday 10:00-11:30
Wednesday 12:00-13:00
Sustainable Development Goals, SDGs(Link URL)
04.Quality Educationinclude experience courses：N
Please respect the intellectual property rights and use the materials and protected electronic files legally. Please respect gender equality.
Update Date, year/month/day：2025/09/11 16:07:54 Printed Date, year/month/day：2026 / 10 / 06
The second-hand book website：http://www.myub.com.tw/