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 英文/EMI N Semester 2025-FALL
Course Description 本課程將介紹離散數學中的極值組合問題。我們感興趣的是有限集合的子集合族所構成的結構。
例如：在集合{1,2,3,...,7}中的這些子集合{1,2,4},{1,3,5},{1,2,6},{2,5,6},{4,5,6}，有甚麼特別的性質?
又如果觀察子集合{1,2},{2,3},{3,7},{1,3,4}{2,5,6},{5,6,7}，它們之間又有什麼關聯?
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
self-directed learning in the course Y
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. Ahlswede-Khachatrian Theorem
6. Turan's Theorem
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 Ahlswede-Khachatrian Theorem (I)
Week 10 Ahlswede-Khachatrian Theorem (II)
Week 11 Erdos-Matching Conjecture (I)
Week 12 Erdos-Matching Conjecture (II)
Week 13 Turan’s Theorem (I)
Week 14 Turan’s Theorem (II)
Week 15 專題報告
Week 16 專題報告
自主學習，於學期中安排學術演講並規定選課同學聆聽
9/9 14:00-15:50 與 9/10 10:10-11:50 有相關之微型課程

自主學習，於學期中安排學術演講並規定選課同學聆聽
self-directed
learning		    01.Participation in professional forums, lectures, and corporate sharing sessions related to industry-government-academia-research exchange activities.
   02.Viewing multimedia materials related to industry and academia.
   03.Preparing presentations or reports related to industry and academia.
   04.Participation in visits or internships at industry, government, or academic institutions.
   05.Participation in various workshops organized by different departments of NCHU.
   06.Participation in field trips and outdoor instructional activities at other NCHU campuses or branches, including experimental forests or test sites.
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
Wednesday 12:00-13:00
Thursday 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 legally.Please respect gender equality.
Update Date, year/month/day：2025/06/26 15:17:06 Printed Date, year/month/day：2025 / 7 / 04
The second-hand book website：http://www.myub.com.tw/