Type of Credit: Partially Required
Credit(s)
Number of Students
This is the second half of a one-year course which has the aim of giving an introduction into combinatorics, a relativ new area of mathematics. Even though some of its problems have been investigated many centuries ago, a systematic development as an independent area of mathematics has started in the middle of the last century (with the notable exception of Graph Theory). Modern combinatorics uses tools from many other areas of mathematics, e.g., topology, algebra, probability theory, analysis, etc. It has many applications, notable in Computer Science, Information Theory, Probability Theory and Biology.
能力項目說明
Getting aquainted with some of the basic tools, theorems and subareas of Combinatorics; this semester will focus on graph theory and extremal combinatorics.
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
In-class Hours: 3; Outside-of-class Hours: 5
Syllabus:
1. Graphs and Trees
2. Graphs and Trees
3. Graphs and Trees
4. Colorings of Graphs and Ramsey's Theorem
5. Colorings of Graphs and Ramsey's Theorem
6. Systems of Distinct Representatives
7. Dilworth's Theorem and Extremal Set Theory
8. Midterm Exam
9. Latin Squares
10. Latin Squares
11. Hadamard Matrices and Reed-Muller Codes
12. Hadamard Matrices and Reed-Muller Codes
13. Designs
14. Designs
15. Designs
16. Codes and Designs
17. Final Exam
Weekly Homework Assignments: 60%
Midterm Exam: 20%
Final Exam: 20%