Note：The course will be delivered on Tuesdays, 19:20-21:45, from May31,2022.

Prerequisites: 

Calculus, Linear Algebra, and some basic algebra (groups, rings and fields). 

Covered Materials: 

We will give a broad introduction to combinatorics. The tentative schedule is as following: 

(1). Enumeration (counting, generating functions, inclusion-exclusion and so on) 

(2). Applications of basic methods (double-counting and pigeonhole principle) 

(3). Basics on graphs (trees) 

(4). Extremal combinatorics (Erdös-Ko-Rado, Turán's Theorem, Ramsey's Theorem) 

(5). Partially Ordered Sets 

(6). Probabilistic methods 

(7). Algebra methods 

(8). Spectral methods 

Textbook: 

We do not have any assigned textbook and will update class notes during the term. However, the following books can be used as references, which should be very helpful. 

• Invitation to Discrete Mathematics, by Jiri Matousek and Jaroslav Nesetril, Oxford University Press 

• Proofs from the book, by Martin Aigner and Gunter M. Ziegler, Springer 

• Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra, by Jiri Matousek, American Mathematical Society

Note: Please register through the following link.

报名链接：https://www.wjx.cn/vj/Q0BxFS5.aspx 

课程微信群：

Notes：

 2022_note_final.pdf  Lecture1-0510.pdf  Lecture2-0512.pdf  Lecture3-0517.pdf Lecture 4.pdf   Lecture 5.pdf   Lecture 6.pdf  Lecture 7.pdf   Lecture 8.pdf  Lecture 9.pdf  Lecture 10.pdf   Lecture 11.pdf   Lecture 12.pdf   Lecture 13.pdf

Videos：

Lecture 1 (May10）：

Lecture 2 (May12）：

Lecture 3 (May17）：

Lecture 4 (May19）：

Lecture 5 (May24）：

Lecture 6 (May26）：

Lecture7-13（May31-July12）：

http://archive.ymsc.tsinghua.edu.cn/pacm_course?html=combinatorics.html