Combinatorics

Speaker:Prof. Jie Ma (USTC)
Schedule:Tues.19:20-20:55, Thur.9:50-11:25, May 10 -May 26;Tues.19:20-21:45, May 31-July 12 (updated)
Venue:Zoom Meeting ID: 271 534 5558 Passcode: YMSC
Date:2022-05-10~2022-07-12

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