Combinatorics

主讲人 Speaker:Prof. Jie Ma (USTC)
时间 Time:Tues.19:20-20:55, Thur.9:50-11:25, May 10 - July 14, 2022
地点 Venue:Zoom Meeting ID: 271 534 5558 Passcode: YMSC

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:

 ClassNotes.pdf Lecture1-0510.pdf   Lecture2-0512.pdf  Lecture 4.pdf  2022_5_24_note.pdf  Lecture 5.pdf


Videos:

Lecture 1 (May10):

Lecture 2 (May12):

Lecture 3 (May17):

Lecture 4 (May19):

Lecture 5 (May24):