Combinatorics

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_5_30note.pdf Lecture1-0510.pdf Lecture2-0512.pdf Lecture3-0517.pdf Lecture 4.pdf Lecture 5.pdf Lecture 6.pdf Lecture 7.pdf

Videos：

Lecture 1 (May10）：

Lecture 2 (May12）：

Lecture 3 (May17）：

Lecture 4 (May19）：

Lecture 5 (May24）：

Lecture 6 (May26）：