Calculus, Linear Algebra, and some basic algebra (groups, rings and fields).
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
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.
ClassNotes.pdf Lecture1-0510.pdf Lecture2-0512.pdf Lecture 4.pdf 2022_5_24_note.pdf Lecture 5.pdf
Lecture 1 (May10）：
Lecture 2 (May12）：
Lecture 3 (May17）：
Lecture 4 (May19）：
Lecture 5 (May24）：