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.

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