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Syllabus

**Lecture outline will be updated during the semester. [Update: see Combinatorics2020 for a complete collection]**

Week 1
** Countings; Binomial Theorem; Estimating.
Week 2
** Inclusion-Exclusion principle; Generating function.
Week 3
** Integer partition, the Catalan number, Randon walk; Exponential Generating function.
Week 4
** Exponential Generating function; Basic of graphs; Sperner's Lemma.
Week 5
** Double counting, Sperner's Theorem, Turan type problems on C4 and K3.
Week 6
** Trees, Cayley's formula (first and second proofs).
Week 7
** Cayley's formula (third proof); Erdos-Ko-Rado Theorem.
Week 8
** Erdos-Ko-Rado Theorem (second proof); Partially ordered set (poset).
Week 9
** Erdos-Szekeres Theorem; Pigeonhole Principle, Ramsey's Theorem.
Week 10
** Ramsey's Theorem, Random graphs.
Week 11
** The Probabilistic Method.
Week 12
** The Probabilistic Method II.
Week 13
** The Probabilistic Method III.
Week 14
** The Algebraic Method.
Week 15
** The Algebraic Method II.
Week 16
** The Algebraic Method III; Finite Projective Plane.
Week 17
** Finite Projective Plane II .

**Homeworks:**

HW 1 . If you want to use the tex file of the problem set, download Tex1

HW 2 , Tex2

HW 3 , Tex3

HW 4 , Tex4

HW 5 , Tex5

HW 6 , Tex6

HW 7 , Tex7

HW 8 , Tex8

HW 9 , Tex9

HW 10, Tex10

HW 11, Tex11

HW 12, Tex12