Lec #  Topics  KEY DATES 

1  Course Introduction Ramsey Theorem 

2  Additive Number Theory Theorems of Schur and Van der Waerden 

3  Lower Bound in Schur's Theorem ErdösSzekeres Theorem (Two Proofs) 2Colorability of Multigraphs Intersection Conditions 

4  More on Colorings Greedy Algorithm Height Functions Argument for 3Colorings of a Rectangle Erdös Theorem 

5  More on Colorings (cont.) ErdösLovász Theorem Brooks Theorem 

6  5Color Theorem Vizing's Theorem 
Problem set 1 due 
7  Edge Coloring of Bipartite Graphs Heawood Formula 

8  Glauber Dynamics The Diameter Explicit Calculations Bounds on Chromatic Number via the Number of Edges, and via the Independence Number 

9  Chromatic Polynomial NBC Theorem 
Problem set 2 due 
10  Acyclic Orientations Stanley's Theorem Two Definitions of the Tutte Polynomial 

11  More on Tutte Polynomial Special Values External and Internal Activities Tutte's Theorem 

12  Tutte Polynomial for a Cycle Gessel's Formula for Tutte Polynomial of a Complete Graph 

13  Crapo's Bijection Medial Graph and Two Type of Cuts Introduction to Knot Theory Reidemeister Moves 

14  Kauffman Bracket and Jones Polynomial  Problem set 3 due 
15  Linear Algebra Methods Oddtown Theorem Fisher's Inequality 2Distance Sets 

16  Nonuniform RayChaudhuriWilson Theorem FranklWilson Theorem 

17  Borsuk Conjecture KahnKalai Theorem 
Problem set 4 due 
18  Packing with Bipartite Graphs Testing Matrix Multiplication 

19  Hamiltonicity, Basic Results Tutte's Counter Example Length of the Longest Path in a Planar Graph 

20  Grinberg's Formula Lovász and Babai Conjectures for Vertextransitive Graphs Dirac's Theorem 

21  Tutte's Theorem Every Cubic Graph Contains Either no HC, or At Least Three Examples of Hamiltonian Cycles in Cayley Graphs of S_{n} 

22  Hamiltonian Cayley Graphs of General Groups  
23  Menger Theorem GallaiMilgram Theorem 
Problem set 5 due 
24  Dilworth Theorem Hall's Marriage Theorem ErdösSzekeres Theorem 

25  Sperner Theorem Two Proofs of Mantel Theorem GrahamKleitman Theorem 

26  Swell Colorings WardSzabo Theorem Affine Planes 
Problem set 6 due 
27  Turán's Theorem Asymptotic Analogues 

28  Pattern Avoidance The case of S_{3} and Catalan Numbers StanleyWilf Conjecture 

29  Permutation Patterns Arratia Theorem FurediHajnal Conjecture 

30  Proof by Marcus and Tardos of the StanleyWilf Conjecture  Problem set 7 due 
31  Nonintersecting Path Principle GesselViennot Determinants BinetCauchy Identity 

32  Convex Polyomino Narayana Numbers MacMahon Formula 

33  Solid Partitions MacMahon's Theorem Hookcontent Formula 

34  Hook Length Formula  
35  Two Polytope Theorem  
36  Connection to RSK Special Cases 
Problem set 8 due 
37  Duality Number of Involutions in S_{n} 

38  Direct Bijective Proof of the Hook Length Formula  
39  Introduction to Tilings Thurston's Theorem 