Lec #  Topics  Lecture Notes 

1  Course Introduction Ramsey Theorem 
(PDF) 
2  Additive Number Theory Theorems of Schur and Van der Waerden 
(PDF) 
3  Lower Bound in Schur's Theorem ErdösSzekeres Theorem (Two Proofs) 2Colorability of Multigraphs Intersection Conditions 
(PDF) 
4  More on Colorings Greedy Algorithm Height Functions Argument for 3Colorings of a Rectangle Erdös Theorem 
(PDF) 
5  More on Colorings (cont.) ErdösLovász Theorem Brooks Theorem 
(PDF) 
6  5Color Theorem Vizing's Theorem 
(PDF) 
7  Edge Coloring of Bipartite Graphs Heawood Formula 
(PDF) 
8  Glauber Dynamics The Diameter Explicit Calculations Bounds on Chromatic Number via the Number of Edges, and via the Independence Number 
(PDF) 
9  Chromatic Polynomial NBC Theorem 
(PDF) 
10  Acyclic Orientations Stanley's Theorem Two Definitions of the Tutte Polynomial 
(PDF) 
11  More on Tutte Polynomial Special Values External and Internal Activities Tutte's Theorem 
(PDF) 
12  Tutte Polynomial for a Cycle Gessel's Formula for Tutte Polynomial of a Complete Graph 
(PDF) 
13  Crapo's Bijection Medial Graph and Two Type of Cuts Introduction to Knot Theory Reidemeister Moves 
(PDF) 
14  Kauffman Bracket and Jones Polynomial  (PDF) 
15  Linear Algebra Methods Oddtown Theorem Fisher's Inequality 2Distance Sets 
(PDF) 
16  Nonuniform RayChaudhuriWilson Theorem FranklWilson Theorem 
(PDF) 
17  Borsuk Conjecture KahnKalai Theorem 
(PDF) 
18  Packing with Bipartite Graphs Testing Matrix Multiplication 
(PDF) 
19  Hamiltonicity, Basic Results Tutte's Counter Example Length of the Longest Path in a Planar Graph 
(PDF) 
20  Grinberg's Formula Lovász and Babai Conjectures for Vertextransitive Graphs Dirac's Theorem 
(PDF) 
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} 
(PDF) 
22  Hamiltonian Cayley Graphs of General Groups  (PDF) 
23  Menger Theorem GallaiMilgram Theorem 
(PDF) 
24  Dilworth Theorem Hall's Marriage Theorem ErdösSzekeres Theorem 
(PDF) 
25  Sperner Theorem Two Proofs of Mantel Theorem GrahamKleitman Theorem 
(PDF) 
26  Swell Colorings WardSzabo Theorem Affine Planes 
(PDF) 
27  Turán's Theorem Asymptotic Analogues 
(PDF) 
28  Pattern Avoidance The case of S_{3} and Catalan Numbers StanleyWilf Conjecture 
(PDF) 
29  Permutation Patterns Arratia Theorem FurediHajnal Conjecture 
(PDF) 
30  Proof by Marcus and Tardos of the StanleyWilf Conjecture  (PDF) 
31  Nonintersecting Path Principle GesselViennot Determinants BinetCauchy Identity 

32  Convex Polyomino Narayana Numbers MacMahon Formula 
(PDF) 
33  Solid Partitions MacMahon's Theorem Hookcontent Formula 
(PDF) 
34  Hook Length Formula  (PDF) 
35  Two Polytope Theorem  (PDF) 
36  Connection to RSK Special Cases 
(PDF) 
37  Duality Number of Involutions in S_{n} 
(PDF) 
38  Direct Bijective Proof of the Hook Length Formula  (PDF) 
39  Introduction to Tilings Thurston's Theorem 
(PDF) 