This section contains documents created from scanned original files, which are inaccessible to screen reader software. A "#" symbol is used to denote such documents.
These lecture notes were taken by Amanda Redlich, a student in the class, and were used with permission.
Lecture notes files.
| 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
Erdös-Szekeres Theorem (Two Proofs)
2-Colorability of Multigraphs
Intersection Conditions |
(PDF)# |
| 4 |
More on Colorings
Greedy Algorithm
Height Functions Argument for 3-Colorings of a Rectangle
Erdös Theorem |
(PDF)# |
| 5 |
More on Colorings (cont.)
Erdös-Lovász Theorem
Brooks Theorem |
(PDF)# |
| 6 |
5-Color 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
2-Distance Sets |
(PDF)# |
| 16 |
Non-uniform Ray-Chaudhuri-Wilson Theorem
Frankl-Wilson Theorem |
(PDF)# |
| 17 |
Borsuk Conjecture
Kahn-Kalai 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 Vertex-transitive 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 Sn |
(PDF)# |
| 22 |
Hamiltonian Cayley Graphs of General Groups |
(PDF)# |
| 23 |
Menger Theorem
Gallai-Milgram Theorem |
(PDF)# |
| 24 |
Dilworth Theorem
Hall's Marriage Theorem
Erdös-Szekeres Theorem |
(PDF)# |
| 25 |
Sperner Theorem
Two Proofs of Mantel Theorem
Graham-Kleitman Theorem |
(PDF)# |
| 26 |
Swell Colorings
Ward-Szabo Theorem
Affine Planes |
(PDF)# |
| 27 |
Turán's Theorem
Asymptotic Analogues |
(PDF)# |
| 28 |
Pattern Avoidance
The case of S3 and Catalan Numbers
Stanley-Wilf Conjecture |
(PDF)# |
| 29 |
Permutation Patterns
Arratia Theorem
Furedi-Hajnal Conjecture |
(PDF)# |
| 30 |
Proof by Marcus and Tardos of the Stanley-Wilf Conjecture |
(PDF)# |
| 31 |
Non-intersecting Path Principle
Gessel-Viennot Determinants
Binet-Cauchy Identity |
|
| 32 |
Convex Polyomino
Narayana Numbers
MacMahon Formula |
(PDF)# |
| 33 |
Solid Partitions
MacMahon's Theorem
Hook-content 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 Sn |
(PDF)# |
| 38 |
Direct Bijective Proof of the Hook Length Formula |
(PDF)# |
| 39 |
Introduction to Tilings
Thurston's Theorem |
(PDF)# |