PART I: INFINITE and finite RAMSEY THEORY on Graphs & Hypergraphs

Jan 28 Intro to the Course

Infinite Ramsey Thm For Graphs

APP: Thin Set Thm

Infinite Ram to Finite Ram For Graphs

Finite Ram Thm For Graphs

Infinite Ramsey Thm For 3-Hypergraphs

Finite Ramsey Thm For 3-Hypergraphs-TOW bounds

APP: Logic, NOTES

Prim Rec functions

Goodstein Sequences

Better Bounds in 3-hyper Ramsey

Large Ramsey Thm

VERY LARGE RAMSEY NOTES

PH(1) LE 8,: PH(2) LE 14,MAIPH(1) LE 7,PAPER on PH Nums

SLIDES: Inf Can Ram,Inf Can Ram NOTES

Mileti's proof of Can Ram,Mileti NOTES

a-ary Can Ram

APP: Distances and Areas

PART II: FINITE RAMSEY THEORY

Small Ram Num

Two Triangles and Ramsey Multiplicity

Lower Bounds on Ram Numbs

Better Lower Bounds on Ram Numbers,PAPER with better LB

Prob Method: Turan's Thm (last part)

PART III: Graph Ramsey Theory

Graham's GRT

Irving's GRT

Spencer's GRT

APP: Convex Sets

Prob Meth for LB on Ram Numbs,

PAPER with better LB

Prob Method: Turan's Thm (last part)

PART IV: Van Der Waerden's Thm

Grid Coloring SLIDES

Coloring the 15 x 15 grid SLIDES

Dom Set HW Sol SLIDES,

Sq Theorem

VDW

Are There Better Bounds on the VDW Numbers?

Poly VDW,BOOK with pvdw,PAPER with pvdw

Scratch Notes on NT

Extended VDW Theorem

Application to NT

Extra minicoures on Finite Geom and Ramsey

Rado's thm SLIDES

Rado's thm HS SLIDES

Folkman's thm SLIDES

Schur + FLT(4) imply primes infinite SLIDES

W(3,k) SLIDES

Multi Party Comm Comp SLIDES

GKKZP polyvdw paper

Distinct Rado

Distinct Rado NOTES

Multi Comm Comp

PART V: Euclidian Ramsey Theory

Intro to ERT and Chrom Numb of Plane

C4 Ramsey (needed for Unit Sq)

Unit Sq

Area 1

PART VI: Roth’ Theorem

History of VDW bounds

Roth's Theorem

Roth's Theorem by Kelin