PART I: INFINITE RAMSEY ON Graphs & Hypergraphs

Intro to the Course

Infinite Ramsey Thm For Graphs, NOTES

Infinite Ramsey Thm For 3-Hypergraphs

APP: To proving Programs Terminate. OPT, PAPER

Infinite Ram on Z

omega-squared, Latex of omega-squared talk.

Inf Can Ram

a-ary Can Ramsey

HW 01, the Not-ONTO problem

Kruskal Tree Theorem, NOTES, Paper with Proof of Kruskal Tree Theorem

Computable Ramsey, My Notes on Computable Ramsey

AC and Equiv

Ramsey over the Reals

PART II: FINITE RAMSEY ON Graphs & Hypergraphs

Feb 4 Finite Ram Thm For Graphs,NOTES

Feb 6 App to Logic SLIDES,NOTES

OPTIONAL Paper on Spectrum by GrandJean

OPTIONAL Paper on Spectrum by Fagin

Feb 6 Your Top Math Songs, and Mine

Feb 11 Small Ram Num SLIDES,

App to History PAPER, Paper that mentions the app to History, Slides that mentions the app to History

Jan 29 Infinite Ram to Finite Ram For Graphs

Feb 13 Finite Ramsey Thm For 3-Hypergraphs-TOW bounds

Feb 13 Prim Rec, The Language for Bounds on -ary Hypegraph Ramsey

Feb 13 Goodstein Sequences SLIDES

Feb 18 Much Better Bounds on 3-Hypergraph Ramsey

Feb 18 Large Ramsey Theorem

March 6 Convex Sets

PART II: FINITE RAMSEY: Graphs & Hypergraphs

March 11 Projects Done By Students In This Class

March 11 Small Ram Num FOR HS STUDENTS

March 11 Small Ram Num SLIDES

March 11 App to History PAPER TO READ FOR THE QUIZ,

March 11Survey that Includes App to History

March 11 Slide Survey that Includes App to History

March 13 Slight Improvement To Upper Bd on R(k)

March 13 Two Triangles SLIDES

March 25 More on Ramsey Kings

March 25 Even More on Ramsey Kings

March 25 Erdos on R(5) and R(6)

March 25 Garrett approach and Standard approach to Ram. Mult.

March 27 Lower Bounds on Ramsey Numbers I

March 27 Lower Bounds on Ramsey Numbers II, Spencer paper with better lower bounds

March 27 Prob Meth for Distinct Diff Sets

March 27 AC and Equiv

March 27 Ramsey over the Reals

March 27 Prob Meth for Sum Free Sets

OPTIONAL Prob Meth for Turan's Theorem

OPTIONAL Prob Method for Dominating Set

PART III: GRAPH RAMSEY THEORY

April 1 Graham's GRT

April 1 Irving's GRT

April 3 Spencer's GRT

PART IV: VDW and related.

April 8 Grid Coloring SLIDES

OPTIONAL 15 by 15

April 10 Sq Theorem

April 10 VDW SLIDES

April 10 Are There Better Bounds on the VDW Numbers?

April 15 Poly VDW SLIDES,

April 15 Poly VDW Cheat Sheet I: Statement of Lemmas

April 17 Poly VDW Cheat Sheet II: Useful Notation

April 17 Write up of Lemma for Quad VDW

April 17 Small Poly VDW

April 22 Arvind's Guest lecture, a few slides

April 24 Roth's theorem

April 24 Extended VDW Theorem

April 24 Application to NT

April 29 You'll See

April 29 Rado's thm SLIDES

PART V: EUCLIDEIAN RAMSEY THEORY

April 29 Intro to ERT and Chrom Numb of Plane

May 1 C4 Ramsey (needed for Unit Sq),Alt Proof. OPT

May 1 Unit Sq,PAPER on R4

May 1 Open Problems Col on Unit Sq

May 1 Area 1

May 6 There is a mono equil-Tri of size… OPT

May 6 L2-L2 WRITEUP

May 6 L2-L3

DIDN"T DO L3-Lbig

DIDN"T DO L3bigpaper.pdf WRITEUP

DIDN"T DO L2bigpaper.pdf WRITEUP

DIDN"T DO cheatL2bigpaper.pdf WRITEUP

NEED THIS has sign change lemma

PART VI: Topics that I missed earlier

W(3,k) and 3-free sets

Funny Math Stuff

Multi Party Comm Comp

Schur + FLT(4) imply primes infinite

List of our ‘‘Applications’’

What we Didn't Cover