Structure and Randomness: An Invitation to Arithmetic Combinatorics 2010 University of Georgia Research Experience for Undergraduates

Instructors:
Neil Lyall
Mariah Hamel
Alex Rice

Participants:
Stephanie Bell (University of Montana)
Cliff Blakestad (Caltech)
Bryan Gillespie (Penn State)
Will Grodzicki (Pomona College)
Hans Parshall (Humboldt State)
Lucia Petito (University of Rochester)
Catherine Ha Ta (University of California, Irvine)
Frank Xiao (Princeton University)

Expository notes and exercise sheets:
Exercise sheet 1
Schur's Theorem and exercise sheet 2
Exercise sheet 3
A proof of van der Waerden's Theorem
Roth's Theorem and Exercise sheet 4
Behrend's construction
Szemeredi's proof of Roth's theorem
Roth's theorem in random sets
Probability sheet

Projects:
"Rotated corners in the integer lattice" by Hans Parshall
"Roth's 1/4-theorem" by Cliff Blakestad
"Extensions of Varnavides proof on arithmetic progressions" by Lucia Petito
"Monochromatic corners on the integer lattice" by Frank Xiao
"Using Szemeredi's regularity lemma to prove Roth's theorem" by Stephanie Bell and Will Grodzicki
"Szemeredi's proof of Roth's thoerem" by Catherine Ha Ta
"On Randomness" by Bryan Gillespie
"Fourier coefficient visualizer" This program was written by Bryan Gillespie.  It requires Python.


Around Athens:
Flagpole magazine
UGA gym
Outdoor pool at UGA
Farmers market
Sandy Creek Nature Center and Park