Visualizing Discrete Fourier Coefficients

Over the course of the 2010 University of Georgia REU, we spent an extensive amount of time understanding and applying properties of the discrete Fourier transform to topics in arithmetic combinatorics. In order to get an intuitive idea of what we were really looking at, I wrote a GUI program in Python to visualize the . . . [Read More]

Behrend’s Construction

How large can a set of integers be without containing any 3-term arithmetic progressions? German mathematician Felix Behrend provided a construction in 1946 which gave an example of a fairly large set lacking such progressions. The main idea of the work is to use the fact that a line may intersect with a sphere . . . [Read More]