Ultrafilters and the Spectrum of the Power Set of the Natural Numbers -
Ultrafilters are collections of subsets of N that have some surprising properties. In this talk, we’ll define filters and ultrafilters, and provide as many examples as possible. Then, at the end we’ll show that the power set of the natural numbers has a ring structure, and that the ultrafilters are in bijective correspondence with the prime ideals for this ring.

Since this talk really only involves subsets of the natural numbers, Math 112 and 113 students are particularly encouraged to attend!