An introduction to uniform distributions and Weyl's Criterion

Abstract

This report is an exploration into the basics of the uniform distribution of sequences and a proof of Weyl's Criterion. After describing what it means for a sequence to be uniformly distributed, we develop the tools to prove Weyl's Criterion. In order to do this, we split Weyl's Criterion into two theorems and prove each of them. Finally, we will show an example which applies Weyl's Criterion to prove that a certain sequence of irrational numbers is uniformly distributed.