Abstract: A Beatty sequence is a sequence of the form [a*n], where a is an irrational number and the bracket denotes the floor function. A remarkable result, called Beatty's Theorem, says that if a and b are irrational numbers such that 1/a+1/b=1, then the associated Beatty sequences "partition" the natural numbers. That is, every natural number belongs to exactly one of these two sequences. It is known that Beatty's Theorem does not extend directly to partitions into three or more sets, and finding appropriate analogs of Beatty's Theorem for such partitions is an interesting, and wide open, problem, which has applications to optimal scheduling questions. The goal of this project is to explore different constructions of partitions of integers into perturbed Beatty sequences and possible applications to optimal scheduling algorithms.