AIM Ph.D. Program Requirements The requirements for the AIM Ph.D. program are designed to offer maximal flexibility in the pursuit of interdisciplinary study while simultaneously ensuring full rigor of training. These requirements differ substantially from those of the Mathematics Ph.D. degree and are detailed below. The order of this list of requirements mirrors the order in which the requirements should be completed. AIM Preliminary Examinations Coursework Thesis Proposal, Oral Examination, and Advancing to Candidacy Research, Writing, and Defense of Dissertation