The degree of Doctor of Philosophy in Applied Mathematics and Computational Science is an advanced degree designed for those who wish to pursue a career involving applied mathematics research. It is conferred in recognition of marked ability and high attainment in advanced applied and computational mathematics, including the successful completion of a significant original research project. The Ph.D. program is designed to guide students, year-by-year, toward becoming researchers in applied mathematics. Typically the program takes four or five years to complete, including the dissertation (although it can be completed in less time, depending on the student). There are several stages to the Ph.D. program. The first, which is centered on the course requirements and the Written Preliminary Exam, is designed to help the student acquire a broad background in applied mathematics and computational methods. The second stage includes the Ph.D. Oral Exam, and participation in seminars. Depth is one of the goals of this second stage, but the main objective at this point is to assist the student in choosing a field of specialization and in obtaining sufficient knowledge of this specialized field, including recent research developments, to begin to do independent research. Ph.D. students also have an opportunity to earn a masters degree at this stage. The third and key stage of the Ph.D. program is the dissertation (or Ph.D. thesis), in which the student will make an original contribution to applied mathematics and computational science.