To obtain the Ph.D. degree, a student is required to:

1. Complete 12 term courses (including reading courses) at the graduate level, at least two with Honors grades. Among these 12 courses, within the first year, a student should finish 4 core courses in each of the methods of applied analysis, numerical computation, algorithms, and probability. To meet the minimum Graduate School quality requirements for the Ph.D., students must achieve the grade of Honors in at least one full-year or two full-term graduate courses, taken after matriculation in the Graduate School and during the nine-month academic year. The Honors requirement must be met in courses other than those concerned exclusively with dissertation research and preparation.  In addition to the above, all first year students  must successfully complete one course on the responsible conduct of research (e.g. MATH 991 or CPSC 991) and AMTH 525 Seminar in Applied Mathematics.

A student who has not met the Honors requirement at the end of the fourth term of full-time study will not be permitted to register for the fifth term. In exceptional circumstances, the Director of Graduate Studies may petition the appropriate dean that a student who has not met the Honors requirement be permitted to continue to register.

2. Participate in teaching.  Each student is required to teach as a teaching fellow two undergraduate courses by the end of their second year;

3. Pass a qualifying examination on their general applied mathematical knowledge (in algebra, analysis, probability and statistics) by the end of their second year;

4. Find an adviser. By the time the student has  passed the qualifying exam, he/she is expected to have found an adviser. The advisor has to be approved by the Director of Graduate Studies, and students are encouraged to find an advisor sooner rather than later. In collaboration with his/her adviser, the student prepares a dissertation prospectus, a short document that outlines plans for the research and demonstrates familiarity with relevant literature. The prospectus is expected to have been approved by the dissertation committee before the end of the third year.

5. Be in residence for at least three years. The residence requirement must normally be met within the first four years of study. Any exception to the residence requirement must be approved by the department and by the appropriate associate dean.

6. Complete a dissertation that clearly advances understanding of the subject it considers.