Skip Navigation

Requirements for the Ph.D. Degree

Qualifying Exam Webpage

Doctoral study consists of the following four stages. There are no specific course requirements for the Ph.D. in Applied Mathematics and Statistics.

  1. Mastery of core knowledge in preparation for study in one of the five disciplinary areas. Mastery is demonstrated by passing the Common Qualifying exam, which is normally taken at the start of the second semester.
  2. Mastery of the theory and techniques of one of the five disciplinary areas. Mastery is demonstrated by passing an Area Qualifying exam, which is normally taken at the start of the fourth semester. At the same time, a thesis advisor is selected.
  3. Development of a thesis topic. Completion of this step is marked by passing the preliminary examination and advancing to candidacy.
  4. Completion of dissertation research. Completion is marked by a successful dissertation defense.

Research Advisor
After completion of at least one year of full-time residence and prior to taking the preliminary examination, a student must select a research advisor who agrees to serve in that capacity.

Preliminary Examination
This is an oral examination administered by a committee and given to a student when he or she has developed a research plan for the dissertation. The plan should be acceptable to the student's dissertation advisor. A committee approval request form  must be filled out at least 4 weeks before the scheduled date of preliminary examination and submitted to Christine Rota (Math Tower, Room P141; (631) 632-8360;   The write up for the preliminary exam must be sent to committee members one week in advance of the exam.  

Note: The outside committee member is optional at this stage. The preliminary presentation is usually 45 minutes long including a novel topic, a thorough literature review, and outline for future work. Please include an additional 15-30 minutes, for Questions/Answers -- Please book the seminar room with Christine as well:

For Fall 2022, the students must take and pass their prelims by Friday, August 26 in order to be considered as advanced to candidacy for the Fall 2022 semester.  ***Please email your signed (by your entire committee) Prelim Signature Form to by 1:00 pm on Friday, August 26  in order for her to submit the form to the graduate school in time.

Language Requirement
As part of their preliminary exam, students must write up background readings and initial research results in a paper of at least 20 pages. This page will be carefully reviewed for English writing as well as research content. For details, see English Writing Requirement. 

Advancement to Candidacy
After successfully completing all requirements for the degree other than the dissertation, the student is eligible to be recommended for advancement to candidacy. This status is conferred by the vice provost for graduate studies upon recommendation from the departmental graduate studies director. 

Dissertation Defense
The most important requirement of the Ph.D. degree is the completion of a dissertation, which must be an original scholarly investigation. The dissertation must represent a significant contribution to the scientific literature and its quality must be comparable with the publication standards of appropriate and reputable scholarly journals. Students must advance to candidacy at least one academic year before the beginning of the semester in which they plan to defend their dissertation (an academic year is defined as the Fall and Spring semesters, in either order, that immediately precede the semester of defense).

The student must defend the dissertation before the dissertation examining committee. The draft dissertation must be sent to the committee members at least two weeks in advance of the defense. On the basis of the recommendation of this committee, the Department of Applied Mathematics and Statistics will recommend acceptance or rejection of the dissertation to the vice provost for graduate studies. All requirements for the degree will have been satisfied upon successful defense of the dissertation.

Procedure for the PhD thesis defense:

1. Select a dissertation committee with the assistance of one's advisor. The committee must include at least three faculty members from the department and one outside member. Submit a request for committee approval to the AMS Graduate Secretary. All PhD defense committee approval requests should be submitted from the program to the Graduate School at least five weeks prior to the defense date. Please note that changes in the make up of the committee can be made later if needed, but sufficient time will still be needed to approve these changes. 

2. The candidate needs to send the defense announcement to the Graduate Director through email at least four weeks prior to your defense date. The Graduate Director will then forward the announcement to the Graduate School, which again needs approval

3. Apply for graduation on the graduate school website by the posted deadline (which for Fall 2022 is Wednesday, November 9, 2022)
4. Once a thesis is successfully defended, the thesis must be submitted to the graduate school office by the posted graduate school deadline (which for Fall 2022 is Thursday, December 15th) or no later than 3 months after the date of your defense, whichever comes first.  ***Please check the Graduate School website for updated information:

Minimum Residence
At least two consecutive semesters of full-time study are required.

Time Limit
All requirements for the Ph.D. degree must be completed within seven years after the completion of 24 graduate credits as a student enrolled in the doctoral program. The time limits for the qualifying and preliminary examinations and advancement to candidacy are described in the following section on Academic Progress.

* * * * *

Joining a Research Group: 
Satisfactory progress for a student funded by the department (TAship or Fellowship) requires joining a research group.
Students entering with a B.S. have up to three semesters from the start of graduate studies in the department to join a research group. Students entering with an M.S. in the mathematical sciences, or equivalent course work, have one year to join a research group. 

Support after Joining a Research Group
Once a research group is joined, the student's advisor and the Graduate Program Director will jointly decide, on a year-to-year basis, whether the student is eligible to continue on a Teaching Assistantship (TAship.) Most students in research teams are supported with Research Assistantships (RAships), and only a limited number of students can stay on TAships after joining a research group. Supported students who plan to join a research group with little external funding have a substantial chance of losing financial support.