Requirements for the Ph.D. Degree
Academic Progress Expectations
Qualifying Exam Webpage
- Mastery of core knowledge in preparation for study in one of the four disciplinary areas. Mastery is demonstrated by passing the Common Qualifying exam, which is normally taken at the start of the second semester.
- Mastery of the theory and techniques of one of the four 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.
- Development of a thesis topic. Completion of this step is marked by passing the preliminary examination and advancing to candidacy.
- Completion of dissertation research. Completion is marked by a successful dissertation defense.
Qualifying Examinations
The qualifying exams for each track are based largely on the M.S. course requirements for each track. Thus, in the first three semesters, the bulk of a doctoral student's coursework is what an M.S. students in that track would take. The qualifying exams are given in two parts. The first part, called the Common Exam, has a two-hour section on undergraduate linear algebra and advanced calculus that all students must take. The third hour is, depending on a student's track, either a test of probability or a test of analysis and more advanced linear algebra. The Common Exam is normally taken after one semester. The second part of the exam is specific to each track. Some tracks have a take-home component to the test. For details of the courses on which qualifying exams are based and for copies of past exams, go to Quals Website.
The qualifying exams are given twice each year, in late January and in late May. Students have two chances to pass the exams. Students who fail to pass the exams are required to withdraw the doctoral program. Typically, these students leave with an M.S. degree. Doctoral students are expected to pass the Common Exam by the end of the first year and the Area Exam by the end of the second year.
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 research advisor. A committee approval request form must be filled out at least 4 weeks before the scheduled date of prelimary examination.
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.
The student must defend the dissertation before the dissertation examining committee. 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 either be submitted from the program to the Graduate School by day 15 of classes of the semester the student is defending (which for Fall 2009 is Friday, September 18th), or four weeks prior to the defense date, whichever comes first. In other words, for students defending later in the semester the graduate school needs these sent to them from the program by day 15 of classes, while for students defending at the beginning of the semester we will still need a four week advance submission. 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. This change in policy is intended to help students avoid issues of not having committees approved before they defend, and to give programs a more uniform date for handling these requests.
2. The candidates needs to send the defense announcement to the Graduate Director through email at least three weeks prior to your defense date. The Graduate Director will then forward the announcement to the Graduate School, which again needs approval.
3. 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 2009 is TBA) or no later than 3 months after the date of your defense, whichever comes first.
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 progam. The time limits for the qualifying and preliminary examinations and advancement to candidacy are described in the following section on Academic Progress.
Academic Progress Expectations of Doctoral Students
As noted above, doctoral study in the Department of Applied Mathematics consists of the following four stages:
- Mastery of core knowledge which is demonstrated by passing the Common Qualifying Exam. This exam is expected to be taken at the start of the second semester.
- Mastery of the theory and techniques of one of the four disciplinary areas. which is demonstrated by passing an Area Qualifying Exam. This exam is expected to be taken at the start of the fourth semester.
- Development of a thesis topic which culminates in a Preliminary Exam. This exam is expected to occur by the end of the fifth semester.
- Completion of dissertation research, which is demonstrated by a successful dissertation defense. The dissertation is expected to be completed by the end of the fifth year, at the latest.
A doctoral student must complete these stages in the time frames given above to be in good academic standing.
Second attempts
Doctoral students who fail either qualifying exam on their first attempt are allowed a second attempt which is expected to occur at the end of their second semester for the common exam; and at the end of their fourth semester for the area exam.
Delay in attempting an exam
A student needs the permission of the Graduate Program Committee to delay the time, beyond the semesters listed above, of their first or second attempt of either qualifying exam. Permission is also needed to delay advancement to candidacy beyond the end of the fifth semester. When a student is expected to take an exam, not taking the exam will count as a zero on the exam.
Failing Students
A doctoral student who fails a qualifying exam twice will normally have any departmental support terminated and be asked to leave the graduate program. A failing student supported on faculty research grants may be allowed to remain in the program to complete a project. In extenuating circumstances, a student may be allowed to continue in the graduate program by special vote of the full faculty.
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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.
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Entry into doctoral program from Masters program.
A Masters student may petition the Graduate Program Committee to be admitted to the Doctoral program. In addition to a strong performance in coursework at Stony Brook, a student will be expected to have passed at least the common qualifying exam. Admission will become effective at the start of the next semester. A student seeking departmental support, upon admission to the doctoral program, must meet the same deadlines as new students applying for admission with support.
Switching areas
A doctoral student who wishes to change areas must consult with the graduate program director as well as the faculty member in the proposed area. Switching areas typically requires decisions be made on stipend support, additional coursework, and qualifying examinations.
English Writing Requirement for the Ph.D.
The Department has replaced the doctoral degree foreign language requirement by an English writing requirement. This writing requirement
is associated with the preliminary oral examination. The student must submit a document, typically 20 to 25 double-spaced pages long, containing a discussion of: the foreseeable goals of the dissertation; a synopsis of the appropriate literature relevant to the problem; the research work accomplished to date (if any); and a discussion of the initial/next methods that will be undertaken to achieve progress towards those goals.
The document must have written approval for good English and writing style as well as correct content by the student's thesis advisor and a faculty reader, appointed by the graduate program director, who is not a member of the Preliminary Examination Committee. This document must be given to the advisor and the reader at least two weeks before the oral presentation. The document should be given to the remaining members of the Preliminary Examination Committee at least one week before the oral presentation.
If the scientific content of the document is satisfactory, as evaluated by the Preliminary Examination Committee, but the writing needs improvement, the student will be advanced to candidacy, but the student must have a revised document approved by the end of the following semester. If the deadline for approval is not met, the student will be deemed not to be making satisfactory progress and may be subject to a reduction or termination of financial support.
International students may need extensive writing assistance from the ESL Tutoring Center established to provide exactly this kind of technical writing tutorial support. Tutorial assistance in writing, if needed, will also be provided to native students.
Below are some reference texts you might find helpful.
Betty Schrampfer Azar, Understanding and Using English Grammar (3rd edition). Prentice Hall.
Nicholas J. Higham, Handbook of Writing for Mathematical Sciences, SIAM, 1998.
Jan Peterson and Stacy A. Hagen, Better Writing Through Editing. McGraw Hill -College.
Jan Frodesen and Janet Eyring, Grammar Dimensions: Form, Meaning, and Use.
Heinle and Heinle (Thomson Learning). (Series director: Diane Larsen-Freeman.)