Requirements for the Ph.D.
The following requirements need to be met in the order they are presented.
- Passing the Doctoral Comprehensive (written) Examination.
- Passing the Doctoral Preliminary (oral) Examination.
- Demonstrating proficiency in reading mathematics in two languages other than English that are relevant to the candidate's field of study.
- Advancement to candidacy.
- Two consecutive semesters of full time study as a student at Stony Brook University in a program approved by the Mathematics Department.
- Satisfactory completion and defense of the Dissertation.
The Doctoral Comprehensive Examination
The Doctoral Comprehensive Examination (known in the department as “Comps'') is a written examination based on the syllabi of the seven core courses listed here. The purpose of the Comps is to test the mastery of the fundamentals in several core areas of mathematics. The examination is offered twice each year, in January and in August (shortly before the start of each semester).
Description of the Exam: The exam is split in two parts, each four hours long, and consisting of six questions based on the syllabi of the seven core courses, but slightly more difficult than the questions on the final exams of these courses. Thus the total number of questions is 12. A student passes the exam if they answer six problems completely correctly.
Sample questions, as well as past exams, are available on request from the Graduate Secretary.
Evaluation of Comps: Identities of students are concealed by use of a coded designation for each individual. All answers to each question are graded independently by two faculty members. Scores of the exam are tabulated by a faculty member designated by the Graduate Studies Director. These tabulations are the basis of the evaluations made at a meeting of the Graduate Program Committee with the graders. The graded examination papers are available during the meeting should detailed comparison become appropriate.
When all examinations have been evaluated, the individual identities are made known. At that time, some negative decisions may be converted to positive decisions on the basis of course work and reports from faculty (this is a one way street; no positive decisions may at this time be changed to negative). Before the meeting, the Graduate Studies Director solicits reports from teachers of core courses on their students. These reports, together with all information volunteered by interested faculty members, is available at this last step of the evaluation meeting.
Students have the right to see their graded examination papers, and to discuss them with the graders. They can check for themselves that scores were added correctly, that no answer was overlooked, and that their intended meaning was understood by the grader. A student who wishes to do this should see the faculty member in charge of the examination.
Timetable for Taking/Repeating Comps: A student may take the Comps any time that they are given, but a maximum of three times. As a general rule a student should have passed the Comps before the start of the fourth semester, i.e. January of their second academic year. It is recommended that students take the exam in the August before their first semester as well – which will not count towards the three attempts.
If a student has not passed the Comps before the start of the fourth semester, then they are not making satisfactory progress and will be subject to dismissal from the program at the end of the academic year. A student may petition the graduate director for an alternative to dismissal. This will only be approved in rare cases and requires the approval of the Graduate Committee.
The Doctoral Preliminary Examination
This examination is known in the Mathematics Department as "Orals", and only students that have passed the comps are eligible to take it. It is an oral examination administered by a faculty committee. The examination tests both the student’s ability to learn advanced mathematics, and the student’s preparation for research in their major area. The emphasis on the test is a mixture of knowledge and application: one not only has to know the important results, and the interrelationships among them, but one also has to know how to apply these results in particular cases.
Orals Committee and Syllabus: Each Orals Committee has three members: a major advisor, chosen by the student, a minor advisor, also chosen by the student, but in consultation with, and with the approval of, the major advisor, and a third member, chosen by the Graduate Studies Director. All committee members must be of professorial rank, including assistant and associate professors, in the Mathematics Department; exceptions to this rule must have the approval of the Graduate Studies Director.
The oral examination will cover two topics: a major topic and a minor topic. First a student should look for an advisor who is likely to become the student's dissertation advisor. This advisor will develop with the student a syllabus for the major topic. The material for this syllabus should be in quantity equal to that of a yearlong course, although it should not be the subject of an actual course given regularly/biannually in the math department. Part of the point of the preparation for the oral examination is for the student to read independently, pose questions about what they are reading and work out examples. During the preparation for the oral examination there should be interaction between the student and the advisor which will facilitate the advisor's directing the student after the examination is passed.
The minor topic can be suggested by the major advisor or by a second (minor) advisor. The minor topic can be complementary to the major topic or it can be a completely different second interest of the student. The material for the minor syllabus should be in quantity equal to that of a one semester course, although it should not be the subject of an actual course.
The oral examination should be taken within a year of passing the written comprehensive examination (comps). For a student to remain in good academic standing, the oral examination must be passed within one and a half years from the time of passing the comprehensive examinations and at most three years from the beginning of graduate study. Students who begin their study with a master's degree will be expected to follow a shorter schedule.
If at some point the major advisor and student agree that it is best for a student to find another advisor, then the Graduate Studies Director should be immediately informed.
Eligibility for Orals: Students on probation may not organize an Orals Committee without the approval of the Graduate Studies Director; also, a student must pass the Comps before taking Orals.
Procedures: When a student is ready to organize their Orals Committee, they, in conjunction with their major and minor professors, fill out a form (obtainable from the Graduate Secretary) listing the major advisor, the minor advisor, the syllabus for the examination, and a date by which the examination must be taken. This form should be given to the Graduate Secretary. If the Graduate Studies Director approves, then they will add a third member to the Committee. These arrangements must be made at least three weeks before the date of the examination, in order to allow time for the Graduate School to approve the membership of the Committee. It is then the student's responsibility to make all the arrangements for the Orals. They should arrange the date, time, and place (often, the office of the major advisor) with the members of the Orals Committee. They must notify the Graduate Secretary of these arrangements at least one week in advance of the date. The graduate secretary will provide the members of the committee with a copy of the syllabus, and will prepare an Orals report Form for the committee to complete.
Members of the faculty who are not on the Committee may observe the Orals Examination only with the student's permission, and the permission of the major advisor.
After the examination, the Orals report form is signed by the members of the Committee and is then given to the Graduate Secretary; it is then placed in the student's file.
There are three possible outcomes to the Oral Examination: pass, pass with distinction, and fail. The Committee decides that a student's performance on the Orals merits a verdict of pass with distinction only if the student's performance has been outstanding in both major and minor topics.
If the Committee decides that the student has failed the examination, then the Committee must also decide whether or not to recommend a repeat. If the recommendation for a repeat is positive, then the Orals Committee will be supplemented by a fourth faculty member, chosen by the Graduate Studies Director. The repeat must ordinarily be scheduled within six months of the first attempt. A majority vote (3-1 or 4-0) of the Committee is required for a pass on the second attempt.
Ordinarily, the recommendation to repeat is withheld only when the Orals Committee decides, on the basis of the Orals Examination, that the student is very unlikely to improve sufficiently to pass on a second attempt.
The approval of the Graduate School is required for a second repeat.
Examiners' Responsibility: Since the oral exam is the last step before the doctoral thesis, the examiners should make sure that any student who passes the exam has a thesis advisor available. It is most common that the major advisor becomes the thesis advisor, but any examiner may become the thesis advisor and any examiner may find a thesis advisor for the student. It is the major advisor's responsibility to ensure that a thesis advisor is available to a student who passes the oral exam even if they have to become the thesis advisor themselves.
The Language Proficiency Examinations
The Mathematics Department requires that students show reading proficiency in two languages, other than English, in which there is substantial mathematical literature. The standard foreign languages are Chinese, French, German, Italian, and Russian; these are always available to students to choose from. Satisfaction of this requirement with any other foreign language requires approval of the Graduate Studies Director.
For students whose native language is not English, a note from the thesis advisor asserting that there is significant literature in the student's native language will satisfy the requirement for one of the two languages.
Normally, a student is expected to complete this requirement during the first four years of graduate study.
The examiner must be a Department member of professorial rank or someone else approved by the Graduate Director. The examiner chooses the pages to be translated (from an appropriate book or journal article), and sets a reasonable time limit. The student then writes out a translation of these pages. The examiner evaluates the translation, and enters the result on the Language Examination Form. It is the student's responsibility to then give the completed form to the Graduate Secretary.
Advancement to Candidacy
This is primarily a formality; a form is filled out, and sent to the Graduate School. It takes place after the student has met all degree requirements above (comps, orals and language exam), except for the dissertation.
A student cannot Advance to Candidacy and then immediately defend their dissertation. That is, at least one year, i.e. two semesters, must pass between the moment the student Advances to Candidacy and the moment they defend their dissertation.
Students who have Advanced to Candidacy are regarded by the Graduate School as working independently on their dissertations. Tuition Scholarships for such students are limited to nine credits per semester; these must consist of six credits of MAT 699 (Dissertation Research) as well as a topics course, unless otherwise approved by the Graduate Studies Director.
Time Limitation: There is a Graduate School requirement that a candidate for a Ph.D. must satisfy all requirements for that degree within seven years after completing 24 hours of graduate courses in the Mathematics Department. Except for authorized Leave of Absence, this is an absolute limitation.
One can petition to extend this time limit, provided the petition is endorsed by the Graduate Studies Director. The Department, and/or the Graduate School may require evidence that the student is still properly prepared for the completion of work. In particular, the student may be required to pass a new Oral Preliminary Examination in order to be permitted to continue work.
Maintenance of Matriculation: The Graduate School requires that students who withdraw (that is, who are registered during one semester and do not register for the following semester) must apply for readmission to resume their graduate work at Stony Brook. Students should note that the time limitations are suspended only for students who are on official Leave of Absence.
If a student finds it necessary to interrupt their matriculation, they may ask the Graduate Studies Director to seek approval from the Graduate School for a Leave of Absence for one year (this can be renewed for a second year). The student should however be aware that, after a Leave of Absence, they will need to be readmitted to the Graduate School; the conditions for readmission should be stated in the Leave of Absence Form.
The Dissertation
After passing Orals, a student may ask any member of the faculty of professorial rank (including assistant and associate professors) to accept formal designation as thesis (dissertation) advisor. Under unusual circumstances, a thesis advisor may be chosen from outside the Mathematics Department; such a choice must be approved, before the fact, by the Graduate Studies Director, and by the Graduate School.
The usual choice of thesis advisor is the major advisor, or another member, of the Orals Committee. However, the student is under no obligation to make that choice. Indeed, after passing the Orals, the student may choose to work in an entirely different branch of mathematics. However, the members of the Orals Committee are likely to be the faculty members most familiar with the student, and they voted to pass the student, certifying that the student is adequately prepared to begin thesis research. There is, then, a presumption that at least one of the members of the Orals Committee would be willing to accept the student as a thesis student. It is the responsibility of the Committee to assist the student in finding an adequate thesis advisor. A student wishing to change subject is free to approach any faculty member of professorial rank to inquire if they would serve as thesis advisor.
In any event, the thesis advisor/advisee relationship commences and continues by mutual agreement and may be terminated by either party, although the Mathematics Department expects that members of its faculty and graduate students will not act arbitrarily in such matters (or any other matters), but will only take action for reasonable cause. If the agreement is terminated, the Graduate Studies Director should be notified immediately.
The Mathematics Department depends heavily upon reports of thesis advisors to make renewal of support decisions. It is therefore to the student's advantage to keep the Graduate Secretary informed of their thesis advisor's identity, and to keep the thesis advisor informed of the students activities.
When a student's thesis advisor decides that the thesis is complete, they, together with the advisor, and with the approval of the Graduate Studies Director, choose the members of the students Dissertation Examining Committee. That Committee consists of the thesis advisor, at least two other members of the Mathematics Department of professorial rank, one of whom will serve as chairman, and at least one outside member. The outside member must also have professorial rank, either in the mathematics department of another university, or in another department of this university. The outside member should be knowledgeable in the student’s field.
The student must prepare their written thesis in a form acceptable to the Graduate School. The Graduate School publishes a set of rules in the Graduate Bulletin that a student should consult before writing the final draft of their thesis. The final copy must be written in accordance with the rules stated there.
The Graduate Studies Director must submit the membership of the Dissertation Examining Committee to the Graduate School for approval. This approval is contingent on the student's Advancement to Candidacy having already taken place.
The student is responsible for making all arrangements for the thesis defense. Specifically, they should provide the members of the Dissertation Examining Committee, and the Graduate Studies Director, with printed or electronic copies of the thesis and should arrange with them a date, time, and place for the thesis defense. The student should notify the Graduate Secretary of these arrangements and the graduate secretary will then post announcements of the pending thesis defense, and distribute copies of the announcements to the members of the Committee. The defense must be open to all interested parties.
Note: Public announcement of the thesis defense must occur at least one week prior to the defense.
An electronic copy of the thesis given to the Graduate Studies Director and the Graduate Secretary will be available to any interested person. The thesis must be submitted to the Graduate School via ProQuest.
The formal form which the committee uses to approve the thesis is electronic and is generated by the student (as per instructions by the Graduate Secretary).
Graduation
When a student has met all requirements for a degree, the Graduate Studies Director so informs the Graduate School. If a student wishes to graduate (that is, to participate in Commencement and/or to receive a diploma), another formality must be attended to: the student must submit a signed degree card to the Registrar. Consult the Academic Calendar for each semester's deadline for submitting degree cards, as well as for other relevant deadlines.
To graduate at the end of a term (Fall semester, Spring semester, or Summer session), the student must be registered during that term for at least one credit hour, and all degree requirements must be met before a certain degree deadline for that term (this deadline is listed on the Academic Calendar). If the degree requirements are met after the deadline, but before registration for the following term, a student may graduate the following term (provided a Completion Statement has been submitted by the Department to the Graduate School before the beginning of the next semester). There is no need to register for the following term.