# PhD Requirements

Requirements for the Ph.D.

1. Passing the Doctoral Comprehensive (written) Examination.
2. Passing the Doctoral Preliminary (oral) Examination.
3. Demonstrating proficiency in reading mathematics in two languages other than English that are relevant to the candidate's field of study.
4. Two consecutive semesters of full time study as a student at Stony Brook in a program approved by the Mathematics Department.
6. Satisfactory completion and defense of the Dissertation.

The Doctoral Comprehensive Examination

The purpose of the Doctoral Comprehensive Examination (known in the department as Comps'') is to test the mastery of the fundamentals in several core areas of mathematics. It is a written examination based on the syllabi of the seven core courses listed  here. The examination is offered twice each year, in January and in August.

Description of the Exam

The exam is 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. A student gets a perfect score if he or she does 10 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 your 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 by the end of his or her third semester.

If a student has not passed the Comps by the end of his or her third semester, then he or she is not making satisfactory progress and may be subject to dismissal from the program at the end of the academic year. A student may petition the graduate director for permission to take the Comps one last time (at the end of his or her fourth semester), by presenting the graduate director with evidence of significant progress since the last time he took the exam or with strong letters of recommendation from the faculty. The graduate Director will then seek the advice of the Graduate Committee.

The Comps Requirement can be waived

In rare cases students who enter with a master's degree from another university and who show convincing evidence of being prepared for research, may have the requirement of passing the Comprehensive Examination (Comps'') waived. This requires the approval of the Graduate Committee. A student who has the Comps waived must pass the Doctoral Preliminary Examination (Orals'') before the end of the second semester after admission.

The Doctoral Preliminary Examination

This examination is known in the Mathematics Department as Orals''. It is an oral examination administered by a faculty committee. The examination tests both your ability to learn advanced mathematics, and your preparation for research in your 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, and a third member, chosen by the Graduate Studies Director. The major and minor advisors 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. Part of the point of the preparation for the oral examination is for the student to read independently, pose questions about what he/she is 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 comprehensive examinations. For a student to remain in good 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.

The names of the committee members, and the syllabi, are recorded on a form that is available from the Graduate Secretary. This form also records a deadline, before which the examination must take place. This form is submitted to the Graduate Studies Director for approval and for the selection of a third member of the committee, who must also be of professorial rank in the Mathematics Department. The form is then sent to the Graduate School for approval.

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 (see 5.1 and 5.2).

Procedures

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 Chairman of the Orals Committee.

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 Orals 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 he or she has to be the thesis advisor.

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 French, German, and Russian; these are always acceptable. 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.

When a student is ready, he or she should choose one or two appropriate books and/or substantial journal articles to translate, and communicate this choice to the Graduate Studies Director (on a form available from the Graduate Secretary). After approving the choice, the Graduate Studies Director will help you find an examiner. The examiner must be a Department member of professorial rank or someone else approved by the Graduate Director.

The examination must take place within one month. The examiner chooses the pages to be translated, and sets a reasonable time limit. The student then writes out a translation of these pages, using a dictionary if desired. The examiner evaluates the translation in accordance with the above criterion, 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.

The Residence Requirement

Two consecutive semesters of full time study are required. The purpose of the residence requirement is to ensure that students experience the stimulation of regular mathematical interaction with other students and with the faculty.

This is primarily, but not necessarily, a formality; a form is filled out, and sent to the Graduate School. It takes place after you have met all degree requirements, except for the dissertation.

A student must have Advanced to Candidacy one year; that is, two semesters before he defends his or her 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 nine credits of MAT699, 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. You should note that the time limitations are suspended only for students who are on official Leave of Absence.

If you find it necessary to interrupt your matriculation, you 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). You should however be aware that, after a Leave of Absence, you 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 chairman, 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 he or she is adequately prepared to begin thesis research. There is, then, a presumption that at least one of the faculty members of the 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, in the subject in which the student was examined. A student wishing to change subject is free to approach any faculty member of professorial rank to enquire if he or she 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.

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 his or her thesis advisor's identity, and to keep the thesis advisor informed of your activities.

When your thesis advisor decides that your thesis is complete, he or she, in consultation with the Graduate Studies Director, chooses the members of your Dissertation Examining Committee. That Committee consists of your 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 your field.

The Graduate Studies Director also designates a second reader; this is done in consultation with the thesis advisor. The thesis advisor and second reader are each required to submit a brief written evaluation of the thesis to the Graduate Studies Director. These evaluations both confirm the technical correctness and originality of the main results in the thesis, and include reasons why the thesis should be accepted as a doctoral dissertation. (G. H. Hardy's criteria were: Is it true? Is it new? Is it interesting?'') The written reports of the two readers must be circulated to the members of the Dissertation Examining Committee before the thesis defense takes place. The reports then become a permanent part of the student's file.

The student must prepare his or her 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 your 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, he or she should provide the members of the Dissertation Examining Committee, and the Graduate Studies Director, with typed 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.

The copy of the thesis given to the Graduate Studies Director will be placed in the office of the Graduate Secretary for examination by any interested person.

The student should prepare, or ask the Graduate Secretary to prepare, a thesis approval page for the Committee in the form specified by the Graduate School. All signatures on this page must be in permanent black ink (not felt tip).

After the thesis defense, the student must submit to the Graduate Studies Director a photocopy of the signed thesis approval page. He or she must also submit three copies of the thesis to the Graduate School, each copy containing a signed thesis approval page. One copy, after being bound, goes to the Mathematics Department for inclusion in the Department's public thesis collection. A second bound copy is placed on the open shelf in the Library Thesis Room. The original thesis is placed unbound in the Library Archives.