# Graduate Handbook

### Doctor of Philosophy

In addition to satisfying the University regulations, each candidate for the Doctor of Philosophy (PhD) must

- Complete 72 credit hours with minimum of six full terms in residence. The 72 credit hours may be obtained through formal course work, directed study, and thesis research. (for details see below).
- Complete at least 10 courses at the 2000 or 3000 level at grade B or better, excluding the orientation seminars, independent study, and courses designated as preparatory to the preliminary examination.
- Complete three two-course sequences. The approved sequence couse list is available at Approved Graduate Sequences.
- Achieve an overall course average of B or better.
- Pass a written preliminary examination within 2 years.
- Pass a comprehensive examination within 3 years.
- Complete an oral overview/prospectus examination and be admitted to candidacy within 4 years.
- Write and defend a dissertation embodying an extended original investigation of a problem of significance in an area of mathematics.
- Participate in a teaching assignment of at least one lecture or recitation section per term for a minimum of two terms. This requirement can be waived by the Graduate Committee.

It is, of course, the satisfactory writing of the dissertation that is the most important goal of the PhD candidate. All other requirements, except that of item 8, support this objective.

The requirements must be completed within 10 years from the date of admission (8 years if already obtained a Master's Degree prior to admission).

#### Special requirements for a PhD in Mathematics

As of January 1, 2015, the following courses will no longer be included in the count toward the 72 credit hour requirement: Internship (3900), Independent Study (2990), Thesis MS (2000).

**Non-Math courses**: A student may take up to 1 course per semester from other University disciplines if they are in areas relevant to the proposed program of study. The student’s advisor must submit a request to the Graduate Committee prior to course registration in order for the credits to count toward the departmental 72 credit hour requirement and the 10 course requirement.

**Repeated courses**: For selected topics courses, documentation is required indicating the unique course material offered in a repeated course in order for the credits to count toward the department 72 credit hour policy. For all other courses, if repeated, the credits and grade (regardless of which is higher) of the course taken the first time around are removed from the transcript.

To receive a PhD in mathematics, a student must complete at least 10 mathematics courses at the 2000 or 3000 level with grade B or better. This excludes reading courses, directed-study courses, and the preparatory courses for the preliminary examination, such as Progress in Mathematics, Matrices and Linear Operators I and II (2020, 2370, 2371).

These courses must include at least three one-year sequences chosen from a list developed and kept up to date by the Graduate Committee. Sequences may not overlap, i.e., any particular course can only be counted in one of the required sequences. The courses should adhere to a coherent plan of study for the student's interests. The plan must be designed by the student's advisor with input from the student and consulting examples of such plans of study. It is to be submitted to the graduate committee for approval.

As many as two courses outside the mathematics department are permitted in these 10 courses, provided that all the following are satisfied.

- The programmatic necessity for the course is explained in writing to the Graduate Committee by the student's advisor and the courses are approved by the Graduate Committee.
- The courses are at the 2000 or 3000 level and are completed with a grade of B or better.

The exclusion of reading courses is not absolute. Faculty advisors can appeal to the Graduate Committee asking that a reading course on a topic count toward the 10 with documentation that it corresponds in requirements, student workload, and material to a real course.

10-course policy for Center for the Neural Basis of Cognition (CNBC) students: The PhD requirement for mathematics PhD students accepted into the CNBC program will be the three CNBC courses (Cognitive Neuroscience, Cellular Neurophysiology, Systems Neuroscience), Computational Neuroscience (Math 3375), plus an additional six mathematics courses at the 2000 level or above. This excludes reading courses, directed-study courses, and the preparatory courses for the PhD (Preliminary Examination, Progress in Mathematics, Matrices and Linear Operators I and II, Math 2020, 2370, 2371)

The course requirement at the 2000 and 3000 level is to ensure that the graduating PhD has a reasonable breadth in mathematics. Students with advanced degrees may be allowed credit for as many as four courses.

The overview/prospectus involves the formation of the student's doctoral committee and the presentation of a proposed research topic. The research should lead to a dissertation describing an extended original investigation and containing a definite contribution to mathematics. The thesis defense constitutes the final step in achieving the PhD.

A well-prepared student who is unencumbered by other obligations can complete the PhD requirements in four years. This can be done by enrolling in six courses per year, passing the preliminary evaluation after one year, the comprehensive examination after two years, and the overview/prospectus at the end of the third year. The dissertation is then written during the final year. For most students, this ideal minimum time is not possible. However, no more than two years should be needed to write a thesis and finish the remaining requirements. Thus, a maximum of five years is anticipated to accomplish the doctorate. In exceptional cases, the Graduate Committee will grant an additional year.

For part-time students, no rigid schedule can be imposed. Such candidates are encouraged to complete the requirements as rapidly as possible, but the only upper limit is the University's statute of limitations of 10 calendar years from the date of admission to graduate study.

#### The PhD Preliminary Examination

According to the Graduate and Professional Bulletin as published in the FAS Graduate Bulletin, the preliminary examination "should be designed to assess the breadth of the student's knowledge of the discipline, the student's achievement during the first year of graduate study, and the potential to apply research methods independently. Students who have full graduate status should be evaluated formally by approximately the end of the first year of full residence." The PE "is used to identify those students who may be expected to complete a doctoral program successfully and also to reveal areas of weakness in the student's preparation."

Accordingly, the examination covers advanced undergraduate and beginning graduate material, specifically material covered in Math 1530 and 1540 (Advanced Calculus I and II) and Math 2370 and 2371 (Matrices and Linear Operators I and II). The PE is given in April, just after the final exams, and August of each academic year. It is a written examination and consists of questions pertaining to the areas studied in the for courses just mentioned. The examination is prepared by a committee in which recent instructors of Math 1530, 1540, 2370, and 2371 will be involved. The preliminary exam consists of two parts taken on different days. Each part consists of a single set of questions related to either linear algebra or analysis (advanced calculus), according to a schedule that will be posted in advance. Syllabi and sample exams are available at: http://www.mathematics.pitt.edu/graduate/enrolled-students/graduate-hand...

Each part of the examination takes four hours. The two parts are graded separately. A student will receive a credit for passing one of the exams if he or she receives a passing grade on that exam and scores above a specified threshold in the second exam. The student then will need to pass only the second exam. The date at which the second exam is passed will be the official date of passing the preliminary exam. Each time the exams are offered, the exam committee will determine for each of the exams both the passing score and the acceptable threshold.

Under normal circumstances, PhD students are allowed to attempt the preliminary exam for a period of three years, starting from the time of enrollment. In order to receive continued financial support, PhD students must pass the preliminary before the end of their second year in the program. If a student has not passed the preliminary exam by the beginning of the third year, his or her financial support will be halted. The student may remain enrolled in PhD program and attempt to pass the exam in their third year. If the student passes the exam by the end of their third year, his or her financial support will be reinstated. If a student has not passed the preliminary exam by the beginning of the fourth year, his or her enrollment in the PhD program will be discontinued. At that time, the student will have the option of switching his or her degree objective to Master of Arts or Master of Science.

The passing of the PE automatically fulfills the Master of Arts comprehensive examination requirement. Thus, a student who has passed the PE and satisfied items 1 and 2 under general requirements for the master's degree is entitled to a Master of Arts degree.

#### The PhD Comprehensive Examination

The *Graduate and Professional Bulletin* states that "The comprehensive examination should be designed to assess the student's mastery of the general field of doctoral study, the student's acquisition of both depth and breadth in the area of specialization within the general field, and the ability to use the research methods of the discipline. It should be administered at approximately the time of the completion of the formal course requirements and should be passed at least eight months before the scheduling of the final oral examination and dissertation defense. In no case may the comprehensive examination be taken in the same term in which the student is graduated."

In contrast to the preliminary examination, the comprehensive examination is suited to the individual needs of each student and is created and administered by a specially formed examining committee of three faculty members, which includes the student's advisor. The comprehensive examination should maintain a proper balance between specialization and generality.

The comprehensive examination will consist of a written component and, at the discretion of the examining committee, a subsequent oral component.

The content of the components should be determined by the examining committee, taking into consideration the chief interests of the student. The examining committee also shall decide whether the student has passed the comprehensive examination. Prior to administering the examination, the examining committee will submit an outline of the exam's areas and the questions comprising its written component to the Graduate Committee for approval.

It is the responsibility of the student to verify that the necessary approvals have been secured before taking the comprehensive examination.

Students are expected to pass the comprehensive examination by the end of the the third year of full-time study.

#### Overview/Prospectus Examination and Admission to Candidacy

After passing the comprehensive examination, the student should secure a prospective thesis advisor in an area in which he or she wishes to perform research. The thesis advisor will guide the student in further course work and directed study in the appropriate areas. At that time, the student may begin research toward the doctoral thesis.

In contrast to both the preliminary and comprehensive examinations, the overview examination is an oral examination whose form may vary from student to student. In order to take the overview, a student must have worked long enough with his or her advisor to have begun work on a thesis topic. At a mutually agreed-upon time (but no later than one year after the comprehensive examination and at least eight months prior to the thesis defense), the thesis advisor will form an overview committee consisting of at least four members of the graduate faculty. At least one member must be from outside the department. If a committee member is not a member of the University of Pittsburgh faculty, prior approval must be granted by the graduate faculty of arts and sciences office. **The Graduate Committee will be informed in writing and must approve the selection prior to the overview.**

The exam begins with a presentation of approximately one hour in which the student discusses his or her thesis topic and gives some ideas on where the research may lead. Then there is a period for questions and comments by the committee. Because the question-and-comment period can take a variety of forms, the length and format of the exam cannot be predicted.

If a student is deemed to have passed the examination, admission to candidacy forms are submitted by the examining committee to the Graduate Committee. Normally, the PhD Thesis Committee for the Final Oral or Defense of Thesis will be the same as the Overview Committee. If there is a change in committee members, then the student's advisor must request this in writing, and the Graduate Committee must approve it, as well as the dean of the faculty of arts and sciences.

If the committee is not pleased with the student's performance, then he or she will be asked to retake the examination at a later date. After the second examination, the committee will recommend whether the student will be allowed to continue toward the PhD.

#### Thesis Defense

The thesis defense is conducted by the student's doctoral committee as outlined in the *Graduate and Professional Bulletin.* Successful completion of this final examination marks the end of studies for the PhD degree.

#### Thesis Format

The proper format for a doctoral dissertation at the University of Pittsburgh is described in detail in the Style and Form Manual.

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