Program Requirements

General Program Requirements:
Number of Credits Required Beyond the Baccalaureate: 54

Required Courses:

Students are required to take at least 16 graduate courses, which are chosen with the advice and consent of the student's advisor. These courses should be taken during the first two years of graduate study and include foundational 8000-level courses for the topics in which the student plans to take the Ph.D. Comprehensive Examination. Students who have had graduate courses in these subjects prior to admission may omit some or all of the courses with the consent of their advisor and the Graduate Committee.

Students also take six additional credit hours of:

MATH 9994Preliminary Examination Preparation1-6
MATH 9998Pre-Dissertation Research / Elevation to Candidacy1-6
MATH 9999Dissertation Research2 minimum

Culminating Events:
Written Comprehensive Examination:
The Ph.D. Comprehensive Examination is a written exam comprised of three separate sections selected from the following areas:

  • Algebra
  • Applied Mathematics
  • Complex Analysis
  • Differential Geometry and Topology
  • Partial Differential Equations
  • Real Analysis

Students can choose any three of these sections for their examination. After exams in three different topics have been attempted, an exam in a fourth topic can only be taken under exceptional circumstances, and only after specific approval by the Graduate Committee. Each section is a three-hour test based primarily on the corresponding two-term 8000-level graduate course sequence. The separate section tests are given on different days, during one two-week period, twice a year: once in August just before the beginning of the Fall term, and once in January during the two weeks prior to the beginning of the Spring term. Students do not have to take all three of the section tests during the same two-week period. Each section test may be repeated once to obtain a higher grade.

Each of the three-hour section tests is further divided into two parts. Part I contains four questions, of which the student is asked to answer three. These questions are designed to test mastery of the facts of the subject. Part II contains three questions, of which two are to be answered. These questions test the ability to solve in-depth problems in the subject.

Students should begin taking the components of the Comprehensive Exam as soon as possible after finishing the corresponding coursework. Students are expected to complete and pass the Comprehensive Examination by August of their second year of study. While some delay in this schedule may be permitted, under exceptional circumstances, students not making good progress toward completing and passing their Comprehensive Examination in a timely fashion will be asked to leave the Ph.D. program.

Incoming students may, with approval of the Graduate Chair, take up to three of the written Ph.D. Comprehensive Examination sections once prior to their first term of enrollment. Upon request by the student, any of these pre-enrollment attempts can be removed from the student's record.

Each section is graded independently by two faculty members, using a scale of 0 to 25. The grades are compared and reconciled in the event of a discrepancy. A total score of at least 60, with a score on each individual section test of at least 13, is required to pass. If a student falls slightly short of this standard, the Graduate Faculty may, at their discretion, recommend a grade of pass based on the whole of the student's academic record.

A student who achieves a total score of at least 40 from the three sections of the Ph.D. Comprehensive Examination, with no individual section below 8, has obtained a master's pass on the examination and has fulfilled the examination requirement for the M.S. degree. If one of the individual exam scores falls below 8 points, that exam may be repeated once, or the exam in a different topic may be attempted once, or the student may take the Master's Comprehensive Examination. As above, such arrangements are subject to approval by the Graduate Committee, and if a student falls slightly short of the required standards, then the Graduate Faculty may, at their discretion, recommend a grade of pass, basing their decision on the student's entire academic record.

Preliminary Examination:
The preliminary examination is a two-hour oral exam. It should be taken by the end of the sixth term and must be passed by the end of the seventh term. The Ph.D. preliminary examination can be repeated, in whole or in part, only once. No student is permitted to take the preliminary examination before passing the written Ph.D. Comprehensive Examination and satisfying the foreign language requirement.

The student chooses a chief examiner with the advice and consent of the Mathematics Graduate Committee and with the consent of the proposed chief examiner. The chief examiner, in accepting his/her assignment, implicitly offers to be the student's dissertation supervisor if the examination is passed. Approximately one-half of the preliminary examination is conducted by the chief examiner, who asks questions in the area that the student has chosen as a specialty. The other half of the examination is devoted to questions asked by other faculty members on two or more elementary topics related to the area of specialization. The exact description of the elementary topics to be included in the examination is determined by the chief examiner, who is also responsible for assigning examiners to cover the topics. The examination committee consists of the chief examiner, the examiners for the elementary topics, and any other faculty who choose to attend. All faculty in attendance may vote on the outcome of the examination. The examination is considered passed if the chief examiner and at least one-half of the other faculty present vote in favor of passing.

Students who are preparing to write their preliminary examination should confirm a time and date with the chair of their Doctoral Advisory Committee and register with the department. The student and chair receive confirmation of the time, date, room, and proctor for the examination.

Dissertation:
The candidate's dissertation must be a distinctive and original contribution to research in mathematics. It must be an individual work, with only one author. Previously published work by the candidate may be included, if it represents research done while the student was enrolled in the Ph.D. program in Mathematics at Temple University and was not used to obtain any other degree. Joint work that cannot be attributed to the candidate alone must not be included in the body of the dissertation, but may be attached as an appendix. All previously published work must be logically connected and integrated into the dissertation, with a common introduction, conclusion, and bibliography. Existing copyrights must not be violated.

Preparation of the dissertation is supervised by the student's Doctoral Advisory Committee (DAC). This committee must include at least three Temple graduate faculty, two of whom must be in the Mathematics Department. The chair of the committee must be a member of the Temple University Mathematics Department. The DAC may include members of other Temple University departments. It is also possible for faculty from other universities or expert advisors employed in non-university settings to be included in the DAC.

The first step in preparing the dissertation is to write a dissertation proposal, which must be approved by the candidate's DAC. The proposal is kept on file, and if it becomes necessary to alter the proposal, the changes should be approved by the DAC and filed with the proposal.

The dissertation defense may be attended by faculty and graduate students from Temple University or other institutions, as well as mathematicians or scientists employed in a non-academic setting. The candidate's Dissertation Examining Committee (DEC) must attend the defense. This committee includes the candidate's DAC and at least one additional member, who must be a faculty of some Temple University department other than Mathematics or a faculty member of another university. The DEC meets at the conclusion of the dissertation defense and decides, by majority vote, if the candidate was successful.

If a student needs to change a member of a committee, the new member must be approved by the Mathematics Graduate Committee and registered with the department and the Graduate School.

When the dissertation is deemed complete by the candidate and the DAC, a defense is scheduled. Students who are preparing to defend their dissertation should confirm a date and time with their DAC and register with the department at least 20 days before the defense is to be scheduled. The Graduate Chair arranges the date, time, and room. The appropriate forms are forwarded to the student.

This dissertation defense must be announced in writing at least 10 days in advance of its occurrence. Copies of the announcement must be directed to each member of the candidate's DEC, each faculty member of the Mathematics Department, the Dean of the College of Science and Technology, and the Graduate School. Copies of the announcement are to be posted at the Department Office, the College Office, and on the Graduate School website.