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 three years of graduate study and include foundational 8000-level courses for the topics in which the student plans to take the PhD 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:
| Code | Title | Credit Hours |
|---|---|---|
| MATH 9994 | Preliminary Examination Preparation | 1-6 |
| MATH 9998 | Pre-Dissertation Research / Elevation to Candidacy | 1-6 |
| MATH 9999 | Dissertation Research | 2 minimum |
Culminating Events:
Written Qualifying Examination:
The PhD Qualifying Examination (Comprehensive Examination) is a written exam comprised of two separate sections selected from the following areas:
- Algebra (Math 8011-8012)
- Numerical Analysis (Math 5043-44)
- Geometry and Topology (Math 8061-62)
- Real Analysis (Math 8041-42)
Students can choose any two of these sections for their examination. After exams in two different topics have been attempted, an exam in a third 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 year-long graduate course sequence. The separate section tests are given on different days, during a one-week period, twice a year: once in August just before the beginning of the Fall term, and once in January just before the beginning of the Spring term. Students do not have to take both of the section tests during the same one-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 Qualifying Exam as soon as possible after finishing the corresponding coursework. Students are expected to complete and pass the Qualifying Examination by August of their second year of study, and are required to pass it no later than the January of their third year of study. Students not making good progress toward completing and passing their Qualifying Examination in a timely fashion will be asked to leave the PhD program.
Incoming students may, with approval of the Graduate Chair, take one or two of the written PhD Qualifying 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 100, with each problem worth 20 points. The grades are compared and reconciled at the level of individual problems. A written account of the grading is returned to the student.
An average score of 75 points per section is required to pass. If a student falls slightly short of this standard, the Graduate Committee may, at its discretion, recommend a grade of pass based on the whole of the student's academic record.
A student who achieves an average score of at least 55 on the two sections of the PhD Qualifying Examination, with no individual section score below 30, has obtained a Master's pass on the examination and has fulfilled the examination requirement for the MS degree. If one of the individual section scores falls below 30 points, that exam may be repeated once, or the exam in a different topic may be attempted once. Such arrangements are subject to approval by the Graduate Committee, based 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 PhD 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 PhD 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 their 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 PhD 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 faculty of some Temple University department other than Mathematics or faculty at 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.