About the Mathematics Doctoral Program
Foreign Language. No requirement.
Seminars. Advanced topics seminars which contribute to the student’s overall mathematical background will be offered each semester. It is expected that each student will participate in seminar work in his/her area of specialty.
Preliminary Examination. Only those students who have passed the preliminary examination requirement are eligible to take MATH 8000 . Students should check with the instructor of record in the year the preliminary exams are administered to find out the exact list of topics for the preliminary exams. For more information about the preliminary examination requirements for the doctoral program, students must contact the graduate director or advisor.
Dissertation. A dissertation is required of every candidate for the doctoral degree. This requirement is separate and apart from other requirements in the doctoral program. Consequently, successful performance in other areas does not necessarily guarantee the acceptance of a dissertation. The dissertation should embody a significant contribution to new information to the subject.
Qualifying Examination (Oral Comprehensive). After passing the required preliminary examinations, the next required step towards candidacy is passing the qualifying exam. It consists of a public presentation by the candidate, after which the audience is asked to leave, and the examination continues between candidate and committee. The decision (pass/fail) is recorded in writing and signed by the committee.
Dissertation Defense. A final oral examination over the student’s dissertation topics is required of every candidate for the doctorate. It consists of a public presentation by the candidate, after which the audience is asked to leave, and the examination continues between candidate and committee. The decision (pass/fail) is recorded in writing and signed by the committee.
Students who pass a preliminary exam without having taken the corresponding course sequence in the department are exempt from that specific sequence requirement. Students must complete the remaining number of foundational sequences and courses for their concentration. The rules 2b and 3a for transfer credit would apply.
Tracks
The doctoral program offers concentrations in five areas of study: applied mathematics, pure mathematics, statistics, mathematical finance, and mathematics education. The program consists of 60 hours of graduate coursework and 12 hours of doctoral dissertation. The program requirements listed below are in addition to the university and Graduate School requirements. Specific questions concerning interpretation of these policies should be directed to the graduate advisor. A student in the doctoral program must fill out a degree plan after the end of the second long semester and before the start of the third long semester in the program.
Guidelines for Ph.D. Tracks
Applied Mathematics
1. Foundational coursework (24 hours):
Three sequences from the following, with at least one sequence from Group A and at least one sequence from Group B.
Group A: MATH 5320 -MATH 5321 , MATH 5322 -MATH 5323 , MATH 5324 -MATH 5325 , MATH 5332 -MATH 5333 , MATH 5340 -MATH 5341 .
Group B: MATH 5330 -MATH 5331 , MATH 5334 -MATH 5335 , STAT 5328 -STAT 5329 , STAT 5373 -STAT 5374 .
At least two other courses (not necessarily in a sequence) chosen from Group A and Group B. Course choices will be performed after consulting with the graduate advisor or departmental leadership, subject to course availability, graduation deadlines, and the subfield that the graduate student performs research in. These courses prepare students for preliminary examinations and build the foundation necessary for doctoral degrees.
2. Additional coursework: Thirty-six additional hours selected with the approval of the student’s dissertation advisor and the director of graduate studies. These may include courses offered by the Department of Mathematics and Statistics relevant to the student’s area of research or courses offered outside the department relevant to the student’s area of research.
3. Twelve hours of MATH 8000
Pure Mathematics
1. Four sequences from the following list: MATH 5320 -MATH 5321 , MATH 5322 -MATH 5323 , MATH 5324 -MATH 5325 , MATH 5326 -MATH 5327 , MATH 5330 -MATH 5331 , MATH 5332 -MATH 5333 . Course choices will be performed after consulting with the graduate advisor or departmental leadership, subject to course availability, graduation deadlines, and the subfield that the graduate student performs research in. These courses prepare students for preliminary examinations and build the foundation necessary for doctoral degrees.
2. Thirty-six additional hours selected with the approval of the student’s dissertation advisor and the director of graduate studies. These may be courses offered by the Department of Mathematics and Statistics relevant to the student’s area of research or courses offered outside the Department of Mathematics and Statistics relevant to the student’s area of research.
3. Twelve hours of MATH 8000 .
Statistics
1. All of the following courses: STAT 5328 , STAT 5329 , STAT 5371 , STAT 5373 , STAT 5374 , STAT 5380 , MATH 5382 .
2. Four courses from: STAT 5326 , STAT 5370 , STAT 5372 , STAT 5375 , STAT 5378 , STAT 5379 , STAT 5386 .
3. Twenty-seven additional hours of statistics courses selected with the approval of the student’s dissertation advisor, the director of graduate studies, and the statistics coordinator. These may be statistics courses offered by the Department of Mathematics and Statistics (excluding STAT 5302 -STAT 5303 and STAT 5384 -STAT 5385 ), mathematics courses relevant to the student’s area of research, or courses offered outside the Department of Mathematics and Statistics relevant to the student’s area of research. These courses must be chosen with approval by the student’s dissertation advisor and the director of graduate studies. Note that a Preliminary Examination in pure mathematics must be passed.
4. At least 12 hours of MATH 8000 .
Mathematical Finance
1. All of the following eight courses:
2. At least four of the following courses:
3. Twenty-four additional hours selected with the approval of the student’s dissertation advisor and the director of graduate studies. These may include courses offered by the Department of Mathematics and Statistics (excluding STAT 5302 -STAT 5303 and STAT 5384 -STAT 5385 ) relevant to the student’s area of research or courses offered outside the department relevant to the student’s area of research.
4. Twelve hours of MATH 8000 .
Mathematics Education
1. Foundational coursework (24 hours):
- STAT 5328 -STAT 5329
- At least two sequences from the following, including at least one sequence from Group A and one sequence from Group B:
- At least two other courses (not necessarily in a sequence) chosen from Group A and Group B.
2. Additional coursework (36 hours) selected with the approval of the student’s dissertation advisor and the director of graduate studies. These may be courses offered by the Department of Mathematics and Statistics relevant to the student’s area of research or courses offered outside the Department of Mathematics and Statistics relevant to the student’s area of research. (It is assumed that these courses will include a significant number of graduate Education courses chosen in consultation with the student’s dissertation advisor.)
3. Twelve hours of MATH 8000 .
