Ph.D. Requirements - Mathematics

The Ph.D. requirements include both graduate credit requirements (including basic required courses) and examinations. Depending on the background of the student, the basic required courses and Ph.D. Qualifying Examinations can be completed within one to two years.

Course Requirements: 72 hours of graduate credit (or 36 hours for students who enter with an approved Master's degree) is required for the degree. In this 72 hour requirement, students must satisfactorily complete certain basic required courses: two semesters of Real Analysis (Math 7350 and Math 7351), two semesters of Algebra (Math 7261 and Math 7262), one semester of Complex Analysis (either Math 6361 or Math 7361), and one semester of Topology (either Math 6411 or Math 7411). More details on course descriptions and requirements can be found in the Graduate Catalog. See the Graduate handbook for any additional departmental policies.

Ph.D. Examinations: 1. the Ph.D. Qualifying Examination, which is normally completed after the first or second year of graduate studies (depending on the student's background); 2. the Ph.D. Comprehensive Examination, which is normally taken after the student has begun his/her dissertation work; and 3. the Dissertation Defense, which occurs at the completion of the program.

1. Ph.D. Qualifying Examination: The PhD Qualifying Examination consists of two components: Analysis (covering material in Math 7350 and Math 7351) and Algebra (covering material in Math 7261 and Math 7262). The two components, Analysis and Algebra, may be taken at the same term or in different terms. Normally, both exams should be completed by the beginning of the third year of graduate studies, but some flexibility may be negotiated with the approval of the Graduate Committee. The exam is typically offered during the week prior to the start of the Fall Semester and the start of the Spring Semester. Further information on syllabi for basic courses and previous Ph.D. Qualifying Examinations can be found here.
   
   Note that the Ph.D. Qualifying Examination structure changed effective January 2014, so some previous examinations may contain parts no longer relevant in the current structure.
   
   
2. Ph.D. Comprehensive Examination: The comprehensive exam consists of two parts: the completion of the qualifying exam and a talk in preparation for the Ph.D. Dissertation. This talk must be announced to the department and evaluated by a committee of at least three faculty members. Upon completion of these two parts, the Comprehensive Exam Results Form must be completed and returned to the Graduate School.
3. Dissertation Defense: Students are expected to defend their dissertation during their last year in the program. Then the Dissertation Final Defense Results Form must be completed and returned to the Graduate School.

Completion of the basic course requirements leading to the successful completion of the Ph.D. Qualifying Examinations can be summarized by the following tables.