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.

Ph.D. Examinations: The Ph.D. requires three 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 normally occurs after the student has begun his/her thesis research; and 3. the Dissertation Defense, which occurs at the completion of the program.

  1. Ph.D. Qualifying Examination: The PhD Qualifying Examination will consists of two exams, Analysis (covering material in Math 7350 and Math 7351) and Algebra (covering material in Math 7261 and Math 7262). The two exams, Analysis and Algebra, may be taken at the same time 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 approval of the Graduate Committee. The exam will be given in 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: This is an oral examination in preparation for the Ph.D. Dissertation and primarily covers specialized material related to the Dissertation topic. Upon completion of this exam the Comprehensive Exam Results Form must be completed and returned to the Math Department.
  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.

To take the Ph.D. Qualifying Examinations after the first year of the program
Fall Spring
1st year Math 7350 Real Variables I
Math 7261 Algebraic Theory I
Math 6411 or Math 7411 Topology
Math 7351 Real Variables II
Math 7262 Algebraic Theory II
Math 6361 or Math 7361 Complex Variables

To take the Ph.D. Qualifying Examinations after the second year of the program
Fall Spring
1st year Math 6350 Intro to Real Analysis I
Math 6261 Abstract Algebra
Math 6411 or Math 7411 Topology
Math 6351 Intro to Real Analysis II
Math 6361 or Math 7361 Complex Variables
Math 6000-8999 Elective
2nd year Math 7350 Real Variables I
Math 7261 Algebraic Theory I
Math 6000-8999 Elective
Math 7351 Real Variables II
Math 7262 Algebraic Theory II
Math 6000-8999 Elective