PhD Mathematics


This program is intended for individuals who wish to develop careers in mathematical research and mathematics education at the university level or mathematical research in various industry and government sectors. Students of this program gain necessary exposure to significant results and trends in their chosen fields of specialization.

 Degree Requirements

To be admitted into the program, the applicant must have completed all the requirements for the M.S. in Mathematics degree. Then, s/he must fulfill the following:

  1. Complete a total of twenty-seven (27) units of graduate courses in mathematics consisting of nine (9) units of required courses and eighteen (18) units of electives.
  2. Pass a comprehensive examination, a written exam covering three areas, two of which are algebra and analysis. The third area may be chosen by the student from other fields covered by the courses s/he has taken.
  3. Submit a doctoral dissertation which is considered by the Mathematics Department an original contribution to existing knowledge. The dissertation will count for twelve (12) units toward the total thirty-nine (39) units required.
  4. Proof of submission of a paper containing results of the dissertation to a Science Citation Indexed journal (ISI) or a reputable referred international journal.
  5. Presentation of dissertation results in an international or national conference in mathematics.


The student is required to complete nine (9) units of required courses:

  • MA 251: Algebraic Structures II
  • MA 295A.2: Seminar in Real Analysis II
  • Any one of the following courses:
    • MA 260: Topological Structures
    • MA 295C.1: Seminar in Finite Geometry
    • MA 295C.4: Seminar in Groups and Design
    • MA 295C.8: Seminar in Hyperbolic Geometry
    • MA 295C.9: Geometric Crystallography
    • MA 295C.10: Seminar in Color Symmetry
    • MA 295C.11: Seminar in Tilings and Patterns

The student must also complete eighteen (18) units of electives in mathematics.

 Comprehensive Exams

This is a written exam that covers algebra, analysis and a third area. The third area may be chosen by the student from other fields covered by the courses s/he has taken.

 Dissertation and Oral Defense


Prospective students may go to the Admissions page to learn more about the application procedure.