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Ph.D. Program

Earn admissions to a nationally ranked program

Incoming Ph.D. students are expected to pass qualifying examinations by the end of their third semester in the Ph.D. program.

After passing the qualifying examinations, students are expected to select a thesis adviser and form a doctoral committee. The committee administers the comprehensive examination (no later than the end of the sixth semester of study) and offers counsel to the student as his research progresses.

  • No credit will be given for any course in which a grade of less than B is received.
  • A minimum grade point average of 3.0 is required for graduation for all advanced degrees.


  1. American English Oral Communicative Proficiency Test (AEOCPT)-International students only (Graduate School requirement) This exam must be taken upon arrival during the week of orientation. Students who pass the exam may teach without restrictions; marginal or failing students must register for the appropriate ESL course.
  2. SARI/CITI (Scholarship and Research Integrity/Collaborative Institutional Training Initiative) (Graduate School requirement) The SARI@PSU program is composed of two parts: an online course, and an interactive, discussion-based component; and encompasses content that is both interdisciplinary and discipline-specific. The online portion Part 1), offered through the Collaborative Institutional Training Initiative (CITI), provides a common language and understanding of the history and principles of the responsible conduct of research. This requirement must be completed within the first two weeks of the semester of arrival. The discussion-based component Part 2)provides an opportunity for in-depth exploration of important issues unique to each field of study. Part 2 is completed by attendance at the Graduate Student Seminar (see below).
  3. Qualifying Examinations (Departmental requirement) Ph.D. students are expected to pass four qualifying examinations out of the following areas: real analysis, linear algebra, abstract algebra, complex analysis, functional analysis, topology.  All students are required to pass real analysis and complex analysis. Students may then choose between linear and abstract algebra and functional analysis and topology.  Exams must be completed by the end of their third semester in the Ph.D. program. The system of qualifying examinations is explained in detail  here: Qualifying Exams.
  4. Colloquium Attendance Requirement (Departmental requirement) Students year one (1) through the semester of the Ph.D. Oral Comprehensive Examination are required to attend at least 12 colloquium talks each academic year. Four (4) of the talks may be substituted by Departmental Seminars. First-year students (only) may substitute Student Colloquium talks for some of the required Departmental Colloquium talks. Students post-comprehensive are required to attend six (6) colloquium talks with NO substitutions.  Colloquium Attendance Form for 2022-23.
  5. Graduate Student Seminar Requirement (Departmental requirement) This is a three credit course offered every spring. It is a requirement that every student successfully completes the seminar before his or her third year of study.
  6. Ph.D. Candidacy (Graduate School requirement) The Department of Mathematics will recommend Ph.D. candidacy after a student has passed all qualifying examinations and successfully completed 18 credits of Mathematics courses. Admission to candidacy is conferred by the Graduate School.
  7. Oral and Written English Competency (Graduate School and Departmental requirement) A candidate for the degree of Doctor of Philosophy is required to demonstrate high-level competence in the use of the English language, including reading, writing, and speaking, as part of the language and communication requirements for the Ph.D. Oral competency is assessed by the GTA (Graduate Teaching Assistant) Oversight Committee. Written competency is evaluated by the students' advisor. For additional detail, please see Oral and Written English Competency.
  8. Advisers and Doctoral Committees (Graduate School requirement) Consultation or arrangement of the details of the student's semester-by-semester schedule is the function of the adviser. General guidance of a doctoral candidate is the responsibility of a doctoral committee consisting of four or more active members of the Graduate Faculty, which normally includes at least two faculty in the major field and is chaired by the student's adviser. This committee is appointed by the Graduate Dean through the Office of Graduate Programs, upon recommendation of the Director of Graduate Studies. A student should have an adviser by the end of their fourth semester and must have an adviser by the end of their fifth semester in the Ph.D. program.
  9. Course Requirements (Departmental requirement) Students must receive a minimum grade of B in at least eleven 3-credit 500-level mathematics courses. Students must take the Graduate Student Seminar before the third year of study.
  10. Ph. D. Oral Comprehensive Examination (Graduate School requirement) The comprehensive examination is scheduled by the Graduate School after the student has passed all qualifying examinations, has been admitted to candidacy, and agreed on a thesis adviser and a research program. Doctoral students must pass their comprehensive examination by the end of their sixth semester. A doctoral committee chaired by the thesis adviser determines whether the proposed problem is acceptable for the thesis and whether the student has the necessary background to pursue the work proposed. The committee is at liberty to inquire into any aspect of the student's preparation and progress.
  11. Ph.D. Thesis (Graduate School requirement) The ability to do independent research and competence in scholarly exposition must be demonstrated by the preparation of a thesis on some topic related to the major subject. It should represent a significant contribution to knowledge, be presented in a scholarly manner, reveal an ability on the part of the candidate to do independent research of high quality, and indicate considerable experience in using a variety of research techniques. The contents and conclusions of the thesis must be defended at the time of the final oral examination. A draft of the thesis must be submitted to the doctoral committee a month before the final oral examination.
  12. Final Oral Examination (Graduate School requirement) The final oral examination is primarily a defense of the thesis and is scheduled by the Graduate School at least three months after the date of passing the comprehensive examination and no more than seven years after admission to candidacy.
  13. Residency Requirement (Graduate School requirement) After being admitted to candidacy, the student must be a full-time graduate student as defined by the Graduate Bulletin for two consecutive semesters (excluding summers) before comprehensive examinations can be scheduled.
  14. Continuous Registration (Graduate School requirement) After a Ph.D. candidate has passed the comprehensive examination and has met the two-semester full-time residency requirement (above), the student must register continuously for each fall and spring semester (beginning with the first semester after both of the above requirements have been met) until the Ph.D. thesis is accepted and approved by the doctoral committee.