PSU Mark

Mathematics Department

Graduate Program

Eberly College of Science Mathematics Department

List of Requirements

The Ph.D. Program

Incoming Ph.D. students are expected to pass qualifying examinations by the beginning of their second year in the Ph.D. program. The system of qualifying examinations is explained in details here.

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 fifth semester of study) and offers counsel to the student as his research progresses.

The D.Ed. Degree

This program is designed for students who are primarily interested in teaching rather than research. In order to qualify for admission to the D.Ed. program, a student must have at least three years teaching experience at the college level. Experience gained as a teaching assistant may not be used to satisfy this requirement.

Requirements for Degree Programs

The following requirements apply to all degree options.

The Ph.D. Program

  1. Qualifying Examinations (Departmental requirement). Ph.D. students are expected to pass two qualifying examinations, in Algebra and Analysis, by the beginning of their second year in the Ph.D. program. The system of qualifying examinations is explained in details here.

  2. 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.
  3. Colloquium Attendance Requirement (Departmental requirement). All students in our PhD program are required to attend at least 12 Mathematics Department Colloquium talks each academic year. First-year students (only) may substitute MASS colloquium talks for some of the required Departmental Colloquium talks. Attendance will be taken to enforce this requirement.

  4. 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. Click here for details.

  5. Ph.D. Candidacy (Graduate School requirement). The Graduate School will recommend candidacy after a student has passed all qualifying examinations and demonstrated satisfactory progress toward (2) above. Admission to candidacy is conferred by the Graduate School.
  6. Residence 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.
  7. Continuous Registration (Graduate School requirement). After a Ph.D. candidate has passed the comprehensive examination and has met the two-semester full-time residence requirement (5) 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.
  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 must have an adviser by the end of their fifth semester in the Ph.D. program.
  9. 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. It is Penn State's policy that students who are non-native speakers of English be certified as competent to teach in English by the Department of Speech and Communication. The oral competency of both native and non-native (once certified) speakers of English is assessed by the Graduate Studies Committee before the end of the second year of study based mainly on faculty evaluations of the student's classroom performance while teaching undergraduate mathematics courses, which are returned to the Associate Chair of the Department every semester. In the cases when students have not had the opportunity to teach before the end of their second year, oral competence may be assessed based on a faculty report on student's presentations made in seminars. Students whose oral competency is judged to be substandard will be assigned a faculty mentor who will work with them to improve their oral presentation skills. In particular, the student may be required to enroll in the Graduate Student Seminar or to give a presentation in one of the departmental seminars. The faculty mentor will certify in writing to the Director of Graduate Studies when the student has attained the required standard of oral competency. Non-native speakers of English may be required to take and to pass with a B or better SPCOM 114G (Basic ESL).

    To satisfy the written competency, a student should prepare a short expository paper (approximately 4 pages) on topics related to proposed dissertation research. The adviser and one other mathematics graduate faculty member evaluate the paper and report the result to the Director of Graduate Studies (in the case of disagreement the Director will have the paper evaluated by a third member of the graduate mathematics faculty). Students whose written competency is judged to be substandard will be required to take and to pass with a B or better one of the following courses: ENGL 202 (Effective writing), ENGL 418 (Advanced Technical Writing and Editing), ENGL 198G (Writing in the Disciplines) for native speakers of English, and SPCOM 116G (ESL: Reading and Writing) for non-native speakers of English.

    Competence must be formally attested by the Graduate Studies Committee before the doctoral comprehensive examination is scheduled. (International students should note that passage of the minimal TOEFL requirement does not demonstrate the level of competence expected of a Ph.D. from Penn State.)

  10. 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.

The D.Ed. Program

To be admitted to this program, the student must have three years of teaching experience at the college level. Experience gained as a teaching assistant may not be used to satisfy this requirement.

  1. Qualifying Examinations (Departmental requirement). Passage of the qualifying examinations in algebra and analysis. These examinations are subject to the same conditions as discussed in requirement (1) of the Ph.D. program. In particular, students who do not pass both examinations before the beginning of the second year of study may not continue in the program. Entering D.Ed. students who do not pass at least one pre-entrance examination must take at least one of the basic sequences in algebra or analysis.
  2. Course Requirements (Graduate School and Departmental requirement). 90 course and research credits of which at least 30 must be earned at the University Park Campus (see requirement 5 below). 15 credits in educational foundation courses approved by the College of Education (see requirement 7 below). 45 credits of approved mathematics courses, including 24 credits of 500-series courses and 15 credits of 600-series research credits. In order to receive credit for a course, the student must receive a grade of B or better.
  3. Candidacy (Departmental requirement). The Department will recommend candidacy after a student has passed 1 of the 2 qualifying examinations and demonstrated satisfactory progress toward (2) above. Admission to candidacy is conferred by the Graduate School.
  4. Residence Requirement (Graduate School requirement). A minimum of six semesters of full-time graduate study and research (15 credits per semester), or their equivalent in credits (90 credits), of which at least 30 credits must be earned in residence at University Park Campus is required for the D.Ed. dgree. A candidate may register for a maximum of 30 credits of research in absentia, but none of these may count toward the minimum of 30 credits that must be earned at University Park Campus. It is expected that students will register for a minimum of 15 credits of thesis research. The maixmum credit load permitted a student who is employed full time is 6 credits per semester.
  5. 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, soon after the student is admitted to candidacy.
  6. Major Program and Minor Field (Graduate School requirement) The program of study includes a major and either a minor or a group of general studies. A majority of the courses offered in fulfillment of the requirements must be in the major program. A candidate choosing a major outside the fields of professional education (such as mathematics) shall have a minor consisting of no fewer than 15 graduate credits in professional education, as recommended to the dean of the Graduate School early in the major program with the approval of a faculty adviser from the minor area.
  7. Comprehensive Examination (Graduate School and Departmental requirement). The comprehensive examination is scheduled by the Graduate School after the student has passed two qualifying examinations, has satisfied the language requirement, has been admitted to candidacy, and agreed on a thesis adviser and a research program. The comprehensive examination will cover three areas to be chosen by the student from those listed below. It will be based on the contents of the following 400-level series courses in these areas: applied analysis (MATH 411), geometry (MATH 427), logic (MATH 457), number theory (MATH 465), numerical analysis (MATH 455-456), probability and statistics (MATH 414) and topology (MATH 429).
  8. Thesis (Graduate School requirement). Evidence of a high degree of scholarship, competence in scholarly exposition, and ability to select, organize, and apply knowledge must be presented by the candidate in the form of a written thesis. The candidate must demonstrate a capacity for independent thought, as well as ability and originality in the application of educational principles or in the development of a new generalization under scientific controls. A thesis may be based upon a product or project of a professional nature, provided scholarly research is involved. In order to be an acceptable thesis, the professional project must be accompanied by a written discourse demonstrating the nature of the research and including such theories, experiments, and other rational processes as were used in effecting the final result. The topic and outline of the proposed thesis must have the approval of the doctoral committee. A draft of the thesis must be submitted to the doctoral committee a month before the final oral examination.
  9. 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 after admission to candidacy.