(1) Qualifying Examinations (Departmental requirement). All doctoral students are required to take three written qualifying examinations. Two of these examinations must be completed prior to the beginning of the student's second year of graduate study, and third prior to the beginning of their third year. The written qualifying examinations are in the areas of Analysis, Algebra, and Topology/Geometry.
[ Note: Pending approval of the Logic and Foundations option, the following additional information will appear at this point:
Students who elect the Logic and Foundations Option will take a written qualifying examination in Logic/Foundations instead of Topology/Geometry. ]
Students who fail a qualifying examination twice after enrolling may not continue in the Ph.D. program. Students who do not pass all three examinations by the beginning of their third year may not continue in the Ph.D. program.
The examinations are offered starting approximately 10 days before the beginning of the fall semester and at the end of the spring semester each academic year. Basic one-year sequences in each subject are offered annually to help prepare the student for the examinations. Typically, an entering Ph.D. student takes two of the basic sequences in the first year and the third basic sequence in the second year of study, and takes the qualifying examinations in the spring after completing the corresponding courses.
However, entering Ph.D. students may take any of the examinations on arrival in August without penalty. If a pre-entrance examination is failed, the student still has two more opportunities to pass it. Entering Ph.D. students are advised to take at least two basic sequences (in the subjects they did not pass qualifying examinations on arrival) and the subsequent qualifying examinations in the first year of graduate study.
Some qualifying exam problems from previous years are available, along with a selection of problems from some first-year graduate courses. There are also outlines of the first-year courses on which the qualifying examinations are based.
(2) Course Requirements (Departmental requirement). Students must receive a minimum grade of B in at least 11 3-credit 500-level mathematics courses.
(3) Language Requirement (Departmental requirement). Before scheduling their comprehensive examination, students must pass a reading examination in one language, chosen from French, German, and Russian, which is not their native language. Doctoral students must pass the language exam before the end of their third year. The candidate must translate (the equivalent of) four typewritten pages of mathematics (selected from a journal or textbook) into English with the aid of a dictionary. The translation must be accomplished in two hours or less. The material to be translated is usually selected by the student's advisor. It is subject to approval by the Director of Graduate Studies.
(4) Ph.D. Candidacy (Graduate School requirement). The Graduate School will usually recommend candidacy after a student has passed 2 of the 3 qualifying examinations and demonstrated satisfactory progress toward (2) and (3) above. Admission to candidacy is conferred by the Graduate School.
(5) 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.
(6) 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.
(7) 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.
(8) 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 advisor 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.)
(9) Comprehensive Examination (Graduate School requirement). The comprehensive examination is scheduled by the Graduate School after the student has passed three qualifying examinations, has satisfied the language requirement, has been admitted to candidacy, and agreed on a thesis advisor and a research program. Doctoral students must pass their comprehensive examination by the end of their seventh semester. A doctoral committee chaired by the thesis advisor 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.
(10) 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.
(11) 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.