Mathematics (MPhil)
专业详情
The Master of Philosophy in mathematics is a terminal professional degree that is designed for students who want to go beyond the usual masters degree. Entering students should have previously completed either an undergraduate or a regular masters program in mathematics. The degree is typically earned one or two years after beginning to take courses that go beyond the regular master of arts degree.
Students who already have a regular masters degree take six additional graduate courses numbered 600 or above to earn an M.Phil. degree. Students who enter the program with just an undergraduate degree will fulfill the usual masters course requirements plus an additional six (for a total of 14 courses). Students in this program also need to pass the Graduate Preliminary Exam and an oral exam in one area of mathematics, and to submit and defend an M.Phil. thesis (which is somewhat longer and more in depth than a thesis in the usual masters program).
Detailed requirements:
- Admission to candidacy: A Bachelors degree (but not a masters degree) is required for entrance to the program. Admission to M.Phil. candidacy is achieved by passing the Preliminary Exam by the end of the first year in the graduate program, and the oral M.Phil. Preliminary Exam (described below). If the student so requests before the exam, the Masters General Examination can serve as the M.Phil. Preliminary Exam. In this case, the exam will test the depth and breadth of knowledge expected of entering M.Phil. candidates.
- M.Phil. Preliminary Exam: This is an oral exam in the subfield of mathematics which is the student’s intended area of specialization. The student should demonstrate both depth and breadth of knowledge, as well as real mastery of basic material and the ability to apply it to specific examples. Typically, the content of this exam will be somewhat more than that of a one-semester graduate course at or above the 610 level.
- Course requirements: A minimum of six units of graduate courses (beyond the course requirements for the Masters) at the University of Pennsylvania, numbered 600 and above, is required for the M.Phil. Degree, including at least four taken in the Mathematics Department. These courses cannot include any that are counted towards a Masters degree. Students who do not have a Masters degree must in addition satisfy the course requirement of a Masters degree (while those who already have a Masters degree need take just these six). Among these six courses, every student must take at least a semester of graduate courses in two of algebra, analysis and geometry-topology.
- Language requirement: There is no foreign language requirement for the M.Phil. Degree.
- Seminar requirement: The student must satisfactorily present a lecture in one of the department’s graduate or research seminars, and answer questions about the material. The intention of this requirement is to help the student gain experience in digesting and presenting advanced material and fielding questions about it before an audience of mathematicians. Guidance in the preparation of these lectures is provided by faculty members in the department.
- M.Phil. Thesis: Each student must write, under the supervision of a Mathematics Department faculty member, a satisfactory M.Phil. thesis, which is typically expository in nature, but may also be a research paper. The preparation of this thesis should involve the mastery of some area of mathematics beyond the curriculum of the courses that the student has taken. (To obtain an M.Phil. degree, it is not necessary to have previously written a masters thesis. But a student in the M.Phil. program who previously submitted a masters thesis cannot resubmit that thesis toward the M.Phil.)
- The M.Phil. Comprehensive Examination: Following submission of the M.Phil. thesis, the student will take a Comprehensive Examination for the M.Phil. degree. This exam will consist of a presentation by the student of the content of the thesis, followed by questions from the faculty on the topic presented and related areas of mathematics.
- Some important administrative details:
- The administrative details listed earlier in connection with the Masters Degree program apply to the M.Phil. program as well. In addition, we have the following:
- When the student asks that the Masters Gen’l Exam serve as the M.Phil Prelim exam, there are two possible positive outcomes: Pass at the M.Phil level, which requires demonstration of the required depth and breadth in the subject matter; Pass at the M.A. level (described in the requirements for that degree). If the student does not pass at either of these levels, he may retake the exam one more time; if on the initial exam, the student passes at a level below the desired outcome then he may also retake the exam one more time. In either case, the single retake of the exam must occur before the end of the next semester.
- Timing: The program leading to the M.Phil. must be completed within two years of full time study (after completion of the masters course-work). Part time study, when allowed, will have a corresponding timetable set in each case by the Graduate Group Chair.
- Course requirement: Approval of the Graduate Group Chair is required for courses taken outside the Penn Mathematics Department to be counted toward the course requirement for the M.Phil. Degree in Mathematics.
- The M.Phil. Comprehensive Examination Committee is appointed by the Graduate Group Chair after consultation with the student. It will consist of two or more faculty members, at least one of whom must be tenured, and one of whom will ordinarily be the supervising faculty member. The Graduate Group Chair will notify the entire mathematics faculty of the exam; all faculty are explicitly invited to attend, and those who do are full voting members of the Exam Committee.
- If the M.Phil. Comprehensive Examination is not passed on the first try, it may be taken just once more, and this must occur before the end of the following semester.
