Ph.D. Program
Degree requirements.
In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.
- Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics
- Pass the six-hour written Preliminary Examination covering calculus, real analysis, complex analysis, linear algebra, and abstract algebra; students must pass the prelim before the start of their second year in the program (within three semesters of starting the program)
- Pass a three-hour, oral Qualifying Examination emphasizing, but not exclusively restricted to, the area of specialization. The Qualifying Examination must be attempted within two years of entering the program
- Complete a seminar, giving a talk of at least one-hour duration
- Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee
- Meet the University residence requirement of two years or four semesters
Detailed Regulations
The detailed regulations of the Ph.D. program are the following:
Course Requirements
During the first year of the Ph.D. program, the student must enroll in at least 4 courses. At least 2 of these must be graduate courses offered by the Department of Mathematics. Exceptions can be granted by the Vice-Chair for Graduate Studies.
Preliminary Examination
The Preliminary Examination consists of 6 hours (total) of written work given over a two-day period (3 hours/day). Exam questions are given in calculus, real analysis, complex analysis, linear algebra, and abstract algebra. The Preliminary Examination is offered twice a year during the first week of the fall and spring semesters.
Qualifying Examination
To arrange the Qualifying Examination, a student must first settle on an area of concentration, and a prospective Dissertation Advisor (Dissertation Chair), someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective advisor, the student forms an examination committee of 4 members. All committee members can be faculty in the Mathematics Department and the chair must be in the Mathematics Department. The QE chair and Dissertation Chair cannot be the same person; therefore, t he Math member least likely to serve as the dissertation advisor should be selected as chair of the qualifying exam committee . The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval, it is to be circulated to all faculty members of the appropriate research sections. The Qualifying Examination must cover material falling in at least 3 subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one section of the department. Sample syllabi can be reviewed online or in 910 Evans Hall. The student must attempt the Qualifying Examination within twenty-five months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the re-examination must be held within thirty months of the student's entrance into the PhD program. For a student to pass the Qualifying Examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student.
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Mathematics, PhD
The Department of Mathematics of the University of Pennsylvania offers a full Graduate Program in Mathematics, conferring the degrees of Master of Arts (A.M.), Master of Philosophy (M.Phil.), and Doctor of Philosophy (Ph.D.). The educational aim of this program is to provide well-rounded mathematical training for a career of research and teaching in mathematics, as well as for other careers which use advanced mathematics in a substantial way. Students are offered the possibility of a dual Ph.D. degree in Mathematics and a Masters degree in other subjects, including physics and computer science.
This program covers a variety of areas, including analysis, geometry-topology, algebra, mathematical physics, combinatorics, logic, and probability. See our Graduate Mathematics Page and our Math Department home page for detailed information about other aspects of this program and of the Penn Math Department as a whole, including its colloquia, seminars and lecture series, and the research interests of the faculty.
Full time Ph.D. students receive financial support for five years, at least two of which are in the form of a fellowship.
In addition, Penn offers an interdisciplinary graduate program in Applied Mathematics and Computational Science , for which there is separate application process.
For more information: https://www.math.upenn.edu/graduate/
View the University’s Academic Rules for PhD Programs .
Sample Plan of Study
A total of 20 course units are required for graduation.
The degree and major requirements displayed are intended as a guide for students entering in the Fall of 2024 and later. Students should consult with their academic program regarding final certifications and requirements for graduation.
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