ADMISSIONS AND PLACEMENT
Applicants to the mathematics graduate program are evaluated on the basis of their transcripts (courses taken and grades earned), letters of recommendation, GRE scores, TOEFL or TSE scores (for non-native English speakers), personal statement, and other material in their applications. The entire application package is considered, and no one portion guarantees admission (although weaknesses in one area should be compensated by strengths in another area). Applicants should have taken courses in advanced calculus/analysis and in abstract and linear algebra with proofs; and mathematics course grades should be mostly A or A- (or the equivalent). Letters of recommendation should be from mathematics professors who can evaluate the applicant's knowledge and ability, concerning mathematical material at an advanced level.
Scores on the Advanced Math Subject Test of the GRE should be at least 690, though applicants with somewhat lower scores may be admitted if the rest of their application is sufficiently strong. The average GRE scores of the students who entered our Ph.D. program in the recent past were: Verbal: 597; Quantitative: 789; Advanced Math Subject Test: 731. For all those who were admitted (including those who did not matriculate at Penn), the corresponding figures were: Verbal: 589; Quantitative: 790; Advanced Math Subject Test: 739. (In the most recent year, the figures for entering students were 590, 794, and 751, while the figures for all those admitted were 571, 791, and 743.) Non-native English speakers should have a TOEFL score of at least 250 on the computer-based exam, or at least 600 on the paper-based exam; scores on the TSE should be at least 50. Among those admitted to our program in recent years who took the TOEFL, the average score was 268 on the computer-based scale, or 634 on the paper-based scale.
Over the past five years (2000-2004), the average number of applications submitted to our graduate program per year was 170. We admitted an average of 39 students per year to our Ph.D. program. Of these, an average of 14 entered our program per year. In the most recent year, the figures were 173, 33, and 15. In years prior to 2000, the figures were lower, with smaller entering classes in the 1990's.
There were 31 Ph.D.'s awarded during 2000-2004, primarily from students who entered the program during the period 1995-1999. Of these, 24 (or 77%) took academic jobs in mathematics following their Ph.D. The other seven (or 23%) took other mathematically related jobs, in consulting, finance, or in the field of computers. This academic year we expect to award eleven Ph.D.'s (from a larger entering class).
Graduating students receive help from the Mathematics Department in their employment search. This includes guidance about how to apply in an effective way; financial help (e.g. covering the costs of mailing and photocopying); logistical help with submitting letters of recommendation; and help in providing information about the applicant's teaching and research to potential employers.
STUDENTS AND SUPPORT
Currently there are 60 Ph.D. students in our graduate program. Of these, almost all are full-time. Almost half of our graduate students entered our program from colleges or universities outside the United States, from a wide variety of countries including Bulgaria, Chile, China, Germany, Ghana, Romania, Russia, South Korea, Switzerland, and Turkey. About one quarter of our Ph.D. students are women. Students typically receive their Ph.D.'s in five years, and our financial support package lasts for five years for students making good progress toward their Ph.D. (so ordinarily there are no "off years").
The University has announced that during 2005-06, all full-time fully-funded Ph.D. students in the School of Arts and Sciences will receive a stipend of at least $17,500, in addition to a full-tuition scholarship and free health insurance (for up to six years, when fully funded). In addition to the academic year stipend, Mathematics Ph.D. students are also offered a fellowship stipend for the summer following their first year; and they frequently receive a stipend for teaching or research in later summers, also supplementing their academic year stipends. (Students are expected to be in residence at least during the nine-month academic year; to be eligible for summer funding, students are expected to be in residence during most of the summer as well.) Mathematics graduate students also receive office space with a computer, and access to the Mathematics Reading Room and the Math-Physics-Astronomy Library.
COURSES, REQUIREMENTS AND MENTORING
The Penn Mathematics Graduate Program offers three degrees: the masters degree (A.M.), the M.Phil. degree (in between the masters and the Ph.D.), and the Ph.D. The Ph.D. is a research degree; the M.Phil. is a terminal professional degree; and the masters degree can be earned either as a professional degree or as a step in the Ph.D. program.
Ph.D. students take four courses each semester that they are on fellowship (including the first year), and three courses in other semesters, until they complete the course requirement. There are many courses to choose from, but all Ph.D. students must either take, or place out of, the following required courses:
Ph.D. students can receive a masters degree on the way to the Ph.D. by completing the requirements for that degree (eight graduate courses, with at least one each in algebra, analysis, and geometry-topology; passing the Masters Preliminary Exam; and submitting and successfully defending a masters thesis. Apart from the masters thesis (which is optional for Ph.D. students), Ph.D. students are expected in their first year to complete the requirements for the masters degree, and to achieve a distinguished pass on the Masters Preliminary Exam. (By doing this and by doing well in their classes, students satisfy the Qualifications Evaluation.) Ph.D. students are expected to take their oral Ph.D. Preliminary Exam by the end of the second year, unless given an extension by the Graduate Group Chair.
Students receive mentoring from both their faculty advisor and the Graduate Chair. Students are assigned to a faculty advisor upon entering the program, and students can change advisors if they wish. Following passage of the oral exam, students select a Ph.D. thesis advisor, who becomes their main mentor. Students also receive mentoring concerning their teaching (as TAs) from the faculty and senior grad students who coordinate the TA training program. They also receive additional mentoring from their Ph.D. Advisory Committee, with whom they discuss the topic of their dissertation (Ph.D. thesis). These discussions are in lieu of a formal written dissertation proposal.
More information about requirements for the masters, M.Phil, and Ph.D. programs.