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Grad program overview

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.

Non-native English speakers should preferably have a TOEFL score of at least 100 on the ibt exam (and at least 20 on the spoken English portion of that exam), or at least 250 on the computer-based exam; scores on the TSE should be at least 50.

Over the past few years, the average number of applications submitted to our graduate program per year was around 300. We admitted about 20-30 students per year to our Ph.D. program. Of these, an average of 10-12 entered our program per year.

A majority of our Ph.D.'s take academic jobs in mathematics following their Ph.D. The remainder take other mathematically related jobs, in areas such as computer vision, genomics, medical imaging, mathematical finance, or artificial intelligence.

Graduating students receive help from the Mathematics Department in their employment search. This includes guidance about how to apply in an effective way; logistical help with submitting letters of recommendation; and help in providing information about the applicant's teaching and research to potential employers.

More information.

Students and Support

Currently there are about 55 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 Australia, Brazil, Bulgaria, Canada, Chile, China, Germany, Ghana, Greece, India, New Zealand, Norway, Pakistan, Romania, Russia, Korea, Singapore, Switzerland, Thailand and Vietnam. We strive to have a diverse community of students including women and those from other groups that are under-represented in mathematics.

Our financial support package lasts for five years for students making good progress toward their Ph.D., and students typically complete their Ph.D.'s within this time frame. The support package includes at least four semesters with no teaching required, as well as three summers of funding with no teaching required. The current academic year stipend for Ph.D. students is $40,500 for twelve months, which includes the summer stipend, in addition to a full-tuition scholarship and free health insurance. (Students are expected to be in residence on campus during the summer months when they are funded, unless they arrange otherwise with the graduate chair of the program & their advisor.) Mathematics graduate students also receive office space with a computer, and access to the Mathematics Reading Room and the Math-Physics-Astronomy Library. All Penn students have access to a free gym membership to Pottruck Recreation, including the basketball and tennis courts, and the swimming pool. Students also have access to Penn Transit which operates an evening shuttle service, providing transportation free of charge to and from campus pick-up locations to any address within the service boundaries.

More information.

Courses, Requirements and Mentoring

The Penn Mathematics Graduate Program offers three degrees: the masters degree (A.M.), the M.Phil. degree (for students who already have a masters degree), 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 typically take four courses each semester during their first year, and three courses in other semesters when they teach, until they complete the course requirement (a total of 20 courses). There are many courses to choose from, but all Ph.D. students must either take, or place out of, the following required courses:

  • In geometry-topology: Math 600, 601.
  • In algebra: Math 602, 603.
  • In analysis: Math 608, 609.


These courses are usually taken in the first year of the program. Students who place out of these courses, by demonstrating their knowledge of the material to the instructor, may take other courses instead. In the second year, students typically take courses related to their areas of greatest interest, and in preparation for their oral exam (the Ph.D. Preliminary Exam). In the third year, students concentrate on their research, and typically complete their course requirement by taking topics courses in the area of their dissertations, independent studies, reading seminars, etc. (Students can complete their course requirement sooner by transfering up to eight courses taken as a graduate student elsewhere.)

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 have a pre-thesis advisor from the time they enter the program. Following passage of the oral exam, students select a Ph.D. thesis advisor, who becomes their main mentor. 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. Students also receive mentoring concerning their teaching (as TAs) from the faculty and senior grad students who coordinate the TA training program.

More information about Graduate Courses.

More information about requirements for the masters, M.Phil, and Ph.D. programs.


Penn has a PhD student leave of absence policy. The policy is available in the Pennbook, though its essential elements are as follows:

PhD students can be granted a leave of absence for military duty, medical reasons, or family leave. Military, medical and family leave “stops the clock” on time to completion. Personal leave for other reasons may be granted with the approval of the Graduate Group Chair in consultation with the Graduate Dean, but does not, absent exceptional circumstances, “stop the clock” on time to completion. While on leave, a student’s funding from the University is deferred until the student returns from leave. Students receiving funding from external sources, such as government grants, are subject to the conditions established by the funding source. Students whose University funding includes coverage of the Penn Student Health Insurance Plan will continue to receive coverage for their individual health insurance while on medical or family leave for one full semester. The procedures for requesting and returning from leave are outlined here. For information regarding the Penn Student Insurance Plan (PSIP) while on leave, see:

Following a leave, students are expected to fulfill any/all unmet service obligations.