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I. Graduate Fellowships 
II. Financial support package for Ph.D. students 
III. Ph.D. Thesis

I. Graduate Fellowships

There are various fellowships available for graduate students. We mention in particular:

a) Benjamin Franklin Fellowships --Ph.D. students are offered five years of support as Benjamin Franklin Fellows. During this time they receive a full tuition scholarship, a generous stipend each academic year, and coverage of fees and health insurance. The ten month academic year stipend during 2020-21 is $30,940. As Benjamin Franklin Fellows, students will typically serve as teaching assistants during their second, third, and fifth years, but not have teaching or grading duties during their first or fourth years. Benjamin Franklin Fellows are expected to make good progress toward their degrees.

b) Summer fellowships --Ph.D. students who are offered full support will be offered three summers on fellowship, during which they will receive a stipend and have no teaching or grading responsibilities. The summer 2020 stipend is $4,880 and the 2021 stipend will be $5,085. This is expected to rise in future years, as it has in the past. Students receiving summer fellowship stipends are expected to work on their mathematical studies and to be in residence at Penn for the bulk of the summer (unless the Graduate Chair makes an exception in advance due to specific circumstances). Students may also request summer teaching assignments to gain additional teaching experience; an extra stipend is provided to those grad students who teach in the summer.

c) Math Department Research fellowships --These are fellowships awarded to selected Ph.D. students, for the purpose of working on research projects that are funded by the National Science Foundation or other agencies. Each year a number of these are awarded.

d) Calabi Fellows and Scholars --Incoming graduate students are eligible to be considered for fellowships from the Mathematics Department's Calabi Scholars Fund, started in 1997 and named in honor of Prof. Eugenio Calabi. A small number may be granted by the Mathematics Department each year. Those who are named as Calabi Fellows or Calabi Scholars receive additional supplements to their stipends each year of their support package that they are in good standing and making timely progress toward their Ph.D.

e) Dean's Dissertation Fellowships --These are one year fellowships awarded in a School of Arts and Sciences competition to senior graduate students who are working on their Ph.D. theses. The Department of Mathematics recommends several of our most qualified students every year.

f) NSF Fellowships --These fellowships, which are awarded by NSF, provide three years of fellowship support with no teaching or grading required. The deadline for applying for these fellowships is early December. These fellowships are restricted to U.S. citizens and permanent residents. Applications are accepted from students in their last year of undergraduate study or in their first two years of graduate study. Further information is available on the NSF website and on the Graduate Fellowship program website.

g) AAUW Fellowships --These fellowships are awarded by AAUW, the American Association of University Women. They provide one year of fellowship support to women graduate students. More information is available on the AAUW Fellowshipwebsite.

h) Microsoft Graduate Fellowships --These fellowships are awarded by Microsoft Research. They provide two-to-three years of fellowship support; graduate students may apply in their second or third year of a Ph.D. program. More information is available on theMicrosoft Graduate Fellowship website.

i) NDSEG Graduate Fellowships --These US government fellowships provide three years of graduate support in mathematics and other scientific fields with no teaching required during that time. These fellowships are restricted to U.S. citizens or nationals who are at or near the beginning of their graduate studies. The application deadline is in early January, and more information is available on the NDSEG website.

II. Financial support package for Ph.D. students.

The number of years indicated below starts with the student's enrollment as a graduate student at Penn. It does not include graduate work done elsewhere, or years on leave.

  1. The usual financial support package is for five years, for students in good standing who are making satisfactory progress toward the Ph.D. Students are given at least two years of support with no teaching expected, including the first year and typically the fourth year. They are also given three summers of support with no teaching expected, and may ask to teach (for a stipend) for their other summer.
  2. Performance in the first year courses and on the Preliminary Examination will be taken into consideration before a second year of financial support is given.
  3. Before a third year of financial support is given, the student must have taken the Ph.D Preliminary exam (unless given an extension by the Graduate Chair).
  4. Before a fourth year of financial support is given, the student must have passed the Ph.D Preliminary exam, and fulfilled the seminar requirement, and must be in good standing. At this point the student should be maturing as a growing mathematician, should be attending seminars and colloquia on a regular basis, and should be giving evidence of very serious immersion in mathematics as a professional.
  5. A fifth year of financial support is dependent on making substantial progress toward the Ph.D, and having a plan to complete the thesis in a reasonable period of time.
  6. If approved by the thesis advisor and graduate chair, students may be permitted to stay for a sixth year, if they are close to completing their thesis. At that point their financial support plan will have expired, but they may apply to be an "outside TA" for a reduced stipend. Students in their sixth year are responsible for their tuition, which drops substantially after the fifth year.
  7. Good performance as a teaching assistant is expected, for continuation in that capacity. Such performance is also important when applying for academic jobs.
  8. Students whose native language is not English are required to pass a test of spoken English given by the University's English Language Program. This test is given shortly before the beginning of each semester. It is best to pass this exam prior to the beginning of the first year. It must be passed before the start of the second year in order to receive funding in the second year as a TA. (By law, non-native speakers of English cannot be TAs without first passing this exam.) International students are strongly urged to speak English at every opportunity and to attend departmental colloquia and social functions.
  9. During the regular academic year, students receiving financial support from the University (in any form) must inform the Graduate Group Chair in writing and receive permission in writing before they may receive financial compensation from jobs outside the University. Because of conflict of interest, a student serving as a teaching assistant for a given course may not receive payment for tutoring other students enrolled in that course (this includes students enrolled in a different section of the same course).
  10. In case of financial difficulties the student should consult the Graduate Group Chair.

III. Ph.D. Thesis

The Ph.D. thesis (dissertation) is the heart of the Ph.D. program. It consists of a significant piece of original research in an area of mathematics. Students generally begin work on the topic of their Ph.D. thesis in their third year in the program, and should finish writing it by the end of their fifth year. Work on the thesis is done in consultation with a thesis advisor, who is ordinarily a member of the Penn Mathematics Department. In case a student desires to do dissertation work under a person not on the graduate faculty at Penn, the student must obtain the approval of the Graduate Group Chair before beginning the thesis work.

When a student nears completion of the dissertation, the Graduate Group Chair, in consultation with the student and the Thesis Advisor, will appoint a committee to examine and approve the thesis. This Thesis Examination Committee consists of three or more faculty members, at least one of whom is a tenured member of the Penn Mathematics Department, and at least one of whom is outside the area of specialization of the thesis. The Chair of the committee should be someone other than the Thesis Advisor competent to judge the technical merits of the dissertation. The Thesis Advisor or the Chair of the committee (but not necessarily both) should be a tenured member of the Mathematics Department.

The Graduate Group Chair will organize the date, time and place of the examination and issue a memorandum to all faculty members concerning the exam.

It is the responsibility of the student to provide members of the Thesis Examination Committee with copies of the thesis before the University's "final date for presentation to faculty of completed doctoral dissertations". A copy of the thesis should also be left in the Department office by this date so that any other interested faculty member may read it before the Final Ph.D. Examination. In particular, the Thesis Advisor and the Chair of the Examination Committee should have an ample opportunity to suggest changes in the manuscript before it is typed in final form. Students should consult the Graduate Secretary and the Office of the Graduate Faculties concerning the format of the dissertation and the rules regarding its submission.

The final typed version of the thesis must be read and approved by the Thesis Advisor and the Chair of the Examination Committee by the "final date for faculty reports on acceptance of dissertations". This is a University-wide rule and no exceptions can be made.

After the dissertation is approved by the Thesis Advisor and Chair of the Examination Committee, the Final Ph.D. Examination will be scheduled. This examination must take place before the University-wide "final date for deposit of Ph.D. dissertations and for faculty reports on satisfaction of degree requirements". At the examination, the student will be expected to give a short exposition of the results of the thesis work and to answer questions concerning not only the thesis but also areas related to it. All faculty members of the Graduate Group in Mathematics will be invited to attend the examination. Those who do so are full voting members of the Exam Committee.