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University of Pennsylvania Course/Program Name
Application closes on
National :15 Dec 
International :15 Dec 

MPhil Mathematics

 Course Level
Masters / PG
Full Time

2 Years
 Start month

 Tuition fee

4526 USD
4526 USD

Application fee

International 80 USD
National 80 USD
Department of Mathematics
Scores accepted
IELTS (min)7
TOEFL-IBT (min)100
TOEFL-PBT (min)600
GRE (avg)307
GMAT (avg)732

World University Ranking

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About this course

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 Masters 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).

Check further details on University website

Eligibility Criteria

Eng lang – On the TOEFL-iBT exam (Internet-Based Test), competitive applicants tend to have a composite score of 100 and above (the exam is scaled from 0-120, with 120 being a perfect score) with demonstrated consistency on each section of the exam (reading, listening, speaking, and writing). On the Paper- Based TOEFL, Penn tends to admit students with a score of 600 and above (the exam is scaled from 310 to 677, with 677 being a perfect score).

  • IELTS - 7.0
  • GRE - 307
  • GMAT - 732


Check further details on University website

Course Modules

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 Masters Preliminary Exam, 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. 
  • Concentrations in Applied and Computational Mathematics: Since M.Phil. degree students may wish to pursue a course of study which emphasizes either applied or computational mathematics, the Mathematics Department recognizes this by offering Masters degrees with concentrations. Courses given in the Mathematics Department or elsewhere in the University can be designated by the Graduate Group Chair as being in the applied or in the computational mathematics concentration (some courses may be in both concentrations). To receive an M.Phil. degree with a concentration in Applied Mathematics or in Computational Mathematics the student must fulfill the requirements for a M.Phil. degree in Mathematics. In addition both the M.Phil. Thesis and at least two of the courses taken for the M.Phil. degree must be designated as being in that concentration.

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.

Check further details on University website

How to Apply

Additional information:

(1) Applicants should check that their applications are complete and correct before submitting them, since the online system does not allow changes to be made after that. Complete applications contain the following items:

  • Application form
  • Transcripts (can be unofficial at this stage)
  • Statement of purpose
  • CV/resume
  • Letters of recommendation (at least 3, at most 5)

The application form consists of these sections:

  • Personal information
  • Program information
  • Academic background
  • Standardized tests
  • Additional information

No additional writing sample is needed in the application.

Applicants should submit scores for the GRE math subject test and the TOEFL (unless exempt from that). Scores on the basic GRE test are also requested. Exemptions from the TOEFL are granted to applicants whose native language is English; to those who did their entire undergraduate studies in the United States or Canada; and to those whose spoken English skills have been adequately demonstrated to our admissions committee.

Transcripts are uploaded to the Academic Background section, after entering the other requested information there. The transcript can be unofficial. Those applicants who are admitted will be required to submit an official transcript prior to matriculating in the Penn Math Graduate Program.

(2) The deadline for submission of applications is December 15, in the case of applications that request financial support. If some of the material related to the application (letters of recommendation or score on the GRE or TOEFL) is received a few weeks later, the application can still be considered. But since the Admissions Committee reads the files during January, and then meets near the end of January, material must arrive by then in order to be considered during the admission process.

If supplementary application materials are submitted after January 1 (whether or not financial support is being requested), a follow-up email message should be sent to the Mathematics Department's Graduate Group Chair, indicating what has been submitted. This includes letters of recommendation.

(3) In order to submit an on-line application, it is necessary to list at least three people (generally mathematics professors) as writers of letters of recommendation. Once your application is submitted, you cannot arrange for any additional letter writers (beyond those you listed in your application) to upload letters directly to the online system. Instead, if you wish to get additional letters beyond those you indicated on your application, you can ask the additional letter writers to email their letters to the Mathematics Graduate Coordinator, Reshma Tanna. In their message they should state that this letter is for your application to the Mathematics Graduate Program and that the letter should be uploaded to your application.

(4) Admissions decisions are made by the Mathematics Graduate Admissions Committee, and not by individual professors. Therefore, requests for admission should not be sent to individual members of the faculty, and instead should be submitted as indicated above. Nevertheless, applicants may wish to contact specificprofessors with whom they may have a particular interest in working, in order to discuss the possibility of applying and in doing research in their area (but should not send mass emails to professors).

(5) Applicants cannot be considered for possible admission (and no admission decision can be made) until an official online application form is submitted by the applicant and is received by the Mathematics Graduate Admissions Committee.

(6) Applicants may wish to visit the Penn Math Department in person, to get a better sense of the department and the graduate program. Such visits can be helpful to applicants in deciding where to apply and what offers to accept (but are not part of the Admissions Committee's decision process).

(7) Those who are admitted will be notified by email and letter. Those who are rejected will have their status indicated on the online application website. While some decisions will be made in February or early March, others will not be made until close to the uniform reply date of April 15, since our admissions committee must wait for replies from those admitted in the first round before being able to make offers to those on our waitlist.

Check further details on University website

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