Penn Arts & Sciences Logo

Masters Program

The Masters of Arts program in AMCS is intended for students who wish to go into professional careers in Applied Mathematics, or wish to obtain sufficient background in Applied Mathematics to be a strong candidate for a doctoral program in Applied Mathematics, Mathematics, Statistics, Financial Mathematics etc. While an undergraduate degree in Mathematics, or Applied Mathematics is not required, applicants to the program should have taken sufficiently many advanced undergraduate mathematics courses so that their interest in and aptitude for mathematics can be assessed. Beyond Calculus, two semesters of Mathematical Analysis, a semester of Linear Algebra, a semseter of Probability, and a semester of Complex Analysis are strongly recommended. The masters degree is typically earned in 3 to 4 semesters, depending upon the student's background.

Students in the masters program take at least eight graduate courses from the list of approved courses numbered 500 and above, including at least one each in applied algebra, applied analysis,  probability and statistics,  and numerical methods. With permission of the Graduate Group Chair, certain courses with a 400-number may be counted toward the course requirement for the Masters degree. The other courses can be in  pure mathematics, applied mathematics, and courses offered by other departments, which make essential usage of advanced mathematics. Every student's program of study must be approved by the graduate group chair. There is also a requirement to pass the Written Preliminary Exam and to submit and defend a Masters thesis, or take two additional courses in lieu of the Masters thesis, with the approval of the Graduate Group Chair. To receive the Masters degree a student must have at least a 3.0 cumulative grade point average in courses counted toward the degree.

The masters degree can also be earned by Penn Math Ph.D. students, on the way to their Ph.D. In addition, Penn Ph.D. students in allied fields of study can apply to enter the masters program in Applied Mathematics and Computational Science. Successfully completing the requirements for this program would allow them to earn both degrees simultaneously.

Undergraduates at Penn can request permission to submatriculate into the AMCS Masters degree program.  AMCS does not allow double counting of courses: you must take 8 courses, not counted toward any other degree, and write a Masters thesis, or take two additional courses on an advanced topic, which are also not being counted toward another degree. To be admitted as a submatriculant a student must demonstrate a high level of mathematical aptitude and proficiency, usually by taking undergraduate mathematics courses at the level of MATH 312/512, 360-1, 370-1, 410, 425, 430, and receiving excellent grades. Typically submatriculants are not permitted to use 500-level Mathematics courses, other than MATH 546-7, 570-1, 580-586, toward their list of required courses, and must take a preponderance of Mathematics courses.  Submatriculants should have an adequate background to pass the Written Preliminary Examination upon admission to the program.

Detailed requirements:

    1. Course requirements: A minimum of eight units of graduate courses at the University of Pennsylvania, numbered 500 and above (or, rarely, 400-level courses with the permission of the Chair), is required for the Masters degree. Other than MATH 546-7, most 500 level Mathematics courses are only accepted in extenuating circumstances at the discretion of the AMCS chair. This list of courses must usually include courses in applied algebra, applied analysis, probability and statistics, and numerical methods.  The list of courses must be approved by the Graduate Group Chair of the  AMCS graduate group. To be approved there must be a preponderance of graduate-level mathematics courses. To receive the Masters degree a student must have at least a 3.0 cumulative grade point average in courses counted toward the degree.
    2. Admission to candidacy: Admission to Masters candidacy is achieved by passing the Written Preliminary Examination, at the masters level, and by satisfactory performance in course-work.  Masters students must pass the Written Preliminary Exam in order to graduate.
    3. Language requirement: There is no foreign language requirement for the Masters degree.
    4. Masters thesis: Each student may either write a Masters thesis, or take two additional courses at an appropriate level. The Masters thesis, to be written under the supervision of a AMCS graduate group  faculty member, should be of modest length. It 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 applied mathematics, or computational science beyond the curriculum of the courses that the student has taken, and should ordinarily take  one semester to complete. Following submission of the Masters thesis, the student will take the Masters Oral Examination. This exam consists of a presentation by the student of the content of the thesis, followed by questions from members of the faculty on the topic presented and related areas of applied mathematics.
    5. In lieu of writing a Masters thesis, a student may take two additional (1 credit) courses. These courses, which must be approved by the Graduate Group Chair, should be at the level of a Masters thesis, and give the student a solid background in a more advanced topic. That is: both course should be on the same topic. These courses must be passed with a grade of B, or higher.
  1. Some important administrative details:
    • Administration of the Graduate Program: The Graduate Group Chair directs and oversees the administration of the graduate program, advises the graduate students in this program, and assesses their progress on a continuing basis. The Graduate Group Chair is aided in this by the subcommittees of AMCS graduate group.
    • Timing: The program leading to the Masters degree should ordinarily be completed within two years of full time study, and in any case must be completed within three years of full time study. Part time study, when allowed, will have a corresponding timetable set in each case by the Graduate Group Chair.
    • Written Preliminary Exam: Students entering the masters program will normally be expected to take the Written Preliminary Exam at the beginning of their first semester along with the new doctoral students. For masters students this first attempt at the Written Preliminary Exam will be regarded as a placement exam, and will help determine their choice of first year courses. Masters students will have two more chances to pass the Written Preliminary Exam. Passing this which is a requirement for graduation.
    • Course schedules: Each semester, the student's course schedule must be approved in advance by the Graduate Group Chair and the student's advisor. Students are reminded that, while the course requirements for the masters degree include at least a semester of graduate courses in each of algebra, analysis, probability and statistics, and numerical methods, the course requirements for the Ph.D. include a full year in most of these subjects at a possibly higher level, and may want to take this into account when planning their course schedules.
    • Course requirement: Approval of the Graduate Group Chair is required for courses to be counted toward the course requirement for the Masters Degree in AMCS.
    • For students writing a thesis, the Masters Oral Examination Committee is appointed by the Graduate Group Chair after consultation with the student and his/her advisor. It will consist of two or more faculty members, at least one of whom must be in the AMCS faculty and tenured, and one of whom will ordinarily be the supervising faculty member. The Graduate Group Chair will notify the entire AMCS faculty of the exam; all faculty are explicitly invited to attend, however only those appointed by the Graduate Group Chair are voting members of the Exam Committee.
    • If the Masters Oral 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. Passing the Masters Oral Examination on the second try, at the latest, is a requirement for remaining in the graduate program.
    • Satisfactory performance in the graduate program is determined by the Graduate Group Chair, with the advice of AMCS faculty members. Satisfactory performance, which includes maintaining a B average every academic year, and meeting requirements in a timely manner, is a requirement for remaining in the graduate program.
    • Financial aid: Students enrolled in a terminal masters program will not ordinarily be offered financial aid.