upenn math phd admission

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Department of Mathematics

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The University of Pennsylvania has two graduate mathematical programs. One is the regular program in mathematics, discussed below. The other is the program in Applied Mathematics and Computational Science , which is more interdisciplinary.

Our graduate program in mathematics offers three degrees: a masters degree (A.M.), a master of philosophy (M.Phil., between the masters and Ph.D.), and a doctorate (Ph.D.). Applications to any of these programs may be submitted in the final year of study in a bachelors degree program in mathematics. More information about the application process is available here .

Courses are offered in both pure and applied mathematics, and it is possible for students to take courses in related departments such as Physics and Astronomy , Computer Science , and Statistics (and even to get a masters degree in a related department, along with a Ph.D. in Mathematics).

Generous financial support is provided to Ph.D. students. Our Ph.D. students serve as teaching assistants in some years and receive fellowships that do not require teaching in other years (including the first year in the program and at least two later semesters). In connection with the assistantship or fellowship, Ph.D. students receive a full tuition scholarship and a stipend, for five years. They also receive three summers of funding, and can receive additional summer support if they teach during a summer. In conjunction with their support, Ph.D. students also receive university-provided health coverage.

Students who have graduated from our program have taken jobs in a variety of areas. Many now have faculty positions in colleges or universities , teaching and doing research. Others have taken positions in industry or research labs, in such areas as bioinformatics, robotics, mathematical finance, and computer science. There are currently about fifty graduate students in the Penn Math Department, with a faculty of about forty (plus visiting faculty). Students can work in research areas that include algebra (number theory, algebraic geometry, ring theory), analysis (classical analysis, PDE's, functional analysis, operator algebras), geometry-topology (differential geometry, symplectic geometry, topology of manifolds, applied topology), logic (including mathematical foundations of computer science), combinatorics, probability, and applications such as mathematical physics, medical imaging and mathematical finance.

The Penn Math Graduate Program is structured so as to guide each student, year by year , in the transition from having been an undergraduate to becoming a professional mathematician. During the first year in the graduate program at Penn, students typically take courses in algebra, analysis, and geometry-topology. At the end of that year, students work in groups on mathematical topics of their choice. In the second year, students begin to take more specialized courses and to concentrate on their area of interest. Ph.D. students typically begin work in the area of their thesis after the end of their second year, while masters students typically complete their thesis in the second year. Those who have previously done more advanced work can place out of courses and begin research sooner.

In addition to taking courses, students attend seminars, which are offered in a broad spectrum of topics and levels. Every Friday, there is a Pizza Seminar , open only to students, at which a grad student will present a topic that he or she has found interesting; the Math Department provides pizza and drinks during the talk. Other seminars , open both to students and faculty, include the Department Colloquium, graduate student reading seminars, and advanced seminars specializing in areas such as Mathematical Physics, Geometry-Topology, Analysis, Algebra, Logic and Computation, and Combinatorics and Probability, among others.

Students at the Penn Math Department interact a lot with each other and with faculty. Students regularly work with each other on assignments, on seminar talks, and on research, and talk quite a bit with faculty about mathematics. Interactions take place in seminars, after class, in offices (grad students share offices), in the hallways, and at the daily teas in the Departmental Lounge -- as well as at seminar dinners, at graduate student social events, etc. This helps create a lively atmosphere, in which much of the learning takes place outside of formal lectures (though there are also plenty of those).

The Penn Math Department is located in David Rittenhouse Laboratory (DRL), which it shares with the Department of Physics and Astronomy . Facilities include the Mathematics Reading Room (with a non-circulating mathematical book collection, computers, and pleasant surroundings including lounge chairs and stained glass windows) and the Math-Physics-Astronomy library (a circulating library of books and journals). Adjacent to DRL are Shoemaker Green, an athletic center, the Palestra basketball arena, and the university stadium (Franklin Field). DRL is at the eastern end of the University of Pennsylvania campus, a few blocks from downtown Philadelphia .

Written Preliminary Exam

The Written Preliminary Exam is taken by all incoming AMCS graduate students at the University of Pennsylvania, just before the start of the fall semester (generally in late August). It plays three roles:

• It serves as a placement exam, to help determine whether students should begin with 500-level courses or with 600-level courses (or with a mixture).
• It is a requirement for each of the graduate degrees in applied mathematics, to ensure that those who receive graduate degrees have a solid mathematical foundation.
• It provides an incentive for incoming grad students to review basic material, which will then help them in their beginning graduate classes.

PhD students who do not pass the exam on their first attempt will have one more chance to pass it at the end of the spring semester (generally in late April or early May).  PhD students who do not pass the exam by the end of their first year will be asked to leave the program.

Masters students who do not pass the exam on their first attempt will have two more opportunities to pass this exam. Students who fail the exam are required to retake the exam the next time it is offered. If a student does not do so, they will be given a score of zero, and lose that opportunity to retake the exam. While we strongly encourage master students to prepare before their arrival, intending to pass the exam on their first try, this first attempt serves primarily as a placement exam.

All students who do not pass the Written Prelim on the first try are strongly encouraged to take the Proseminar (MATH 504, 505), which helps to prepare you for this exam. You will also be directed to other 400/500-level math courses during your first year, to strengthen your problem-solving ability, and background in mathematics.

The written preliminary exam focuses on the material from an undergraduate mathematics program that is most important to those entering an applied mathematics graduate program. The exam is given in two 2.5-hour sessions, either on a single day or consecutive days. Each part consists of 6-8 problems.

The exam contains problems in linear algebra, advanced calculus, basic complex analysis, and probability. Some problems are computational, some ask for proofs, and some ask for examples or counterexamples. Each part of the exam contains a mixture of types of problems and a mixture of subjects.

The key to success on the preliminary exams is practice!  AMCS Preliminary Exam Examples

Books that cover the material at an appropriate level are as follows.  We list more than one book in some areas only to maximize the probability that the list contains a book you are familiar with.

Linear algebra: Strang, Gilbert “ Linear Algebra and its Applications”

Real analysis: Rudin, Walter “ Principles of Mathematical Analysis ” or Strichartz, Robert “ The Way of Analysis “

Probability theory: Ross, Sheldon “ A First Course in Probability ” or Hoel, Port and Stone “ Introduction to Probability Theory “

Complex Analysis: Conway, John B. “ Functions of One Complex Variable” or Bak and Newman “ Complex Analysis ” or Alfors, Lars “ Complex Analysis: An Introduction to The Theory of Analytic Functions of One Complex Variable “

Graduate Admissions

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Graduate and professional programs at Penn emphasize the integration of knowledge across boundaries and disciplines. More than 16,000 graduate and professional students study at Penn, pursuing more than 300 degree and certificate offerings, from Accounting to Women’s Health.  Explore our graduate programs  and click on the programs that interest you to learn more about admissions and academic requirements.

Spotlight on Research

Penn is a nationally-ranked research university, one of the top recipients of competitive research grants in the U.S.  More than 170 research centers and institutes  play a major role in advancing the university’s intellectual agenda. Learn more about research activity in Penn’s graduate and professional schools through  Research at Penn .

Contacts Below

Penn’s graduate and professional programs are housed in 12 schools on one campus. Each graduate program has a separate admissions process. Applicants apply directly to the  program of interest . All questions about the admissions process should be directed to the  program of interest .

Spring 2020 Recognizing the challenges of teaching, learning, and assessing academic performance during the global COVID-19 pandemic, Penn’s admissions committees for graduate and professional programs will take the significant disruptions of the COVID-19 outbreak in 2020 into account when reviewing students’ transcripts and other admissions materials as part of their regular practice of performing individualized, holistic reviews of each applicant. In particular, as we review applications now and in the future, we will respect decisions regarding the adoption of Pass/Fail and other grading options during the period of COVID-19 disruptions. An applicant will not be adversely affected in the admissions process if their academic institution implemented a mandatory pass/fail (or similar) system for the term or if the applicant chose to participate in an optional pass/fail (or similar) system for the term. Penn’s longstanding commitment remains to admit graduate and professional student cohorts composed of outstanding individuals who demonstrate the resilience and aptitude to succeed in their academic pursuits.

Required Tests For PhD applicants: Most, but not all, PhD programs at Penn require the Graduate Record Examination (GRE). The University’s institution code is 2926, you only need to send your scores to one Penn code and it will be matched to your application. Each graduate program has a different GRE requirement; please refer to your program of interest for more information. For information about the administration of the GRE, see the  Educational Testing Service website .

For professional program applicants: Some, but not all, professional programs at Penn require standardized test scores, such as the GRE, LSAT, MCAT, GMAT, etc. Each program has a different requirement and a different institution code. Please refer to your program of interest for more information.

International Applicants Applicants who are non-native English speakers may also be required to report scores from the Test of English as a Foreign Language (TOEFL), Pearson’s PTE Academic , or International English Language Testing System (IELTS). Please refer to your program of interest for detailed requirements.

Penn is a leader among its peers in welcoming students from every part of the world. The division of International Student and Scholar Services offers help, advice, and information on all matters connected to immigration, employment, adjustment to a new culture, and living in Philadelphia.

Application Materials Please note that all application materials become property of the University of Pennsylvania and will not be returned. Remember to retain a personal copy of your application.

Offline Recommendation Penn strongly prefers that recommenders submit letters of recommendation online through the admissions system. If, however, your recommender is unable to submit an online recommendation, please follow these instructions:

1) Select the “Recommendation Form PDF Download” and download the form . 2) Complete the first section. Be sure to include the address of the appropriate admissions office — refer to the “Contact Graduate Admissions” list below. 3) Print out the form and provide it to your recommender.

Please note:

• If you are applying to a program in Nursing, print out and provide your recommender with these special instructions for completing your letter of recommendation.
• If you are applying to a program in the School of Social Policy & Practice, print out and provide your recommender with these  special instructions  for completing your letter of recommendation.

4) Your recommender should send the form directly to the admissions office you designate, along with the letter of recommendation.

Visiting Penn You are welcome to visit the campus. Interviews are generally by invitation only. Applicants may contact their prospective program to inquire about the availability of tours, open houses, and information sessions. If you plan to visit campus, make sure to visit  other attractions in Philadelphia too.

Privacy Policy Prospective students and applicants should review  Penn’s Privacy Policy.

Penn’s graduate tuition and other fees vary by school. Consult the individual schools and programs for details. Penn awards some loans based on financial need. These awarded loans are only made by Penn as part of a student’s financial aid package. The loans are repayable by the student after completion of his/her education or withdrawal from school and are not subsidized.

Students in Ph.D. programs generally receive multi-year financial packages to cover tuition, fees, health insurance and a living allowance or stipend.  The terms of the award may vary according to field of study. Contact individual programs for details. Most programs require that PhD students teach or conduct research for two or more years during their course of study, as part of their academic preparation.

Penn’s professional schools provide limited assistance in the form of grants based on financial need. Some schools award merit-based scholarships or provide support in return for service.  Contact your school for information on its policies and application procedures for grants and scholarship funding.

Penn’s  Student Financial Services  provides up-to-date information the  cost of attendance , as well as  loans and other resources for support . U.S. citizens and permanent residents may be eligible for federal loans (i.e., Direct Loan, Grad PLUS). In addition, private  alternative loan programs  are available for credit-worthy borrowers. Generally, international students must have a qualified co-signer who is a U.S. citizen or permanent resident.

A stimulating intellectual and social community of students and scholars from across Penn’s 12 schools form a vibrant graduate network. The campus offers extensive resources for academic support and personal enrichment.

Penn is a leader among its peers in welcoming students from every part of the world. The division of  International Student and Scholar Services  offers help, advice, and information on all matters connected to immigration, employment, adjustment to a new culture, and living in Philadelphia.

Graduate Student Center Penn’s Graduate Student Center  provides a home base for graduate and professional students. Located in the heart of campus on Locust Walk, the Center hosts a variety of activities including recreational outings, dissertation support workshops, game nights, and more.

Graduate Student Organizations As the University-wide graduate student government,  GAPSA  — the Graduate and Professional Student Assembly – advocates for students, funds initiatives, and plans events. A wide variety of other  graduate and professional student organizations  flourish at Penn, including school governments, as well as professional, social, athletic, and cultural groups.

Campus Resources The  Grad Student’s Guide to Thriving at Penn , published by the Grad Center, comprehensively outlines all of the many resources serving graduate and professional students at Penn. Of special importance to many students are these resources:

• Family Resource Center  for students with children
• Campus Cultural Resource Centers
• LGBT Center
• Student Disabilities Services
• Health & Wellness Resources
• Recreation & Gyms
• Career Services

Across 12 Schools, more than 16,000 graduate and professional students, and more than 5,000 faculty members, we become one university: a wide-ranging, ever-changing community that draws its strength from a multitude of races, ethnicities, nationalities, genders, sexual orientations, historical traditions, ages, religions, disabilities, veteran status, interests, perspectives, and socioeconomic backgrounds.

Penn has a number of policies and initiatives that support its efforts to foster inclusive excellence. Diversity and inclusion related data, progress reports on initiatives, a timeline of selected milestones, and stories about members of the Penn community are available  here .

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Famous as the birthplace of life, liberty and the pursuit of happiness, Philadelphia is a vibrant city offering countless things to do: fascinating museums, vibrant parks, national historic sites and famous (and delicious) food.

Learn more  about the great City of Philadelphia.

Philadelphia neighborhoods each have a distinctive personality. The University of Pennsylvania is located in the University City section of Philadelphia. While most students live in University City and the adjacent Center City neighborhoods, there are  many other areas to explore . 

Penn’s  Office of Off Campus Services  assists students with finding housing in Philadelphia, as well as assistance with leases, landlords, utilities and more. New graduate and professional students are encouraged to start looking for housing 3-4 months before arriving at Penn. Each spring, the University offers  online sessions  about housing so that incoming graduate students can get this critical information before arriving on campus. 

The Graduate Student Center’s  Resources for New Grad Students  includes a section on Moving to Philadelphia, which includes more information on transportation, parking, dining, and more.

Contact Graduate Admissions

There is no one central Office of Graduate Admissions. All questions about the admissions process should be directed to the academic program of interest.  Carefully research the admissions information available online through  the Penn Catalog  for your prospective program.  If you are unable to find the information you require, contact the appropriate School Admissions Office:

3620 Walnut Street Philadelphia, PA 19104-6220

215-573-6349

PhD Programs

Graduate Division 3401 Walnut Street, Suite 322A Philadelphia, PA 19104-6228

215-898-8101

The College of Liberal & Professional Studies

3440 Market Street, Suite 100 Philadelphia, PA 19104-3335

215-898-7326

Robert Schattner Center 240 South 40th Street Philadelphia, PA 19104-6030

215-898-8943

GSE Admissions Office 3700 Walnut Street Philadelphia, PA 19104-6216,

215-898-6415

Engineering Admissions

109 Towne Building 220 South 33rd Street, Philadelphia, PA 19104-6391

215-898-4542

Law Admissions

3501 Sansom Street, Philadelphia, PA 19104-6204,

Claire M. Fagin Hall 418 Curie Blvd., Suite M-5 Philadelphia, PA 19104

215-898-4271

3701 Locust Walk Philadelphia, PA 19104-6214

215-898-5539

3800 Spruce Street, Suite 106 Philadelphia, PA 19104-6008

215-898-5434

110 Meyerson Hall, 210 South 34th Street Philadelphia, PA 19104-6311

215-898-6520

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Application Requirements

The application for fall 2024 is now closed. the application for fall 2025 admission will open september 15, 2024 and deadline to apply is december 15th, 2024 11:59 p.m. eastern standard time. a complete application includes a completed online application and supplemental application materials. we recommend that you begin the application process early as it may take longer than expected. allow enough time to complete your online application, gather and submit your materials, and take the necessary standardized tests..

Wharton only accepts applications submitted via our online application system.

Letters of Recommendation

The Admissions Committee requires three recommendations. The recommendations must be submitted using our online system.

When you apply online, you will provide the names and email addresses of three recommenders. These recommenders will receive an email with a password, login, and link to our site that will enable them to submit their recommendation directly to our office via the online system.

To submit letters of recommendation via Interfolio, please follow the instructions from Interfolio:  https://product-help.interfolio.com/en_US/about-dossier-accounts/dossier-quick-start-guide

Assistance for applicants or the Interfolio agent can write to  [email protected] .

Transcripts & Academic History

You must submit transcripts of your academic work by scanning and uploading copies of your transcripts through the online application system. The file cannot exceed 600 KB in size and should be in .doc, .wpd, .rtf, .xls, .pdf, .docx, .xlsx or .txt format. For Mac users, please note that the filename must include the appropriate three- or four-letter extension. Also, please do not attempt to upload a document that is password-protected or that contains macros. This will cause the process to fail.

If you are offered admission, you will be required to provide official transcripts of all previous academic work to verify the information provided. If there are discrepancies between the self-reported academic work and official records, the offer of admission will be revoked. Offers of admission are not binding until academic records are verified.

When applying, list all post-secondary educational institutions you have attended, including technical and professional schools. Use the full, actual names of the institutions attended, and provide the titles of all diplomas or degrees earned. If you have attended more than one institution, submit official records from each institution, with the exception of study-abroad programs. If academic records and diplomas are not issued in English by the institution, both the official record and an authorized English translation must be submitted.

All translations should be complete and literal renditions of the original record. Records should show the date of enrollment, courses taken, units of credit or time allotted to each subject during each term or year, your marks or ratings in each subject, and, if available, your rank in the total class or group.

The institutional grading scale or other standards of evaluation, including minimum passing and failing marks and definition of grades between them, should appear on official records or be provided as an attachment.

Pursuant to the Family Educational Rights and Privacy Act of 1974, as amended, personally identifiable information can be disclosed to persons outside the University only with the written consent of the student or alumnus/alumna. The complete confidentiality statement is available in the University’s graduate academic bulletins.

You must complete the Personal Statement essay question on the online application.

There is also an optional essay question where you may provide additional information or clarification on other points of your application.

Standardized Test Scores

The Wharton Doctoral Programs requires ALL applicants to take and provide scores for either the Graduate Management Admissions Test (GMAT) or the Graduate Record Examination (GRE). Test requirements vary by program, as described below. Applicants whose native language is not English must also take the TOEFL.

Self-reported test scores may submitted in the application, pending receipt of your official scores.

We no longer accept late test scores due to Covid-19. Please plan accordingly to ensure test scores and materials are submitted by the December 15 deadline.

Accepted applicant GMAT and GRE test scores usually fall within the top 10 percent. For the TOEFL test, a high level of proficiency is expected. You can find information about the average GRE and GMAT scores for our most recent fall matriculates in our FAQ section.

To expedite the processing of your application, you must self-report your scores via the online application. In addition, you must request that the ETS send an official copy of your scores to the Wharton Doctoral Office.

We strongly encourage applicants to take the necessary tests in the fall at the latest so that the test scores reach the Wharton Doctoral Office before the December 15 deadline. It has been our experience that students often underestimate the time it takes for the School to receive grade transcripts and test scores. Since this time period may be as long as two months, students are well advised to send requests for grade transcripts and to schedule the appropriate tests as early as possible. Note: Late arrival of test results prevents evaluation of your application.

GRE & GMAT Requirements by Program

• Accounting: GRE or GMAT
• Applied Economics: GRE only
• Ethics & Legal Studies: GRE or GMAT
• Finance: GRE or GMAT
• Health Care Management & Economics: GRE or GMAT
• Management: GRE or GMAT
• Marketing: GRE or GMAT
• Operations, Information & Decisions: GRE or GMAT
• Statistics and Data Science: GRE only

We will accept GMAT and GRE scores that are up to 5 years old. If your test scores are more than 5 years old (taken prior to July 2019), you will have to take the test again and submit the new scores. Please see the GRE and GMAT websites for further information on taking those tests.

The GMAT and GRE in-person and home tests will both be accepted.

We evaluate only GMAT and GRE results from tests taken prior to the receipt of your application. The highest score is used — we do not combine multiple scores. This requirement cannot be waived; there are no exceptions.

Ask the Educational Testing Service (ETS) to report your test scores using the following Wharton Doctoral Programs’ ETS codes:

• GRE: 2954-5199 or 2954-0000
• GMAT: G56-97-12

TOEFL Applicants whose native language is not English must take the TOEFL. You may request a TOEFL waiver if you have earned an undergraduate or master’s degree (or will receive the degree by June 2025) in an English-speaking country or from an institution in which English is the language of instruction.

To waive the TOEFL, you must submit your request under the optional essay section of the application and have it documented that your medium of education was English. Your transcripts may serve as documentation that English was the language of instruction.

TOEFL scores are valid for two years. If your TOEFL test was taken prior to July 2022 you will need to submit new scores.

• TOEFL: 2954-02 or 2954-00

Please note:

• The TOEFL IBT and TOEFL ITP in-person and home tests will be accepted.
• We do not accept IELTS scores in place of TOEFL scores

Application Fee

A nonrefundable application fee of $80 must accompany your application. Credit card payments, made with a Visa or MasterCard only, are processed through Wharton’s secure server using Cybersource. The application fee cannot be waived; there are no exceptions.*

* McNair, Fulbright,  Leadership Alliance, IDDEAS and GRE Fee Reduction recipients applicants may waive the application fee. Please follow the instructions in the application.

Application Deadline

To begin your studies in Fall 2025, you must make sure that all your supporting materials (letters of recommendation, transcripts, and either GMAT or GRE scores) and your application are submitted no later than December 15, 2024.

As states on our website, please submit your application by December 15, 2024, 11:59PM ETS.

Prior Convictions Information

If an applicant has ever been convicted of, or plead guilty or no contest to, any felony or misdemeanor (excluding minor traffic violations), he or she must report that information. We offer a secure site for the applicant; answers will be reviewed by the Wharton Doctoral Programs Review Officer.

This information will not be provided to the admissions committee as part of the regular academic review process. If you have questions, you may contact the Review Officer directly at  [email protected] .

Generative AI Policy

The Wharton School embraces the use of generative AI technology and sees it as an important tool for business scholars in this rapidly changing world. While we believe that generative AI will continue to provide utility to all students, your work contained within this application must be your own. We recommend applicants treat generative AI as you would the guidance or writings of another person. For example, this means that, as it is unacceptable to have another person substantially complete a task like writing an admissions essay, it is also unacceptable to have AI substantially complete the task.

By embracing AI responsibly, Wharton aims to uphold the integrity of the application process while leveraging technological advancements to enrich the admissions experience. The Wharton School of the University of Pennsylvania requires that the work in your application must be completely accurate and exclusively your own, and may use its own proprietary and/or licensed AI solutions in order to identify AI-authored elements of applications. Any such flagging will result in a more holistic investigation of an application.

Recognizing the challenges of teaching, learning, and assessing academic performance during the global COVID-19 pandemic, Penn’s admissions committees for graduate and professional programs will take the significant disruptions of the COVID-19 outbreak in 2020 and 2021 into account when reviewing students’ transcripts and other admissions materials as part of their regular practice of performing individualized, holistic reviews of each applicant. In particular, as we review applications now and in the future, we will respect decisions regarding the adoption of Pass/Fail and other grading options during the period of COVID-19 disruptions. An applicant will not be adversely affected in the admissions process if their academic institution implemented a mandatory pass/fail (or similar) system for the term or if the applicant chose to participate in an optional pass/fail (or similar) system for the term. Penn’s longstanding commitment remains to admit graduate and professional student cohorts composed of outstanding individuals who demonstrate the resilience and aptitude to succeed in their academic pursuits.

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The Bridge to PhD master’s program will no longer accept new students. This program has recently transitioned into a fellowship opportunity for applicants to our PhD program. Please read more about Bridge Fellowships on our graduate admissions page https://www.math.upenn.edu/graduate .

ABOUT THE PROGRAM

Bridge to PhD is a master’s program in mathematics offered by the University of Pennsylvania. The goal of this program is to increase the number of PhD’s awarded in mathematics to members of groups that are traditionally underrepresented. The program will be supported by the mathematics department at Penn, by the School of Arts and Sciences, and by the National Science Foundation .  A committee of mathematics faculty will coordinate the program.

Applicants must be permanent residents of the United States to be eligible, and the application deadline for Fall entry is December 31. We encourage prospective students to visit this link for more  information on applying. The admission process will include interviews, which may  be in-person or via video. Each admitted applicant will have a chance to visit Philadelphia before accepting.

The program will be two years long, and we anticipate admitting 2 to 3 bridge program students each year. Students will receive an annual stipend, which is currently  $25,000. In their second year, Bridge students will serve as teaching assistants, typically in an introductory calculus class, in addition to taking courses and working  on their master’s thesis . The students who complete the Bridge to PhD program and are admitted to the PhD program will receive credit for the work they have done towards their PhD.

One of the requirements for the program is a preliminary examination . All math  graduate students, including those in the Bridge to PhD, will take this exam. Bridge students may choose to take this exam when they arrive, or they can wait until later to take and pass it. It is permissible to take it several times, and there will be a seminar to help students pass this exam. For all other program requirements, please visit our graduate studies page.

University of Pennsylvania School of Arts and Sciences Penn A-Z Penn Calendar

Department of Mathematics David Rittenhouse Laboratory 209 South 33rd Street Philadelphia, PA 19104-6395

Robin Toney  [email protected] (215) 898-8178 & 898-8627 Fax: (215) 573-4063

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Ph.D. Degree Requirements

The Ph.D. requirements include the completion of a minimum of 10 course units of graduate level work beyond the undergraduate program with a grade-point average of at least 3.0, satisfactory performance in the Ph.D.-related exams, presentation of a departmental seminar, completion of the teaching practicum, and the submission and successful defense of an original and significant dissertation. The milestones in the Ph.D. program are noted in the Ph.D. Handbook .

Course requirements for MEAM PhD students:

• ENM 5200 Principles and Techniques of Applied Math I*
• ENM 5210 Principles and Techniques of Applied Math II
• ENM 5220 Numerical Methods for PDEs
• ENM 5310 Data-driven Modeling and Probabilistic Scientific Computing
• MATH 5000 Topology
• ESE 5000 Linear Systems Theory
• ESE 6050 Modern Convex Optimization
• MEAM 5190 Elasticity and Micromechanics of Materials
• MEAM 5300 Continuum Mechanics
• MEAM 5350 Advanced Dynamics
• MEAM 5610 Thermodynamics: Foundations, Energy, Materials
• MEAM 5700 Transport Processes I
• MEAM 6200 Advanced Robotics
• One graduate course in MEAM beyond the core MEAM courses (depth requirement)
• One graduate course outside MEAM (not ENM 5200/5210) related to student’s research (breadth requirement)
• Three additional graduate courses related to student’s research
• Three semesters of Teaching Practicum (MEAM 8950; normally taken in 3 rd , 4 th and 5 th semesters)
• Six semesters of the MEAM seminar (MEAM 6990)
• Responsible Conduct of Research in Engineering (EAS 9000; mandatory in the first year)

Notes: Neither MEAM 8990 (Independent study) nor MEAM 9990 (Research) can be used to satisfy the above course requirements.

* Students should check their preparedness for ENM 5200 by reviewing the syllabus before registering for the course.  If this material is unfamiliar, the student should take ENM 5100 prior to taking ENM 520.

Course Selection Approval:

No courses shall be taken without the prior approval of the student’s advisor. Each student must prepare a tentative course plan and obtain the approval of his/her advisor and the Graduate Group Chair before the end of the second semester after his/her matriculation. A copy of the course plan will be maintained in the student’s file. Any deviations from the course plan must be documented and approved by the Graduate Group Chair.

Obsoleteness:

The Ph.D. program, culminating in a successful defense of the doctoral dissertation, must be completed within a period of 10 years from the year of matriculation as a graduate student in the School of Engineering and Applied Science of the University of Pennsylvania.

Teaching Practicum

This course provides training in the practical aspects of teaching. The students will work with a faculty member to learn and develop teaching and communication skills. As part of the course, students will participate in a range of activities that may include: giving demonstration lectures, leading recitations, supervising laboratory experiments, developing instructional laboratories, developing instructional material, preparing homework assignments, and preparing examinations. Some of the recitations will be supervised and feedback and comments will be provided to the student by the faculty responsible for the course. At the completion of the 0.5 c.u. of teaching practicum, the student will receive a Satisfactory/Unsatisfactory grade and a written evaluation from the faculty member responsible for the course. The evaluation will be based on comments of the students taking the course and the impressions of the faculty.

Doctoral Program:

• Ph.D. Handbook

Staff Contact:

Peter Litt Associate Director of Graduate Programs 229 Towne Building Phone: 215-746-6737 Email: [email protected] Current Student Appointments

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Admissions information to the ph.d. program in economics.

Students may enter the Ph.D. program  only in the fall . Applicants must present evidence of a baccalaureate degree or its equivalent, or show that they can expect such a degree by the time they begin graduate work. The University requires that applicants utilize the on-line application system (new link coming soon). Applicants must upload a personal statement and their transcript (unofficial or official) from each university attended. If an applicant is accepted into our program then they must provide an official transcript mailed directly to the Graduate School of Arts and Sciences. Three letters of recommendation are also required, usually from professors who can judge the student's potential for high-quality academic work. Results of the Graduate Record Examination (GRE) must also be submitted. This test should be taken as early as possible to ensure that the results are received in time to be considered by the admissions committee.  Our GRE institution-department code is 2926-1801 . International students must submit a TOEFL score unless they have or will receive an undergraduate degree from a college/university in the US, Canada, UK, Australia, New Zealand, South Africa, or Ireland or they have completed, at the time of application, four semesters of graduate study at an institution in the above mentioned countries.

The program's goal is to admit 16 students a year. Applicants should be aware that the admissions committee reviews a large number of applications (over 600 last year). Our decisions on admission and financial aid are facilitated when application materials are clearly presented, well written, and concise. The committee tries to form an image of the intellectual and personal qualities of applicants, and then admits those who seem most likely to do high quality work. All applicants are encouraged to provide a personal statement (see below) and any additional information that might help the admissions committee in their task. For example, students might wish to submit research papers that they have written or a description of some major job experience related to economic analysis. 

Mathematics prerequisites

Proficiency in mathematics is crucial for successful completion of the first year of study, in the Department of Economics, at the University of Pennsylvania.

A minimal level of preparation  consists of two years of mathematics courses in college, including courses in:

• multivariable calculus
• probability theory and statistics
• linear algebra

An excellent level of preparation  consists of additional courses in:

• real analysis
• point-set topology
• measure-theoretic probability theory

We strongly suggest you obtain an excellent level of preparation, for your application to be competitive.

Requirement for Personal Statement:

In the personal statement, all Ph.D. applications within the Graduate Division of Arts & Sciences should address the following: Please describe how your background and academic experiences have influenced your decision to pursue a graduate degree and led you to apply to Penn. Your essay should detail your specific research interests and intellectual goals within your chosen field. Please provide information about your educational trajectory, intellectual curiosity and academic ambitions. If you have overcome adversity and/or experienced limited access to resources or opportunities in your field of study, please feel free to share how that has affected the course of your education. We are interested in your lived experiences and how your particular perspective might contribute to the inclusive and dynamic learning community that Penn values and strives to create.

In the Economics Graduate Group, we also ask that applicants discuss their relevant research experience, if any, that make Penn Economics a good fit for what you would like to accomplish in your PhD. Your statement can include specific fields of interests and specific faculty members that you think could be potential advisors. 

Deadline for admission:

All applications must be completed and submitted by 11:59pm eastern US standard time on December 15th. The admissions committee then examines completed applications which have been received. Notification of its decision is sent by April 15th.

Follow this link to apply on-line:  “coming soon a new link to the admissions application to the Ph.D. program.”

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Mathematics, MPhil

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 6000 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).

For more information: https://www.math.upenn.edu/graduate

View the University’s  Academic Rules for Research Master's Programs .

A total of 14 course units are required for graduation.

At least four courses must be taken in the Penn Math Department.

The degree and major requirements displayed are intended as a guide for students entering in the Fall of 2024 and later. Students should consult with their academic program regarding final certifications and requirements for graduation.

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