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The University of Pennsylvania's Mathematics Department provides a comprehensive Graduate Program in Mathematics, awarding Master of Arts (A.M.), Master of Philosophy (M.Phil.), and Doctor of Philosophy (Ph.D.) degrees. This program is designed to deliver broad mathematical education for careers in academic research, teaching, and other fields requiring advanced mathematical expertise. This document outlines Penn's graduate mathematics curriculum, which spans diverse disciplines such as analysis, geometry-topology, algebra, mathematical physics, combinatorics, logic, and probability. For further details about the program and the Math Department—including colloquia, seminars, lecture series, and faculty research—visit our Graduate Mathematics Page and departmental website. Penn also features a distinct interdisciplinary graduate program in Applied Mathematics and Computational Science, which requires a separate application.
A Bachelors degree (but not a master’s degree) is required for entrance to the program. Admission to M.Phil. candidacy is achieved by passing the Graduate Preliminary Exam, and the oral M.Phil. Preliminary Exam.
On the TOEFL, we look for total scores of at least 100, and scores of at least 20 on the spoken English portion.