Preliminary Exam

The Preliminary Exam is taken by all incoming mathematics graduate students at the University of Pennsylvania, just prior to the start of the fall semester (generally in late August). It plays three roles: Students who do not pass the exam the first time will have a second chance to pass it at the end of the spring semester (generally in late April or early May). Those students take the Proseminar (Math 504, 505) during their first year, to strengthen their problem solving ability, their ability to present proofs, and their familiarity with material on the prelim.

The prelim exam focuses on the key material from undergraduate mathematics that is most important to those entering a mathematics graduate program. It is given in two parts, either on consecutive days or in the morning and afternoon of the same day. Each of these two parts consists of six problems, and students are given two and a half hours for each part (which is intended to be more time than is necessary for those who know the material).

The exam consists of problems in algebra (including linear algebra), analysis, and basic geometry-topology. Some problems are computational, some ask for proofs, and some ask for examples or counterexamples. Each part of the exam (morning and afternoon) constains a mixture of types of problems, and a mixture of analysis and algebra problems.

The following list of topics gives a general idea of the material that is covered on the exam:

Sample Prelim Exam.

Some Old Prelim Exams.

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