Preliminary Examination

All students must pass the Preliminary Examination in order to continue with the program.

The Preliminary Examination consists of written examinations in the following three subjects: algebra, analysis, and geometry/topology.

Incoming students are strongly encouraged to take the Preliminary Examination upon entrance. There is no penalty for failing to pass a preliminary examination taken upon entrance to the program.

Incoming students are required to take each of the first-year courses (Algebra, Analysis, and Geometry-Topology) for which they do not pass the preliminary exam.

The rules for the Preliminary Examination are posted here.

The Preliminary Examination is given during New Student Week in September and at the end of the academic year (typically June). Graduate students must take the Preliminary Examination in all three subjects by the end of their first academic year. Students who do not pass the Preliminary Examination by the end of their first year must pass a make-up examination in September of their second year in order to continue in the program beyond the first quarter of the second year.

An award is offered at the end of each academic year to the student who has achieved the best performance in the Preliminary Examination. The award is accompanied by a monetary prize when sufficient funds are available.

Students who do not pass the Preliminary Examination by the end of their first year must pass a make-up examination in September of their second year in order to continue in the program beyond the first quarter of the second year. This rule may be waived with the permission of the instructor and the approval of the Graduate Committee.

To help the graduate students (including incoming and prospective students) better prepare for the exams, we provide here some sets of problems from past years. Trying to solve these problems is an excellent way to find out in which areas more work is needed. We encourage prospective graduate students to study books and audit courses related to the material of these exams while still in college.

Previous Exams

Algebra (470)

Analysis (Real and Complex) (410)

Geometry and Topology (Pre-2009)

Prior to Fall 2009, Topology and Geometry were courses with separate examinations; these examples should be used only as a source of problems, not as guidelines to the syllabus for or the structure of current exams. The current syllabus is below under Geometry/Topology (440). 

Geometry/Topology (440)