# Past exams

The written PhD qualifying exam, also called the PhD Comprehensive Examination, is administered twice yearly, during the two weeks just prior to the start of the Spring semester (January exam) and Fall semester (August exam). The qualifying exam is offered in six separate sections, out of which students need to pass three:

• Applied Mathematics (Thursday)
• Geometry & Topology (Friday)
• Abstract Algebra (Monday)
• Complex Analysis (Wednesday)
• PDEs (Thursday)
• Real Analysis (Friday)
The sectional exams are given in the above order on the indicated days. The sections Algebra, Complex Analysis, PDE and Real Analysis take place during the week just before the start of the semester; the sections Applied Mathematics and Geometry & Topology at the end of the week prior to that. Each section of the exam begins at 10:00AM and ends at 1:00PM.

The Geometry & Topology and Partial Differential Equations sections were added in August 2013 and 2011, respectively, while the Applied Mathematics exam was offered for the first time in August 2014. Two Applied Mathematics practice exams are available here and here. In addition to the past PDE exams listed below, two sample PDE exams are available here and here. Sample problems for the Geometry & Topology exam are posted here.

Please consult the Graduate Handbook for current rules and timelines about taking the exam.

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