# 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
• Geometry & Topology
• Abstract Algebra
• Complex Analysis
• Numerical Analysis
• PDEs (discontinued)
• Real Analysis
The sectional exams are given during the week just before the start of the semester. Each section of the exam begins at 10:00AM and ends at 1:00PM.

The Geometry & Topology section was added in August 2013, while the Applied Mathematics exam was offered for the first time in August 2014. Two Applied Mathematics practice exams are available here and here. Sample problems for the Geometry & Topology exam are posted here. The PDE section was offered for the first time in 2011 and discontinued in 2019. Past PDE exams remain available here.

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

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