The PhD Qualifying Exam is a degree requirement of our PhD programs. Students must attempt the exam the first time it is offered while they are enrolled as a PhD student, and can have no more than two attempts. If a student is unsuccessful on the second attempt, the student’s status will change to Required to Withdraw in the term immediately following the term in which the examination took place. Please see the graduate calendar for complete details.  Please see below for a more detailed description of the topics covered in these written exams, as well as for links to past exams.

Our Qualifying Exams cover material from our undergraduate courses. Each exam will be broken into three separate timed sections. To each section will be tagged a particular undergraduate course, so that if a student does not pass the section, they may instead get a grade of at least 80 in the associated undergraduate course as a condition for a conditional pass (if it is their first attempt at the exam; conditional passes are not possible on the second attempt). If a student already has a grade of at least 80 in said course, they need not write that section. Though the sections have courses tagged to them, the syllabus for the section will differ somewhat from the syllabus of the associated course. The exams will be broken down as follows:

Algebra: Linear Algebra 60min (MATH 245), Groups and Rings 60min (PMATH 347), Fields and Galois 60 min (PMATH 348)

Analysis & Topology: Topology and Real Analysis 60min (PMATH 351), Complex Analysis 60min (PMATH 352), Measure Theory and Fourier Analysis 60min (PMATH 450/451)

Note: We will count having achieved a grade of at least 80 in PMATH 650/651 in place of PMATH 450/451 for the purpose of skipping the Measure Theory and Fourier Analysis section.

Algebra | Analysis and Topology

Algebra Qualifying Examination

Analysis and Topology Qualifying Examination