PhD qualifying examination

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, which will be taken as 60 minute long exams on different days over the course of 3 weeks. 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 (PMATH 347), Fields and Galois (PMATH 348)

Analysis & Topology: Topology and Real Analysis (PMATH 351), Complex Analysis (PMATH 352), Measure Theory (PMATH 450)

Algebra | Analysis and Topology

The 2026 PhD Qualifying Examinations will take place from September 15 to October 1, 2026. The exams will take place on the following dates:

September 15: Linear Algebra

September 17: Topology and Real Analysis

September 22: Groups and Rings

September 24: Complex Analysis

September 29: Fields and Galois Theory 

October 1: Measure Theory 

To sign up for any of the Qualifying Exams, please complete the 2026 Pure Math Qualifying Exam Sign-Up.

Algebra Qualifying Examination

Analysis and Topology Qualifying Examination