Qualifying Exams

The Qualifying Exam is designed to ensure students possess the necessary foundational knowledge in core mathematical areas while offering the flexibility to demonstrate proficiency through coursework.

Core Subject Areas

The exam will evaluate competency across eight core areas:

1. Algebra
2. Analysis
3. Geometry
4. Numerical Analysis and Numerical Linear Algebra
5. Partial Differential Equations
6. Topology
7. Probability
8. Optimization

Schedule and Format

• Annual Administration: The exam will be offered twice a year, in May and August. Incoming first-year students who are prepared may opt to take the exam in May or August prior to the start of their first semester.
• Structure: The exam spans five hours and includes a supervised break. It will encompass four to eight of the core subjects, which will include Algebra and Analysis. The inclusion of the remaining topics will be determined by the specific courses taught over the preceding two semesters. The selected subjects and their corresponding syllabi will be published at the start of each academic year.

Passing Requirements

To satisfy the Qualifying Exam requirement, a student must fulfill one of the following two tracks:

• Track 1 (Exam Only): Pass the exam in 2 out of the 8 core areas.
• Track 2 (Exam + Coursework): Successfully pass the examination in one core area AND complete two approved graduate-level Mathematics courses with a minimum grade of A-. These courses may be distributed across one or two core areas, provided they are distinct from the core area passed in the examination. ( Note: Reading courses do not fulfill this coursework requirement .) Students must complete this coursework requirement by the end of their first year in the program.
• Master’s Degree Pathway: If a student does not successfully fulfill the Qualifying Examination requirement by the beginning of their 3rd semester, they will be with-drawn from the PhD program and receive continued funding only for an additional academic year to facilitate the completion of a Master’s degree.

Doctoral students must pass qualification exams ("quals") in three of the six available areas:

Topics and Related Courses

• Algebra: Math 245 course
• Algebraic Topology: Math 275, 276 courses
• Analysis: Math 133, 245 courses
• Geometry: Math 285 course
• Numerical Analysis and Numerical Linear Algebra: Math 225, 226 courses
• PDEs: Math 255, 256 courses

It's important to note that, in the list above, the courses related to an exam will partially prepare an exam taker for the exam. An exam-taker is expected to know the full list of topics covered in the exam, as provided in the text below.

A few months prior to the exam, doctoral students will receive email reminders to sign up for quals. Please see section 2.4 of the PhD Handbook for more details on the exams and for all policies and procedures related to the exam. If you have further questions, please consult with your advisor.