New Qualifying Exams (effective Fall 2017)

Qualifying Exams

New Qualifying Exams (effective Fall 2025)

Old Qualifying Exam information and exam examples can be found here.

All doctoral students are required to pass a single multi-part examination that is composed of three written qualifying examinations and the completion of one required course with a grade of A- or better. All qualifying exams and the course must be completed by the end of students' third semester (excluding summer sessions) of entry into the doctoral program.

-The real analysis qualifying exam is mandatory for all students.
-Students will choose one of the following qualifying exams: linear algebra or abstract algebra.
-Students will choose one of the following qualifying exams: functional analysis or topology
- Students will choose and pass with a grade of A- or better one of the following courses: Complex Analysis (MATH 502), Differential Manifolds (MATH 528), Mathematical Logic (MATH 557), Algebraic Number Theory I (MATH 567), Numerical Analysis I (MATH 523), PDE 2 (MATH 514). This list may be modified after approval by the graduate studies committee of the program.

• Optional route: students may choose to take both the functional analysis and topology qualifying exams, and not be required to complete the course requirement above.

Qualifying examinations are offered twice a year: in May, after the end of the Spring semester and in December/January, after the end of the Fall semester. The corresponding semester-long graduate-level courses that prepare for these qualifying exams are offered every year: Linear algebra (MATH 535), Abstract algebra (MATH 536), Real analysis (MATH 501) in the Fall semesters, and Functional analysis (MATH 503) and Topology (MATH 527) in the Spring semesters.

The other courses are offered at least once every two years. They are required to have a final exam, and their final grade must be based at least for 60% on written tests (quizzes, midterm, final exam).
After passing all three qualifying exams and the course, students are expected to select a dissertation adviser and form a Ph.D.committee. The committee administers the comprehensive exam (no later than the end of the sixth semester of study) and offers counsel to the student as their research progresses..

Linear Algebra and its Applications	Math 535
Abstract Algebra	Math 536
Real Analysis	Math 501
Complex Analysis	Math 502
Functional Analysis	Math 503
Topology - Topics Covered this Year (2019-20)	Math 527