# Qualifying Exams

After the 1^{st} year, and ideally by the end of their 2^{nd} year, but no later than by the end of their 3^{rd} year, every student must pass three written Qualifying Exams. The purpose of the Qualifying Exams is to verify that the student has acquired the necessary general knowledge, to serve as the basis for her/his dissertation research.

Each Qualifying Exam will be based on a syllabus of topics available below. The syllabi are based on material covered in classes relevant to each subject, the classes for each exam are listed below. Each Qualifying Exam is a 3 hour long, written exam, and the exams will be offered once per semester. During the semester the students takes her/his last qualifying exam, she/he must be enrolled in Math 795.

Students must pass the Qualifying Exam in:

- Analysis (based on MATH 713, 714, 715),

and two Qualifying Exams from this list:

- Algebra (based on MATH 731, 732),
- Topology (based on MATH 641, 741, 742),
- Numerical Analysis and Approximation (based on MATH 701, 702),
- Operations Research (based on MATH 687, 751, 752), or
- Probability (based on STAT 705).

Students will be allowed a maximum of two attempts at each of the exams in the first three years of the Ph.D. program. Each exam can be passed at M.S. level (low pass) or Ph.D. level (high pass). To proceed with the Ph.D. program all exams must be passed at the Ph.D. level. If all exams are passed at the M.S. level but not all at the Ph.D. level, and other requirements for the M.S. degree are satisfied, the student will end her/his program with an M.S. degree in Mathematics.