Mathematics

Written Qualifying Examinations

The written qualifying examinations are given twice a year, in January and August, just before the start of the Spring and Fall semesters. A Ph.D. candidate is required to pass three written qualifying examinations chosen from the following set of subjects (corresponding course numbers are included in parenthesis):

• algebra (6310-6320)

• applied mathematics (6710-6720)

• differential equations (6410-6420)

• numerical analysis (6610-6620)

• probability (6040)

• real and complex analysis (6210-6220)

• statistics (6070)

• topology and geometry (6510-6520)

Each exam lasts three hours and is written at a first-year graduate level. Entering students are recommended to take the 6000-level course corresponding to a particular exam and use the course materials to prepare for the exams. Students with particularly strong backgrounds can choose to take the exams without taking the courses. Copies of past exams from the last ten years can be obtained by contacting the Graduate Coordinator.

Oral Qualifying Examination

This exam is conducted by the student’s supervisory committee and it can take one of the following two formats: a general exam to measure the student’s overall mathematical maturity and breadth, or a presentation of the proposed dissertation project. The exam also evaluates the student’s skill at chalkboard exposition and verbal exchange.

Teaching Requirement

Each Ph.D. candidate is required to teach a minimum of two courses or equivalent tutorials, or supervise laboratory sessions.

Final Oral Examination

This examination consists of a public thesis defense that summarizes the candidate’s thesis work.