The Qualifying Examination

Valid starting Autumn Quarter 2009.

The qualifying examination is used as a reinforcement tool to ensure that students have assimilated the graduate-level material (and its background material) necessary for completion of a PhD in Applied Mathematics to a degree where its use becomes second nature. The examination is not meant as a filter to eliminate students from the PhD program, but rather to ensure that students are well prepared for it.


The Qualifying Examination is offered by the Department during the week before the start of classes in September, and again during the Finals Week of Autumn Quarter. Ph.D. students are expected to take the Qualifying Exam following their first year of full-time study (or the first time the exam is offered after taking AMATH 567, 568, 569, 581 or 584, 585, and 586, or equivalent).


In order to sit for the Qualifying Examination, students have to provide the Examination Committee (consisting of three members of the Applied Mathematics faculty) with a written summary of the research accomplished with their research advisor over the summer of their first year. The summary should be at least two pages. This research summary is to be handed in on the first day of the Qualifying Examination. Failure to do so will be counted as a failed Qualifying Examination.

The bulk of the Qualifying Examination consists of three exams of three hours each, spread over three days. The exams cover a core of undergraduate and graduate material necessary for successful completion of the Ph.D. program. These core areas are the material covered by AMATH 567, 568, 569, 581 or 584, 585, 586, and calculus, ordinary differential equations, linear algebra, advanced calculus and complex analysis.

Questions do not necesarily correspond to one of these core areas, but may require the synthesis of different concepts from different areas, as well as the employment of different approaches. The solution of some questions will involve the use of a computer, including some programming.

Exam questions are collected from the entire AMATH faculty. Questions are arranged in order of increasing difficulty from the first day to the third day.

The exams are written, except on the third day, which starts with a written preparation and ends with an oral examination with the Examination Committee.


In order to pass the qualifying examination, students are expected to provide their research summary on day 1, perform excellent on day 1 and very well on days 2 and 3.


If a student did not pass the qualifying exam he/she may choose to retake the qualifying exam once. This retake is expected to occur at the first occasion the exams are offered again. If a student does not pass the qualifying exam after two attempts, he/she will not be allowed to continue in the Ph.D. degree program.