The Qualifying Examination

Effective starting Autumn Quarter 2018.

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.


In order to sit for the Qualifying Examination, a student has to provide the Examination Committee (consisting of three members of the Applied Mathematics faculty) with a written statement on his/her tentative research plan or accomplished research work. This document should be at least two-pages long, and it is to be handed in on the first day of the Qualifying Examination. A student who fails to do so will be disqualified to sit for the Qualifying Examination.

The bulk of the Qualifying Examination consists of three exams of three hours each, spread over four days. The exams of the first three days focus respectively on the materials in the sequences 567, 568, 569 (Mathematical Methods), 561, 562, 563 (probability and statistics), and 581/584, 585, 586 (numerical methods). A student chooses to sit for two out of the three exams. The exams on the first three days are written; the last day is an oral examination with the Examination Committee.

The solution of some questions may involve the use of a computer, including some programming.

Exam questions are collected from the entire AMATH faculty.


In order to pass the Qualifying Examination, students are expected to provide their research plan/summary on day 1, perform excellently on the first two days and very well on the oral exam.


If a student does not pass the qualifying exam, he/she may choose to retake the Qualifying Examination 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.