Doctoral Qualifying Examinations

General Description

Doctoral qualifying examinations are given in Applied Mathematics and in Applied Probability and Statistics. These consist of (I) written preliminary exams, each composed of three parts, and (II) an oral exam.

Updated: October 26, 2015

I.   Preliminary Exam

Applied Mathematics

  • Part A. Applied Mathematics
  • Part B. Analysis
  • Part C. Linear Algebra and Numerical Methods (LA/NUM)

Applied Probability and Statistics

  • Part A. Probability Distributions and Regression Analysis Methods
  • Part B. Real Analysis and Statistical Inference
  • Part C. Probability Theory and Design and Analysis of Experiments

The timing of the Qualifying Examination sequence is based on the assumption that students commence the Ph.D. program in the Fall semester. Students who start in the Spring must consult with their advisor as to the timing of their Qualifying Examinations. Spring starts are not encouraged.

Ph.D. students take Part A at the beginning of their second (Spring) semester in the program and take Parts B and C soon after the end of their second (Spring) semester. Any deviations from this schedule will be permitted only under extenuating circumstances, and must be agreed by the Director of the Graduate Program. Any one part of the preliminary exam can be taken at most twice. Exam grades are: A pass, B fail (some understanding of subject but not sufficient to pass), F fail (understanding is more deficient). More information about each part of the preliminary exams is given by following the links above.

II.  Oral Exam

Ph.D. students usually take the oral exam at the beginning of their fourth semester in the program.

Applied Mathematics:

  • For students following the Applied Mathematics track, the oral exam will be based on a research topic that they study with a chosen faculty advisor. For many students this research and study will begin over the summer, following completion of their first two semesters on the Ph.D. program. The project will continue in the student's third (Fall) semester, when they will register for pre­doctoral research credits (Math 792B) with their chosen advisor. For students who elect not to take part in the optional Ph.D. summer program, their research and study will begin at the start of the third (Fall) semester with Math 792B. Students in this category will most likely take the oral exam at a later stage, towards the end of the fourth (Spring) semester. The faculty advisor is responsible for convening an examining committee of three faculty members (one of whom is the advisor), and for designating seminal research papers in the chosen research area with which the student must be familiar. The student will be examined both on this key literature, and on the research that he or she has carried out. Students may, if they wish, change advisors after successful completion of the oral exam.

Applied Probability and Statistics Oral Exam:

For students following the Applied Probability and Statistics track, the oral exam will be based on specific courses that students take:

More information about topics for the oral exam is given by following the links above. 


To maintain status in the doctoral program (and to progress from doctoral student to doctoral candidate) students must successfully complete the preliminary and oral components of the qualifying exam within two years of beginning the Ph.D. program.

The components of the exams are usually offered at the following times of the year:

  • August: Preliminary Exams Parts B and C (retakes)
  • January: Preliminary Exams Part A
  • May: Preliminary Exams Parts A (retakes), B, C
  • Oral Exam: By arrangement with the Committee

Additional Information

Copies of past qualifying exams are available here.