PhD Qualifying and Preliminary Exams (Semesters)

All PhD students must pass one of the two following qualifying exams.

  • Advanced Calculus and Linear Algebra based on the two-semester sequence Advanced Calculus MATH6001-6002 and the one semester course Advanced Linear Algebra MATH6003. (See sample problems.)
  • Statistics based on the two two-semester sequences Mathematical Statistics STAT6021-6022 and Applied Statistics STAT6031-6032.

All incoming PhD students are required to take at least one qualifying exam before the beginning of their first semester. Students who do not pass this exam at the PhD level are placed in the appropriate 6000 - level courses. In order to remain in the PhD program, the student must pass the Qualifying Exam (at the PhD level) by the beginning of the Fall Semester following their admission into the program.

All PhD students must also pass four of the following ten preliminary examinations. Exams are primarily offered in May and August of every academic year and can be attempted at most twice. Exams taken by incoming students in August do not count against this two-attempt rule.

  • Real Analysis
  • Complex Analysis
  • Algebra
  • Topology
  • Ordinary Differential Equations
  • Partial Differential Equations
  • Multivariate Analysis
  • Theory of Linear Models
  • Statistical Methods
  • Probability

Note: From 2013-2018 there were five Prelim exams covering two subjects each:

Note on semester conversion: The above preliminary exams were offered for the first time in May 2013. Students transitioning from the quarter-based preliminary examination system to the new one should consult the rules on preliminary exams during the conversion to semesters.