Comprehensive Examination

The Comprehensive Exam tests knowledge of graduate-level mathematics. The purpose is to ensure that each student has the necessary knowledge to conduct research in his or her area of concentration. This exam must be passed by the end of the eighth semester in the program (summer semesters do not count).

Exam Structure

The examination will consist of three tests; two three-hour, written subject tests and one specialty test that can be oral and/or written.

Exam Topics

Topics depend on your area of concentration.

Applied Mathematics

Chose two.

  1. Ordinary Differential Equations SyllabusSample problems
  2. Partial Differential Equations SyllabusSample problems
  3. Numerical Linear Algebra/Numerical Optimization SyllabusSample problems

Discrete Mathematics

Chose two.

  1. Algebra SyllabusSample problems
  2. Coding Theory and Cryptography Syllabus Sample problems
  3. Design Theory SyllabusSample problems


Chose two.

  1. Mathematical Statistics SyllabusSample problems
  2. Linear Models SyllabusSample problems
Exam Archive (use ISO password)

Specialty Test

The specialty test may be written, oral, or a combination of both formats, to be determined by the student's advisor


The Comprehensive Exams are administered twice a year, usually during weeks three or four of fall and spring semesters. Students are notified by email of the registration deadline approximately six weeks prior to the exam.