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PhD Comprehensive Exams

Written comprehensive exams

One of the milestones on your progress toward the PhD is successful completion of your written comprehensive exams. These exams cover material from the 500-level graduate sequences. The written comprehensive exams are given in August of each year, the week before the Fall semester starts. The student must schedule his or her comprehensive exams with the Graduate Coordinator at the end of the preceding Spring semester.

There are three possible grades for a written comprehensive: Fail, Pass at the MS level, and Pass at the PhD level. The exact rubric for each grade is up to each Exam Committee.

A PhD student must pass (at the PhD level) written comprehensive exams for three of the 500-level graduate sequences.

Written comprehensive exam topics

Written comprehensive exams are offered for each of the twelve 500-level graduate sequences. A committee of graduate faculty members and department professors in the exam area is created each spring to prepare and grade the exams. The exams topics and corresponding sequences are listed below.

  • Abstract Algebra, corresponding to MATH 565-566
  • Advanced Linear Algebra, corresponding to MATH 561-562
  • Algebraic Topology, corresponding to MATH 537-538
  • Applied Statistics, corresponding to STAT 530-535
  • Complex Analysis, corresponding to MATH 575-576
  • Experimental Statistics, corresponding to STAT 521-522
  • Mathematical Statistics, corresponding to STAT 523-524
  • Numerical Analysis, corresponding to MATH 555-556
  • Ordinary Differential Equations, corresponding to MATH 583-584
  • Partial Differential Equations, corresponding to MATH 595-596
  • Real and Functional Analysis, corresponding to MATH 573-574
  • Topology, corresponding to MATH 535-536

Rules and regulations

  • A PhD student must pass, at the PhD level, written comprehensive exams for three of the specified 500-level graduate sequences.
  • A PhD student must pass, at the PhD level, at least one written comprehensive exam by the end of the summer of his or her second full year in the program.
  • A PhD student must complete the written comprehensive exam requirement by the end of the summer of his or her fourth full year in the program.
  • A student may attempt any particular exam at most two times.
  • A student who schedules a particular exam may give a cancellation notice to the Graduate Coordinator no later than one week before the exam. A student who does not take a scheduled exam and does not give notice of cancellation in time will be considered to have taken and failed the exam. Exceptions to the above will be considered by the Graduate Coordinator in the event of special circumstances, if a request is made formally and in writing by the student.
  • Copies of some old written comprehensive exams may be available on request from the Graduate Coordinator; the availability depends on the approval of the corresponding examination committee. Please check with the Graduate Coordinator.

Oral comprehensive exam

Another milestone on your progress toward the PhD is successful completion of your oral examination. Before scheduling the oral examination, the student must first fulfill the written comprehensive examination requirement, and successfully complete a year of 600-level coursework in his or her proposed area of specialization.

The oral examination is intended to demonstrate that the student is prepared to begin research in his or her proposed area of specialization, has a sufficient command of the relevant materials, and can discuss them intelligibly. As such, it should take place either just before, or very shortly after, the student begins said research. Ideally, it should not be too close to either the completion of the written comprehensive exam requirements, nor to the oral defense of the dissertation.

In preparation for the oral exam the student must assemble a committee of at least three mathematics faculty members who are also members of the graduate faculty. One of these committee members must be the student's proposed thesis supervisor (Major Professor). The voting members of the committee are those members who are also graduate faculty members.

The committee will make specific decisions about the exam content, but the exam will generally cover the student's 600-level course work in the proposed area of specialization and related 500-level material.