Ph.D. Qualifying Examination in Mathematics

  1. The examination is offered in three separate emphasis areas: mathematics, computational and applied mathematics, and statistics. Each candidate must successfully complete an examination in one area of emphasis.

Mathematics Emphasis

Candidates for the PhD program in mathematics are required to choose and pass four individual qualifying examinations from the following list of seven Missouri S&T courses:

  • Math 5105 (Modern Algebra I)
  • Math 5215 (Introduction to Real Analysis)
  • Math 5302 (Intermediate Differential Equations)
  • Math 5325 (Partial Differential Equations)
  • Math 5351 (Introduction to Complex Variables)
  • Math 5585 (Introduction to Topology)
  • Stat 5643 (Probability and Statistics)

In addition, the Ph.D. qualifying exam is subject to the operational guidelines below.

Statistics Emphasis

All candidates will be examined over the contents of Missouri S&T courses Stat 5643 (Probability and Statistics), 5644 (Mathematical Statistics), and 5346 (Regression Analysis).

Candidates are also examined over one out of the following six courses:

  • Stat 5814 (Applied Time Series Analysis)
  • Stat 6343 (Nonparametric Statistical Methods)
  • Stat 6344 (Design and Analysis of Experiments)
  • Stat 6545 (Multivariate Statistical Methods)
  • Stat 6553 (Linear Statistical Models I)
  • Stat 6841 (Stochastic Processes)

In addition, the Ph.D. qualifying exam is subject to the operational guidelines below.

Computational and Applied Mathematics Emphasis

  1. Required exam: Math 5601 (Introduction to Numerical Analysis).
  2. Three courses of the following
  • Math 5215 (Introduction to Real Analysis)
  • Math 5302 (Intermediate Differential Equations)
  • Math 5325 (Partial Differential Equations)
  • Math 5602 (Mathematical Foundation of Finite Element Methods)
  • Math 5603 (Methods of Applied Mathematics)
  • Stat 5643 (Probability and Statistics)

Furthermore, candidates can complete a significant individual computational project in place of one of the remaining three exams in 2.  Candidates must first find two faculty members who agree to serve on the student’s computational project committee.  The faculty member committee will oversee and judge the computational project.  If a candidate does not find two faculty members who are willing to serve on the student’s computational project committee, then the candidate is not eligible to substitute a computational project in place of one of the remaining three exams.

The computational project must consist of one or more significant computational mathematics problems whose difficulty requires the completion of at least one 5000 or 6000 level mathematics course.  The project must contain material that advances beyond the material covered in the relevant 5000 or 6000 level course(s).

In addition, the Ph.D. qualifying exam is subject to the operational guidelines below.

Operational Guidelines for the Ph.D. Qualifying Examination

A syllabus will be prepared for the examination over each course and will be available to interested parties. A copy can be obtained from the department secretary.

A student must perform adequately on each examination (i.e., each examination on each of the courses) to be given a pass. If a student passes one, two or three exams but not four exams, the student will be given a partial pass and is required to take the failed exams in a second attempt.  Students may change their emphasis area after the first attempt at the qualifying exam (irrespective of the outcome), but they will be given only one attempt to pass the qualifying exam in the new emphasis area.

A student must retake failed examinations subject to the timing requirements below, and also no later than 13 months after their first attempt.

If a student fail to pass all four exams in two attempts, the department will terminate the student's pursuit of the Ph.D. Degree in Mathematics at Missouri S&T and the student will be ineligible for renewal of his or her teaching assistantship.

The qualifying examination will be offered twice each academic year, once in the fall semester and once in the spring semester.  The qualifying exam must be completed by the end of the third week of the semester in which it is given.  Exam scheduling is subject to approval by the Director of Graduate Studies.

Timing requirements for completion of the Ph.D. qualifying exam:

The Ph.D. qualifying exam must be completed within a certain time period, which is specified below. In the timing requirements that follow, semesters of enrollment will be counted from the first semester the student enrolls as a full-time student in our doctoral program but will not cover semesters in which the student was enrolled as a probationary student.

    • The Ph.D. qualifying exam will be administered no later than the beginning of the student’s third or fourth semester of enrollment.  Students who fail the exam (completely or partially) may re-take the exam no later than the beginning of their fourth (or fifth) semester of enrollment.  If the qualifying exam is not successfully completed by the end of the fifth semester of enrollment, then the student will no longer be eligible to be on the doctoral program in the department of Mathematics & Statistics.
    • Note: Students with catalog year up to 2019-2020  have until the end of the sixth semester of enrollment to successfully 
      complete the qualifying exam.

(Revised 10/16/2021)