### Ph.D. Qualifying Examination in Mathematics

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

**Mathematics Emphasis**

All candidates will be examined over the contents of the Missouri S&T courses MATH 5302 (Intermediate Differential Equations), MATH 5105 (Modern Algebra I), MATH 5215 (Introduction to Real Analysis), MATH 5585 (Introduction to Topology), and 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), STAT 5644 (Mathematical Statistics), and STAT 6553 (Linear Statistical Models I).

All candidates will be examined over the contents of two of the following seven Missouri S&T courses:

- MATH 5107 (Combinatorics)
- MATH 5215 (Introduction to Real Analysis)
- STAT 5346 (Regression Analysis) (or COMP SCI 5204)
- STAT 6841 (Stochastic Processes)
- STAT 6343 (Nonparamteric Statistics)
- STAT 6344 (Design of Experiments)
- STAT 6545 (Multivariate Analysis)

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

**Computational and Applied Mathematics Emphasis**

Candidates are examined over five out of the following nine 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 6417 (Functional Analysis I)
- MATH 6601 (Numerical Analysis)
- MATH 6602 (Mathematical Foundation of Finite Element Methods)
- STAT 5643 (Probability and Statistics)

In addition, at least one of the five exams must be either MATH 5215 (Introduction to Real Analysis), MATH 6417 (Functional Analysis I), or MATH 6601 (Numerical Analysis).

Furthermore, candidates can complete a significant individual computational project in place of one of the remaining four exams. 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 four 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. A student who performs adequately on all but one or two examinations in their first attempt will be given a partial fail and will be required to retake those failed examinations within 13 months of completing the first attempt . Students who fail more than two exams will be required to retake all five subjects they were tested on previously and do so within 13 months of their first 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.

The second unsuccessful (fail or partial fail) attempt on the examination 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 master’s or doctoral program but will not cover semesters in which the student was enrolled as a probationary student. In addition, summer semesters will not be counted towards the semesters of enrollment. Furthermore, define the “beginning of the semester” as the time period from the start of the semester until the end of the third week of the semester.

- For students who enter our graduate program without a master’s degree in mathematics or statistics:
- The Ph.D. qualifying exam will be administered no later than the beginning of the student’s fifth semester of enrollment. Students who fail the exam (completely or partially) may re-take the exam no later than the beginning of their sixth semester of enrollment. If the qualifying exam is not successfully completed by the beginning of the student’s sixth semester of enrollment, then the student will no longer be eligible to be on the doctoral program in our department.

- For students who enter our graduate program with a master’s degree in mathematics or statistics:
- The Ph.D. qualifying exam will be administered no later than the beginning of the student’s third semester of enrollment. If the qualifying exam is not successfully completed by the beginning of the student’s fourth semester of enrollment, then the student will no longer be eligible to be on the doctoral program in our department.

Exceptions to the above exam schedule may be allowed by the department’s graduate policy committee after appeal by the student and due consideration by the graduate policy committee, but such an exception will be allowed only under extenuating circumstances.

(Revised 8/18/15)