Ph.D. Qualifying Examination in Mathematics

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 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)

· 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 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

All candidates will be examined over the contents of Missouri S&T course Math 5601 (Introduction to Numerical Analysis).

Candidates are also examined over three out of the following courses

· 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 5604 (Introduction to Numerical Methods for Differential Equations)

· Stat 5643 (Probability and Statistics)

Furthermore, candidates can complete a significant individual computational project in place of one of the remaining three 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 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-level or 6000-level mathematics course. The project must contain material that advances beyond the material covered in the relevant 5000-level 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

The individual examinations of the Ph.D. qualifying examination will be offered twice each academic year. Exam scheduling is subject to approval by the Director of Graduate Studies.

· To pass the Ph.D. qualifying examination, a candidate must pass four (4) individual examinations by the end of their fifth semester of enrollment in the Ph.D. program.

· A candidate must attempt at least one individual examination before or during their third semester of enrollment in the Ph.D. program.

· A candidate may take any number (1, 2, 3, or 4) of individual examinations each time the qualifying examination is offered.

· A candidate has two attempts to pass any individual examination.

· If a candidate fails the first attempt of a specific individual examination and changes to a different individual examination, then the candidate only has one attempt on the new individual examination. (The failure in the first attempt is not erased by the change to a different individual examination.)

· For any individual examination, if a candidate fails the second attempt, then the candidate cannot continue in our Ph.D. program.