The Ph.D. in Mathematical Sciences Program

The Ph.D. in Mathematical Sciences program is an interdisciplinary program designed to ensure that students acquire knowledge across a broad spectrum of the mathematical sciences and develop expertise in a chosen field of concentration, understand how it relates to other areas, and are able to apply this knowledge to solve real-world problems. Students in the Ph.D. program are provided with opportunities to gain consulting experience through the Center for Statistical and Mathematical Services in the department, as well as opportunities to participate in research projects through other facilities on campus, such as the Engineering Research Center for Computational Field Simulation. As a result, the Ph.D. program prepares students to work in industry, government, or academia.

Note

The student should earn at least 53 semester hours of graduate credits in the program. Required courses for the Ph.D. program include Mathematics/Statistics Core Courses for the Master's Degree, as described at https://www.math.msstate.edu/graduate/masters-mathematics or https://www.math.msstate.edu/graduate/masters-statistics.

Breadth Requirements for the Ph.D.

In keeping with the emphasis of the doctoral program that each student acquires breadth in the mathematical sciences, each student in the program will demonstrate a satisfactory grasp of each of the areas listed below.

  1. A Programming Language;
  2. Matrices/Linear Algebra;
  3. Probability/Statistics;
  4. Advanced Calculus;
  5. Computational Mathematics/Statistics.

The GCC members will determine a student's satisfactory grasp of the areas listed above.

Doctoral Committee

Each student in the Ph.D. program is assigned an academic advisor at the beginning of the program. The academic advisor guides the student through the program until the student decides on a major professor to supervise his/her Ph.D. project.

  • Students are encouraged to choose their major professors early in their programs of study; nonetheless, students must choose their major professors no later than the end of the second year of their program.
  • The student and the major professor then select the other members of the Doctoral Committee, consisting of the major professor and four graduate faculty members, with at least three from the Department of Mathematics and Statistics.
  • The Doctoral Committee so formed needs the GCC's approval.

The student and the Doctoral Committee select the courses for the student's program of study with the GCC's approval. The Doctoral Committee also monitors the student's progress.

Examination Procedures

Qualifying Examinations

In order to ensure that the skills and basic knowledge have been acquired to carry out the research necessary for the dissertation, the student must demonstrate competence in three different areas, as follows.

Ph.D. with a Mathematics Concentration:

The student chooses three courses, at least one from A-C and at least one from D-G, from the list below:  

  • A. Real Analysis: MA 8633 - Real Analysis I  
  • B. Functional Analysis: MA 8663 - Functional Analysis I  
  • C. Complex Analysis: MA 8713 - Complex Analysis I  
  • D. Applied Mathematics: MA 8203 - Foundations of Applied Mathematics I  
  • E. Ordinary Differential Equations: MA 8313 - Ordinary Differential Equations I  
  • F. Partial Differential Equations: MA 8333 - Partial Differential Equations I  
  • G. Computational Mathematics: MA 8443 - Numerical Solutions of Partial Differential Equations I

Ph.D. with a Statistics Concentration:

The student chooses two sequences, one from A-B and one from C-D, from the list below:  

  • A. Statistical Inference: ST 6573 - Math Stat II and ST 8733 - Advanced Statistical Inference I  
  • B. Applied Probability: ST 8533 - Applied Probability and ST 8553 - Advanced Probability Theory.  
  • C. Linear Models: ST 8613 - Linear Models I and ST 8413 - Multivariate Statistical Methods  
  • D. Design of Experiments: ST 8603 - Applied Statistics and ST 8853 - Advanced Design of Experiments I  

For a Statistics Concentration, the third area shall be related to the student's concentration and the advisor's area of expertise. This graduate-level course fulfills the program of study of the student's concentration and will be related to the research area for the Ph.D. dissertation. The graduate course will be suggested by the major advisor, which requires the approval of the GCC. Passing this graduate-level course with a grade of at least B will be considered for the third area of the qualifying examinations.

Qualifying Examinations Schedule:

  • Written qualifying examinations are normally scheduled twice a year, once in September and once in February.  
  • To demonstrate satisfactory progress in his/her graduate studies, a student is normally expected to complete his/her qualifying examinations by the beginning of the third academic year of Ph.D. work.  
  • A student is allowed to repeat an examination only once.

The Dissertation Committee

After the qualifying examinations have been passed, the student's Doctoral Committee will be reconstituted to form the Dissertation Committee, which normally consists of the same committee members. In rare cases, the student and the Doctoral Committee's major professor will select the student's Dissertation Committee, subject to the departmental GCC's approval.

  • The Dissertation Committee will consist of at least five graduate faculty members, including a major professor and at least three additional graduate faculty members from the Department of Mathematics and Statistics.
  • The committee's primary responsibility will be to supervise the student's research and writing of a dissertation in the area of specialization, and its members should be chosen with this mission in mind.
  • The student's major professor will enlist a person from outside the Department of Mathematics and Statistics who has expertise in the dissertation area to serve as an external examiner.
  • This person will read the dissertation and submit written comments regarding its quality and significance to the student's committee.
  • The external reviewer's letter will be sent to the Graduate Coordinator for their record.

Preliminary Examination

When the qualifying examinations have been passed, the breadth requirements have been met, and all course work on the program of study has been completed, the student may request the preliminary examination to be scheduled. In the early stages of the research effort, the student will make a formal dissertation proposal to the Dissertation Committee. The dissertation will be an original work that makes a significant contribution to the student's area of specialization. This examination will be in the allied areas as well as an in-depth examination in the area of specialization. It will be administered by the student's Doctoral Committee and must include an oral component. The majority vote of the Dissertation Committee will determine pass or fail. The oral component of the examination is open to the general faculty members and students.

Admission to Candidacy: A Ph.D. student who has successfully passed the preliminary examination is considered to have passed the Admission to Candidacy.

Final Examination

Once all other examinations and the dissertation have been completed, the student's committee will schedule the student's final examination. This examination will consist of an oral defense of the dissertation and will be open to the public. After consultation with the Graduate Coordinator, the major professor will publicize the time and place where the examination will be held. This announcement should be made at least one week prior to the scheduled date of the examination. The major advisor will notify the GCC about meeting the requirements and provide a copy of the external reviewer's letter of support at least one week before the final examination. A pass or fail on this examination will be determined by a majority vote of the student's committee. In making its decision, the committee will give due consideration to the external examiner's dissertation assessment.

Note:

  • To set the final examination, from work completed during the Ph.D. studies, students are expected to prepare at least one manuscript suitable for submission to peer-reviewed journals. This ready-to-submit manuscript shall be acceptable to the major professor.  
  • By the GCC's recommendation and Head's approval, a Ph.D. candidate will be rewarded for each accepted paper in a qualified refereed journal related to the Ph.D. dissertation's research area prior to his/her graduation.