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Graduate Students

picture of McBryde Hall

The Mathematics Department is located in McBryde Hall, pictured above (photo credit: Mia Shu). There are roughly 70 graduate students actively engaged in the mathematics graduate programs. All graduate students have an office/study space for their own use, and are welcome in the Department's Common Room for informal discussion and conversation. 

As a new student you will be given an initial advisor appropriate for the research interests you have expressed. However, those interests will envolve, and you are free to make your own arrangements with any other faculty member to be your advisor. 

Most of our students become involved in some sort of study or research project in addition to their course work. This can range from independent study on a topic of special interest, under the direction of a faculty member, to supporting work on a faculty research project, to the doctoral dissertation of Ph.D. students. Most M.S. students complete their studies with a presentation based on a reading/study/research project that they have carried out under faculty supervision. These opportunities to study with and learn from both student and faculty colleagues is one unique privilege of graduate work in a major research department.

Each year an average of 15 or so students complete their M.S. degrees. Some of the employers of our past Master's Degree graduates are: Cambridge Technology Partners, Bluffton College, Wingate College, U.S. Army Combined Arms Support Command, Mississippi State University, Johns Hopkins University Applied Physics Laboratory, Naval Air Warfare Center, Allied Signal Communications Systems, GEICO and MIT's Lincoln Laboratories. Many go on to become Ph.D. students. With good progress, all M.S. students are invited to do so in our department.

Some of the most popular areas for Ph.D. dissertation work are, PDEs (Applied), Mathematical Physics, Numerical Computation, Control and Systems Theory, Algebra and Number Theory. An average of about 5 students complete their Ph.D. each year. Some employers of recent graduates include: University of Texas, Washington University (St. Louis), University of California - Berkeley, Georgia Tech, Memphis State University, Iowa State University, University of Richmond, University of California - San Diego; Siemens Energy and Automation Inc., Advanced Technologies, Crown Life Insurance, Hollins College, University of Arkansas, University of St. Thomas, Mississippi State University.

We offer programs leading to the Master of Science (M.S.) degree, and a doctoral program leading to the Doctor of Philosophy (Ph.D.) degree. The descriptions below of degree requirements for these programs are only summaries, intended to communicate the nature of the programs to potential students. For complete descriptions see the Policies document linked below. 

The Master of Science degree represents two years of course work and an optional thesis. This degree is intended to provide a basic foundation of graduate level work from which the student can pursue multiple options for the future. Many M.S. degree holders move on to a technically oriented job with an employer in the private sector or with a government agency. For others it is the gateway into the more intense and in-depth study of the doctoral program. There are two M.S. degree options: the nonthesis option and the thesis option. As alternatives to the standard requirements for these options, both are available under a special interdisciplinary plan.

To complete the M.S. degree requirements the student must satisfy some form of final examination requirement. Our current practice is to have the student prepare and give a lecture with written summary on the topic of a short independent study project carried out under the supervision of a faculty member. These Master's Presentations have proven valuable to students in job interviews and in developing professional communication skills, not to mention the interesting mathematical topics they have explored. A standing alternative to the Master's Presentation requirement is the passage of two Ph.D. preliminary examinations. This allows a student to complete the M.S. requirements "automatically" in the first two years of normal progress toward the Ph.D.

The thesis option requirements differ from the above mainly in that the writing of a Master's Thesis replaces some of the course work. The Master's Thesis is a written report resulting from a significant independent study or research project, conducted under the guidance of a faculty advisor. Some course requirements are replaced by Math 5994, a special course designation to account for the time spent in independent study and writing of the thesis. In addition, the thesis option allows a little more flexibility in allowing you to take courses outside the Mathematics Department that may be relevant to your work. The final examination is replaced by a presentation of the thesis and response to questions (the "thesis defense"). This option provides more opportunity for in-depth work in a specific topic or application than would be possible under the nonthesis option.

The interdisciplinary plan is intended only for students having clearly defined interdisciplinary career goals that cannot be adequately served under either the standard thesis or nonthesis options above. The student's program of study is designed by the student and an advisory committee, including at least one faculty member from the related discipline. This allows a program of study to be customized to the student's specific interdisciplinary goals, while insuring a level of quality comparable to the other master's degree options. It is important that the student interested in this option take the initiative to form the advisory committee and plan a program of courses at the very beginning of their graduate studies.

The Doctor of Philosophy (Ph.D.) degree takes the student far beyond the Master's degree in several ways. For one, a broader and more solid basis of advanced mathematical knowledge must be demonstrated. To ensure this, the student must pass Ph.D. preliminary examinations in two of the following four areas: Algebra, Analysis, Partial Differential Equations, and Computational Mathematics. With the prelims complete the student begins the preparations for his/her doctoral research project. The transition into the research phase is marked by the comprehensive exam. This exam is administered by the student's advisory committee. Its structure may vary, but the exam generally includes a discussion of the planned research project. The time required to complete the Ph.D. program is not fixed but typically involves three to five years of study after completion of the M.S..

The centerpiece of the Ph.D. is the dissertation. Under an advisor's guidance, the doctoral candidate engages in a major research project. The dissertation itself is the written document, following professional standards, resulting from this project. Through this dissertation work the doctoral student moves beyond the relatively passive role of receiving knowledge presented in courses to become an active, self-motivated scholar, making a significant contribution to their area of specialty. The work of the dissertation is expected to be of such quality as to merit publication in a scholarly journal, after appropriate revisions. For those continuing in academic research the dissertation topic may initiate a more lengthy research program that forms the beginning of a scholarly career. For those who continue in a nonacademic direction, the dissertation experience is valued because it requires the highest level of creativity and independent thinking.

Most graduate students in the Mathematics Department are supported by Graduate Teaching Assistantships (GTAs). GTAs receive a stipend (paycheck) for the nine-month academic year, as well as a waiver of tuition. As a GTA you are an employee of the Mathematics Department with assigned duties related to teaching undergraduate courses. Students are typically supported for two years in the M.S. program. After admission to the Ph.D. program, four additional years of GTA support can be anticipated for students making satisfactory progress. There are usually a number of GTA positions available for the summer months, awarded on a competitive basis. Faculty with research grants can often provide summer support for students assisting them on their projects.

Some graduate students may find academic year support through their advisor's research grant, or through fellowships or grants. Some of the awards that our graduate students have held are: NSF Graduate Fellowship, DOD Assert grant, Albert Einstein Congressional Fellowship, Willma Lowry Teacher of the year in Mathematics, Presidential Award for Excellence in Science and Mathematics Teaching. 

Our department welcomes students from across the world, and our graduate programs currently include students from nearly every continent. The accommodate international students and meet university guidelines, a few additional requirements apply. If you are an international student you will be required to submit TOEFL scores as part of your application. The University takes on a certain legal responsibility in authorizing the visa for an international student. Once admitted, the Graduate School will administer additional tests for English language skills. You will be required to take special English courses to strengthen your language skills, if necessary. International students are also required to provide evidence of health insurance coverage, or else participate in the University's optional group policy for graduate students.

This section provides semester-by-semester guidance for current graduate students. Students might also want to visit the for Advisors tab on this page, to see flowcharts and check major benchmarks for completing their graduate degree.

First Semester

  • August: An academic advisor is assigned to you based on stated interests; work with your advisor to select courses
  • Attend at least 6 seminars or colloquia
  • November: Attend Research Days to help you identify a research advisor and research topic (for thesis option only)
  • December: complete your Graduate Student Activity Report

Second Semester

Third Semester

Fourth (Final) Semester

  • Complete coursework
  • Apply for graduation and final exams
  • Complete final exam requirements: 2 preliminary exams, a thesis, or a presentation
  • Note that even the preliminary exam option requires that you schedule a final exam, but in that case, there is no actual presentation or defense.
  • If you plan to continue into the PhD program, Request a Change of Degree Status

First Semester

  • August: Attend Orientation; work with your advisor to select courses
  • November: Attend Research Day to help you identify a research advisor and research topic
  • Attend at least 6 seminars or colloquia
  • December: complete your Graduate Student Activity Report

Second Semester

  • Choose your Advisory Committee in consultation with your advisor
  • Complete Ethics and Diversity requirements
  • Attend at least 6 seminars or colloquia
  • April: Request preliminary exams for August

First Semester

Second Semester

First Semester

  • Attend at least 6 seminars or colloquia
  • December: complete your Graduate Student Activity Report
  • Begin conducting dissertation research

Second Semester

First Semester

  • Attend at least 6 seminars or colloquia
  • December: complete your Graduate Student Activity Report
  • Schedule dissertation defense date

Second Semester

Graduate advisors support graduate students in navigating benchmarks in their progress toward degree. The main benchmarks are outlined, semester-by-semester, in the drop-down tab for Current Students. During the first year of graduate school these benchmarks include meeting the university's Ethics requirement and its Diversity, Equity, & Inclusion (DEI) requirement. The Ethics requirement is met if the student participates in Orientation and Research Days and completes a short Canvas course (linked below). The DEI requirement is met when the student completes the Diversity Course in Canvas (also linked below) and writes a diversity statement suitable for a job application--as approved by the advisor. Both of these requirements are checked when the student submits a Plan of Study.


The flowchart below comes from the Graduate School and illustrates step-by-step progress toward the doctoral degree (PhD). Steps for the Master's degree (MS) differ but follow the same general order. Semester-by-semester requirements for both degrees can be found under the Current Students tab. The key checkpoints for Academic progress toward the PhD are as follows:

A) Submit a Plan of Study (step 13)
In addition to coursework, this step includes the formation of a graduate committee, agreed upon by the student and their advisor. As mentioned above, this step also includes verification the student has met the Ethics and DEI requirements (step 17). Students should submit their Plan of Study to the Graduate Program Coordinator at the end of their third semester in the program (second semester for MS students).

B) Pass Two Preliminary Exams (step 15)
Note that the Graduate School refers to these exams as "qualifying exams." Students must take and pass two of the four offered preliminary ("qualifying") exams: Algebra, Analysis, Differential Equations, and Computational Mathematics. These exams are offered in January and August of each year, upon request. If a student fails an exam, they must retake the same exam and must pass it the second time, in order to stay in the program. 

C) Pass Oral Exam (step 16)
Note that the Graduate School refers to this exam as the "preliminary exam." This is a formal defense in which the student's committee determines whether the student is prepared to proceed with dissertation research. This "Prelim Exam" must be scheduled through the Graduate School at least 2 weeks before the defense. See Exam Scheduling flowchart further below.

D) Final Exam (step 21)
The final exam for PhD students is their disseration defense. This Final Exam must be scheduled through the Graduate School at least 2 weeks before the defense, and it must occur at least 6 months after passing the Oral Exam. See the Exam Scheduling flowchart further below. The advisor should announce the defense date to all Math faculty and graduate students so that they might attend the student's presentation.

The second flowchart, below, illustrates the timeline for exam scheduling. Students schedule Prelim (oral) and Final (dissertation or thesis) exams using the the Graduate School's exam system, linked below the flowchart. Students and their advisors can also use that system to check progress in satisying the exams (key checkpoints C and D).