MS Degrees

PhD Degrees

The department offers PhD degrees in mathematics and applied mathematics. Applied Mathematics PhD degrees can also have a concentration in Computational Mathematics. Mathematics and Applied Mathematics PhD degrees can also have a concentration in Interdisciplinary Mathematics. The degree programs are designed to ensure that the student acquires a fairly broad background, then rather quickly acquires the depth of knowledge needed to begin PhD-level research.

For the first year or two, the student takes introductory courses and prepares for the PhD Written Qualifying Examination. In addition, many PhD students acquire early research experience by participating in the Industrial Applied Mathematics Program, or by completing a master's degree with its associated project.

"Each PhD student must take the analysis course MA 515 and the algebra course MA 521 and obtain a grade of B or higher". Moreover, there are lists of additional basic mathematics and applied mathematics courses:

A mathematics PhD. student takes three courses from the first list and one from the second; an applied mathematics PhD student takes two courses from each list.

The PhD Written Qualifying Examination consists of a written examination in each of three subject areas chosen by the student. It is administered twice a year, during January and August. The three subjects are chosen from the following list, each subject being represented by a two-semester sequence of graduate courses. Full details on scheduling and retake policies are found here.

Students opting for the PhD in Applied Mathematics with a concentration in Computational Mathematics meet the requirements for an applied mathematics student. In addition, they must take Numerical Analysis as one of the three subject areas for the qualifying examination, and they must select three courses from a list of computational mathematics courses. The list includes the department's advanced numerical analysis and computer algebra courses, as well as various computer science courses, and computationally intensive courses from other disciplines.

After passing the written qualifying exam, the student chooses a dissertation advisor who supervises the research project and dissertation. The student also chooses three additional faculty members to make up the advisory committee, which is chaired by the dissertation advisor. The dissertation plan is presented to the advisory committee at the Preliminary Oral Examination. Finally, the student produces a dissertation of new and original research in an area of mathematics; the dissertation is defended at the Final Oral Examination.

Concentration in Computational Mathematics (CMA)

CMA students must fulfill all the requirements for the PhD in Applied Mathematics. One of the three subjects for the qualifying examination must be Numerical Analysis such as MA 580 - 780. In addition to MA 580 and 780, CMA students must take three courses from the list of approved CMA courses.

The MAI concentration is available to PhD students in either Mathematics or Applied Mathematics. It is not available to Masters students.

MAI students fulfill all the requirements for the Ph.D in MA or AMA except that they have the option of substituting a qualifier in another field for one of the three required math PhD qualifying examinations.
This substitution requires prior approval of the Director of Graduate Programs (DGP) or Graduate Program Administrator (GPA). The substituted exam does not have to be on the same date as the two math qualifying examinations. The taking of the two math qualifying examinations and the substituted exam will be considered as one set of examinations and the usual departmental retest policies will hold.

In addition to the MA or AMA PhD requirements the IMA student would be required to demonstrate evidence of interdisciplinary work. This would be done as follows:

Required of all MAI students

• Member of committee from other discipline.
• At least 2 courses in the other discipline, at least one of which is not cross-listed with mathematics.
• A formal research proposal to be presented at the preliminary oral exam. The proposal could be as much as several fully developed chapters of the final dissertation or as little as a few pages. The proposal would clearly explain the interdisciplinary research plan. A copy would be filed with the Math Dept Graduate Program
  Office.
  

MAI Students are required to do at least two of:

• Attend and present at a conference in the other discipline.
• Publish in the literature of the other discipline.
• Have a Summer internship.
• Take a Preliminary examination in the other discipline.

The MS degrees are similar in philosophy to the PhD degrees. They are designed to ensure that the student acquires a reasonably broad background in either mathematics or applied mathematics, and that the student studies some area or areas in depth. The MS program with project is described first. The Option B Masters is then described.

The MS degrees require a minimum of 27 hours of course work (nine courses). In addition, each MS student works on a project, which carries three hours of credit. An advisory committee of three faculty members oversees the project. A written report on the project is presented at the Final Oral Examination, which generally includes a short lecture describing the project.

For the MS in Mathematics, the student takes a four-course core consisting of:

• MA 515 (Analysis)
• MA 551 (Topology) or MA 518 (Manifolds)
• MA 520 (Linear Algebra) or MA 523 (Matrix Theory)
• MA 521 (Algebra)

For the MS in Applied Mathematics, the four-course core is:

• MA 515 (Analysis)
• MA 580 (Numerical Analysis)
• Two courses from among:
  • MA 505 (Linear Programming)
  • MA 531 (Control)
  • MA 532 (Ordinary Differential Equations)
  • MA 534 (Partial Differential Equations)
  • MA 546 (Probability)
  • MA 523 (Matrix Theory) or MA 520 (Linear Algebra)

In addition, for either degree there is an in-depth study requirement of two two-course sequences, or one group of three related courses. This requirement can be met, for example, by taking follow-up courses to two of the core courses. Thus, it can be met by as few as two courses in addition to the core courses, which leaves room for three electives. Another way to meet the in-depth study requirement is to complete a three-course minor in a mathematics-related area. The MS programs allow up to three courses in mathematics-related disciplines.

For the MS in Applied Mathematics with a concentration in Computational Mathematics, the student's coursework must include MA 780 and one course from a list of computational mathematics courses. This list includes the department's advanced numerical analysis and computer algebra courses, as well as various computer science courses, and computationally intensive courses from other disciplines.

MS projects are sometimes directed by a faculty member from the student's minor department. Other MS projects have grown out of jobs with local companies or research organizations.

The Option B Masters is an MS in mathematics but with different requirments. For the Option B Maters the student substitutes passing the mathematics department PhD qualifying examination for doing a project. The standards for passing the qualifying examination are identical for MS and PhD students. Option B students must meet all the course requirements of the mathematics masters program as described above. Option B Masters students do not, however, have to have a committee and there is no separate oral exam. Students file a request for the Option B with the Graduate Program Secretary and the request is processed when all requirements are completed. Independent project or masters project course hours cannot be counted toward the Option B Masters. Note that the taking of three qualifying sequences which is necessary for taking the qualifying examination is not required of the conventional MS.

Students who are classified as PhD students and have completed the Option B requirements, may get an Option B masters without switching to the masters classification. They should do this as soon as they pass the qualifying examination. Students close to completing their PhD and students who already have a MS in mathematics or applied mathematics are not eligible for an Option B Masters.