The mathematics and applied mathematics Ph.D. degrees have both a standard track and an interdisciplinary track. This page describes the standard track. The interdisciplinary track is described here. Students completing the interdisciplinary track will receive either a Ph.D degree in Mathematics with a concentration in Interdisciplinary Mathematics or a Ph.D. degree in Applied Mathematics with a concentration in Interdisciplinary Mathematics.
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
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
Basic Mathematics Courses
Basic Applied Mathematics
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
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 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
580 - 780.
In addition to MA 580 and 780, CMA students must take three courses
from the list
of approved CMA courses.
Concentration in Interdisciplinary
The MAI concentration is available to PhD students in either Mathematics or Applied Mathematics in either the standard or the interdisciplinary Ph.D. tracks. It is not available to Masters students. This section describes the standard track MAI. The interdisciplinary track MAI is described is described here.
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
MAI Students are required to do at least two of:
- Attend and present at a conference in the other
- 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:
For the MS in Applied Mathematics, the four-course
580 (Numerical Analysis)
- Two courses from among:
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
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
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.