All students in the applied mathematics graduate programs carry out research as part of their graduate studies. The Master's student presents 1. a Mathematics Seminar paper or 2. a Master's thesis and the doctoral student prepares 3. a Doctoral Dissertation.

1. Mathematics Seminar Paper:

The **Mathematics Seminar paper** is the product of individual
study of some topic or problem by the student under the direction of a member
of the graduate faculty in applied mathematics. The student selects a faculty
member under whom he or she will carry out the study and obtains that person's
permission before signing up for the seminar. For this reason, it is important
that students get to know the faculty and, most importantly, learn of their
research areas. The student will organize and write an exposition of a problem
in applied mathematics. It need not contain original mathematical results but
it should reflect the student's understanding and organization of the topic.
The paper must be approved by the faculty member who agreed to direct the
study and by whoever he or she designates as reader.

2. Masters Thesis:

The **Master's thesis** is an in-depth study of some applied mathematics
topic at a level beyond that of the paper for the Mathematics
Seminar. Some original contribution is expected. The thesis is frequently an
elaboration of a study which was begun under the heading of the Mathematics
seminar. One paper will suffice for both, but the thesis is expected to be
more extensive than the seminar paper. As with the seminar paper, the student
works under the direction of an applied mathematics faculty member. In
addition, the student must prepare the written thesis in the form prescribed by
the Graduate School and present the thesis orally at an open forum.

3. Doctoral Dissertation

The student pursuing the Ph.D. in Engineering Applied Mathematics must present a doctoral dissertation which is the result of the student's extensive research effort. In conjunction with the program's emphasis on providing an interdisciplinary focus on research, the Interdisciplanary Doctoral Committee which the student puts together to help direct this research must be balanced between Mathematical Sciences and Engineering faculty. The student works with his or her dissertation director to develop a research proposal which the student then presents to the committee. This committee advises the student on the appropriateness of the problem to be considered as well as the mathematical approach to this problem. The end result of the research is an extended paper, the dissertation, which describes the problem in detail and elaborates the student's analysis and solution of this problem. This paper should contain results which are publishable in the appropriate scientific literature. The paper and subsequent oral defense will demonstrate the student's ability to represent his or her results to an interdisciplinary audience.