Programs

Masters of Science in Applied Mathematics
(MSAM)

The Department of Mathematics at the University of Notre Dame offers an interdisciplinary master of science in applied mathematics (MSAM) degree. The goal of the MSAM is to produce skilled and creative scholars who will be able to use sophisticated mathematical techniques in their professional activities and go beyond the established mathematical paradigms in their particular areas of interest. The MSAM program does not offer financial support. It is primarily for students who are already at Notre Dame, pursuing a PhD in some other department.

Admission to the Program

Admission is limited to students who are pre-approved. Before formally applying to the Graduate School, a student should find an advisor in the Mathematics Department, who agrees to help the student prepare a plan of study and to supervise, or at least co-supervise, the interdisciplinary project or thesis. The plan of study also needs the approval of the advisor in the department providing financial support. Once the plan of study is ready, then the DGS and the Graduate Studies Committee in the Mathematics Department decide whether to recommend the student to the Graduate School for admission. A student who has been recommended in this way applies formally.

Advisors

The MSAM degree represents work beyond that being done in another department. Ideally, the student will receive input on the interdisciplinary project from two advisors, one in the Mathematics Department, and one in another department. The Mathematics advisor helps the student choose appropriate courses, and to plan an interdisciplinary project that goes beyond what the student may be doing toward another degree.

Plan of Study

The plan of study should both expand the students' mathematical horizons and to develop their expertise in the intended area of application. The Department of Mathematics’ graduate committee will evaluate each student’s proposal in close consultation with appropriate faculty members from other departments. The student’s proposed plan of study, including the mathematical content of the courses of the interdisciplinary component (see below), requires the approval of the DGS in the Department of Mathematics, the student’s adviser and the DGS of the cooperating department. Once approved, the proposed plan of study becomes the student’s official plan of study.

Degree Requirements

The program of study for the MSAM consists of a core mathematics component and an interdisciplinary component for a total course requirement of 24 credit hours.

The Mathematical Core Component

The core component is a solid requirement of mathematics from courses offered by the Department of Mathematics. It consists of either nine or 12 credit hours, depending on both the background and the interests of the student.

1. One requirement is Math 60-690, Numerical Analysis (three credit hours). This course features a thorough discussion of the mathematical foundations of numerical analysis and considers such concepts as ill-conditioning, numerical stability, and error analysis.

2. To ensure a solid mathematical background, the student is required to learn the elements of at least one of the five basic areas of graduate-level abstract mathematics, which can be chosen in an area that parallels the student’s field of interest. For example, a student with an interest in coding theory or computer science could take Math 60-210, Basic
Algebra (three credit hours). If a student’s mathematical objectives concern partial differential equations, control and systems theory, or the mathematics of finance, the choice would be either Math 60-350, Real Analysis (three credit hours), or Math 60-370, Basic Complex Analysis (three credit hours). A student of physics or molecular biology would want to learn the constructions that are pursued in Math 60-430, Basic Topology (three credit hours). Finally, students in electrical or computer engineering would likely study Math 60-510, Basic Modern Logic (three credit hours).

3. The third requirement is a choice of other basic courses or Topics courses in applied mathematics. There are courses given regularly in such areas as partial differential equations and their applications, control and optimization, and geometric methods in mechanics.

The following themes reflect only a small portion of the expertise of applied mathematicians of the Department of Mathematics, and courses based on them are offered by the department at various times.

• Elements of symplectic geometry and nonlinear soliton equations

• Methods and applications of asymptotic analysis

• Geometric theory of nonlinear dynamical systems

• Numerical Methods

• Partial differential equations and free boundary problems

• Toda flows with applications to eigenvalue and optimization problems

The Interdisciplinary Component

The interdisciplinary component accounts for the additional 12 to15 credit hours. These can be met by an appropriate selection of courses in any graduate discipline at Notre Dame that makes serious use of mathematics.

Thesis or Project

The final requirement for the MSAM is a master’s thesis or project.  For a student pursuing another advanced degree, this represents extra work, beyond what is being done for the other degree.

W ith the approval of the adviser, the student may pursue an interdisciplinary master’s thesis under the adviser’s direction. If written and defended in accordance with the standard procedures of the Graduate School, the thesis satisfies six of these credit hours.

A second way in which the student can complete the requirements of the interdisciplinary component is with a meaningful interdisciplinary project carried out under the adviser’s supervision. The written exposition of the project requires the approval of the director of graduate studies of the Department of Mathematics, the director of the cooperating department, the student’s adviser, and the dean of the Graduate School. It is designed to connect the mathematical core to the area of application that the student intends to pursue.

Further Information

For further information regarding the master of science in applied mathematics, please contact:

Dr. Julia Knight
Director of Graduate Studies

Mathematics Department
University of Notre Dame
255 Hurley Building
Notre Dame, Indiana 46556-4618

Telephone: (574) 631-7245
E-mail: knight.1@nd.edu
Web: http://math.nd.edu

 (Revised July 2006)