MTH 1360 & 3360: Seminar in Applied Mathematics

This course is intended to give students of mathematics the experience of utilizing their skills to study problems that arise in industry and other "real-world" settings. It will also provide the opportunity to build on exciting industrial experiences that they may have had through Co-op or other employment. (This course satisfies the academic component of the College of Arts & Sciences Experiential Education Requirement.)

INSTRUCTOR: Robert McOwen, 445 LA.   Phone: 373-5678.   E-mail: mcowen@neu.edu.
REQUIRED TEXT: Industrial Mathematics: A Course in Solving Real-World Problems, by Avner Friedman and Walter Littman, SIAM, 1995.

The course is available to undergraduates (as MTH 1360) and to graduate students (as MTH 3360). It will follow a nonstandard structure in order to build upon student input, learn interesting and relevant mathematics, and get students working on their own projects.

Discussion of Student Experiences and Goals. We shall discuss the experiences that students have already had with industrial mathematics, either through Co-op jobs or employment outside of the university. What mathematics did they use in their work? What would students like to know more about? What kinds of industrial problems would they like to use mathematics to study? The answers to these two questions will have a substantial impact on the rest of the course.

Presentation of Mathematical Techniques and Some Problem Solving. Based upon student input and the instructor's judgment, there will be several topics of industrial mathematics presented in class. These shall illustrate the basic paradigm of applied mathematics:

• Formulate the Mathematical, Model
• Analyze the Model (theoretically and numerically) to Obtain Conclusions,
• Interpret the Conclusions for the Physical System, and Evaluate.

As examples of physical problems that arise in industrial settings, consider:

• Crystal Precipitation in Photographic Emulsion;
• Air Quality Control;
• Electron Beam Lithography.

These physical problems and their mathematical models are studied in Friedman & Littman using differential equations and numerical methods. However, there are many other physical and nonphysical industrial problems that may require different mathematical tools for their treatment. As examples, consider the following:

• Cryptography using sophisticated algebraic structures;
• Modeling physical objects by piecewise polynomial functions called ``splines'';
• Data compression using Fourier analysis or ``wavelets''.

If additional topics of interest to the class are outside the coverage of the textbook(s) or the expertise of the instructor, additional books and/or faculty will be consulted.

Coursework

• Homework: Since some new mathematical techniques will be introduced in this course, homework problems will be assigned to test the students' new skills, and to provide some quantitative evaluation of their performance in the course.
• Student Modelling Project: Each student will select an industrial problem to study. Classroom time will be devoted to discussions of possible solution strategies, analytic tools, and reports upon their success or failure. Bi-weekly written reports will be submitted to chronicle progress, and a final report will be submitted. Students are encouraged to consult with experts as the project proceeds.
• The course grade will be determined equally by performance on the homework and the student project.

GRADING: The course grade will be determined as follows:

• Homework 50%
• Modelling Project 50%

Remarks.

1. The basic structure of this course may be followed by other instructors in other years, although the text(s) and class presentations will very likely change.
2. This course may be taken both by undergraduate math majors and graduate students in mathematics. A higher level of performance will be expected to receive graduate credit.