Careers in Mathematics

Question

1.) What is your major field of expertise and how did you become interested in it? 2.) What suggestions do you have for students who wish to become involved in your field of study?

Answer

My primary expertise is in mathematical modeling, especially dynamic systems. My first job after graduating from college was at the Army Map Service (now the Defense Mapping Agency) where I was assigned the task of transferring a rather primitive satellite orbit theory from the classic Univac I computer to a then modern mainframe. After that I coded a better orbit theory, but for adequate precision I had to adopt numerical methods. Vastly improved observing technologies and the ready availability of computers have moved almost all modeling efforts away from solvable systems and perturbation theories toward numerical methods. This has not trivialized the field, but made it even more challenging. As far as academic training, there is an embarrassment of riches, but most are not in the math department. Good material will be found in the social and biological sciences, as well as the physical sciences. Filtered noise models are used in engineering, geophysics, and business forecasting. The basic tool box consists of differential equations and multiple regression. These in turn require some knowledge of advanced calculus, linear algebra, and complex analysis. The basics of computer science and numerical analysis are needed to transform the math into useful tools. More details and an overall description of the field can be found in my book, The Art of Modeling Dynamic Systems (by Foster Morrison, Wiley, 1991). Most college libraries should have a copy or two. Software packages useful for applications and self-study abound. The Numerical Recipes collection of compiler subroutines (Cambridge University Press, several editions), Mathematica, Matlab, and various specialized tools are among the possibilities. Career opportunities exist, since the math modeling is often the most challenging step in any given project; yet the field has not blossomed as promised by James Gleick, in his optimistic best seller, Chaos: Making a New Science (Viking-Penguin,1987). Scientific revolutions have to be advanced by a new generation and those people are now moving through the academic degree mills from which they will emerge as the leaders in science, technology, and industry. Think about becoming one of them.