Steve Hobbs is a mathematician with the Space and Naval Warfare (SPAWAR) Systems Center (SSC), in San Diego, California. As a member of the Maritime Surveillance Division he helps the SSC with large mathematics and statistics problems that arise in Command & Control, Communications, Radar, and Sonar. "I've worked on various aspects of sonar in my ten years at the lab," Steve explains. "I function as a technical person, solving mathematics and statistical problem that arise."
Steve has a B.S. in mathematics and biology from Point Loma Nazarene College, and an M.S. in applied mathematics and Ph.D. in mathematics from the University of California, San Diego. "As I finished my graduate studies I thought I wanted to teach college level mathematics," Steve explains, "but I was drawn to SSC after talking with a mathematician there; I was impressed with the amount and level of mathematics he used in his work. It seemed to be well beyond what the professionals who were teaching college math courses were using. I also felt my mathematical training in school had left me fairly ignorant of applications of mathematics; I intended to stay at the lab only 3 to 4 years while I remedied this deficiency and then look for an academic job. But I found the applied world far richer than I had expected; and I found the working environment at the lab gave me quite a bit of time to pursue my own 'research' interests in mathematical analysis as well."
"I work with a team of six to twelve people, consisting of a manager with a Ph.D. or master's in engineering, one or two math or engineering PhDs as lead scientists/technical people, several supporting programmers (often with bachelor's in engineering, physics, mathematics, etc.), and several computer (hardware/software) support people (perhaps with bachelor's in CS). Each person has an office, usually shared with one or two others and a personal computer, which is upgraded every five years or so."
The problems in communications, radar and sonar require a good understanding of the mathematical theory involved. To develop models of these systems requires skills mathematicians usually have, such as quantitative assessment and logical thinking. Courses in analysis and algebra are important to the development of these skills. Steve mentions that the two branches of mathematics most used in applications are statistics and numerical methods. "In addition, probability and stochastic processes, differential equations, Fourier analysis, optimization, and some mathematical theory from related fields like mechanics, electricity and magnetism, signal processing, economics, finance, etc. are all valuable. I tend toward analysis myself, but for those inclined to algebra, communications and computer science uses a lot of algebra and I think courses like number theory and algebraic geometry would be very useful. It is also valuable to learn to use the computer; word processing, at least one programming language (at the level of C, Fortran, or Pascal), and higher level applications/languages (Matlab, Mathematica, SPSS, S+, Minitab, etc) are helpful."
It also helps to "learn a little about other disciplines and the mathematical aspects of them. Mathematical depth is very important, but not as narrow and deep a scope is usually needed for the applied person as the pure researcher. Breadth is important for the applied mathematician; an employer will not hire three people when he can get one to do the same job. You have to have at least a basic working knowledge of statistics, numerical methods, stochastic processes, harmonic analysis, differential equations, etc., etc.; often a good undergraduate knowledge is adequate and many deficiencies will be picked up on the job if you have the basic mathematical depth (in analysis and algebra, say) to start with."
