MATH 396 Topics in Applied Mathematics
This course which will cover various topics in applied mathematics. This course may be repeated once for credit.
Computational Mathematics (4 units)
This course investigates the enhanced problem solving techniques realized by the incorporation of the computer and well designed algorithms. We note that in the real world, mathematicians are asked to solve problems vastly more complex than those found in a homework set or final exam. The types of such problems are numerous: problems which are non-linear in nature, large systems of many equations rather than a few, problems which attempt to identify an infinite number of solutions, problems for which only approximate solutions are possible, and much more. We start by noting the basics of how the computer processes data and the fundamentals of decision making, iteration, and memory. We apply this to problems in various areas of mathematics and science. Often, we'll make substantial headway, but run into some limitations only to find that some obscure mathematical property comes to the rescue and allows us to "upgrade" our process to obtain dramatically more or better solutions. Our overall course philosophy favors neither mathematics or computational tools, but the way in which these tools work together to produce amazing results!
Industrial Mathematics (2 units)
This course is a project-oriented introduction to industrial mathematics. Students will be grouped into teams and tasked with creating solutions to actual real-world problems provided by external partners from business, industry and government. Familiarity with a programming language is highly desirable but not required. The goal of this course is to provide students with an experience of what it is like to work as a mathematician in a professional setting.
Mathematical Modeling (2 units)
This course is a project-oriented seminar in mathematical modeling. Concepts from calculus, linear algebra, differential equations and other areas of mathematics will be used to derive, describe and solve mathematical models from the life, physical, and social sciences. Familiarity with a programming language is desirable but not required. The goal of this course is to provide students with multiple examples of how mathematics can be used to explain various phenomena, to describe real-world situations and to make (more quantitatively) informed decisions.
Applied Mathematics (2 units)
This weekly seminar course is an introduction to some of the classic techniques of applied mathematics. Topics will include scaling, dimensional analysis, regular and singular perturbations, and asymptotic matching. The goals of the course are to expose students to important techniques widely used in applied mathematics; to present a different mode of classroom instruction and student involvement where students see themselves as equal participants in the learning process; to provide students with opportunities to practice and hone oral presentation skills; and to become more familiar with using modern computational tools to solve mathematical problems.