| The research and teaching foci of the Department of Applied Mathematics at IIT are primarily in four areas of modern applied mathematics. These areas are briefly described next, and
faculty with primary and secondary interests and expertise are
listed for each of these areas.
Areas of Concentration
There is also a financial
mathematics track, offered together with the
Stuart Graduate School of Business.
APPLIED ANALYSIS
Applied analysis is one of the foundations for interdisciplinary applied mathematics. The principles of (functional) analysis are applied to such areas as partial differential equations, dynamical systems and numerical analysis.
The basic framework, concepts and techniques of modern mathematical analysis are essential for modeling, analysis and simulation of complicated phenomena in engineering and science. Applying the ideas and methods of modern mathematical analysis to such problems has been a thoroughly interdisciplinary effort.
Research and teaching within the applied analysis group
at IIT concentrates on development and application of
new techniques for investigating numerous phenomena in
engineering and science. In particular, members of the
group do research in nonlinear dynamics, approximation theory, numerical analysis, fluid dynamics, materials science, viscoelastic and polymeric fluid flows, biological science, quantum mechanics and electrodynamics, solid mechanics, financial engineering and other disciplines.
Faculty with primary interests in applied analysis:
Abarji, Bielecki, Duan, Edelstein, Frank
Faculty with secondary interests in applied analysis:
Bernstein, Cialenco, Erber, Fasshauer, Li, Lubin, Nair, Rempfer
COMPUTATIONAL MATHEMATICS
The use of computation/simulation as a third alternative
to theory and experimentation is now common practice in
many branches of science and engineering. Many scientific
problems that were previously inaccessible have seen
tremendous progress from the use of computation (e.g.,
many-body simulations in physics and chemistry, simulation
of semi-conductors, etc.). Researchers and scientists
in these areas must have a sound training in the fundamentals
of computational mathematics and become
proficient in the use (and development) of new algorithms
and analytical techniques as they apply to modern
computational environments.
Research and teaching within the computational mathematics
group at IIT concentrates on basic numerical
analysis, as well as development of new computational
methods used in the study and solution of problems in
the applied sciences and engineering. In particular, members of the group do research on complexity theory, the finite element method, meshfree methods, multiscale and multilevel methods, Monte Carlo and quasi-Monte Carlo methods, numerical methods for deterministic and stochastic ordinary and partial differential equations, computational fluid dynamics, computational materials science, computer-aided geometric design and parallel computation.
Faculty with primary interests in computational mathematics:
Fasshauer, Hickernell, Li
Faculty with secondary interests in computational mathematics:
Bernstein, Cialenco, Duan, Fang, McMorris, Rempfer
DISCRETE APPLIED MATHEMATICS
Discrete applied mathematics is a fairly young branch of mathematics and is concerned with using combinatorics, graph theory, optimization, and portions of theoretical computer science to attack problems in engineering as well as the hard and soft sciences.
Research interests in the discrete applied mathematics group at IIT are in discrete methods in computational and mathematical biology, intersection graphs and their applications, discrete location theory, voting theory applied to data analysis, graph drawing, random geometric graphs, communication networks, coding theory, low discrepancy sequences, algorithm design and analysis. Faculty with primary interests in discrete applied mathematics:
Ellis, Kaul, McMorris, Pelsmajer
Faculty with secondary interests in discrete applied mathematics:
Frank, Hickernell
STOCHASTICS
Stochastics at IIT includes traditional statistics (the methods of data analysis and inference) and probability (the modeling of uncertainty and randomness). However, also included are other areas where stochastic methods have been becoming more important in recent years such as finite and infinite dimensional stochastic processes, stochastic integration, stochastic dynamics, stochastic partial differential equations, probabilistic methods for analysis, mathematical finance and discrete mathematics, computational methods for stochastic systems, etc.
The current research and teaching interests in the stochastics group at IIT include asymptotics in statistics, experimental design, computational statistics, stochastic calculus and probability theory, stochastic dynamical systems, stochastic control, stochastic partial differential equations and statistical decision theory.
Laboratory for Stochastics and Dynamics
Faculty with primary interests in stocastics:
Adler, Bielecki, Cialenco, Duan, Fang, Heller, Hickernell
Faculty with secondary interests in stochastics:
Ellis, Frank, Kaul, McMorris |
