What is Applied Mathematics?

Applied mathematics provides the interface between the fundamental mathematical structures and their use in the physical and social sciences. Such applications include numerical analysis, mathematics of engineering, linear programming, optimization and operations research, continuous modelling, mathematical biology and bioinformatics, information theory, game theory, probability and statistics, financial mathematics, actuarial science, cryptography and hence combinatorics and even finite geometry to some extent, graph theory as applied to network analysis, and a great deal of what is called computer science.

The question of what is applied mathematics does not answer to logical classification so much as to the sociology of professionals who use mathematics. The mathematical methods are usually applied to the specific problem field by means of a mathematical model of the system.

Below is a list of topics in applied mathematics being researched by our faculty, showing the broad range of interest and applications it can encompass:

• Signal and image processing/analysis
• Randomized algorithms to handle large data sets
• Elliptic boundary value-eigenvalue problems
• Geophysical inverse problems
• Growth processes
• Random matrix theory
• Statistical estimation in data-poor environment
• Valuation and optimization of financial portfolios
• Equilibrium problems in a stochastic environment
• Diffusion processes in hydrology
• Growth and percolation models in genetics
• Dynamics of quantum systems
• Models of magnetism
• Statistical mechanics
• Control and Systems Theory
• Estimation of Nonlinear Processes
• Control Model Reduction
• Waves/Imaging in random media and stochastic analysis
• Reaction-diffusion in fluid flows and PDEs
• Dynamical systems and model reduction with uncertainty
• Computational fluid dynamics
• Biofluiddynamics
• Mathematical biology