The proliferation of data being collected in almost every scientific field has led to a need for data-driven analysis. Data-driven analysis utilize statistics, machine-learning, and low-dimensional reductions to synthesize, interpret and make predictions based on the known data.
Financial mathematics involves the development of mathematical and computational models used in the financial industry. Banks, energy and insurance companies and other corporations rely on financial mathematics to optimize investment decisions, develop and price new securities and manage risk.
Fluid Mechanics involves the study of fluids (liquids, gases, plasmas) and the forces acting on them. Applications include fluid mixing, turbulence and the stability of fluid, large scale ocean, ferromagnetic and small scale biological flows.
Mathematical Biology pairs mathematical models with theoretical and computational methods. This information is used to investigate a variety of biological and ecological systems and processes. Research areas include: cell and molecular biology, population dynamics, evolutionary biology, neuroscience, medical imaging and epidemiology.
Nonlinear Dynamical Systems
Nonlinear Dynamical Systems involve the study of systems governed by a set of laws over time. This includes difference equations and deterministic and stochastic differential equations. The emphasis is on determining the geometrical properties and the long-time behavior. There are an astounding array of applications that range over all areas of applied science, mathematics, and engineering.
Scientific Computing involves the use of advanced computing systems and numerical algorithms to understand and solve complex problems using simulations. In practice, scientific computation is applied to a large variety of problems in all scientific disciplines.
Statistics involves the collection, analysis, and interpretation of data. By understanding variability in data, statistics enables one to overcome the uncertainty to make informed predictions and decisions. Statistical analysis is applied to numerous scientific, industrial, and social problems.