With the proliferation of data being collected in almost every scientific field, data-driven analysis involves the use of statistics, machine learning, and low-dimensional reductions in order to synthesize and interpret the large data sets, and to make predictions based on the known data.
Financial mathematics involves the development of mathematical and computational models used in the financial industry. Banks, insurance companies, investment firms, energy companies, and other corporations rely on financial mathematics to optimize investment decisions, to develop and price new securities, and to manage risk.
Fluid Mechanics involves the study of fluids (liquids, gases, plasmas) and the forces acting on them. There are a wide variety of applications including the stability of fluid flows, fluid mixing, turbulence, large scale ocean flows, ferromagnetic flows, and small scale biological flows.
Mathematical Biology involves the development of mathematical models and the use of theoretical and computational methods to investigate a wide variety of biological and ecological systems and processes including cell and molecular biology, population dynamics, evolutionary biology, neuroscience, medical imaging, and epidemiology.
Nonlinear Dynamical Systems
Nonlinear Dynamical Systems involves the study of systems governed by a set of laws over time, including 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.