Applied Mathematics
Applied mathematics deals with mathematical concepts and techniques used in various fields of science and engineering. Historically, mathematics was first applied with great success in astronomy and mechanics. Then it developed into a main tool for physics, other physical sciences and engineering. It is now becoming important in the biological, geological, economics, business, etc. With the coming of age of the computer, applied mathematics transcended its traditional style, and now assumes an even greater importance and a new vitality.Compared with the pure mathematician, the applied mathematician is more interested in problems coming from other fields. Compared with the engineer and the physical scientist, he is more concerned with the formulation of problems and the nature of solutions. Compared with the computer scientist, he is more concerned with the accuracy of approximations and the interpretation of results. Needless to say, even in this age of specialization, the work of mathematicians, scientists, and engineers frequently overlaps. Applied mathematics, by its very nature, has occupied a central position in this interplay, and has remained a field of fascination and excitement for active minds.
Applied Mathematics: Current research encompasses analytical and numerical analysis of
deterministic and stochastic partial differential equations, large-scale scientific computation,
fluid dynamics, dynamical systems and chaos, as well as applications to
various fields of physics and biology. The applications to physics
include condensed-matter physics, plasma physics, nonlinear optics,
medical imaging, and the earth sciences, notably atmospheric, oceanic,
and climate science, and solid earth geophysics (see below). The
applications to biology include cellular biophysics, machine learning,
and functional genomics, including collaborations with Columbia's
Center for Computational Biology and Bioinformatics (C2B2), the Center
for Computational Learning Systems (CCLS), the NIH-funded Center for
Multiscale Analysis of Genetic and Cellular Networks (MAGNet), and the
NIH-funded NanoMedicine Center for Mechanical Biology. Extensive
collaborations exist with national climate research centers (the
Geophysical Fluid Dynamics Laboratory and the National Center for
Atmospheric Research) and with national laboratories of the U.S.
Department of Energy, custodians of the nation's most powerful
supercomputers.
Atmospheric, oceanic, and earth physics:
Current research focuses on the dynamics of the atmosphere and the
ocean, climate modeling, cloud physics, radiation transfer, remote
sensing, geophysical/geological fluid dynamics, geochemistry. The
department engages in ongoing research and instruction with the NASA
Goddard Institute for Space Studies and the Lamont-Doherty Earth
Observatory. Five faculty members share appointments with the
Department of Earth and Environmental Sciences.
In addition to the department faculty and graduate students, many others participate in these projects, including full-time research faculty, faculty and students from other departments, and visiting scientists.