Computational mathematics aims to provide approximate solutions and
reliable estimates of accuracy for mathematical problems arising in
science, engineering and industry. One pillar of research is numerical
analysis, the field of mathematics in which the convergence of numerical
approximations is studied and robust error estimates derived. The other
pillar is the practical and efficient implementation of numerical
algorithms on computers, which not only exploits skills in general-purpose
programming languages (C, Fortran, Python, etc.) but also benefits from
working knowledge in several areas of computer science. Nearly every
branch of modern science and engineering relies upon computational
mathematics as a fundamental tool of verification and discovery.
Applied mathematics in the traditional sense of applied analysis remains
one of the most vibrant research fields of modern mathematics. This
includes areas such as ordinary differential equations (dynamical
systems), partial differential equations (applied functional analysis),
asymptotic analysis, and stochastic differential & partial differential
equations. Many of the most challenging problems of the 21st century, such
as climate, environmental and medical sciences, depend upon advancing
knowledge in these fields. Engineering and industry are client applications, as well
as inspirations, for much modern research. While closely linked to
scientific modelling, applied mathematics maintains, at the same time,
diverse connections with pure mathematics,including differential geometry,
Lie algebras, harmonic analysis, functional analysis, probability theory,
stochastic analysis, and many others.
Faculty in GCAM are experts in computational mathematics and various
subfields within applied mathematics, such as dynamical systems, partial
differential equations, applied geometry or image processing and analysis.
Our research is driven by forefront applications in areas such as
geophysics, astrophysics, mechanical and biomedical engineering. Research
is driven by the synergy between theory and application, and welcomes the
participation of students both at the undergraduate and graduate levels.
The students and faculty in GCAM profit from very strong university
affiliations. These include the Applied Physics Laboratory (APL), the
Institute for Data Intensive Engineering and Science (IDIES), The Center
for Environmental and Applied Fluid Mechanics (CEAFM), the JHU Turbulence
Database Group, the Center for Imaging Science (CIS) and the Institute of
Computational Medicine (ICM). These affiliations and associated
collaborations embody the interdisciplinary culture that is characteristic
of the Johns Hopkins University.
For more details about our members, research, and course offerings in
computational and applied mathematics, please explore
the additional tabs.