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.