Our researchers’ deep expertise in computational mathematics and in subfields in applied mathematics, including dynamical systems, partial differential equations, applied geometry, and image processing and analysis, is applied areas that range from geophysics and astrophysics to mechanical and biomedical engineering.
Faculty, along with undergraduate and graduate students, benefit from the department’s numerous affiliations across the university, including with JHU’s 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 school and the university’s interdisciplinary culture.
Research Affiliations at Johns Hopkins University
Primary Areas of Research
Computational mathematics focuses on 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 are 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 and 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.
Complete descriptions appear in the course catalog.
View the semester course schedule.
- EN.553.111/112 Statistical Analysis I/II
- EN.553.171 Discrete Mathematics
- EN.553.211 Probability & Statistics for the Life Sciences
- EN.553.291 Linear Algebra and Differential Equations
- EN.553.310 Probability & Statistics for the Physical and Information Science
- EN.553.311 Probability & Statistics for Biological Sciences and Engineering
- EN.553.361 Intro to Optimization
- EN.553.362 Intro to Optimization II
- EN.553.371 Cryptology and Coding
- EN.553.383 Scientific Computing with Python
- EN.553.385 Scientific Computing: Linear Algebra
- EN.553.386 Scientific Computing: Differential Equations
- EN.553.388 Scientific Computing: Differential Equations in Vector Spaces
- EN.553.391 Dynamical Systems
- EN.553.4/616 Introduction to Statistical Learning, Data Analysis and Signal Processing
- EN.553.4/620 Introduction to Probability
- EN.553.4/630 Introduction to Statistics
- EN.553.4/633 Monte Carlo Methods
- EN.553.4/643 Financial Computing in C++
- EN.553.4/650 Computational Molecular Medicine
- EN.553.4/692 Mathematical Biology
- EN.553.4/693 Mathematical Image Analysis
- EN.553.6/781 Numerical Analysis
- EN.553.730 Statistical Theory
- EN.553.731 Statistical Theory II
- EN.553.735 Topics in Statistical Pattern Recognition
- EN.553.761 Nonlinear Optimization I
- EN.553.762 Nonlinear Optimization II
- EN.553.764 Modeling, Simulation, and Monte Carlo
- EN.553.790 Topics In Applied Math
- EN.553.792 Matrix Analysis and Linear Algebra
- EN.553.793 Turbulence Theory
Research and academic opportunities in computational and applied mathematics