Our researchers’ deep expertise in computational mathematics and in subfields of applied mathematics, that includes dynamical systems, partial differential equations, applied geometry, optimization, and image processing, is applied to various areas that range from geophysics, astrophysics, mechanical and biomedical engineering as well as transportation systems and public health.

Faculty, along with undergraduate and graduate students, benefit from the department’s numerous affiliations across the university,  and the associated collaborations embody the highly interdisciplinary culture within the university and school of engineering.

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, Python, R, MATLAB, CUDA, 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 and wide research fields of modern mathematics. This includes areas such as ordinary differential equations (dynamical systems), partial differential equations, asymptotic analysis, stochastic processes, applied geometry or control theory. 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 modeling, applied mathematics maintains, at the same time, diverse connections with pure mathematics, including differential geometry, harmonic analysis, functional analysis, probability theory, stochastic analysis, and many others.

Related Courses

Complete descriptions appear in the course catalog

View the semester course schedule.   

  • EN.540.4/668 Introduction to Nonlinear Dynamics and Chaos
  • EN.553.111/112 Statistical Analysis I/II
  • 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.553.413 Applied Statistics and Data Analysis
  • EN.553.4/633  Monte Carlo Methods
  • EN.553.4/643  Financial Computing in C++
  • EN.553.4/650  Computational Molecular Medicine
  • EN.553.665 Introduction to Convexity
  • EN.553.669 Large Scale Optimization for Data Science
  • EN.553 688 Computing for Applied Mathematics
  • EN.553.4/681  Numerical Analysis
  • EN.553.4/692  Mathematical Biology
  • EN.553.4/693  Mathematical Image Analysis
  • EN.553.739 Statistical Pattern Recognition Theory & Methods
  • EN.553.761   Nonlinear Optimization I
  • EN.553.762  Nonlinear Optimization II
  • EN.553.763 Stochastic Search and Optimization
  • EN.553.764   Modeling, Simulation, and Monte Carlo
  • EN.553.780 Shape and Differential Geometry
  • EN.553.790  Topics In Applied Math
  • EN.553.792   Matrix Analysis and Linear Algebra
  • EN.553.793   Turbulence Theory
  • EN.553.797 Introduction to Control Theory and Optimal Control

Learn More

Research and academic opportunities in computational and applied mathematics