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Grooms, Ian G Assistant Professor

Positions

Research Areas research areas

Research

research overview

  • My research lies at the intersection of applied mathematics and geophysical fluid dynamics, and my focus is to develop novel mathematical techniques in support of atmosphere and ocean science, from fundamental theory to numerical simulation to data assimilation and forecasting. My main mathematical tools are multiscale and stochastic modeling, asymptotic methods, and numerical analysis; my primary application area is physical oceanography.

keywords

  • applied mathematics, geophysical fluid dynamics, data assimilation

Publications

selected publications

Teaching

courses taught

  • APPM 1360 - Calculus 2 for Engineers
    Primary Instructor - Spring 2019
    Continuation of APPM 1350. Focuses on applications of the definite integral, methods of integration, improper integrals, Taylor's theorem, and infinite series. Degree credit not granted for this course and MATH 2300.
  • APPM 3310 - Matrix Methods and Applications
    Primary Instructor - Spring 2018 / Fall 2018
    Introduces linear algebra and matrices with an emphasis on applications, including methods to solve systems of linear algebraic and linear ordinary differential equations. Discusses vector space concepts, decomposition theorems, and eigenvalue problems. Degree credit not granted for this course and MATH 2130 and MATH 2135.
  • APPM 4510 - Data Assimilation in High Dimensional Dynamical Systems
    Primary Instructor - Fall 2019
    Develops and analyzes approximate methods of solving the Bayesian inverse problem for high-dimensional dynamical systems. After briefly reviewing mathematical foundations in probability and statistics, the course covers the Kalman filter, particle filters, variational methods and ensemble Kalman filters. The emphasis is on mathematical formulation and analysis of methods. Same as APPM 5510, STAT 4250 and STAT 5250.
  • APPM 4720 - Open Topics in Applied Mathematics
    Primary Instructor - Spring 2018
    Provides a vehicle for the development and presentation of new topics that may be incorporated into the core courses in applied mathematics. Department enforced prerequisite: variable, depending on the topic, see instructor. May be repeated up to 15 total credit hours. Same as APPM 5720.
  • APPM 5510 - Data Assimilation in High Dimensional Dynamical Systems
    Primary Instructor - Fall 2019
    Develops and analyzes approximate methods of solving the Bayesian inverse problem for high-dimensional dynamical systems. After briefly reviewing mathematical foundations in probability and statistics, the course covers the Kalman filter, particle filters, variational methods and ensemble Kalman filters. The emphasis is on mathematical formulation and analysis of methods. Same as APPM 4510, STAT 4250 and STAT 5250.
  • APPM 5600 - Numerical Analysis 1
    Primary Instructor - Fall 2018
    Solution of nonlinear algebraic equations, interpolation, integration, approximation, and numerical linear algebra. Department enforced prerequisite: APPM 3310 or MATH 2130 and experience with a scientific programming language.
  • APPM 5620 - Numerical Linear Algebra
    Primary Instructor - Spring 2020
    Develops and analyzes methods for the solution of square nonsingular linear systems, linear least squares problems, eigenvalue problems, and rank estimation. Direct and iterative methods are covered, as well as methods for dense and sparse problems. Requires solid background in linear algebra and proficiency with scientific computing.
  • APPM 5720 - Open Topics in Applied Mathematics
    Primary Instructor - Spring 2018 / Fall 2019
    Provides a vehicle for the development and presentation of new topics that may be incorporated into the core courses in applied mathematics. Department enforced prerequisite: variable, depending on the topic, see instructor. May be repeated up to 6 total credit hours. Same as APPM 4720.
  • APPM 6950 - Master's Thesis
    Primary Instructor - Fall 2019 / Spring 2020
    May be repeated up to 6 total credit hours.
  • ASEN 6055 - Data Assimilation & Inverse Methods for Earth & Geospace Observations
    Primary Instructor - Fall 2019
    Covers a selection of topics in probability theory, spatial statistics, estimation theory, numeric optimization, and geophysical nonlinear dynamics that form the foundation of commonly used data assimilation and inverse methods in the Earth and Space Sciences. Hands-on computational homework and projects provide opportunities to apply classroom curricula to realistic examples in the context of data assimilation.
  • MATH 5600 - Numerical Analysis 1
    Primary Instructor - Fall 2018
    Solution of nonlinear algebraic equations, interpolation, approximation theory and numerical integration. Department enforced prerequisites: MATH 2130 or MATH 2135 or APPM 3310 and experience with a scientific programming language. Instructor consent required for undergraduates.

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