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
APPM 1360 - Calculus 2 for Engineers
Primary Instructor
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Spring 2019 / Fall 2023
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
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Spring 2018 / Fall 2018 / Fall 2020 / Spring 2021 / Spring 2023 / Fall 2024
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 4380 - Modeling in Applied Mathematics
Primary Instructor
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Fall 2021
An exposition of a variety of mathematical models arising in the physical and biological sciences. Students' modeling projects are presented in class. Topics may include: GPS navigation, medical imaging, ocean waves, and computerized facial recognition. Recommended prerequisites: APPM 3310 and APPM 4350 and APPM 4650. Same as APPM 5380.
APPM 4510 - Data Assimilation in High Dimensional Dynamical Systems
Primary Instructor
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Fall 2019 / Fall 2021 / Fall 2023
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
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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 5380 - Modeling in Applied Mathematics
Primary Instructor
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Fall 2021
An exposition of a variety of mathematical models arising in the physical and biological sciences. Students' modeling projects are presented in class. Topics may include: GPS navigation, medical imaging, ocean waves, and computerized facial recognition. Department enforced prerequisites: APPM 2350 or MATH 2400 and APPM 2360. Recommended prerequisites: APPM 3310 and APPM 4350 and APPM 4650. Same as APPM 4380.
APPM 5480 - Methods of Applied Mathematics: Approximation Methods
Primary Instructor
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Spring 2024
Covers asymptotic evaluation of integrals (stationary phase and steepest descent), perturbation methods (regular and singular methods, and inner and outer expansions), multiple scale methods and applications to differential and integral equations. Department enforced prerequisite: APPM 5470.
APPM 5510 - Data Assimilation in High Dimensional Dynamical Systems
Primary Instructor
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Fall 2019 / Fall 2021 / Fall 2023
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
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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
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Spring 2020 / Spring 2022
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
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Spring 2018 / Fall 2019 / Fall 2020
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
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Spring 2020 / Fall 2020
May be repeated up to 6 total credit hours.
APPM 7400 - Topics in Applied Mathematics
Primary Instructor
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Spring 2020 / Spring 2021 / Fall 2021 / Spring 2022
Provides a vehicle for the development and presentation of new topics with the potential of being incorporated into the core courses in applied mathematics. May be repeated up to 6 total credit hours.
APPM 8700 - Mathematical Geosciences Seminar
Primary Instructor
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Fall 2023 / Fall 2024
Research-level seminar that explores applications of mathematical and statistical modeling, analysis, and computation in the geosciences. Provides a vehicle for the development, presentation, and dissemination of new topics in the mathematical geosciences. Formerly offered as a special topics course.
MATH 5600 - Numerical Analysis 1
Primary Instructor
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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.
