Resources and Education for the Mathematical Sciences

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Data-Driven Science and Engineering [View]


This website makes available lectures for the book by S. L. Brunton & J. N. Kutz, “Data-Driven Science and Engineering: Machine Learning, Dynamical Systems and Control” (Cambridge 2019).



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Data-Driven Modeling & Scientific Computation [View]


This website makes available lectures for the book by J. N. Kutz, “Data-Driven Modeling and Scientific Computation” (Oxford 2013). This textbook is used for courses in scientific computing as well as data analysis.



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Inferring Structure of Complex Systems [View]


This website makes available all lectures for AMATH 563, Inferring Structure of Complex Systems. This course provides an broad introduction to a diversity of data-driven methods and machine learning algorithms that help understand networked dynamical systems. It provides an introduction to the power of the numerical algorithms for model discovery using MATLAB programming.



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Beginning Scientific Computing [View]


This website makes available all lectures for AMATH 301, Beginning Scientific Computing. This course provides an introduction to programming and the MATLAB scripting language. It is intended for engineering and physical sciences majors, providing a broad introduction to the power of numerical methods, scientific computing and MATLAB programming.



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Dynamic Mode Decomposition [View]


This website makes available a variety of lectures for the emerging method of dynamic mode decomposition. It includes numerous MATLAB codes as well.



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Data Methods for Biologists [View]


This website makes available a variety of lectures for a new course focusing on data methods used in the biological sciences. It includes numerous MATLAB codes as well as lecture materials and lightboard videos.





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Scientific Computing [View]


This course provides a survey of numerical solution techniques for ordinary and partial differential equations. Emphasis is on the application of numerical schemes to practical problems in the engineering and physical sciences.


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Computational Methods for Data Analysis [View]


Exploratory and objective data analysis methods applied to the physical, engineering and biological sciences. Brief overview of statistical methods and their computational implementation for time series analysis, spectral analysis, filtering methods, principal component analysis, proper orthogonal decompositions, and image processing and compression.



Lightboard Architecture


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Over the Spring and Summer of 2015, I built (with critical help from Derek Franz and Steven Brunton) a lightboard in the Department of Applied Mathematics. The lightboard is a remarkable tool for online education since you can integrate multiple teaching modalities: standard lecturing, powerpoint, MATLAB, and computer drawing programs. This allows the instructor to face the audience, which improves the online engagement over standard methods.

We used this method to film and produce our Data Science for Biologists course which is available on EdX and YouTube.
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