Teaching Materials

Materials developed for courses at the University of Southern Mississippi and Temple University:

Graduate Courses

• Deep Learning Seminar (2023 Fall): Notes on Deep Neural Networks, Convolutional Neural Networks, Recurrent Neural Networks, Transformers, and Generative Adversarial Networks.
• Ordinary Differential Equations (Graduate, 2023 Fall): Comprehensive notes on ODE theory and applications.
• Introduction to PDE (2023 Spring): Foundational materials on partial differential equations.
• Numerical Analysis I (2021 Fall, Temple University): Detailed notes on numerical methods for scientific computing.

Undergraduate Courses

• Calculus I, III, IV: Lecture notes and problem sets for calculus sequence.
• Ordinary Differential Equations (2020 Spring, 2019 Spring): Teaching materials for ODE courses.
• Trigonometry & College Algebra (2018 Fall): Foundational mathematics materials.

Research Notes

Technical documents and working notes from research projects:

• Weak Galerkin Finite Element Methods: Analysis and implementation notes for WG-FEM on various mesh types.
• Nonlocal PDEs and Fractional Diffusion: Mathematical foundations and numerical approaches.
• Stochastic PDEs and Uncertainty Quantification: Methods for solving PDEs with random inputs.
• Virtual Element Methods: Implementation details and error analysis for VEM.
• Computational Neuroscience Models: Mathematical models of calcium dynamics in neurons with endoplasmic reticulum.
• Deep Learning for Scientific Computing: Hybrid approaches combining numerical methods with deep neural networks.