Advanced topics in the theory and application of computer science. Recent topics include geometric modeling and visualization, and high-performance and parallel computing. Three lecture hours a week for one semester. May be repeated for credit when the topics vary.
Recent topics
- Foundations of Predictive Machine Learning (Fall 2020)
Foundational aspects of data sciences, machine (deep) learning and statistical inference analysis.
- Geometric Foundations of Data Science (Fall 2025)
- Geometric Methods in Data Science (Fall 2021)
- Introduction to the Mathematical Theories and Computational Methods for Machine Learning (Fall 2020)
Theoretical and computational aspects of Bayesian inversion framework, MCMC theory, randomization methods for inverse/inference problems, and the theory of machine learning. Focus on mathematical understanding of Bayesian inference, learning problems, and their computations.
- Matrix and Tensor Algorithms for Data (Spring 2024)
Study mathematical foundations of large-scale data processing, design algorithms and learn to (theoretically) analyze them. Explore randomized numerical linear algebra (sketching and sampling), and tensor methods for processing and analyzing large-scale databases, graphs, data streams, and large multidimensional data. Discuss linear algebra concepts of quantum computing.
- Predictive Machine Learning (Fall 2025)
Explore foundational mathematical, statistical and computational learning theory and application of data sciences. Learn modern machine learning approaches in optimized decision making and multi-player games, involving stochastic dynamical systems, and optimal control.
- Scientific Computing in Machine & Deep Learning (Fall 2024)
Selected topics in numerical methods for machine learning and deep learning including non-convex optimization methods and second-order methods, kernel methods, neural ODEs, Bayesian inference, and reduced order methods for scientific machine learning.