Fall 2025

This course provides a rigorous yet accessible introduction to the algorithmic foundations of optimization, with a focus on problems and applications in computer science and engineering. Topics include convex sets and functions; unconstrained methods such as gradient descent and Newton’s method; projection and gradient‐projection; equality and inequality constrained optimization via Lagrange multipliers and KKT conditions; duality theory; stochastic gradient techniques; and subgradient methods for nondifferentiable problems.

Enterprise systems are large-scale software applications to support business operations; they typically include software systems for data management, business process/workflow management, information flows, reporting, and data analytics. Focusing only the data management aspect, a typical enterprise has to struggle with many data integration difficulties, since its data are usually spread around many database systems, workflow systems, file systems, etc. and in a variety of form possibly with no coherent semantics.

This course explores advanced topics in highly scalable Internet services and their underlying systems’ architecture. Software today is primarily delivered as a service: accessible globally via web browsers and mobile applications, and backed by millions of servers.

This course covers advanced topics on neural information retrieval and web search engines. The content to be focused includes indexing, retrieval, ranking, and system optimization for large-scale search services with deep machine learning and NLP models. Recent papers in top conferences will be reviewed, and issues in relevance, efficiency, and scalability will be studied. 

Once the quarter starts, instructor approval is required to maintain enrollment in the course. 

After over 30 years of research and engineering in controllable quantum devices, we are at the cusp of discovering the first real-world applications for quantum computing systems. A critical element that connects high-level applications to low-level quantum system designs is quantum control and metrology.

Computer Science graduate students often encounter research literature that freely uses "continuous" mathematics not covered in their undergraduate coursework. This course builds literacy in these topics in a compressed timeline, including:

- Second-course linear algebra and probability
- Fundamentals of real analysis and point-set topology
- High- and infinite-dimensional vector spaces
- Manifolds and matrix Lie groups

Artificial intelligence holds enormous promise for accelerating scientific discovery, yet its “black box” nature and data-hungry architectures often hinder adoption in domains where interpretability, physical consistency, and sparse data prevail. This course addresses these challenges by developing a unified framework that integrates three complementary, domain-informed representations—topological features, physics-based constraints, and higher-order relational structures—into end-to-end, scalable AI models.

Networks or graphs are a natural way to represent a variety of interacting complex systems - from disease spreading and brain networks, to social networks and political networks.