MCS 548 - Mathematical Theory of Artificial Intelligence
University of Illinois - Chicago
Fall 2025

This course will introduce some of the central topics in computational learning theory, a field which approaches the question "whether machines can learn" from the perspective of theoretical computer science. We will study well defined and rigorous mathematical models of learning where it will be possible to give precise and rigorous analysis of learning problems and algorithms. A big focus of the course will be the computational efficiency of learning in these models. We will develop some provably efficient algorithms and explain why such provable algorithms are unlikely for other models.

Example topics include inductive inference, query learning, PAC learning and VC theory, Occam's razor, online learning, boosting, support vector machines, bandit algorithms, statistical queries, Rademiacher complexity, and neural networks.

This course is represented on the computer science prelim.

Basic Information

Syllabus: pdf
Time and Location: M-W-F 1:00pm - 1:50pm, Computer Design Research and Learning Center (CDRLC) 1405
Instructor Contact Information: Lev Reyzin, SEO 417, (312)-413-3745,
Required Textbook: Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar. Foundations of Machine Learning, second edition (available free online)
Optional Textbook: Shai Shalev-Shwartz and Shai Ben-David. Understanding Machine Learning: From Theory to Algorithms (available free online)
Office Hours: TBD

Presentations

Problem Sets

Lectures and Readings

Note: lectures will have material not covered in the readings.

Lecture 1 (8/25/25)
covered material: intro to the course, preview of learning models
reading: section 7 of Computing Machinery and Intelligence by Turing (1950)