MCS 549 - Mathematical Foundations of Data Science
University of Illinois at Chicago
Fall 2024

This course covers the mathematical foundations of modern data science from a theoretical computer science perspective. Topics will include random graphs, random walks, Markov chains, streaming algorithms, clustering, singular value decomposition, and random projections.

Basic Information

Syllabus: pdf
Time and Location: M-W-F 9:00-9:50 am, 206 Lincoln Hall (LH)
Instructor: Lev Reyzin, SEO 417
Online Textbook: Avrim Blum, John Hopcroft, and Ravi Kannan, Mathematical Foundations of Data Science
Office Hours: T 11:00-11:50am (online), F 10:00-10:50am (in-person)
Piazza site: please sign up via this link

Presentations

Problem Sets

problem set 1 due 10/4/24

Lectures and Readings

Lecture 1 (8/26/24)
covered material: intro to the course, preview of the material
reading: chapter 1

Lecture 2 (8/28/24)
covered material: some concentration inequalitiess
reading: chapters 2.1 - 2.2

Lecture 3 (8/30/24)
covered material: properties of high dimensions, properties of the unit ball
reading: chapters 2.3 - 2.4

Lecture 4 (9/4/24)
covered material: sampling from a high-dimensional sphere, Gaussian annulus theorem
reading: chapters 2.5 - 2.6

Lecture 5 (9/6/24)
covered material: random projections and the Johnson-Lindesnstrauss lemma
reading: chapter 2.7

Lecture 6 (9/9/24)
coveredmaterial: singular value decomposition (SVD), best-fit subspaces, and optimality of greedy algorithm
reading: chapters 3.1 - 3.4

Lecture 7 (9/11/24)
covered material: computing SVD, power iteration
reading: chapters 3.7 and 3.8

Lecture 8 (9/13/24)
covered material: centering data, separation Gaussians with SVD
reading: chapter 3.9