MATH 590STA: Introduction to Mathematical Machine Learning

As of 08 November 2023, enrollment for the class is full. However, if you are still interested in signing up for the course, please email us at and

Spring 2024

MWF 1:25-2:15PM in LGRT 141

Instructors and contact

Benjamin Zhang, LGRT 1632,

Ziyu Chen, LGRT 1630,

Course description

This course will provide an introduction to machine learning from a mathematical perspective. The primary objective of this course is to cultivate in students a sense of mathematical curiosity and equip them with the skills to ask mathematical questions when studying machine learning algorithms. Classical supervised learning methods will be presented and studied using the tools from information theory, statistical learning theory, optimization, and basic functional analysis. The course will cover three categories of machine learning approaches: linear methods, kernel-based methods, and deep learning methods, each applied to regression, classification, and dimension reduction. Coding exercises will be an essential part of the course to empirically study strengths and weakness of methods.


This class is intended for advanced undergraduate and early graduate students. We expect a strong command of probability, multivariable calculus, and linear algebra at the level of STAT 515, MATH 233, and MATH 545, or permission of instructor. Basic programming experience is assumed. Recommended: Familiarity of numerical methods at the level of MATH 551. Some recommended references will be posted before the beginning of the semester.


No required textbook. We will assign selected readings from Probabilistic Machine Learning by Murphy and The Elements of Statistical Learning by Hastie, Tibshirani, and Friedman.

Homework & Grading (subject to change!)

Your grade will be determined by 8 problems sets and a final project.

Students can earn up to 10 points in each homework assignment, with a cap of 60 points over all assignments. A list of suggested projects as well as guidelines for the proposal, final report, and presentation will be released early in the semester. Students are also encouraged to choose their own project with approval from the instructors.

Tentative list of lectures (subject to change!)

Part 0: Introduction and linear algebra review

Part 1: Linear methods

Part 2: Kernel methods

Part 3: Deep learning methods

Part 4: Student presentations