APMA 1930Z: Introduction to Mathematical Machine Learning

Fall 2024

MWF 2:00-2:50 PM in TBD

Instructors and contact

Paul Dupuis, Paul_Dupuis@Brown.edu

Benjamin Zhang, bjzhang@umass.edu

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 weaknesses of methods.


This class is intended for an advanced undergraduate or a first year Master’s student. We expect a strong command of probability, multivariable calculus, and linear algebra at the level of MATH 0520/0540, APMA 1650/1655, and APMA 1690/MATH 1610, or permission of instructor. Recommended: Familiarity of numerical methods. Basic programming experience is assumed. You may program in any language, but most instructional scripts will be provided in Python.


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.

We will be reading selections from

Supplementary readings will be provided for topics not covered in the textbooks.

Homework & Grading (subject to change!)

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

Each homework assignment is worth 8% of the final grade, with a cap of 56% over all 8 assignments. Each problem set will consist of derivations, proof–based questions, and numerical exploration and experimentation of machine learning algorithms.

APMA 1930Z is an experimental course, meaning that feedback will be invaluable for future iterations of this course. Therefore, the instructors ask that students complete short reflections after each class on what they learned and how effectively lectures and homework contributed to their learning. Attendance of lectures will be crucial for receiving credit for minute papers.

An individual final project is required to pass the class. A project proposal will be due in the middle of the semester. Poster sessions showcasing each students’ work will take place on the last week of class. The final project report (7-10 pages) will be due at the end of the semester. A list of suggested projects as well as guidelines for the proposal, final report, and poster session will be released early in the semester. Students are also encouraged to choose their own project with approval from the instructors.

Subject outline

Part 0: Introduction to machine learning and linear algebra review

Part 1: Linear methods and foundations

Part 2: Kernel methods and learning theory

Part 3: Deep learning methods