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Math 535: Mathematical Methods in Data Science

Sebastien Roch, UW-Madison


This course on the mathematics of data has two intended audiences:

Content-wise it is a second course in linear algebra, vector calculus, and probability motivated by and illustrated on data science applications. As such, students are expected to be familiar with the basics of those mathematical areas, as well as to have been exposed to proofs. Moreover, while the emphasis is on the mathematical concepts, students enrolling in this class should be willing to learn a programming language.

Current semester

Website for the current semester (including updated notes):


Websites from previous semesters:

Lectures Notes and Jupyter Notebooks (version: Fall 2020)

A full set of lecture notes and notebooks from Fall 2020 is available below. See the current (above) for the latest version of the notes.

Topic 0: Introduction

Topic 1: Least squares: Cholesky and QR decompositions

Topic 2: Spectral and singular value decompositions

Topic 3: Optimality, convexity and gradient descent

Topic 4: Probabilistic modeling and inference

Programming languages


We will use the following textbooks available online (which will be complemented by the lecture notes and notebooks above):

Last updated: sep 2, 2022