## Math 535: Mathematical Methods in Data Science

### Description

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

• For math majors: it is meant as an invitation to data science from a mathematical perspective.
• For (mathematically-inclined) students in data science (undergrad or grad): it can serve as a mathematical companion to machine learning and statistics courses.
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):

### Archive

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

• Julia: To install Julia and Jupyter notebooks, follow these instructions. Some resources for learning Julia:
• A good place to start learning Julia is this tutorial.
• A more in-depth, but still quick, overview is this video.
• If you are already familiar with MATLAB or Python, this cheat sheet is useful.
• If you do not have much programming experience, this textbook may be helpful.
• Python: Many students will already be familiar with Python. I recommend using Google Colaboratory and I will provide links to notebooks hosted there. Some resources for learning Python (mainly Numpy):

### Textbooks

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

• [Sol] Solomon, Numerical algorithms, CRC Press, 2015 (Chaps 4-7)
• [Bis] Bishop, Pattern Recognition and Machine Learning, Springer, 2006 (Chaps 2, 8, 9, 13)
• [Wri] Wright, Optimization Algorithms for Data Analysis, in: The Mathematics of Data, AMS, 2018 (Sections 2-4)

Last updated: dec 23, 2021