MATH 637: Mathematical Techniques in Data Science

University of Delaware · Fall 2026

Lectures	MWF from 1:50pm–2:45pm in Purnell Hall 236
Office hours	MW from 2:45pm–3:45pm in Ewing Hall 509
Syllabus	Course syllabus (PDF)
Canvas	Canvas course site

Habit de Jardinier, an 18th-century engraving of a gardener dressed in garden tools — *Habit de Jardinier*, engraving by Nicolas de Larmessin (1640–1725)

This course will introduce fundamental techniques for data exploration, prediction, and inference. Our main objective will be to develop a mathematical understanding of data science techniques—their assumptions, properties, and limitations—alongside their practical implementation and use. Several of our meetings will be dedicated to problem-solving and programming sessions. Final projects will evaluate both an understanding of course material as well as the critical thinking skills at the core of effective data science.

Announcements

Aug 11 Welcome! The first lecture will be on Aug 26.
Aug 28 Today’s lecture will motivate dimension reduction and review the linear algebra necessary for Monday’s lecture on principal component analysis.
Aug 30 I’ve posted a Jupyter notebook that we’ll use to demo principal component analysis in lecture 3.
Sep 08 Keep in mind that Homework 1 is due on Sep 14 before class. Tomorrow, we’ll begin our discussion of clustering.
Sep 10 You can now submit your Homework 1 solutions to Canvas.

Lectures

#	Date	Topic	Materials
1	Aug 26	Course overview	Slides
2	Aug 28	Intro to dimension reduction, linear algebra review	Slides
3	Aug 31	Principal component analysis (PCA)	Slides Code
4	Sep 02	More on PCA, and singular value decomposition (SVD)	Slides
5	Sep 04	Quiz 1 and start of PCA/SVD problem set
6	Sep 09	Clustering with k-means	Slides
6	Sep 11	Density estimation

Resources

Mathematics for Machine Learning, Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong
Cambridge University Press, 2020. Free online textbook, and the closest to this course in its presentation of the core topics.
An Introduction to Statistical Learning with Applications in Python, Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, and Jonathan Taylor
Springer, 2023. Free PDF of the Python edition.
The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Trevor Hastie, Robert Tibshirani, and Jerome Friedman
Springer, 2nd edition, 2009. Free PDF of the 12th corrected printing (2017).
Foundations of Data Science, Avrim Blum, John Hopcroft, and Ravindran Kannan
Cambridge University Press, 2020. Free PDF of the 2018 pre-publication draft.
Deep Learning: Foundations and Concepts, Christopher M. Bishop with Hugh Bishop
Springer, 2024. Free online version, readable in the browser.
Veridical Data Science: The Practice of Responsible Data Analysis and Decision Making, Bin Yu and Rebecca L. Barter
MIT Press, 2024. Open-access web version.
Mathematical Methods in Data Science: Bridging Theory and Applications with Python, Sebastien Roch
Cambridge University Press, 2025. Free online version.

← All teaching