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.
Sep 11 If you missed today’s lecture, please make sure to review the slides (posted below) before Monday. We’re going to start from the Gaussian mixture modeling problem in one dimension and build from there. Also, I returned the graded quizzes and went over the solution, which is also posted below.
Sep 14 Now that we’ve completed all parts of the first module, I’d like to gather some anonymous feedback. I’ve made an announcement on Canvas with a link to the form. I’ll ask you to complete it at the start of today’s meeting.
Sep 20 Tomorrow, we’ll begin regression basics.
Sep 24 I forgot to update Wednesday’s reminders slide. It mistakenly said that the homework was due a week from today, when it is in fact still due on Monday before class. I’ve corrected the slides below.
Sep 28 Quiz 3 on linear regression will be on Friday 10/02. It will consist of five multiple choice questions covering material from L9—L11. You will not need to calculate anything.
Oct 05 The midterm will be on Monday, Oct 19 during class. The quiz and discussion questions are representative in terms of style and difficulty of the questions that will be on the midterm. We will have at least one in-class review session.
Oct 19 The Wednesday lecture will be a discussion section like we normally have after quizzes. On Friday, we’ll start on trees.

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, start of PCA/SVD problem set	Notes
6	Sep 09	Clustering with k-means	Slides
6	Sep 11	More on k-means, toward density estimation	Slides
7	Sep 14	Fitting a mixture of Gaussians	Slides
8	Sep 16	More on Gaussian mixture models	Slides
8	Sep 18	Quiz 2, start of density estimation problem set	Notes
9	Sep 21	Least squares regression	Slides
10	Sep 23	More on linear regression	Slides
11	Sep 25	Overfitting and regularization	Slides
12	Sep 28	Cross-validation, the bias–variance decomposition	Slides
13	Sep 30	Priors and MAP	Slides
14	Oct 02	Quiz 3	Notes
15	Oct 05	Regression on indicators	Slides
16	Oct 07	Generative classifiers	Slides
17	Oct 09	Generative classifiers, continued	Slides
18	Oct 12	Logistic regression	Slides
19	Oct 14	Practice midterm
20	Oct 16	Review Q&A
21	Oct 19	Midterm
22	Oct 21	Discussion section for classification basics
23	Oct 23	Trees for classification and regression

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.

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