MTG 7396, Topological Data Analysis and Machine Learning (Advanced Topics in Topology 1)
Across academia and industry there is a huge appetite for new tools to make sense of the vast quantities of data being produced and recorded.
Quantifying and organizing complicated structure is something that mathematics is very good at. The goal of topological data analysis is to use tools rooted in algebra and topology to represent and learn from the shape of data.
The purpose of this course will to be twofold:
- To introduce students to ways in which many topics from pure mathematics are used in data analysis.
- To introduce students to some of the main ideas in machine learning (AI).
Mathematical topics will include: simplicial complexes, homology, linear algebra, Morse theory, category theory, commutative algebra, representation theory of quivers, combinatorics, Hilbert spaces, and kernels.
On the applied side, we will learn some of the central ideas in modern statistics and machine learning (AI). We will learn to use python and python libraries such as scikit-learn and scikit-tda. No prior coding experience will be assumed.
Grading for the course will consist of one computational individual project and a couple of small homework assignments.
This topic has much to offer the aspiring mathematician: interesting new mathematical problems, important applications, conferences with support for graduate students, demand from industry to hire graduates, and demand in academia for postdocs.
Provisional Time and Location
MWF Period 6 (12:50-1:40), Little Hall TBD
Prerequisites
This course will be mostly self-contained. Any student ready for a 4000/5000 level math course is welcome. The main topological construction with which you will be expected to quickly familiarize yourself with is simplicial homology.
Please contact me if you have any questions and/or requests!