## Description

Modern data are high-dimensional, for example, images with millions of pixels, text corpora with millions of words, gene sequences with billions of base pairs, etc. However, these data tend to concentrate on lower-dimensional, nonlinear subspaces known as manifolds. This class covers the mathematical theory of high-dimensional geometry and manifolds and the application of this geometry to machine learning and data analysis.

## Logistics

**Time:**Tue/Thu 2:00 - 3:15 PM**Location:**Olsson 005 / Zoom**Instructor:**Tom Fletcher (ptf8v*AT*virginia*DOT*edu)- Office Hours: Wednesdays, 11 AM - 12 noon, Rice 306

**TA:**Yinzhu Jin (yj3cz*AT*virginia*DOT*edu)- Office Hours: Mondays, 2 - 3 PM, Rice 414

**TA:**Xingbo Fu (xf3av*AT*virginia*DOT*edu)- Office Hours: Thursdays, 3:30 - 4:30 PM, Rice 414

**TA:**Aman Shrivastava (as3ek*AT*virginia*DOT*edu)- Office Hours: Tuesdays, 3:30 - 4:30 PM, Rice 414

**Prerequisites:**You should have basic (undergraduate level) knowledge of Probability, Linear Algebra, Multivariate Calculus, and be comfortable programming in Python**Software:**All homeworks will be done in Jupyter

## Additional Reading

Manfredo do Carmo, *Riemannian Geometry*

Sigmundur Gudmundsson, *Introduction to Riemannian Geometry*

## Example Jupyter Notebooks

For those of you who are relatively new to Jupyter, here are a few notebooks that you might find useful (from my undergraduate course Foundations of Data Analysis.)