## Description

Modern data are high-dimensional, multi-modal, and large-scale, 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. Learning and sampling from this real distribution, hence, is of tremendous value. This class covers the mathematical theory of high-dimensional geometry and manifolds and how it applies to the latest advances in artificial intelligence.

## Logistics

**Time:**Tue/Thu 2:00 - 3:15 PM**Location:**Thronton E316 / Zoom**Instructors:**Tom Fletcher (ptf8v*AT*virginia*DOT*edu) and Aman Shrivastava (as3ek*AT*virginia*DOT*edu)**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**Office Hours:**Tom: Wednesdays, 3:00 - 4:00 pm in Rice 306 & Aman: Mondays, 3:00 - 4:00 pm in Rice 342

## 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.)