# Math 476

**Instructor:** Clayton Shonkwiler

**Time:** Tuesdays and Thursdays 12:30–1:45

**Location:** Online (see Canvas for coordinates)

**Office Hours:** Tuesday 3:00–4:00 and Wednesday 4:00–5:00 (see Canvas for coordinates)

**Email Address:** clay@shonkwiler.org

**Text:** *Matrix Groups for Undergraduates*, by Kristopher Tapp

**Syllabus**

## Overview

Matrix groups are crucially important in areas ranging from computer graphics to quantum information theory to Riemannian geometry. As groups they are algebraic objects, usually realized as the group of symmetries of some space, but matrix groups are also geometric objects in their own right: they are all manifolds, which are higher-dimensional analogs of smooth surfaces. The goal in this course is to provide a geometric introduction to matrix groups, including orthogonal and unitary groups, Lie algebras, and the exponential map.

## Final Project Resources

LaTeX distributions:

- Overleaf — Online collaborative TeX editor: no need to install anything!
- TeX Live — Multiplatform TeX distribution
- MacTeX — TeX Live distribution for Mac OS X; includes TeXShop, a very good editor/viewer
- MiKTeX — Alternative Windows TeX distribution

LaTeX help:

- LaTeX Symbols — Glossary of symbols that can be displayed in LaTeX
- DeTeXify — Draw the symbol you want to enter; (hopefully!) get the code for it