# Math 474

**Instructor:** Dr. Clayton Shonkwiler

**Time:** Monday, Wednesday, Friday 2:00–2:50

**Location:** Engineering E105

**Office:** Weber 216

**Office Hours:** Monday 4:00–5:00, Wednesday 1:00–2:00 and 4:00–5:00, Thursday 9:30–10:30

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

**Text:** *Differential Geometry: A First Course in Curves and Surfaces*, by Theodore Shifrin

**Syllabus**

## Overview

The course provides an introduction to the differential geometry of curves and surfaces, including the relevant notions of curvature, with an emphasis on global theory. Students will develop a deep understanding of the differential geometry of curves and surfaces, including the various relevant notions of curvature. This will require a synthesis of geometric visualization, symbolic and numerical calculation, and rigorous reasoning and communication. At the end of the course, students should be prepared for a graduate course in the differential geometry of manifolds.

The following books may be useful additional resources:

*Differential Geometry of Curves and Surfaces*, by Manfredo P. Do Carmo*Elementary Differential Geometry*, by Barrett O’Neill*Elementary Differential Geometry*, by Andrew Pressley*Differential Geometry of Curves and Surfaces*, by Thomas Banchoff and Stephen Lovett*Geometry from a Differentiable Viewpoint*, by John McCleary

## 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