Clayton Shonkwiler

Math 474

Instructor: Dr. Clayton Shonkwiler
Time: Monday, Wednesday, Friday 2:00–2:50
Location: Engineering E105
Office: Weber 216
Office Hours: Monday 3:00–4:00, Wednesday 11:00–12:00 and 3:00–4:00, Thursday 2:00–3:00
Email Address:
Text: Differential Geometry: A First Course in Curves and Surfaces, by Theodore Shifrin

Lecture Notes



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!
  • ShareLaTeX — Another online TeX editor
  • 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