Math 334: Differential Geometry

Jason Parsley

Announcements

  • Second exam: F., 4/1 -- in-class portion and take-home portion due M., 4/4
  • Office hours on Th., 3/31, are cancelled. I will have them on Tu., 3/29, 2-3:30pm instead.
  • Gentry Lectures: M., 4/4 and Tu., 4/5. The math dept's distinguished annual lecture series features Ravi Vakil (Stanford). Both talks at 4:30 in Annenberg Forum. The usual extra credit is offered for each talk.
  • A list of errata (typos) in do Carmo is posted on the Documents tab.



Course information

Meeting times: MWF 12-1pm, room 124.
My office hours (330 Manchester):

  • M 2-3pm
  • W, Th 2-3:30pm
  • by appointment (please contact me if some of these times don't work!)


Extra-credit talks

  • Th., 1/27, Jeremy Rouse, math club talk
  • W., 2/2, Henry Petroski (Duke), "Scientists and Engineers", Olin, 4-5pm
  • Th., 2/24, Hugh Howards, math club talk (on geometry!)
  • Th., 3/17, Anna Snavely, math club talk
  • M., 4/4, Ravi Vakil, Gentry Lectures, Annenberg Forum, 4:30-5:30
  • Tu., 4/5, Ravi Vakil, Gentry Lectures, Annenberg Forum, 4:30-5:30
  • Th., 4/14, Ben Klein, math club talk

Unless specified, these talks are on Thursdays, 4:15-5:15pm, in Manchester 016. To earn extra-credit, you must submit a 1-2 page reaction paper about the talk.

Website Info

We'll post most everything for the course on this site, including assignments, projects, Maple code, and various other stuff.

Course description

This course will study, in detail, the geometrical properties of curves and surfaces. As we will discover, the subject is remarkably more difficult than your high school geometry class. We will utilize calculus and linear algebra to understand the basic idea of curvature, which is somewhat intuitive for a curve but less so for a surface. One highlight is the Gauss-Bonnet Theorem, which relates the total curvature of a surface to its topology (roughly, how many holes it has). We will talk about the shortest path between two points on a surface, that is a {\it geodesic}, and how to find geodesics. This is an excellent course for anyone planning graduate study in mathematics (or physics).