Elementary Differential Geometry
James Cook's Elementary Differential Geometry Homepage

The initial big picture:

Elementary differential geometry is centered around problems of curves and surfaces in three dimensional euclidean space. We're using Barret Oneil's excellent text this semester.
Oneil uses linear algebra and differential forms throughout his text. I am excited about learning the method of moving frames for surfaces in 3-space. Ideally, I'd like to start reading some papers which generalize this method to surfaces in more exotic three dimensional manifolds. If our course goes very well, perhaps I'll be able to show you something about that other world of ideas at the end.
This course is the natural bridge to abstract manifold theory. I will avoid the temptation to generalize our work as we go. In some sense, advanced calculus is a more abstract course as we insist on treating many questions in n-dimensions. Here, in this course, usually n=3.

Guide to Self-Paced Differential Geometry Course:
In Summer 2015 I wrote these notes:

  • Elementary Differential Geometry:

  • from which I gave the Lectures based on O'neill, Kuhnel for Test 1. Then for Test 2 I simply recycled my old course notes plus a few new hand-written pages for Chapter 4. Then I talked through my notes from Tapp to help build-up to the final exam project. I have links to videos which are not absolutely essential to watch, I think you could get enough from the texts and the notes alone. But, perhaps the videos help. I also included scans of what I wrote in landscape for the Lectures. Rough Notes from my Reading in Oneil:
    As I mentioned, my personal goal is to solve most the problems. However, that seems like a bit much for the class. Missions are given below:

  • Mission 1: homework paired with Test 1 based on my lecture notes, O'neill and perhaps Kuhnel.

  • Mission 2: homework paired with Test 2 based on my lecture notes, O'neill and perhaps Kuhnel.

  • Missions 1-6 detailed I will update this from time to time (it lists the first few Missions as well as my weekly topic targets)

  • I'll probably just let you look at my global solutions for this class. At a minimum, the solutions below should include most of the problems assigned in the Missions.

  • note to self, delete this later: final exam solution.

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    Last Modified: 6-26-15