As I continue preparing for a differential geometry course that might not run, I am assembling a bibliography for my students. (It is far too sad to contemplate that the course won’t run. I will just Keep Calm and Continue Planning.)
I want to hand them an annotated bibliography, with some reasonable commentary about the quality, content and outlook of the texts on the list.
This job is turning out to be a rather large one. There are lots of elementary differential geometry texts. Not quite as many as calculus or linear algebra, but still.
So I will break the job into some more manageable pieces. I’ll start with a simple book list. These are the fruits of an afternoon’s search for possible introductory texts. Later, I will fill in with miniature reviews of the books as I take a more detailed look at them. I have every intention of starting this project strong and then watching it slowly fade into a guilty state of incompletion. But who knows? Maybe this is actually something I can finish.
The Great Elementary Differential Geometry Textbook Review of Winter 2012
A note on the definition of “elementary”: I will only consider texts that I think have some outside chance of serving as a stand-alone introduction to the classical differential geometry of curves and surfaces in . The prerequisites should be no more than courses in multivariable calculus and linear algebra. A few books presuppose a passing familiarity with differential equations. I will allow this, but if the text assumes material past what might reasonably be covered in the course of the regular calculus sequence it will be removed from the list.
I have cut out many books simply because they are too advanced. When I am done with the list of elementary books, I will likely include a short list of my favorite “advanced books” and some other reference material I think is interesting.
I found over 20 books without much effort, so this might take a bit of work.
In no particular order, the books I will look at are:
- Stoker, Differential Geometry
- Wardle, Differential Geometry
- Kreyszig, Differential Geometry
- Willmore, An Introduction to Differential Geometry
- Struik, Lectures on Classical Differential Geometry
- O’Neill, Elementary Differential Geometry
- Oprea, Differential Geometry and its Applications
- Snygg, A New Approach to Differential Geometry Using Clifford’s Geometric Algebra
- Pressley, Elementary Differential Geometry
- Toponogov, Differential Geometry of Curves and Surfaces
- Thorpe, Elementary Topics in Differential Geometry
- McCleary, Geometry from a Differential Viewpoint
- Kühnel, Differential Geometry: Curves – Surfaces – Manifolds, 2nd Ed.
- Bär, Elementary Differential Geometry
- Montiel & Ros, Curves and Surfaces, 2nd Ed.
- Millman & Parker, Elements of Differential Geometry
- do Carmo, Differential Geometry of Curves and Surfaces
- Banchoff and S. Lovett, Differential Geometry of Curves and Surfaces
- Gray, Modern Differential Geometry of curves and Surfaces with Mathematica
- Vaizman, A First Course in Differential Geometry
- Spivak, A Comprehensive Introduction to Differential Geometry, vols 1-5
- Shifrin, Differential Geometry: A First Course in Curves and Surfaces
- Henderson, Differential Geometry: A Geometric Introduction
- Weatherburn, Differential Geometry of Three Dimensions
There are a couple of other texts, I suppose. I found these by going through major publishers websites and looking through UNI’s Rod Library stacks. A few of these have been on my shelf for a while, but I haven’t really taken time to read some significant portion and decide if I like them.
Have I mentioned that I have a problem? Yeah, I spend too much money on mathematics books.