Timeline for Books you would like to read (if somebody would just write them…)
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 20, 2019 at 3:20 | comment | added | Alec Rhea | This would be very nice, but the 'modern' view on differential geometry should probably also mention the synthetic approach (ncatlab.org/nlab/show/synthetic+differential+geometry) in an ideal book. | |
| Jan 25, 2011 at 11:07 | comment | added | John D. Cook | David Bressoud's "Second Year Calculus" combines a typical undergraduate calculus approach with differential forms. It's a start at what I have in mind, but it doesn't go very far. | |
| Jan 24, 2011 at 16:50 | comment | added | arsmath | I've never seen anything like what you have in mind (which would be awesome), but Hicks' "Notes on Differential Geometry" is pretty good about bridging the gap between the differential geometry of curves and surfaces and Riemannian geometry. | |
| Jan 24, 2011 at 13:51 | comment | added | John D. Cook | I've read Spivak's 1st volume. I had good intentions of going further but never made it. What I have in mind is a little different from Spivak in that I'd like to see the comparisons from the beginning. Maybe start with geometry from the viewpoint of Schey's book "Div, Grad, Curl and All That" and show how the vast machinery of differential geometry makes these concepts rigorous. | |
| Jan 24, 2011 at 13:14 | comment | added | Spiro Karigiannis | You should read Spivak's 5 volume "A Comprehensive Introduction to Differential Geometry." In particular, the first 3 volumes. He makes sure to treat almost every single aspect 3 ways: in local coordinates (what you call the physicist's "tensor calculus"), with moving frames (the Cartan/Chern approach), and the modern "invariant" formulation. In my opinion, all differential geometers should be comfortable moving back and forth between all three, because they're all useful in various different situations. | |
| Jan 24, 2011 at 12:39 | history | answered | John D. Cook | CC BY-SA 2.5 |