Timeline for What should be taught in a 1st course on smooth manifolds?
Current License: CC BY-SA 4.0
9 events
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| Jan 4, 2021 at 6:43 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
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| Dec 19, 2018 at 0:40 | history | edited | Anton Petrunin | CC BY-SA 4.0 |
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| Mar 22, 2011 at 0:14 | comment | added | Mariano Suárez-Álvarez | @Igor, for someone who has only "done basic coursework in point-set topology and multivariable calculus" anything beyond dimension $2$ is going to be mumbo-jumbo. There is a real problem which your comment does raise, though: it is extraordinarily sad that first year graduate's knowledge may be so described... | |
| Mar 19, 2011 at 20:43 | comment | added | Gjergji Zaimi | The undergraduate topology/geometry requirement that we have at my school has a term on intro to algebraic topology, a second term on intro to diff.geometry which is similar to what this post describes, and a last term on diff. topology which incidentally uses the same textbooks as in the OP, and I think that's similar to what is being asked here. | |
| Mar 19, 2011 at 13:07 | comment | added | Igor Belegradek | For most graduate students who won't be specializing in geometry/topology their first course on manifolds will also be their last. Focusing on dimension 2 is a great approach for an upper level undergraduate course, but not for the first year graduate one. | |
| Mar 19, 2011 at 12:49 | comment | added | Deane Yang | Agree with Mariano too. | |
| Mar 19, 2011 at 6:19 | comment | added | Mariano Suárez-Álvarez | I could not agree more. In particular, I would avoid all of the big bureaucracy sometimes confused with differential geometry (there is absolutely no need to inflict upon students the general definition of tensors, vector bundles and what not!) | |
| Mar 19, 2011 at 2:57 | comment | added | Deane Yang | I completely agree with this! | |
| Mar 19, 2011 at 2:38 | history | answered | Anton Petrunin | CC BY-SA 2.5 |