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Oct 12, 2018 at 19:33 comment added The Mathemagician Spivak is too difficult for most students on a first pass through the subject. Ideally,you want your students to master curves and surfaces in low dimensions and fully understand the calculus and linear algebra that makes the geometry possible before exposing them to manifolds and forms. I think even if your students are very strong, this is a better way to go in the long run for them.
Sep 14, 2011 at 8:42 comment added Ketil Tveiten In vol. 1 he repeatedly refers to 'Calculus on Manifolds' (in particular any actual calculus required), so it might be prudent to consider that book vol. 0 of his magnum opus. It is probably a bit hard to start on vol. 1 without any previous knowledge.
Sep 14, 2011 at 4:23 comment added Spice the Bird Spivak also wrote a book called "Calculus on Manifolds". Depending on the undergraduate, this might be a nice place to start.
Dec 6, 2009 at 19:57 history made wiki Post Made Community Wiki by Anton Geraschenko
Dec 5, 2009 at 14:07 comment added Akhil Mathew The first two chapters of Vol. 2 require pretty much no prerequisites; they're on curves and surfaces.
Dec 5, 2009 at 6:25 history answered Harry Gindi CC BY-SA 2.5