Space of sections of a vector bundle

The algebra-geometry duality means that there is a strong relationship between the geometry on some space, and the algebra of functions on it. It is thus natural to see how the geometric notion of vector bundles manifests itself on the algebra side. It turns out that they correspond to projective modules. In this video, we indicate how the space of sections leads to this correspondence.

[@trailmixvideo]

It is good to know that you are moving toward projective modules. I hope that you will be able to cover split exact sequences and tensor products, and the correspondence with commutative algebra and extension of scalars. So good to see you moving ahead with these important topics.

[@TheEdwinpako]

Finally found some decent explanation on what is *space of sections*. The fact that base space comes first is the thing that confused me. Now I finally sure about what definition of differential forms says. Thank you a lot for this video. P.S Can I say that set of all smooth vector fields on M is isomorphic to Г(M; TM)?

[@falcon3652]

its a interesting solution, this also learn jus few days ago in my university this also helpfull..by tha by thanks