Online reading needed on manifolds

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xoninhas

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May 25, 2008
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I need ASAP, of some online reading on manifolds (i thought in english was variety...oops). I don't know what kind of manifolds cause in my notes they call it just varieties (in english i found out through wikipedia that its called manifold) . I don't understand what are manifolds... why and how you have to "parametrise" (i have no idea for the english word of doing parametric) how you calculate a manifold's dimension... and what are they used for in calculus...

Thanks for any help on the subject! :)
 
Do a google search with keywords:

mathematics manifold

you'll find 172000 references - you have read one of those. Rest 171999 is awaiting your attention....
 
Ok... in fact I've read quite some... if I asked here it is probably because more than 10 references did not really explained what I wanted, or I didn't understand nothing... and by the way manifold is applicable not only to math...

I'm being quite self-taught and I'm portuguese thus, meaning, a lot of english terms don't even make sense to me...

Thank you for your, for sure, precious time.
 
Let me see if I can explain what a manifold is in laymans terms.

A manifold is a mathematical object which has points(neighborhoods) in Euclidean space but the whole thing can be more complicated.

Let's take the Earth, it is a sphere for all intents and purposes. Looking at it as a whole, a sphere is not in Euclidean space. But locally, it can be represented by a collection of maps in 2 dimensions. For instance, a map of a town is a local point on the sphere we can describe.

For instance, if we go survey a piece of land we can use the rules of Euclidean space; the laws of plane trigonometry. But, looking at it globally and we have spherical trigonometry. A triangle can have more than 180 degree sum of the angles.

Therefore, a sphere (the Earth) is a manifold. See what I mean?. This topic can get complicated, topologically speaking.
 
Hmmm yeah I know it can get complicated that is why I'm asking... I just didn't get it by myself... ok... so maybe with an exercise I can get the better picture... I'll post it as a new topic...

Thank you galactus! :)
 
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