"Advanced" Geometry course

[Waxterzz]

I would like to refresh my "normal" or Euclidean Geometry quickly and then proceed to Non-Euclidean Geometry.

But I don't have a clue where to start. (It's because I want to learn more about Relativity, but my geometry hasn't got an update since long time ago)


I don't know what a manifold is, for starters. :)


Now I Google about Non-Euclidean Geometry and you got more than 1 type of N.E.G.

So, I haven't got a clue where to start.

I remember however this kind of a geometry in high school, where two parallel lines cross each other when going to infinity in a point that doesn't really exist? That's as far as my knowledge of geometry goes (I mean, that was the most advanced of "pure geometry" I encountered)

So how do I refresh my geometry and get ready for more exotic stuff?

I also have no notice from topology, differential geometry or tensor calculus. And what should I do first?

 

[dextercioby]

Diff. geometry is preceded by calculus. You have to take each step at a time. Point set topology comes as a side dish to fundamental (real) calculus. Then you have linear algebra, also before tackling diff. geometry.

 

[Waxterzz]

Ok, so I got Calculus (including multivariable calculus) and Linear Algebra and Differential Equations covered, so the next step is Differential Geometry?

But for me something to learn, I have to look at a lot of premade solutions. So Schaum's Outline Of Differential Geometry in combination with a more theoretical book will do fine?

U got an idea of a good textbook on Differential Geometry?