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"Advanced" Geometry course

  1. Sep 19, 2014 #1
    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?
  2. jcsd
  3. Sep 19, 2014 #2


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    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.
  4. Sep 20, 2014 #3
    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?
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