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itsthemac

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**Advice needed on a "course outline" to teach myself General Relativity**

I want to learn it inside and out. I'm tired of settling for dumbed-down versions of GR, and thus dumbed-down versions of how we describe the very universe we live in, just due to my lack of mathematical understanding. But I don't know what the best path to follow would be to overcome this. Specifically, I want to know what math I should master beforehand, and what order I should learn those maths in.

My math background: I have a decent understanding of basic multi-variate/vector calculus. That's really as far as I've gotten. I have no experience with differential equations (and hence differential geometry), linear algebra, tensors, or Reimannian manifolds (I don't even know what most of this stuff is). I only listed these things because I have heard them thrown around when people discuss the math of GR, but I'm sure there are other things that I'm not even aware of that I would need to learn. I want to know what my "course outline" should be. Given my limited background, what specific types of math should I learn? But more importantly, what order should I learn them in (I'm sure I would need to learn some of these before I could move on to more advanced ones)?

Also, if you have any recommendations for any texts on these topics, I would really appreciate that as well. But my main question is just what math I need to learn, and what order I should learn it in. I'm willing to put in the effort and spend the time (even if it takes a few years) as this is has been a goal of mine for a long time. Thanks in advance.