What branches of math must I master to learn GR?

[Sorcerer]

Based on what I’ve read here, I really have to absolutely kill linear algebra. Maybe some abstract algebra, too. And based on all this talk of manifolds, I’m guessing some topology and differential geometry is in order.

Those of you who know GR, can you offer a math subject prescription so I can finally learn GR?

For the record my math background is currently maxed out here:
*Undergraduate multi-variable calculus

*The barest basics of linear algebra (before you get to more abstract concepts like really understanding vector spaces, basis, kernel, etc).

*Undergraduate differential equations up to some simple partial differential equations (I suppose the furthest I got is separation of variables and utilizing a Laplace transform table).

*A little bit of set theory, truth tables, and some of what you learn in the “Transition” math class undergraduates take before they are allowed to take courses like analysis, abstract algebra, topology and the like.

*A little exposure to group theory, and a couple other very watered down abstract algebra concepts.

Again, thanks to all who respond. I know this is kind of a vague question.

 

[phinds]

I suggest a forum search. This question has been answered here many times.

 

[Sorcerer]

I suggest a forum search. This question has been answered here many times.

(a) That isn’t very efficient as there are countless threads with those key words that only explore one particular issue rather than a simple general summary.

(b) It seems simply answering the question might have taken as much effort as “try the search forum.”

 

[haushofer]

See e.g. Nakahara's book. It covers all the differential geometry, tensor analysis and topology you need to master GR.

 

[PeroK]

Based on what I’ve read here, I really have to absolutely kill linear algebra. Maybe some abstract algebra, too. And based on all this talk of manifolds, I’m guessing some topology and differential geometry is in order.

Those of you who know GR, can you offer a math subject prescription so I can finally learn GR?

For the record my math background is currently maxed out here:
*Undergraduate multi-variable calculus

*The barest basics of linear algebra (before you get to more abstract concepts like really understanding vector spaces, basis, kernel, etc).

*Undergraduate differential equations up to some simple partial differential equations (I suppose the furthest I got is separation of variables and utilizing a Laplace transform table).

*A little bit of set theory, truth tables, and some of what you learn in the “Transition” math class undergraduates take before they are allowed to take courses like analysis, abstract algebra, topology and the like.

*A little exposure to group theory, and a couple other very watered down abstract algebra concepts.

Again, thanks to all who respond. I know this is kind of a vague question.

There are also some Physics prerequisites. Most important, you must have really understood SR. And, you need to have studied Lagrangian Mechanics. Another recent thread is here:

https://www.physicsforums.com/threa...s-for-general-relativity.939528/#post-5940112