Flow Chart of material to learn differential geometry

[jhoffs1]

I am a 3rd year mechanical engineering student at LSU, but my true interest lies in theoretical physics and mathematics (specifically general relativity and differential geometry). I've taken calculus 1,2,3, linear algebra, ordinary differential equations, number theory, discrete math, and statistics (at a local university while I was in high school). My question is, where would I go next after tensor calculus if I want to fully grasp differential geometry/relativity in a full sense (not watered down)? I bought "introduction to tensor calculus and continuum mechanics" and I am almost finished with the tensor analysis (not too difficult) and am trying to find where I need to go next. Sent from my iPhone using Physics Forums

 

[jhoffs1]

Flow chart for general relativity

What classes should be taken/self-taught to fully understand and work with GR? I have taken calc 1,2,3 linear algebra, statistics, number theory, discrete math, and am just finishing "introduction to tensor calculus and continuum mechanics", but where should I go next? Straight to differential geometry?Sent from my iPhone using Physics Forums

 

[WannabeNewton]

You already know enough to delve into a myriad of GR texts.

 

[lavinia]

if you are interested in modern physics I suggest learning Differential Geometry on Manifolds. General Relativity is one entry point to this but pure mathematical texts can be helpful.