I recently started taking an interest in General Relativity, however I am well aware that I simply have no knowledge of the mathematics behind it, especially Riemannian geometry.

That being said, I wish to learn as much as possible about Riemannian geometry, but am a year or so away from even being an undergraduate therefore my knowledge is severely lacking.

I have had a look at some related questions asking for book recommendations and have even (tried to) read some of them, but have found that they expect a far stronger mathematical background than my own, hence my question:

Assuming an undergraduate student in their first or second year at university, what topics would they need a thorough understanding of before they read any introductions to Riemannian geometry?

  • 1
    $\begingroup$ You'll want to know at a minimum: real analysis, linear algebra, general topology, a little algebraic topology, and some smooth manifold theory. $\endgroup$
    – guest
    Feb 11, 2017 at 15:28
  • 2
    $\begingroup$ From my experience as an (ex-)physics student (surrounded by many other physics students), I can tell you that you can understand basic general relativity at some level without much of the background that one would need to rigorously understand the underlying mathematical structures. Whether that's the way you want, or should want, to go is another issue, but many physics students do precisely that. Once you've got a good grip of classical electrodynamics (e.g. all of Griffiths' book) and know some special relativity, you're probably ready to give it a shot. Try Carroll's book. $\endgroup$
    – Danu
    Feb 11, 2017 at 15:54
  • 1
    $\begingroup$ A solid understanding of vector calculus is very important, in particular how Green's Theorem, Stokes' Theorem, and the Divergence Theorem are re-expressed in the language of differential form, and (as mentioned by @Danu) how Maxwell's equations are re-expressed in that language. $\endgroup$
    – Lee Mosher
    Feb 11, 2017 at 16:14
  • $\begingroup$ @LeeMosher In fact, using that the exterior derivative is equal to the antisymmetrized covariant derivative, physics textbooks often get away without even talking about forms much at all---but I agree it is not something that is nice to skip. $\endgroup$
    – Danu
    Feb 11, 2017 at 17:36


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.