Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am reading Road to Reality by Roger Penrose and I although I know about calculus, complex analysis, differential equations I do not know about manifolds, Riemann surfaces and so on. Which books can you recommend me in order to master the topics found on that book?

share|cite|improve this question
James Munkres' "Analysis on Manifolds" and Michael Spivak's "Calculus on Manifolds" are nice accessible texts. – Bill Cook Nov 18 '11 at 0:36
It' can't be done. You need to know the material before you read the book, then you really wouldn't need to read the book unless you really wanted to know what Roger Penrose thoughts. – simplicity Nov 18 '11 at 0:48
@simplicity I think the OP is looking for books to expand on what is discussed in the Road to Reality given he is currently reading it. – Bill Cook Nov 18 '11 at 1:07
I will put in my standard warning about Calculus on Manifolds -- I found it really dense and unmotivated, and disliked it intensely. But people keep recommending it, so it obviously works for a lot of students. And it might work better mixed with Penrose, since he is verbose and extremely intuitive, but lacks the details you'll find in Spivak's book. – David Speyer Nov 18 '11 at 2:06
3 (click on the comic). – Hans Lundmark Nov 18 '11 at 7:50

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.