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?
Preparing for reading Penrose's "Road to Reality"
2
$\begingroup$
calculus
abstract-algebra
complex-analysis
manifolds
-
1James Munkres' "Analysis on Manifolds" and Michael Spivak's "Calculus on Manifolds" are nice accessible texts. – 2011-11-18
-
0It' 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. – 2011-11-18
-
0A really excellent book; I happen to be reading it right now as well! – 2011-11-18
-
2@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. – 2011-11-18
-
2I 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. – 2011-11-18
-
4http://abstrusegoose.com/272 (click on the comic). – 2011-11-18
-
0For learning about Riemann surfaces, I like Forster's book. As far as I recall, you shouldn't have to know about manifolds and differential geometry in order to start reading it. – 2011-11-18