Is Lang's Book on Differential Geometry Suitable for Beginners?

[lurflurf]

Like in the other thread I recommend to toe dippers with "some" calculus and linear algebra and an interest in physical stuffs Curvature in Mathematics and Physics by Shlomo Sternberg. To the sentimentalist who think three dimensions is more than enough try differential Geometry Of Three Dimensions by C.E. Weatherburn.

 

[Mandelbroth]

Sometimes I think the people replying are just trying to show off and "overkill" instead of actually helping the OP.

In the guy's defense, I didn't feel like I understood differential geometry at all until I borrowed a copy of volume 1 of Spivak's introduction. It opens by defining a manifold as a metric space rather than the more general topological space, but other than that it was fantastic. Plus, I like the way Spivak writes. I don't know about anyone else, but it often reads like he's talking to you rather than attempting to talk around your perceived skill level. I appreciate this.

That being said, Spivak doesn't hold much back either.

 

[WannabeNewton]

Spivak isn't a problem. Lots of people use Spivak for a first exposition to differential topology. Only Gauss, Riemann, or Weyl would use Lang as an intro to the subject.

 

[lurflurf]

^I don't see any problem looking at Lang (or Kobayashi and Nomizu) early on. It does not cause your face to melt. Lang is one of the few books with infinite dimensional flavor, and as is often the case with Lang, he presents things as they are best understood instead of easiest understood. Still most people would like to also read a more gentle book. Spivak is pretty chatty which others dislike, but I consider it a strength. I dislike the typeset though and if I recall correctly it is unchanged in the third edition.

 

[deluks917]

The issue I have with Lang is it has no exercises. Otherwise I think it would be a reasonable choice for a dedicated student.

 

[micromass]

^I don't see any problem looking at Lang (or Kobayashi and Nomizu) early on. It does not cause your face to melt. Lang is one of the few books with infinite dimensional flavor, and as is often the case with Lang, he presents things as they are best understood instead of easiest understood. Still most people would like to also read a more gentle book. Spivak is pretty chatty which others dislike, but I consider it a strength. I dislike the typeset though and if I recall correctly it is unchanged in the third edition.

The issue I have with Lang is it has no exercises. Otherwise I think it would be a reasonable choice for a dedicated student.

Man, even my old differential geometry professor said that he looked at Lang and didn't understand much of it because it was so horrible written. And this is a guy who knows differential geometry inside out.