Manifolds

[eyefragment]

About 6 months ago, I got an e-mail from Zev, now a senior at Lawrenceville (my High School).  He had finished the math courses that L'ville could offer, and was wondering what he should do for an independent study.  I recommended working through Rudin or Herstein, but he said that he'd already finished Rudin and done basic group/ring/field theory

Comments

[oxeador]

I seem to remember I liked both books by Do Carmo (one was intro to Differential Geometry, the second was on Riemannian Geometry) and that they had a good collection of problem sets.

[arrowedumbrella]

What about Algebraic Topology by Hatcher or Differential Topology by Guillemin and Pollack?

[sniffnoy]

Hatcher is kind of eh. I remember someone else's complaint about it, that I didn't think of at the time but definitely agree with: It explains pointless obvious stuff in detail, but then leaves out the actually hard parts as obvious.

[leech]

I am very fond of Lee's Introduction to Smooth Manifolds.

I also second Hatcher.