# Study groups for calculus and topology

1. Jul 30, 2012

### micromass

Hello,

Some people on PF are currently self-studying calculus and topology. So we thought we might make a post here so that interested people could join us.

We are doing the following books:
Book of Proof by Hammack (freely available on http://www.people.vcu.edu/~rhammack/BookOfProof/)
Calculus by Spivak
Introduction to topological manifolds by Lee

The idea is to discuss theory with eachother and to make problems.
Communication is currently through facebook, but there are enough chat rooms where we can talk.

If anybody is interested, feel free to PM me. Please only react if you're serious about this. If you're thinking of quitting after a week then this might not be for you.

2. Aug 1, 2012

### zapz

Hey,
This sounds pretty cool. However, I'm not sure if my math skills are up to par with this. What would you consider a "pre-req"? Thanks!

3. Aug 1, 2012

### Number Nine

Outstanding. A sorely underrated book.

4. Aug 2, 2012

### genericusrnme

What is the level of Introduction to topological manifolds by Lee like compared to Loring Tu's Introduction to manifolds?

5. Aug 2, 2012

### micromass

I guess that everybody can do the proofs book. It's not very hard.
To do Spivak, I suggest that you already know at least calculus I. So if you had calculus in high school, then you should be fine. You should be comfortable with continuity and derivatives (not necessarily with epsilon delta's, although that would be nice).

For the Lee book, you should be comfortable with a Spivak level book. You should know continuity and sequences very well and rigorously. You don't need to know metric spaces, although that would be nice.

6. Aug 2, 2012

### micromass

I would say that they're about the same level. But Lee only covers topological manifolds, whereas Tu goes into differentiable structures.
The idea of Lee is to give a basis to later go on to his smooth manifolds book and his Riemannian manifolds.

The three books together cover way more ground than Tu. But Tu goes into smoothness faster.

7. Aug 2, 2012