Study groups for calculus and topology

[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 each other 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.

 

[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!

 

[Number Nine]

Introduction to topological manifolds by Lee

Outstanding. A sorely underrated book.

 

[genericusrnme]

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

 

[micromass]

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!

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.

 

[micromass]

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

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.

 

[ADCooper]

Wish I had seen this at the beginning of Summer, really wanted to do something like this, but now with the semester starting in a few weeks I feel like I'll quit too fast due to classes to make it worth it. Quick aside: is Spivak's book worth getting into having finished an entire calculus sequence already? We used Stewart for 1-2, Rogawski for 3, and then Boyce/DiPrima for Diff EQ (Its normally considered Calc 4 I've heard?). None of those seemed remotely rigorous though.

 

[genericusrnme]

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.

In that case I'll have to give this study group a miss since I'm just finishing Tus book right now.
I may be interested in future study groups however so I'll keep an eye out

Wish I had seen this at the beginning of Summer, really wanted to do something like this, but now with the semester starting in a few weeks I feel like I'll quit too fast due to classes to make it worth it. Quick aside: is Spivak's book worth getting into having finished an entire calculus sequence already? We used Stewart for 1-2, Rogawski for 3, and then Boyce/DiPrima for Diff EQ (Its normally considered Calc 4 I've heard?). None of those seemed remotely rigorous though.

Spivak will get you ready for analysis-y material, if you haven't done any rigorous calculus yet, spivak is a good place to start!