Update, Plan for Diffitopo.

August 16, 2010

I’ve been in the process of moving to New Orleans, so there hasn’t been much updating recently.  In fact, I haven’t been able to do much math at all!  I know, very sad.  I will be posting, next, about some random multivariable topics (primarily those that I need for my placement exam.  ha.) and also beginning to follow the (short, but concise) Topology from the Differentiable Viewpoint by Milnor. 

Lemme just note something quickly about TftDV: it’s an older book, but it comes highly recommended and, as far as I know, is still used relatively frequently as an introduction to the subject.  The problem here is that I learned the subject from a different (and slightly stricter) book; so whereas Milnor talks about manifolds sitting in {\mathbb R}^{m}, I will be talking about maps from the manifold M to {\mathbb R}^{m} explicitly and not assuming the manifold is sitting inside of real space.  

Also note that I am in no way an expert in this field.  Far from it, in fact.  I will be learning along with you!  If I make a careless error, please don’t hesitate to correct me.  In addition, I will most likely be going slightly slower and explaining in more detail many of the topics in the book and simply skipping over or mentioning briefly some of the other topics which I feel are slightly less important or slightly less interesting.  I will also (and this is why I haven’t posted it yet…) be experimenting with scanning pictures that I’ve drawn to illustrate proofs and things, and placing them on this blog.  I don’t have a scanner yet, and I feel that explaining open sets and also manifold mappings and things will be much, much clearer with a picture, so I’ve put it off.

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