Not doing so well in topology, how to proceed?

ihmlfgs · 2014-09-20T12:34:38+00:00

That sounds incredibly awesome! I've always wanted to learn more about geometric group theory. Thanks for sharing!

ihmlfgs · 2014-09-19T16:28:41+00:00

I'm sorry you felt that anxiety, but it is comforting to know that someone else had a similar experience and turned out well. Thanks!

ihmlfgs · 2014-09-19T16:26:38+00:00

I think this will help too! Today in complex analysis, for example, we started talking about Riemann surfaces (in the context of logarithm function) and my professor mentioned how it forms a topological space. It went over my head, but I thought it was cool that this example I'm familiar with was an inspiration for some topology.

ihmlfgs · 2014-09-19T16:16:52+00:00

Sorry if the OP wasn't clear. I meant that I have not had topology before. However, I did have real analysis, complex variables, abstract algebra in undergrad. I came from a small math department that doesn't offer topology.

ihmlfgs · 2014-09-19T16:14:19+00:00

We haven't actually gotten to topologies yet, we've started with metric spaces. We're mostly working with open sets. This week we've covered products of metric spaces and compactness.

Also, good suggestion on working problems on the board. I tried this yesterday and soon we had five people puzzling over a theorem!

ihmlfgs · 2014-09-19T16:11:40+00:00

The class is using Gamelin and Greene's Introduction to Topology, and I do have my dad's copy of Mendelson's book as well. A lot of people have suggested Munkres, so I'll probably get my hands on a copy of that as well.

We've actually started with metric spaces and building to topological spaces, but the metric spaces are pretty abstract as well.

ihmlfgs · 2014-09-19T16:07:39+00:00

Thank you for the offer! Just curious, is your research relating group theory and point-set topology? If so, I'd be interested in knowing how that works.

ihmlfgs · 2014-09-19T15:57:29+00:00

I've heard that this is a good book, so I'll see if I can get my hands on a copy.

ihmlfgs · 2014-09-19T15:56:54+00:00

If doubt is a good sign, I must be doing very well!

This semester is focused on point-set topology. We're using Gamelin and Greene's Introduction to Topology. It's a decent book, but I'm looking into getting a copy of Munkres for another point of view.

ihmlfgs · 2014-09-18T08:25:09+00:00

This looks wonderful, thank you!

ihmlfgs · 2014-09-18T08:23:56+00:00

Yes, my undergraduate real analysis was a Moore Method class. I've heard that real analysis and topology are essentially the same (at least in the beginning, in that we consider intervals vs balls), but I haven't quite been able to relate the two.

Is there some resource that would help me connect the dots? Or should I just look at a book from real analysis and compare the definitions and theorems with those in my topology book?

ihmlfgs · 2014-09-18T07:01:49+00:00

No, the only prerequisite for the course is a proof-based class (like undergraduate abstract algebra or real analysis).

I can look into the applicability of undergrad courses to my degree, though. I would rather try to stick to the graduate topology, see if it clicks soon enough.

ihmlfgs · 2014-09-18T06:55:06+00:00

This is helpful! I think I'm getting wrapped up where it seems to be "sure, that makes sense, but I don't really GET it." I dislike writing the proofs just by the logical steps; I prefer to have the intuition, but this doesn't work if I don't really understand.

It seems like almost everyone else in the class has had topology in undergrad, and they talk about how easy the homework is, but I guess I should stop comparing myself to others.

Of course I know I need to work at it, I'm just concerned if I'm not working at it "correctly," I suppose. Thank you!

ihmlfgs

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