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Analysis self-study

Anonymous Thu 07 May 06:19:17 2020 No.11645639 View Reply Original Report

Quoted By: >>11645645 >>11645661 >>11645700 >>11645747 >>11645766

Anyone know any online resources for studying topology? I can't find any online, with the exception of a few old textbooks.

Anonymous

Anonymous Thu 07 May 2020 06:20:57 No.11645644 Report

Quoted By:

I now realize that I labeled this as "Analysis self- study." whoops. I meant topology, although posting analysis stuff is fine, i guess

Anonymous

Anonymous Thu 07 May 2020 06:21:05 No.11645645 Report

Quoted By: >>11645652 >>11645659

>>11645639
What's that cute little peach all about in the bottom middle

Anonymous

Anonymous Thu 07 May 2020 06:23:34 No.11645652 Report

Quoted By:

>>11645645
it's the self-intersection of a one-sided surface

Anonymous

Anonymous Thu 07 May 2020 06:25:16 No.11645659 Report

Quoted By:

>>11645645
It's called a cross-cap. Because the cross-cap is on a sphere, this specific manifold is a real protective plane

Anonymous

Anonymous Thu 07 May 2020 06:25:26 No.11645661 Report

Quoted By: >>11645673 >>11645681

>>11645639
not being sarcastic, skip topology and learn it as you go in an applied area. keep something like munkres (on libgen) on hand for reference.

there are only a few definitions you should know ahead of time that are shared in all applications, namely connectedness, compactness, (maybe) perfectness, and the basic definitions like open/closed, limit points and so on.

other than that, pick a topic which is topological in nature with extra structure, and learn as you need it. e.g. schemes, manifolds, or logical structures like stone spaces, and the like.

Anonymous

Anonymous Thu 07 May 2020 06:29:04 No.11645671 Report

Quoted By:

that being said, the reason it says cross surface in the picture is because John Conway liked that name, and John Conway is cool, i guess. More often in topology that's called a cross surface, but in projective geometry we call it a real projective plane, as long as you have an affine structure.

Anonymous

Anonymous Thu 07 May 2020 06:31:32 No.11645673 Report

Quoted By: >>11645676

>>11645661
Thanks, I will write the textbook name down.
What applied areas are you referring to? I don't know that many places that use topology

Anonymous

Anonymous Thu 07 May 2020 06:32:43 No.11645676 Report

Quoted By:

>>11645673
never mind, i'm an idiot, I didn't pay enough attention to the whole post

Anonymous

Anonymous Thu 07 May 2020 06:34:43 No.11645681 Report

Quoted By: >>11645689 >>11646839

>>11645661
I suppose a better question might be:
What should I use to study manifolds if I'm going to be learning topology from them?

Anonymous

Anonymous Thu 07 May 2020 06:40:48 No.11645689 Report

Quoted By: >>11646839

>>11645681
everyone loves de cormo, i think it's just ok. it's best for rigid low-dimensional geometry. my fav is "An Introductory Course on Differentiable Manifolds" by shashahani. lee is also good for riemannian geometry. but, I honestly felt the shashahani was the best organized and is the most at the "topological" level.

Anonymous

Anonymous Thu 07 May 2020 06:45:29 No.11645700 Report

Quoted By: >>11645720 >>11645726

>>11645639
do you have a reason why you don't want books ? if it's only because you don't want to pay for them, this can be fixed...

Anonymous

Anonymous Thu 07 May 2020 06:50:55 No.11645720 Report

Quoted By: >>11645751

>>11645700
I'm a high school freshman, so I don't have a professor to teach me anything. Therefore, I am trying to find a Khan academy-esque program for topology/manifolds

Anonymous

Anonymous Thu 07 May 2020 06:53:07 No.11645726 Report

Quoted By:

>>11645700
Also, I'm fine with books, but once again, it's harder to learn from books than from video, at least for me.

Anonymous

Anonymous Thu 07 May 2020 07:04:59 No.11645747 Report

Quoted By: >>11645790

>>11645639
nlab is infamous for being loaded with heavily abstract and autistic infinity category theory but their page Introduction to topology 1 is fine and needs barely any prerequisites

Anonymous

Anonymous Thu 07 May 2020 07:06:16 No.11645751 Report

Quoted By:

>>11645720
read the shape of space by weeks, you're gonna love this. you can find it (and any other math book) on libgen.

Anonymous

Anonymous Thu 07 May 2020 07:12:55 No.11645766 Report

Quoted By:

>>11645639
maybe theres something interesting for you : )

http s://ocw.mit.edu/courses/find-by-topic/#cat=mathematics&subcat=topologyandgeometry

Anonymous

Anonymous Thu 07 May 2020 07:23:48 No.11645790 Report

Quoted By:

>>11645747

at least i dont have to worry about the fking hausdorff dimension anymore. i take my spectra any day of the week

Anonymous

Anonymous Thu 07 May 2020 16:07:46 No.11646839 Report

Quoted By:

>>11645681
>>11645689
omg forgot about this absolutely fantastic youtube series on manifolds

https://www.youtube.com/watch?v=7G4SqIboeig

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