Linear algebra next! I know matrices suck sometimes but the field of linear algebra is so interesting
@highviewbarbell
4 ай бұрын
Spivak has a 5-volume set on Differential Geometry that's so beautiful but is way above my current knowledge; though I have the full set. I would love nothing more than to see that field covered
@Math.A-level-student
4 ай бұрын
interesting and inspiring
@ProfessorNoobster
4 ай бұрын
Dang, just when it was getting good, lol.
@virajbansal3509
4 ай бұрын
10:20 I am bit confused on the construction of Sn here. He's talking about creating a set of points in the intersection of U and Qv that have a d(x,U^c) >= 1/n, but U^c is a set. What distance is he referring to here since a point can have a whole range of distances to a set in R^n? Is it implied that we are possibly talking about max(d(x,U^c)) >= 1/n?
@PhDVlog777
4 ай бұрын
For a fixed set A in R^n, and metric d(x,y), the distance function d(x, A) is defined as d(x,A)=inf{ |x-a| : a in A }.
@rogerr4220
4 ай бұрын
11:15 The sets Sn are a nice construction! But I have the following critiques: The fact that the union of Sn equals U intersect Qv is not obvious. (It's contingent on the fact that U is open.) Omitting the proof of this detail might be innocuous. But, it's chained with another lack of clarity in the proof. It's a proof by cases, and each case ends with the conclusion that f(U intersect Qv) is Borel, implicitly. This should be made explicit. Like, why do we care that f(Junk) is Borel? That f(Union Sn) is Borel? That f(Qv) is Borel? That f(0) is Borel? It's because Junk = U intersect Qv.
@rogerr4220
4 ай бұрын
Using dyadic cubes to cover the case that U is a subset of Qv is a fun idea. It's overkill though, because in this situation U intersect Qv is non-empty, and you already covered that case. Well... sparing the possibility that U is empty ;)
@KurtGodel-po3zl
4 ай бұрын
very interesting comment. May I ask, are you a PhD student as well?
@rogerr4220
4 ай бұрын
@@KurtGodel-po3zl Nope, but I've waffled over going back to graduate school for years.
@user-ho8yz2cs3q
4 ай бұрын
Please recommend a good book on functional and measure with solution
@thomasarnoldussen263
4 ай бұрын
The book Measures, Integrals and Martingales by Schilling was an absolute godsend when I took a course in measure theory, solutions to the exercises can easily be found online as well. For functional I'd recommend Linear Functional Analysis by Rynne and Youngson, very friendly in terms of exposition and solutions to exercises are included in the book.
@gabejagnoun2107
2 ай бұрын
As a guy who studied "upper level" undergraduate Engineering math classes, I have no clue why you are speaking Chinese right now!
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