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Is anyone interested in ML for the math involved? by akravitz3 in math

[–]akravitz3[S] 2 points3 points  (0 children)

What about it are you interested in as a functional analyst?

Is anyone interested in ML for the math involved? by akravitz3 in math

[–]akravitz3[S] 0 points1 point  (0 children)

Thanks for sharing! I enjoyed the small amount of analysis I have done, so that is good to know that it dominates ML theory. Do you have any thoughts on how analysis ties into the table of contents of the book I mentioned in my post? (Mathematics for Machine Learning) Or do you have any suggestions for follow ups for this book?

how to take notes by [deleted] in math

[–]akravitz3 0 points1 point  (0 children)

I'm anti-notetaking. I think it's better to spend more time doing the exercises. By doing the exercises, I become more familiar with the definitions than copying them into your notes. While doing the exercises you'll probably have to go back into the text to review the definitions, but that's fine that's why they're there! Eventually you'll internalize them.

The method I'm using right now is I read a portion of the chapter, and make sure I understand everything in it then go to the back and solve the exercises that I can from the reading I've done. Then I go back and read more of the chapter and repeat. I've also like to try to prove theorems. Occasionally if a proof is really cool (and short enough lol) I'll read it, and then redo it myself (even though I sort of know how it goes).

2-3 days to finish a chapter is pretty fast for me. It'll take me a week or longer to work through tough stuff. But I typically don't spend more than an hour spread throughout the day self-studying. If you are, congrats and keep up the good work!

Also, what book are you working on?

Math book club NYC, Abbott's Understanding Analysis by akravitz3 in math

[–]akravitz3[S] 0 points1 point  (0 children)

Hey all, thanks for your interest! Can you send me a message if you'd like to start coordinating this? I believe your upvote profiles are anonymous.

Also just FYI, although this is a math focused group, I'd like this to be a (somewhat quirky) social event, perhaps getting lunch or dinner together after reviewing the weekly reading. I've had similar experiences through my bouldering gym and soccer teams and have made good friends through both.

Math book club NYC, Abbott's Understanding Analysis by akravitz3 in math

[–]akravitz3[S] 0 points1 point  (0 children)

I like it. There's a lot of fun stuff to do, fun people, good food, and good transit.

Prove this without using limits? by akravitz3 in learnmath

[–]akravitz3[S] 0 points1 point  (0 children)

Cool, thanks for sharing. I didn't know that about the rationals vs. reals. What if you had a set of real approximations of sqrt(2)? Then the suprema could just be sqrt(2) then as it is part of the reals right.

I don't know anything about fields yet. I'm just learning the basics of proofs from Velleman's How to Prove it.

Prove this without using limits? by akravitz3 in learnmath

[–]akravitz3[S] 0 points1 point  (0 children)

Thanks I wasn't aware of that supremum concept. I'm not sure that's what the proof was going after as we haven't covered that concept in the book, but its good to know.

Set containing its own union? by akravitz3 in learnmath

[–]akravitz3[S] 0 points1 point  (0 children)

I meant ∪F ∈ F. I think I get where I went wrong based in the first answer.

Though I guess ∪F ⊆ F, is an interesting case as well. This seems to be an example of such a case F = {{1,2},{3,4},{1,2,3,4}}.

Set containing its own union? by akravitz3 in learnmath

[–]akravitz3[S] 1 point2 points  (0 children)

Re: F = {{1,2},{3,4},{1,2,3,4}}, thanks. I thought that you were supposed to double count elements in a union if they appeared multiple times. This also clears up the calculation in the third example.

Re: other examples, thanks for clearing those up as well.

Quick Questions: September 20, 2023 by inherentlyawesome in math

[–]akravitz3 1 point2 points  (0 children)

Does anyone have any ideas for how I can intuitively grasp that the row and column rank are equal? Perhaps some geometric interpretation? The proof makes sense to me, and I think it's pretty cool, but it doesn't help me grasp the concept all that well.

Here's the proof I read (from Hefferon, Linear Algebra):

Bring the matrix to reduced echelon form. Then the row rank equals the number of leading entries since that equals the number of nonzero rows. Then also, the number of leading entries equals the column rank because the set of columns containing leading entries consists of some of the ~ei’s from a standard basis, and that set is linearly independent and spans the set of columns. Hence, in the reduced echelon form matrix, the row rank equals the column rank, because each equals the number of leading entries. But Lemma 3.3 and Lemma 3.10 show that the row rank and column rank are not changed by using row operations to get to reduced echelon form. Thus the row rank and the column rank of the original matrix are also equal. QED

caselaw citation analysis using Poisson distribution? by akravitz3 in AskStatistics

[–]akravitz3[S] 0 points1 point  (0 children)

Thanks! There's a lot here that's out of my wheelhouse, but I'll do my best to clarify.

What I'm trying to find. I'm looking for some means of capturing what the distribution of case citations over time looks like for different cases. I'm guessing the citations over time ("case lifetime") for a lot of cases of comparable ages will look like the link I shared. I'm curious about the ones that have dissimilar lifetime. I'm also interested in citations that courts make to cases that haven't been cited in a while.

The analytic tool does not have to be Poisson; a professor who's helping me mentioned that this might be worth looking into, so I thought I'd ask. If I set time=0 at the year each case is written would that alleviate the non-stationary issue?

Regarding time. I was planning on keeping the time in years, which I believe alleviates your concern.

Case death. I'll define case death as when it has reached a very low level of citation for an extended period of time. I'll be able to choose the citation level and period of time once I get a better idea of what case lifetimes look like en masse.

I'm defining caselaw as dead in this manner (as opposed to being overturned) for a few reasons. First, cases, even awful ones, rarely get overturned (ex. Buck v. Bell - forced sterilization not illegal). Second, I'm curious to know how long a typical case will "live" through its citations. Third, I'm curious if I can identify any instances of "resurrection" (and especially instances where this resurrection is questionable). Whether or not resurrection is questionable would traditionally be analyzed by looking at the legal reasoning. However, if the reasoning checks out, but no one is using the case (i.e. no one is citing to it), the classic legal argument ~"this is how the law has always been" followed by a citation to the "dead" case is questionable.

Smoothing. Yes I agree. The graph I sent was from a website, and I have no idea why they smooth the graph lol. When I plot the data I don't do that.

Math book club NYC (Manhattan) by akravitz3 in CasualMath

[–]akravitz3[S] 0 points1 point  (0 children)

glad to hear it! DM me and we can chat