ℝolliℵg M∀th Thr∑a∂

RIP

My "aha" moment in getting the Kalman filter was when deriving a simple version of it myself as a special case of the Bayes theorem, iirc.

can you show us?

Proof is left to the readers.

The proof is obvious

Or is it?

*leaves thread*

*time passes*

Yes, it's obvious

Been a long time, I'll see if I can reproduce the aha. :-)

https://twitter.com/AnalysisFact

http://www.johndcook.com/blog/twitter_page/

Euler buy this for your wife for xmas ;-) http://r4ds.had.co.nz/introduction-1.html

looks good!

Still pondering making a mod request to delete my miscalculation of the first few Catalan numbers.

FYI Artificial intelligence still has some way to go

https://www.youtube.com/watch?v=b0HzWMqLeiE

In a lecture that started talking about https://en.m.wikipedia.org/wiki/Classical_Wiener_space#Classical_Wiener_measure

And finding it very hard not to bust out giggling

hope you don't run into Tits groups then

Nah this is way funnier

I asked unthread for a readable analysis book and I chanced upon a pretty good one somehow. I'm reading Abbott, Understanding Analysis just for comprehension and it's going pretty well, in that a bunch of half-remembered things from high school math suddenly seem important in light of the careful construction of R and proofs about sequences and limits. On to continuity.

yeah, i had high school math flashbacks when i took intro analysis. "wait, haven't i done this before? oh wait, it all fits together."

Makes me wish they just taught me Analysis in 9th and 10th grade, it would have all seemed less directionless.

I have a question re: the hairy ball theorem.

We know that combing the hairs on one ball flat will leave at least one tuft of hair sticking out unable to be flattened. But what about two hairy balls that are touching? Can we perform a smooth combing over them?

i hate podcasts but this is good imo

http://www.csbookclub.com/

crüt: depends what you mean by "touching" and how you define a vector field on the resulting space.

If by touching you mean, cut a hole in each ball and glue them together along the boundary, then the resulting surface is still a sphere so the hairy ball theorem still applies

If by touching you mean identified at a single point, then it gets a bit tricky.

You can comb each ball in the following way, such that they have only one "pole" or cowlick:

https://upload.wikimedia.org/wikipedia/commons/6/6e/Hairy_ball_one_pole_animated.gif

then you can identify the pole on each ball. The resulting space is no longer a manifold, so the question then becomes, how do you define a tangent vector at that point (the wedge)?

One possibility is to just ignore the "bad point", the complement of which *is* a manifold. If you mean that, then by construction (taking a vector field on each sphere whose only zero is at the bad point), you do indeed get a non-vanishing vector field.

On the other hand: if the two spheres are touching tangentially, then the tangent planes to the two spheres at the bad point line up, so we can still talk about a tangent vector at that point, and so it still makes sense to talk about a vector field on the whole thing.

OK i have a math question. something I should know how to do and surely learned at some pt at school but I forgot and I don't know what topic to look up

Let's say you have a function F from integers between 1 and 100 to R. generally a well-behaved function but locally can get spiky

I want to approximate it by a function G that is

1) as similar to F as possible
2) as smooth as possible
3) integrates to the same value as F: G(1) + G(2) + ... + G(100) = F(1) + F(2) + ... + F(100)

I know we did this stuff in Numerical Analysis and had to write Matlab scripts that did this sort of thing all the time. Condition (3) is straightforward, but (1) and (2) seem to be in tension; maybe I have to minimize some loss function of MSE and some measure of spikiness?

This seems as good a place as any to mention that Don Knuth has announced his experimental work for pipe organ.

http://www-cs-faculty.stanford.edu/~uno/fant.html

flopson: maximum entropy seems like one tack to take? http://www.lacan.upc.edu/arroyo/Site1/Research/Entries/2012/9/12_Maximum_entropy_approximation.html

let me restate to be sure i understand tho -- "i have an assignment of the integers from 1 to 100 to 100 respective values in R. i would like to make a new assignment of the same form N_[1-100] -> R, but with the condition that the sum of values in the codomain agree with the prior one, and with some sort of smoothing applied."

If that's correct, yeah, you need to decide the tradeoff yr willing to make, towards what end, between similarity and smoothness. i mean a lazy and decent thing to do is just to take some sort of quadratic or cubic interpolation on the points, then "bump" it into shape with a second pass that makes the sum tie out while minimizing MSE as you describe.

that's correct. looking for something simple and quick

friend linked me to: https://en.wikipedia.org/wiki/Mollifier

neat!

was led by this tweet

https://twitter.com/sigfpe/status/811704836622159872

to this book:

https://arxiv.org/abs/1612.06373

wiki:

In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it on the floor, and flattening it.

lol, awesome

You mean like orbifolds?

<3 sigfpe

https://en.wikipedia.org/wiki/Cox%E2%80%93Zucker_machine

Man if I had endless time I would read that Ghys book linked above

otm

why need endless time? do you read novels in your spare time? think of it as one of those!

maybe you can read math books at the same speed as you do novels, not me

why does it have to be at the same speed?

at one point in my life I had the habit of reading a page of Hilbert's Geometry and the Imagination a day. I never finished it but it doesn't matter; it was a blast

:)

https://sites.tufts.edu/gerrymandr/

"A 5-day summer school will be offered at Tufts University from August 7-11, 2017, with the principal purpose of training mathematicians to be expert witnesses for court cases on redistricting and gerrymandering."

that's hot. I wish I could audit that

Is there in iPhone app that I can use to solve or graph or factor algebraic equations? Basically do what my old TI-89 could do back in my high school days, (except in color obv.)?

love to read stats bantz http://davegiles.blogspot.com/2011/09/micronumerosity.html

asically do what my old TI-89 could do back in my high school days, (except in color obv.)?

this is a betrayal