Mathematics - 2020-12-16 (page 3 of 3)

user2103480

23:00

I mean, what do you want to do anyways @Thorgott?

If you're not lucky with the academic track you'll probably end up somewhere that's superficially statistics, so at least you can say you have a basic understanding of that

and else, measure theory is good for the basics of functional analysis, from where you can quickly move to operator algebras

John_Krampf

@user2103480 I agree with this a lot.

Mike Miller

on the opposite spectrum i have done plenty of PDE and only ever, ever, cite the basic measure theory stuff if i really need to use dominated convergence or whatever.

user2103480

@John_Krampf yep, and if one doesn't have a tenure track position, then studying some additional math topic can be pretty tiresome

damn there's a spider on the ceiling and my gf is sleeping

How shall I kill it

Mike Miller

pick it up, set it in her hand, and squeeze her hand so that she crushes it for you

user2103480

throwing a cushion, which es effectuve against many bugs, will probably end up in me chasing it over the ground

Mike Miller

23:04

to pick it up you may need to buy a stepladder

spiders are your friends anyway you just dont know it yet

user2103480

@MikeMiller invaders must die

It would eat me if it could

Also, the risk of it crawling back and scaring her is greater than the cost of terminating it

Mike Miller

@user2103480 while this is admittedly a traditional german view of foreign entities i have to say that did not pan out well for your people, historically speaking

user2103480

I think people here view me as more german than I actually am

Edward Evans

what

user2103480

the only "pure" german part is my mother's father; her mother was of ukrainian descent. Admittedly of german descent, but she didn't look very german. More eastern.

I literally have a nazi document from my grandmother who fled to germany in WW2. They categorized her as a "class 4 human german", which is like a retarded german to them

Edward Evans

23:16

jeeeeesus

Class 4 Human German

that's so

national socialist

user2103480

Class 5 would have been rejection and, possibly, death

Mike Miller

sorry if i poked a sore spot --- obviously it's a very serious matter and i don't mean to suggest you have anywhere near comparable opinions

user2103480

And from my father's side I'm palestinian

nono don't be

Edward Evans

why do convos with you always end up being about nazis

Mike Miller

@EdwardEvans HMMMMM

user2103480

23:16

I don't assume ill intent hahaha

Edward Evans

hMmMmMm

Mike Miller

still i get your point

can you say anything about the random variable X_1 + ... + X_n where X_i are iid uniform distributions

Lucas Henrique

hey c[h]at

lol

Mike Miller

I liked hey cat more

Edward Evans

@user2103480 The grandparents of a friend have a NS salad bowl from their Gauleiter or smth that they were gifted on their wedding day

user2103480

23:18

@MikeMiller random walk, martingale, CLT, but I don't know whether there's a nice and easy distribution

Lucas Henrique

how are you doing @Mike?

Thorgott

Irwin–Hall distribution

In probability and statistics, the Irwin–Hall distribution, named after Joseph Oscar Irwin and Philip Hall, is a probability distribution for a random variable defined as the sum of a number of independent random variables, each having a uniform distribution. For this reason it is also known as the uniform sum distribution. The generation of pseudo-random numbers having an approximately normal distribution is sometimes accomplished by computing the sum of a number of pseudo-random numbers having a uniform distribution; usually for the sake of simplicity of programming. Rescaling the Irwin–Hall...

Mike Miller

oh i see the point lol

i see a puzzle today that asks me to work out the number of dice so that rolling a sum of 521 has the same probability as rolling a 200

user2103480

I think it's a nasty convolution

Mike Miller

but the point is that it's symmetric and peaks in the middle

Thorgott

23:19

@user2103480 we actually dont have analysis 3 here, instead its two small lectures, one is measure and integration theory, the other is complex analysis and ODEs

Mike Miller

@LucasHenrique tired

Thorgott

but we already did basic measure theory up to caratheodory at the end of analysis 2

user2103480

@Thorgott Ah really? We had differential forms and integration

Lucas Henrique

hey @Thorgott! didn't know you were around

user2103480

for submanifolds of R^n

Thorgott

23:20

yeah, I heard some profs do differential forms in measure and integration theory, but I only learned them once I took a course on manifolds

we just did integration on submanifolds of R^n "by hand"

hey Lucas

Mike Miller

here differential forms on R^n are covered in the second analysis class

Lucas Henrique

guys, I'm reading about algebras and I'm a bit confused because it seems that every algebraist has a different def on what an algebra is

Thorgott

it's just that I don't think I've integrated a single function that hasn't been smooth ever since I finished measure theory

guess that's what happens when you decide to work with nice spaces

Karim Mansour

it is covered by royden measure theory @Thorgott

user2103480

tbh it wasn't as much a point as an anecdote, but at least I can safely say I'm pretty detached from *that* german part. Especially since my german grandfather died before I was born

But don't let that deter you from edgy jokes, I'm really not sensitive when it comes from people who grasp the scope of what actually happened

Lucas Henrique

23:22

I'm trying to define it in the most general way - $A$-module, $A$ may not be unital and the product over $M$ is may not be associative

Karim Mansour

sorry not Royden but folland

Thorgott

Folland is a great book

Lucas Henrique

I mean, I think it's fair to assume that $A$ is unital and commutative

user2103480

@Thorgott that is way better anyways

Karim Mansour

Yeah Folland is a great book

I always have it on my shelf

Mike Miller

23:23

@user2103480 Right, I understood the moment you said you were eastern european, I think most aren't aware how horrifying and successful GPO was

Thorgott

I really should read the remaining chapters

it's the book I learned most of the little Fourier theory I know from

Karim Mansour

yeah his later chapters are great especially Hausdorff measures

user2103480

@Thorgott polish spaces are nice spaces

Thorgott

@Lucas have you ever seen an algebra that isn't associative

Mike Miller

@LucasHenrique I think in real life everything is associative, in some people's real life you have non-commutative things but usually not non-unital things unless you are in specialized circumstances

I would be surprised to see a theory developed for non-associative algebras

Thorgott

23:24

@user2103480 I once calculated that convolution by hand for like n=4

will never get back the time I wasted on that

Lucas Henrique

@Thorgott nope. but my advisor works with lie and jordan algebras which aren't, apparently

user2103480

@Thorgott this

Mike Miller

Oh, but I would just define those each by hand Lucas

I think of Lie algebras and associative algebras as just... different

and a Jordan algebra is rather strange and specialized

Karim Mansour

I don't want to ever touch non-associative things

Lucas Henrique

hmm, ok

Thorgott

23:26

ok fair, Lie algebras aren't associative, but they're not really algebras in the classical sense

I don't think you will come up with a unifying definition that encompasses both Lie algebras and k-algebras without making it so broad that it's useless

Mike Miller

I've gotta agree on that one

Thorgott

Lie algebras obey a rather specific set of axioms that's very different

Mike Miller

I think when you get to that level of generality you probably want to invent operads

user2103480

@MikeMiller or stop

Thorgott

of course, there's a relationship between them

Mike Miller

23:27

well I would stop before I get to that level of generality

Thorgott

every associative algebra gives rise to a Lie algebra

Karim Mansour

the only intuition I get from non-associative things is what I call non-associative rectangle in 4d space x(yz) has different area than (xy)z in that 4 dimensional rectangle.

Alessandro Codenotti

@MikeMiller How's your cat by the way

Mike Miller

ah jeez

user2103480

@AlessandroCodenotti the important stuff

Karim Mansour

23:28

rectangle not cube

Mike Miller

He and my girlfriend's cat didn't get along, we tried for 2-3 months and no matter what method we tried they always ended up fighting

Thorgott

@Mike LaWvErE tHeOrY

Lucas Henrique

so let's assume associative product. bla bla bla. $(M, A, \lambda)$ is a $A$-algebra if $M$ is a ring and $\lambda\colon A \to M$ is an homomorphism such that $\mathrm{im}\ \lambda \subseteq Z(M)$

would that be it?

Mike Miller

He now lives happily in a friend's house where he can clamber around

Thorgott

yup, I like that definition

Alessandro Codenotti

23:28

@user2103480 Last time I heard Mike talk about the cat it had stolen a chicken wing from him

Mike Miller

@LucasHenrique That works

Alessandro Codenotti

He argued that the cat deserved it after the successful heist iirc

Mike Miller

It's true

Alessandro Codenotti

@MikeMiller I see, that's a good ending

Karim Mansour

anyway back to work

Mike Miller

23:29

It took us a long time to find him a home but I am glad we did

user2103480

@AlessandroCodenotti understandable

Mike Miller

Her cat is great too, whenever it's dinner time we make him jump or stretch to get the scoop I hold the food in before feeding him

oftentime he has to think about strategy before he can reach it

it's very cute to watch the struggle

Alessandro Codenotti

Sounds like a smart cat though

My flatmate in Bonn had two cats and one was dumb as a brick

Very cuddly, cute, affectionate and whatnot, but still very dumb

John_Krampf

@AlessandroCodenotti sometimes dumb just means you have priorities in order, instead of wasting your 20s in grad school

Mike Miller

I'd definitely be in better mental shape if I sat in a pineapple home and ate kibble instead of going to grad school

user2103480

23:34

@John_Krampf It wasted its time with someone wasting their 20's in grad school

John_Krampf

@user2103480 the cat was happy though

user2103480

@John_Krampf maybe just not enough computation power to realize that there are better options!

John_Krampf

@user2103480 i.e. contentment!

user2103480

fair point

user91411

anybody here ?

copper.hat

23:58

no

John_Krampf

@user91411 hello

copper.hat

time for me to pretend to run. apparently i need a hip replaced but am currently too scared to do it.

Transcript for

$Mathematics$ Mathematics