Mathematics - 2021-03-18 (page 1 of 2)

robjohn

00:00

Yeah, I rarely use anything bigger than 24. Let's just toss the rest. Dead weight.

Edward Evans

@LeakyNun wat

Ted Shifrin

How're your 4-leaf clovers doing today, @robjohn?

robjohn

@TedShifrin Not many 4 leaf clovers, but things are pretty good.

robjohn

00:35

However, we just had corned beef and cabbage, with potatoes, and are watching a webinar from UCLA.

Ted Shifrin

00:46

How very American of you!

anakhro

01:09

@TedShifrin quick check: a Mobius transform fixes \infty if and only if it is of the form $\frac{az + b}{cz + d}$ where $c=0$, right?

It's at least sufficient. And I think if c is not zero then infinity has to be mapped to a/c and then yeah, it's a bijection so a/c, etc.

Ted Shifrin

Yup.

You can also think in terms of $GL(2)$.

Wilson

It is fairly intuitive that if I have $f:A\to B$ where A is countable and B uncountable, then $f$ is not onto. How do I prove it though?

Suppose $f: A \to B$ was onto, then why should $A$ be uncountable?

(if B was uncountable)

Edward Evans

@user2103480 normal mag ich keinen Deutschrap aber holy shit hat der's gekillt hahaha youtu.be/QuUO4ZafFwE?t=255

Ted Shifrin

Because an uncountable set is not countable.

Wilson

is that i?

it*?

Ted Shifrin

01:23

The image of a countable set is at most countable.

Wilson

i see, thx

that was dumb question lol

Ted Shifrin

It depends on definitions, tools, etc.

Ryan Unger

tea is a good idea

Ted Shifrin

01:38

When did you last have tea in Fine Hall?

Ryan Unger

01:48

Illegally or legally

legally? march I guess

last march

:(

Ted Shifrin

Well, hopefully, everyone will soon be vaccinated.

Ryan Unger

It'll be some months before regular activities restart, I'm sure

Ted Shifrin

Maybe fall ...

Ryan Unger

and then everyone will travel for the summer

Ted Shifrin

I want air travel to require vaccine proof.

BigSocks

01:56

@TedShifrin I keep hearing stories of people claiming they are a professor/essential something at wallgreens & they are not required proof. they get the vaccine relatively easily. I fear this will make it so people not willing to lie like this will not get it for a long time

Ryan Unger

I am an essential linear algebra grader

BigSocks

lol

I am an essential student

Ryan Unger

balarka is an essential singularity

Ted Shifrin

I hope it will sort out and everyone can get it within a few months. The big issue is all the ignorami who refuse on political grounds.

I have never been essential.

When I got cancer, the department still functioned.

Ryan Unger

are there any essential mathematicians by that criterion

Ted Shifrin

02:01

Probably not.

BigSocks

they have very high connectivity. I guess lots of structures nowadays are like that. I don't think big companies would go under were they to lose their ceo

robjohn

@RyanUnger complex analysts are singularly essential.

Ryan Unger

I thought balarka does applied math now

motion of molecules

robjohn

@TedShifrin I last had tea in Fine Hall in 1985

robjohn

02:51

@RyanUnger I hadn't seen your earlier comment regarding Balarka, so I was confused why Balarka became a subject here. Now I understand.

Ted Shifrin

03:04

I still don't understand.

AMDG

Good evening! Is there a method available in calculus of variations that I can use to find the locus of values for which a given function has zero curvature?

Doesn't have to be calculus of variations, but from what I've understood, that seems to be the best place to look. Otherwise, I want to solve this for the variable $d$: $\operatorname{arcosh}\left(d\cos\left(\frac{\pi x}{2}\right)+1\right)=\operatorname{arcosh}\left(d+1\right)\sqrt{1-x^{2}}$ and that should give me the value I want.

Ted Shifrin

03:23

Nothing with calculus of variations. What are you talking about with curvature of a function?

AMDG

I suppose the function of the osculating circle that best approximates a function at any point (x, f(x))

Ted Shifrin

So you're talking about the curvature of the graph.

AMDG

Sorry, but I don't know what that means.

Ted Shifrin

Patience.

AMDG

Yes, the curvature of the graph

Ted Shifrin

03:26

So you need $f’’(x)=0$.

AMDG

Yeah, but what if you don't have $f(x)$ explicitly, only an equation containing $f(x)$?

Ted Shifrin

Find $f’$ and then $f’’$ by implicit differentiation.

AMDG

I'm trying to solve for the locus of points $d$ where $\cosh\left(2y\sqrt{1-x^{2}}\right)-1=d\cos\left(\frac{x\pi}{2}\right)$ is a constant. Presumably, some constant close to ~1.89009185 satisfies this set of constraints.

Alright, I'll try that.

Ted Shifrin

Where what is a constant ? This makes no sense..

AMDG

err locus of values. My bad.

Well alternatively, I'm looking for the locus of values where the difference of the LHS and RHS is zero.

Ted Shifrin

03:38

That locus is different for every $d$. The problem still doesn't make sense .

What is the precise statement of the question? You brought in curvature from nowhere.

AMDG

Yes, and I'm looking for a particular $d$ which is presumably a constant which makes the difference of the LHS and RHS some constant value with domain $\lbrace-1 \leq x \leq 1\rbrace$.

The idea of curvature comes from the fact that the graph appears to have a curvature of zero for a specific constant value of $d$.

Sayan Chattopadhyay

Hello @TedShifrin

Ted Shifrin

Wait, you’re still saying it wrong .

AMDG

Probably. I'm more of a programmer than a mathematician.

This might help: desmos.com/calculator/bhig7ewyqf

Change $d$ and you'll see what I'm talking about.

Ted Shifrin

Too much crap for me. I think my original advice is right. Solve for the derivative and see if a value of $d$ makes it constant.

Hi Saysn.

AMDG

03:50

Alright

Sayan Chattopadhyay

How are you doing @Ted? How's your health?

dc3rd

ted doesn't like excessive use of algebra and symbols unless absolutely called for.....

Ted Shifrin

Still alive, Saysn.

AMDG

Yeah, well this is all algebra and symbols as far as I'm concerned. lol

Ted Shifrin

Is there a reason this question is of interest, AMDG?

AMDG

03:56

I've been looking for a real-valued, closed form set of trig functions. This appears to be the border of said set of trig functions.

(Which doesn't require complex numbers explicitly)

Ted Shifrin

Makes no sense to me.

Mixing cosh and cos ... shrug

AMDG

I mean if I have a real-valued set of trig functions, then the effort to compute more and more accurate values of them (especially in real time applications) should be less and less than using other existing approximations (in theory at least).

robjohn

@TedShifrin Ryan Unger had said, "are there any essential mathematicians by that criterion" To which I replied, "complex analysts are singularly essential." I had not seen that earlier, Ryan had said, "balarka is an essential singularity", so I'm guessing Ryan thought that I was referring to Balarka when I made my comment, and so he said, "I thought balarka does applied math now"

AMDG

That's the motivation.

Ted Shifrin

Hard to believe anything beats the CORDIC algorithm.

AMDG

04:00

/shrug

Ted Shifrin

Do you know that?

AMDG

I mean if it is available in hardware: great. I don't think I want to implement software CORDIC for arbitrary precision.

Ted Shifrin

It's how computers and calculators compute trig, exponentials, etc. Maybe you should go learn it.

AMDG

Well the idea is to get it into a form where I can get some sufficient level of precision by approximating one or more constants in the function (disregarding any other approximations used to compose the function which might affect the accuracy).

Ted Shifrin

Have fun.

AMDG

04:07

I think I've mentioned it before. If I have a way to compute $a^b$ for real a and real b, then I can approximate $e$ and substitute $a$ for $e$ to compute $e^x$ using $a^b$. I want to apply this in principle to the trig functions.

Though actually $2^x$ would probably have been a better example since we're dealing with floats and base two and computing that is relatively cheap by itself as far as I know, but you get the point I'm sure.

Ted Shifrin

A reasonable computer science person would understand the technology that is already out there.

AMDG

Yes, well most people aren't writing their own standard library functions either.

Ted Shifrin

Doesn’t excuse being ignorant.

AMDG

What, you think I didn't know about CORDIC?

There are times when using a particular software implementation is more convenient than a hardware implementation, especially if it's faster; other times, it's the only option.

FSIN on x87 is microcoded.

(at least on modern ryzen CPUs)

Ted Shifrin

I find you difficult to understand at all. I am certainly no expert on these matters, so I'll leave you to your fun. I only engaged because you used the word curvature.

copper.hat

04:15

it is not clear what you are asking. is this floating point finite bit width computation?

AMDG

That's probably how I'll implement it, though I'm probably going to try using some other formats as well. Whatever is most computationally convenient to work with.

copper.hat

what exactly are you trying to do?

AMDG

Also, the derivatives of both of those equations are not very nice-looking.

copper.hat

do you have a question?

AMDG

Yes, I'm trying to solve for a variable $d$ in the equation $\cosh\left(2y\sqrt{1-x^{2}}\right)-1=d\cos\left(\frac{x\pi}{2}\right)$. Not quite posed in a question, but... yeah.

Specifically for a particular value of $d$ where the difference of the LHS and RHS is zero.

The graph of this function appears to be a constant distance from the x axis for some constant $d$ of around ~1.89009185

And here's my workspace if it's of any use: desmos.com/calculator/uj0sr9k0ew

copper.hat

04:24

ok, that's a change from implementing computations.
are $x,y$ given constants and you are looking for a numerical solution?

AMDG

No, $x$ and $y$ are variables and I'm looking for a value of $d$ which makes the difference of the LHS and RHS zero.

Zero by some constant value for all values of $d$ if that's the correct phrasing.

copper.hat

you lost me.

AMDG

Well if you look at the graph of the equation pictured there and you change the value of $d$, you'll notice there's a point where there appears to be zero curvature on the graph. I'm looking for that specific value.

copper.hat

i am even more lost. ok, i don't want to waste your time. hopefully someone else can assist you.

AMDG

:L

I don't get how what I'm saying isn't clear, honestly.

Ted Shifrin

04:32

Because you keep saying the same nonsense.

AMDG

Well everyone's going to continue to be lost and I'm going to keep saying the same nonsense if no one tells me what isn't clear and why.

Ted Shifrin

The LHS and RHS are equal by definition. You are looking for the value of $d$ for which $y$ is essentially constant.

AMDG

Yes, that's what I've been trying to say.

Ted Shifrin

I already went through this.

AMDG

Yeah, you said to find the implicit derivatives.

Neither of which equation produces a very "friendly", less complicated implicit derivative.

Ted Shifrin

04:34

You keep not understanding that an equation means LHS = RHS.

Nope. This thing is an unmanageable disaster.

AMDG

Yes, I understand what an equation is.

My saying "the difference of both sides" is the same as rearranging the terms so that one side is equal to zero.

robjohn

@AMDG is $d$ the only variable being solved for? If so, then why does division not work?

AMDG

Because that gives me all values of $d$ which satisfy the equation. I only want a subset which is presumed to be a constant.

robjohn

there is one value of $d$ that satisfies the equation. if you want something else, please clarify.

AMDG

I am looking for the value of $d$ for which $y$ is constant.

As Ted said

robjohn

04:55

@AMDG well, you're never going to get $y$ constant, but perhaps you want the first derivative of $y$ with respect to $x$ to be $0$. Are you looking near $x=0$?

AMDG

The graph of the equation suggests there is a set of values where $y$ is constant. I have to say, I'm not entirely sure how finding the derivative of $y$ to be 0 will help me here.

The graph also suggests there are at least two solutions, and of course we can't see the imaginary part of the function, but I started with $f(x) = \cosh\left(\sqrt{1-x^{2}}\right)$ and I ended up eventually at this equation to figure out to determine the point at which this (or some function similar to it) equals $\cos\left(\frac{x\pi}{2}\right)$.

The value of the function at $x=0$ is $y=\frac{\operatorname{arcosh}\left(d+1\right)}{2}$ and one of the solutions to the equation is $\frac{\operatorname{arsinh}\left(\frac{\sqrt{d}\sqrt{\cos\left(\frac{\pi x}{2}\right)}}{\sqrt{2}}\right)}{\sqrt{1-x^{2}}}$.

Given the assumption that $y$ is constant at some point for both of these functions for some value of $d$, I figured I'd try finding the function that yields a constant for $y$ and where both functions have a difference of zero. That gave me the equation $\operatorname{arcosh}\left(d\cos\left(\frac{\pi x}{2}\right)+1\right)=\operatorname{arcosh}\left(d+1\right)\sqrt{1-x^{2}}$.

So, presumably, given the domain $\lbrace -1 \leq x \leq 1 \rbrace$, the difference of their sets of $y$ values is zero.

I would also like to note that at least in the complex domain, $\cosh(\sqrt{1 - x^2}) = \cos(\sqrt{x^2 - 1})$ apparently.

AMDG

05:37

Also, you should be able to get the original function that you found the derivative of if I find the derivative of both sides of an equation and simplify, then integrate the simplified equation, right?

The integral of the sum of two terms is equal to the sum of the integrals of the individual terms, so I figured I'd try it with $\frac{1}{x^{2}+1}=\frac{\arctan\left(x+h\right)-\arctan\left(x\right)}{h}$ by differentiating both sides individually to get more information about $\arctan(x)$.

Didn't quite work after simplifying $-\frac{2x}{\left(x^{2}+1\right)^{2}}=\frac{1}{h\left(\left(x+h\right)^{2}+1\right)}-\frac{1}{h\left(x^{2}+1\right)}$ and then integrating whether the actual resulting function, or integrating both sides individually of which the latter yields $\sqrt{\ln\left(x\right)-\frac{3x^{2}}{2}}=h$, the significance of which only the Tootsie Pop owl can fathom.

Wolgwang

Can someone recommend a number theory book for a beginner who is in high school?

copper.hat

06:21

ask again when the room is a little busier. i am not particularly number theory aware.

Wolgwang

Ohk :-)

StudySmarterNotHarder

07:04

0

Q: How could we encode the Submultigraph Isomorphism problem in terms of the integer factorization problem?

Let $G = (V_G, E_G)$ be an undirected graph, and $H$ be another graph. My goal is to encode the submultigraph isomorphism problem using integer multiplication. For the graph $G$, we encode connectivity as follows. For each edge $\{i,j\} \in G$ choose a unique pair of primes $p_{\varphi(i,j)}, p_...

love_sodam

07:38

0

Q: Chain map between two exact rows

I want to construct the chain map between two exact rows: Let $M$ be an $R$-module and $(A_{\bullet},f_\bullet), (B_\bullet,g_\bullet)$ be a chain complexes where $A_\bullet,B_\bullet$ are $R$-modules (Here, we define $A_{-1} = M = B_{-1}$). If two chains are exact i.e. $\cdots\to A_2\to A_1\to ...

modules homological-algebra

can anyone answer this question?

Benny

09:42

Hi everyone, I've recently asked a well written question that didn't got attention and went down to the unanswered questions graveyard. I hope that this is the place to cheer up my pity question :). It about probability, but the main issue is an integral in $R^3$, I hope that someone can assist. Here it is: math.stackexchange.com/questions/4064768/…

Astyx

10:10

@Benny you want to compute the area of the annulus projected onto the hemisphere

Edward Evans

Hey @Astyx

Astyx

hi

howdy?

Edward Evans

Howdy doody or smth

as murricas would say

how's it going?

Astyx

Can't seem to be able to fix my sleep schedule

But good nonetheless

wby ?

Edward Evans

lol sad

Yeah alright, just got back from having blood taken

the nurse screwed it up so my arm is aching now lmao

Astyx

10:15

Oh damn

I remember getting an injection for something and the nurse completely screwing up and my blood spilling on the table onto my clothes

Edward Evans

oh shiet hahahaha

i had one last year where the (brand new student) nurse missed completely and went straight into muscle and I immediately went white and threw up on her

probably a good experience for her

Astyx

nice

What's the blood taken for?

Edward Evans

yum yum

Astyx

Are you a donor or is it for some test?

Edward Evans

to measure levels of various drugs in my blood lol

i mean like legal ones

Jakobian

10:34

Let $A\subseteq \mathbb{R}^n$ be open and $f:\mathbb{R}^m\to \mathbb{R}^n$ be $\mu$ locally integrable where $\mu$ is a Radon measure.

how do I construct compact continuous functions $\varphi_k:\mathbb{R}^m\to \mathbb{R}^n$ with $|\varphi_k|≤1$ and supports contained in $A$ so that $$\int \varphi_k\cdot f \mathrm{d}\mu \to \int_A |f|\mathrm{d}\mu$$

Benny

@Astyx I honestly don't really understand what does it mean, though I would try to look it up. that question is taken from a past exam on "Introduction to Probabilty" course, where the lecturer is known of throwing at us random questions from Feller's "An Introduction to Probability Theory and Its Applications". he even gave a question that need's to be solved with Markov chains on one of his exams...needless to say, none of us undergraduate CS students know's what is a Markov chain :\

Jakobian

PM 2Ring

@Wolgwang Take a look at Karl-Dieter Crisman's Number Theory: In Context and Interactive. I think it should be very accessible to a motivated above-average high school student. There's a downloadable version, but the online version has lots of examples using SageMathCell

Jakobian

I'll just make a question I guess

Balarka Sen

10:56

@EdwardEvans @Astyx I have encountered the statement "Let $B$ be a quaternion algebra ramified at two places, $p$ and $\infty$ [over $\Bbb Q$]"

What does this mean?

Edward Evans

Quoted from MO question: if $v$ is a place of a field $K$ and $B$ is a quaternion algebra over K either $B_v \cong M_2(K_v)$ or $B_v$ is the unique division algebra over $K_v$. That $B$ is ramified at $v$ means that $B_v$ is the unique division algebra over $K_v$ and not $M_2(K_v)$.

mathoverflow.net/questions/125043/….

Astyx

It's the opposite notion of splitting right?

Edward Evans

also (if you didn't know) a place of a number field is an equivalence class of absolute values

Balarka Sen

I guessed that's the case

Astyx

An algebra M splits over a field K if $M\otimes K$ is a matix algebra

Balarka Sen

11:01

Hmm, so some classification of quaternion algebras over local fields

Astyx

I'm guessing you're taking $K = \Bbb R$ or $\Bbb Q_p$

Balarka Sen

Ya I'm happy with this

Edward Evans

Keith Conrad's answer is cool

Astyx

$\Bbb F_p$, not $\Bbb Q_p$

Edward Evans

why F_p ?

Balarka Sen

11:03

@EdwardEvans Yeah, makes sense

Astyx

You want torsion I think?

Edward Evans

bleh idk

Astyx

No you're right, it's $\Bbb Q_p$

Balarka Sen

Dude what am I reading this is getting out of hand

Astyx

A quaternion algebra is ramified at a finite even number of places

Edward Evans

11:06

I'll teach you all some juicy facts about this stuff at the end of the semester ;)

hahaha

Balarka Sen

Let $B$ be a quaternion algebra ramified at $p$ and $\infty$. Let $R$ be a fixed maximal order in $B$ and $\{I_1, \cdots, I_n\}$ be ideals representing the ideal classes of $R$. Let $I_1 = R$ and $R_i$ be the right order of $I_i$, and let $w_i = |R_i^\times/\{\pm 1\}|$.

Eichler's mass formula states that $\sum_{i = 1}^n 1/w_i = (p - 1)/12$ wtf

I just wanted to understand Ramanujan graphs

What is this pure algebra

Edward Evans

I signed up for the seminar and asked for a talk describing the Brauer group of a local field and the organiser moved me over to a talk whose description is "This is one of the deepest results in algebraic number theory"

didn#t sign up for this shit

I'm just gonna fail and drop out again

Astyx

What's the result?

Edward Evans

Albert-Brauer-Hasse-Noether

Balarka Sen

lol

Edward Evans

11:19

but more importantly it's the fact that the sequence we were talking about is exact

Astyx

Oh yeah

Yeah that's deep

Wolgwang

@PM2Ring Thanks :-)

PM 2Ring

11:42

@Wolgwang No worries. I discovered that site last year, when I was learning how to solve general quadratic Diophantine equations. I quite liked his style, and the interactive Sage stuff, so I decided to go through it as a kind of refresher course. I didn't completely finish it, though. And it looks like he's added a few new things.

Balarka Sen

11:56

this is kind of insane

Astyx

ANT?

Balarka Sen

(1) You can define a zeta function for a graph, called the Ihara zeta function, a la Siegel's zeta function for Riemann surfaces but with prime cycles instead of prime closed geodesics
(2) Sunada observed that Ihara zeta satisfies Riemann hypothesis for a regular graph iff the graph is Ramanujan (very good approximators of regular trees)
(3) Ihara observed that for graphs of the form $\Gamma \backslash PSL_2(\mathbf{Q}_p)/PSL_2(\mathbf{Z}_p)$ for discrete subgroups $\Gamma$ of $\text{PSL}_2(\mathbf{Q}_p)$ aka $p$-adic symmetric spaces, his zeta function is the reciprocal of the Hasse-Weil z…

This is how these nutcases constructed Ramanujan graphs back in the day

Astyx

(5) ???
(6) Profit

Balarka Sen

lol I meant (4) yeah

Edward Evans

lol wtf

Astyx

12:01

Seems pretty straightforward to me

Balarka Sen

imagine constructing graphs using the theory of automorphic forms

over p-adic curves

Astyx

Where are you reading about this?

Balarka Sen

Can't find a proper resource, but this is my impression going back and forth between papers

These are outdated constructions so modern books on Ramanujan graphs do not mention these

But it seems they were already known to Serre-Ihara

But yeah I don't understand, need to read more

Astyx

I feel like I will never understand this stuff

it's killing me

Balarka Sen

Who cares, it's just for fun

Astyx

12:13

Fair enough

It's just maths' the only thing I've ever been good at, and now I realize I'm worthless anyway :p

Edward Evans

relate

Astyx

I guess everyone goes through this at some point

Balarka Sen

yeah lol i get it completely

i also think you're just, like, way better than me at it.

Astyx

no way man

Edward Evans

lma

o

Balarka Sen

12:15

it doesn't matter, my point is none of this really matters

its just for fun

id read novels if i was paid for it

Edward Evans

it's a game

it's puzzles with lots of rules

Balarka Sen

yeah man

Edward Evans

if I win the lottery tomorrow I'm finishing the master in like 20 semesters and then I'm going to study something even more retarded

Balarka Sen

loool

Edward Evans

always wanted to do smth like norse studies

so I'd live the dream

Astyx

12:18

archeology

Balarka Sen

it'll probably never pay as much for you to live the dream

but i get what you mean

i'd study eng. lit. if i could

Astyx

or be the next david attenborough

The dude must have had such an amazing life

Balarka Sen

lol yeah

Edward Evans

Born with one of the coolest voices on earth too

Balarka Sen

imagine going everywhere and just narrating

chill

shoulda done film studies and shot documentaries

apparently tarkovsky spent 5 years or something with a mining crew in sibera and that changed him as a person

Edward Evans

12:20

there's so much cool shit to learn in the world and I'm here classifying made up structures

Balarka Sen

yeah lol

this is what i feel tbh

100%

Astyx

but eTaLe cOhOmOLoGy

Edward Evans

aye

Balarka Sen

math should be a hobby

it was never meant to be an academic discipline

Edward Evans

at least when you start out in a theory the questions are somehow tangible and you could see how they'd be relevant and then a couple of years down the line you're shitting yourself over stuff that means nothing to anyone

Balarka Sen

12:22

do something else as a job, be in a mining expedition in sibera

at night you can do math

Astyx

I'm actually thinking of doing that

Edward Evans

be like Fermat

troll the whole world

Astyx

I'm scared of not having the time to do math then

But that might be a good thing

Edward Evans

yeah idk, I feel comfortable in mathematics

Balarka Sen

@EdwardEvans because math is exponentially growing and now we're doing p-adic solid derived hodge cohomology

Edward Evans

12:23

it's easy to sit tight

hahaha

Balarka Sen

its not a malleable field anymore

mathematicians should step back

@Astyx same

Edward Evans

POV three math students contemplate the relevance of their entire lives

Astyx

gone wrong scared emoji

Balarka Sen

lmao baleeted

Astyx

I follow the Camus approach

If everything is meaningless, there's no meaning in trying to stop it

Balarka Sen

12:28

i read Sisyphus but never related to it

im more a dostoyevskian

but it makes sense that a Frenchman would follow the Camus approach

Astyx

proud marseillaise noises

Balarka Sen

have you read Arthur Rimbaud

he's one of my favorites

love_sodam

is there anyone can answer my problem?

Astyx

Some of it

Balarka Sen

A Season In Hell is his peak i think

PM 2Ring

12:31

I read Camus' L'Étranger in French. I don't think I ever fully recovered. ;)

Balarka Sen

Camus famously said Rimbaud was the only person who was able to surgically remove poetry out of themself; i think he stopped writing poetry at age 21 and then became involved in coal business

never wrote a single piece of poetry again and lived a happy life

Astyx

@PM2Ring It's such a good book

@BalarkaSen I'll read it!

Balarka Sen

age 17-20 he was a complete vagabond

PM 2Ring

It's an excellent, important book. But rather depressing.

Astyx

Much of Camus is depressing

PM 2Ring

12:32

Exactly

Balarka Sen

Astyx

Sartre is such a brat

Balarka Sen

lol yeah

Edward Evans

apparently i'm Kafka

Balarka Sen

never liked him much

Astyx

12:36

lol "probably an insect"

PM 2Ring

Sartre goes to a café and orders an espresso with no cream. The waitress returns, apologising that they are out of cream, and asks if an espresso with no milk would be acceptable.

Balarka Sen

This is some Slavoj Zizek bit rofl

I have heard him say it at some interviews

PM 2Ring

I heard it decades ago, I can't remember where.

Balarka Sen

He also like the "old tale from Slovenia": One day God comes to a Slovenian farmer and tells him he will grant anything that the farmer asks of him, only that he will grant twice that to his neighbor

The farmer says, ok, take one of my eyes out

Astyx

understandable

Edward Evans

12:50

(don't forget the Springer yellow sale)

just had an email about it lmao

Balarka Sen

yeah me too haha

Astyx

What's that?

Edward Evans

Just discounts on Springer textbooks

until 30th of June

discounts are usually pretty substantial though

Jakobian

1

Q: Approximating $f/|f|$ using compactly supported functions.

Let $A\subseteq \mathbb{R}^n$ be open and $f:\mathbb{R}^n\to \mathbb{R}^m$ be $\mu$ locally integrable, where $\mu$ is a Radon measure (on $\mathbb{R}^n$). How to construct compactly supported continuous functions $\varphi_k:\mathbb{R}^n\to\mathbb{R}^m$ with $\text{spt}\varphi_k\subseteq A$ and $...

real-analysis measure-theory

Astyx

still expensive af

Edward Evans

12:52

yeah I only buy books with long names to put on my shelf to impress women

like "Trees"

Astyx

I have a few Springer books I've never read too

Edward Evans

hahaha rel

Astyx

Like "Mathematical methods of Classical Mechanics" by Arnold

Edward Evans

I bought Intro to Cyclotomic Fields but haven't gotten around to reading it yet

can do that together if you wawnt

Astyx

Actually all maths/physics related books of my parents are on my shelf for some reason, and I have not read 90% of them

Edward Evans

12:56

lol

Balarka Sen

@EdwardEvans lol

i dont buy books

Astyx

I borrow them from my russian friend

Balarka Sen

indeed

anakhro

Mathematical methods of CM is pretty good, @Astyx

Astyx

I guess it is, but I never found the motivation to read it

I don't find classical mechanics that interesting any more

anakhro

12:58

Arnold is a little bit idosynchratic in terminology sometimes, but otherwise some great gems in that book (e.g. constructive proof of Darboux's theorem).

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$Mathematics$ Mathematics