serious-discussion

[mint canopy]

Just mute it ✨

Muting channels is self-care ✨

You don't have to participate™️ in the discourse™️

[maiden bear]

there are some good convos

for example the one ryc started to end another bad discussion yesterday

[surreal sapphire]

lets start bad conversations, so ryc can come and save us

[fading tusk]

same

[plucky verge]

is there a stochastic processes channel in this server

[surreal sapphire]

#advanced-probability

[plucky verge]

ok thanks

[sacred arch]

I was playing around with phi based numbers just for fun and while they're obviously utterly pointless they're actually quite fun to play with

[jolly junco]

Curious if you all think it would be worth taking a calculus 2 course? At my uni in order to sign up for a probability theory course the prerequisites are Calc 2, Multivariable calc 1 and 2, and ordinary differential equations. I was thinking that learning about probability theory might be interesting because then it would give me a foundational understanding of when to apply different statistical techniques in the sciences and when and help me understand statistical techniques in scientific/sociological journal articles better but I'm not sure if it's worth it. thoughts?

[bright hill]

Not to sound elitist but it's always decent when it's mostly the core community

[fading tusk]

are u core?

are u in the kernel sir?

[bright hill]

Or at least a couple that're capable of guiding the conversation

[mint canopy]

I do agree, but it's usually not the core community that speaks there

Which ironically makes #serious-discussion far less annoying lmao

[manic ginkgo]

Hmm what happened? The last few times I checked it didn’t seem particularly bad

[bright hill]

a LOT of low quality content

sooo many cranks

• the occasional homophobes or trolls but those aren't new and are dealt with quickly so they're not much of problem

[manic ginkgo]

ah I see

I guess I've been lucky so far on the times I checked in there

[open aspen]

But then #serious-discussion is either #math-discussion -2 or empty

And when it's math discussion 2 it's not very accessible to most users

Which is like, whatever, but it's not really a replacement for casual conversation

And #chill is just a hellscape

Or it's meta I guess to cover the current topic I guess lmao

[mint canopy]

empty isn't necessarily a bad thing tbh

It means you can actually have conversations

Oh yourself. Look at the last few messages! It's remarkable that this discussion point has continued for so long, with the topic remaining so consistent

[open aspen]

No that wasn't a sarcastic so true

It was a genuine so true

I don't know how to use emojis I'm a geezer in a 22 year olds body

[mint canopy]

Shockingly similar to me! I just read most of the emojis here as sarcastic 😔

[manic ginkgo]

I guess I'm a bit more naïve but I always take them at face value

mostly because I despise it when they're used sarcastically

[mint canopy]

I find it harder to read emojis like or

The 🤔 emoji is already so dripping with sarcasm...

Or criticism, idk

[manic ginkgo]

Hmm dunno I would use it for when I really didn't get something or not sure

[severe swallow]

I have not opened overleaf in like 2 months, but I wanna know who tf thought it was a good idea to remove the button from that corner that allowed you to comfortably switch between code+pdf and pdf instantly

[manic ginkgo]

I've found vscode with the latex workshop plugin works pretty well for that kind of thing btw, if you don't really need the collab features of overleaf

[severe swallow]

no idea what that is, also I do need my supervisors to be able to see the file at some point

[manic ginkgo]

are you comfortable with coding? have you used git or some other VCS before?

[severe swallow]

lets just say I can code, but I'm terrible with Computer stuff in general if that makes any sense

[fading tusk]

is vcs a version control system?

[manic ginkgo]

vscode is a text editor: https://code.visualstudio.com/

[manic ginkgo]

yep

[fading tusk]

it lets u control versions of ur project?

[manic ginkgo]

yeah, you can commit and rollback changes at any time so you don't lose any progress

[manic ginkgo]

latex workshop is a plugin for vs code that lets you work with latex files and generate pdfs: https://marketplace.visualstudio.com/items?itemName=James-Yu.latex-workshop

there's some setup involved depending on your machine

but the result is that I can run a command that generates the pdf and let's me view them both side by side in different panes

[severe swallow]

also, I just found the solution to this, I just need to click on layout and then I can easily switch perspective

[fading tusk]

nice workflow sir

[manic ginkgo]

and if you use a vcs for your local repo - you can undo and replay changes at any time

similar concept as overleaf but it's all on your machine

[fading tusk]

how often do u push ?

u use git?

u add repo to a github or gitlab sort of thing?

or just local

[severe swallow]

I feel like this is slightly overkill, but it does become practical for backups and for the rare cases where I have no internet and need to work on my projects

[manic ginkgo]

yeah, I use github. Generally I push on every commit

[fading tusk]

and how often u commit

[manic ginkgo]

dunno, really depends - anytime I think I've done some significant changes

[manic ginkgo]

yeah there's some setup cost but then you get full control and can use it for any other project really

[fading tusk]

u can make private repos?

for free?

[severe swallow]

I'll consider it, thx for the suggestion

[manic ginkgo]

yeah github has unlimited free private repos since it got acquired by microsoft in the last couple of years or something

[fading tusk]

are u both chess experts?

oh I see, glad microsoft is improving it

[mint canopy]

I am an expert on losing chess games to people who aren't that good at chess, yes 😎

[fading tusk]

I heard there was a lot of drama 😦

[mint canopy]

Chess has had some funny things happen lately

[manic ginkgo]

aye, same here

[mint canopy]

Lmao high five

[teal lion]

Yoooooo

Grandmaster Shadow Morgue

[manic ginkgo]

I have some friends really into chess so I just tag along for the social part - but I just can't be bothered to really get good at it

[teal lion]

Don’t cut yourself on that edge

[manic ginkgo]

huh?

[teal lion]

I’m making a joke about the edgy username, think nothing of it

[manic ginkgo]

ah I see lol. been a while since someone's pointed it out

well I was 12 and needed a cool gamer name so here we are

I'm too set in my ways to change it now

[teal lion]

Cool

[fading tusk]

how is it edgy name

[teal lion]

I have this username because most people don’t like Serge Lang for some reason, and I’m here to change their minds

Hopefully, by the time I start college I’ll have all my math books finished

[manic ginkgo]

heh, is it that guy who's infamous for leaving ridiculously hard problems as exercises for the reader?

[teal lion]

Not that I’m aware

Definitely not his undergrad books

For grad level, that describes a lot of mathematicians

Like, Hartshorne assigns openness of the flat locus as an exercise

[manic ginkgo]

I wish I knew enough to get why that problem is hard lol

[manic ginkgo]

Yeah, I dunno why but that's the name which popped up - I remember some post with a whole bunch of ridiculous problems where someone complained the author was trolling at this point

[manic ginkgo]

huh, I couldn't even find a wikipedia page for that

[teal lion]

There should be one for flat morphisms generally

a Wikipedia article, that is

I wouldn’t recommend using Wikipedia for anything other than a bibliography, imo

[manic ginkgo]

yeah, it's nice to find related topics and definitions though

[teal lion]

you’ll find that in actual books on the subject, rather than those written by people like me, who don’t know shit

[cyan goblet]

need some input on whether or not i should drop a class:

i'm taking a "pre-measure theoretic probability class" which uses the textbook "Knowing the Odds: An Introduction to Probability" by Walsh; as the course name implies, it's not required to know measure theory. both the textbook and professor claim to follow this as well. however, the textbook makes little to no sense to me (i'm on chapter 2 and it's already mentioned "Lebesgue measure" many times) and class is equally just as confusing. week 1, he didn't mention anything about Lebesgue measures. week 2, he was like "you don't need to know measure theory, but if you do, this should look familiar." week 3, and he's like "you cannot use this concept on Lebesgue measure zero." looking around the class, i see plenty of people who seem to understand and plenty of people scratching their heads and furrowing their eyebrows.

however, the issue with dropping the class is that i won't get a refund for it. at which point, i have the dilemma of "is it better to push through and somehow make sense of all of this" or "drop it and not risk damage to my gpa"

today is the last day that i can drop a class without getting a W on my transcript

the textbook was also like "Let (Omega, F, P) be a probability space" without defining what a probability space was until like 2 subheadings later

[neat frost]

That seems like a really terrible solution. Can you try talking to the professor and bring up your concerns?

[cyan goblet]

i could try

[little vine]

Are you toast in the class? Or could you pass

If I were you I'd stick it out

@cyan goblet do you have to calculate the Lebesgue measure of wonky sets or is it mostly plain geometric shapes? I.e elementary sets?

[fluid rapids]

hehehehaw 💀

[viral cipher]

As I can’t find a decent connective between harmonic functions and cybersecurity: what are some excellent applications (or extremely important problems) that are solved via harmonic functions and their properties? Any input is appreciated.

[cyan goblet]

nah, theres no calculating lebesgue measures, he just mentions it a lot

[cyan goblet]

no clue rn, only 3 wks in

[little vine]

I would stick it out. You'll probably surprise yourself

[neat frost]

Could you send the syllabus for your class? Because maybe someone could find you a good book that covers the material so you can teach what your professor isn’t teaching well

[hallow scaffold]

https://ocw.mit.edu/courses/18-04-complex-variables-with-applications-spring-2018/resources/mit18_04s18_topic5/

well I never really messed around with harmonic functions, but harmonic functions and analytic functions are kind of the same thing.

so in terms of use, where ever complex analysis is used: Like analytic number theory (PNT), I am also told that physics and the applied side use them a bunch

[cyan goblet]

(lowkey im slowly rereading it rn and its slowly making sense)

(i think i was just freaking out a bit)

but yeah heres the list of topics

[viral cipher]

I’ll look into that. Yeah, an analytic function is just a complex-valued function where u and v are harmonic and harmonic conjugates of each other. I have it in my research paper so I’m sure I can talk about it in applications.

[hallow scaffold]

I think they are good for modeling fluid flow and other diff eqs too, but I know nothing about physics.

[open aspen]

my advisor just mentioned discord to me and now im sweating

[bright hill]

that one is full on sarcastic

I use and interchangeable to mean "I'm still here, I'm just thinking"

[open aspen]

the latter has a "im humoring you" vibe idk

[chilly hull]

i like

[fading zealot]

It's probably just that I haven't dig deep enough, but are there good visualizations of constructing stellated polyhedra using star polygons?

[chilly hull]

but again i use because i love cat

[fading zealot]

Everything I found is about using triangles or other shapes, for construction of real life models

[little vine]

I use sincerely

[fading zealot]

Also the great dodecahedron

[zealous garden]

my use is up to reader interpretation

[fading zealot]

Not sure if I'm just dumb but it's been hours and I'm struggle how do you put polygons in space to construct these shapes

I want to be able to use my finger to point at something and say “this is a pentagonal face” and “this is another face” and “these two faces are made of different pentagons”

“Nobody is asking this so normal people must be able to understand them” I tell myself

[toxic sky]

guys, how does one become not terrible at analysis

i can just stare at something for literal hours and not see my way into it

[zealous garden]

stop staring

start doing math

[toxic sky]

ok but actually though

[little vine]

Trust the process

[zealous garden]

what background do you have

[toxic sky]

so

my undergrad was in applied math

im fine with most applied math

im in grad school rn for ee

but im taking real analysis for shits and giggles

and its railing me

[little vine]

Oh yes

[zealous garden]

lmfao

[little vine]

Your first pass will be tough

[frigid matrix]

You have to learn how to apply definitions

[toxic sky]

i took like, the required foundations class in undergrad

and i sucked at that too

i would say this may be marginally less sucky but

still sucks

[little vine]

I can recommend you a great book

[toxic sky]

hit me

[little vine]

That is really well motivated

Abbott "Understanding Analysis"

[toxic sky]

lol

[little vine]

Doesn't have everything

[toxic sky]

thats the text we're using

[little vine]

OH then idk

[toxic sky]

hue

[little vine]

It's a great book

What part are you on?

Don't despair. I understand a bit now and don't know how

The brain is just like that.

[toxic sky]

nearing the end of chapter 1 i think

bijections and cardinality

[open aspen]

id once again like to recommend royden fitzpatrick for real analysis

im a R/F shrill

[little vine]

So you know how to show a function is bijection?@toxic sky

[toxic sky]

err

like broadly sure

[chilly hull]

once i finish schroder

[little vine]

So for one to one start with f(x)=f(y)

[chilly hull]

i will put out a review

[honest veldt]

isn't that like

[little vine]

And you can move things around

[honest veldt]

a couple levels beyond abbott

[little vine]

Until you get x=y

[open aspen]

well they said theyre in grad school

so its time to suffer anyway

[honest veldt]

Yeah but they're struggling with abbott, let's ease the suffering for now

[open aspen]

i didnt actually read much of what was said tbh, I saw "real analysis" and took my shot

[chilly hull]

oh yeah i also got artin today

[open aspen]

if struggling with abbott though yeah maybe not

[chilly hull]

(it doesnt have galois theory though )

[honest veldt]

Of course lmao, always a chance to shill

[chilly hull]

using international version

(im broke)

[open aspen]

gotta take those

im the only R/F shrill in here i think

bunch of rudin fans

[little vine]

Onto, start with anything in the codomain call it y and push stuff around until you find x in the domain where f(x)=y. Really you're probably having a hard time because you never had a basic proofs class @toxic sky

I'm guessing

[toxic sky]

well

i did take the intro proofs class in undergrad

i sucked at it ofc

[little vine]

Oh

Do you understand Cantor's diagonal argument?

[toxic sky]

no

professor was going over it in class

and i was completely lost

[honest veldt]

I think abbott does a good job explaining it

have you tried reading it

[little vine]

Yeah he does

[toxic sky]

yeah i need to review it

[little vine]

Study that proof

[toxic sky]

im also working full time though so ive not had as much time to review notes and book as id like

[little vine]

Until you get and cardinality should be more ckear

[honest veldt]

The book is good, I can tell you that

Take the time to read through it diligently

It might take a few tries, but you'll be on your feet movin in due time

[odd narwhal]

royden is good

[open aspen]

not quite the shrill energy but i appreciate the support ✊

[gray snow]

yee bro

suppa

[gentle bluff]

What is matrices and linear algebra used for I kind of just blindly learned this first year and have no idea how to apply it to useful life

[gray snow]

graphics bro

[willow patio]

im legit having an existential crisis about the nature of reality trying to program a visualization of curvature

[gray snow]

show bro

[willow patio]

lol the code doesnt even work yet, its spaghetti af

[gray snow]

which lang

[willow patio]

it has to do with dimensions and how time seems to play a role in iterations obviously with quantization

Python skeleton code but I was gonna do some C++ if it gets too bulky

Like I worked out how you can just use Stern-Brocot approximations to give maze instructions to a robot

You take the Left Right turn sequences, plot it on the binary tree of rational approximations, give the robot that number, and it'll decode its the instructions

The Golden Ratio is an eternal LRLRLRLRLR sequence because its the most perfectly irrational number lol

[gray snow]

broo why tikz so good though

[willow patio]

lol

[gray snow]

you dont get anything showing yet?

[willow patio]

i should by tonight

[gray snow]

why does it take so long to get anything showing

[willow patio]

I'm trying to develop a physics theory where curvature is the only form of actual energy, whether its true or not is different lol

[gray snow]

that shit complicated af?

[gray snow]

right

so what this some diff geo bullshit?

[willow patio]

not even sure lol i could just be a loony nutjob

[gray snow]

meanwhile im doing actual physics he bro

real shit

[willow patio]

shiett

I just think we live in a hologram, the nature of information probably has to do with those oscillations is my gist

[gray snow]

actually jk its just physic simulation

[willow patio]

any irrational number becomes an infinite sequence of L-R directions

[gray snow]

not real physik

[willow patio]

lol

[gray snow]

fourier bro

[willow patio]

lol i do audio, FFT is my shit

Even and Odd numbers are just 2 poles of symmetry

Square wave, Pulse wave, Triangle wave, all have only odd harmonics; the Triangle wave has even harmoncis because its asymmetrical

thats why hard clipping a sine wave gives you a square wave, its just 3 5 7 9 x multiples of the original so the waveform stays symmetrical

[gray snow]

bro you implement fft in cpp?

[willow patio]

Sorta

[gray snow]

ye bro where hub

that fast though?

[willow patio]

You can use the Sinc(x) and Rect(x) functions to start with

[gray snow]

fft but without fast

[gray snow]

when grafik though

get yourself some DJ veach

[willow patio]

lol gimme 5 min and ill make a demo visual

maybe someone can point me in the right direction, im sorta lost on where to go

[gray snow]

that real demo though

does it fit under 2KB

the binary

[willow patio]

a droplet that doesnt merge with the fluid body for whatever reason can be driven at a frequency to glide across the fluid carried by its own previous wave

[gray snow]

tf bro

how u make vibrate

[willow patio]

you can put water on top of a speaker and oscillate it

[gray snow]

this brom bok?

[willow patio]

oil is better

than you drop a water droplet on it and set the driver frequency to how fast its jumping

[gray snow]

bro where you got this shit from

this shit smoking

[willow patio]

lmfaooo

Pilot Wave Dynamics

my concept of "nothingness" its that just a fluid oscillating at the same rate as matter

so it perfectly resists matter against itself, and something remains equally itself (mass/energy conservation)

now I'm trying to work with a concept where I shape a boundary for a wave to travel and I shape the boundary to form the wave into something more complex

and I see what kind of boundary conditions produce complex forms

[gray snow]

broo why you got all these concepts though

you just come up with that shit?

[willow patio]

lol its sorta philosophical/spiritual

Symmetry is the ultimate concept from which literally anything can be constructed, the extremes of self-symmetry are Nothingness and Infinity

There's no meaning in a dimension without symmetry

[gray snow]

shiit bro you smoking too much

[willow patio]

im smoking the same stuff Joseph Fourier was, that good shit

I'm just fascinated by the concept that physics could be an illusion of numbers trying to be rationally approximated and failing

[gray snow]

bro check I made figure with latek

so good

[willow patio]

lol ayo

sometimes i lay in bed thinking about how we're probably within an infinite dimensional object who only produces quantization through renormalization

[gray snow]

sounds like smoking in bed

[willow patio]

nah its in quantum mechanics, Feynmann diagrams

[gray snow]

just make sure your sheet dont catch fire bro

dangerous

[willow patio]

If you try to sum the energies of some quantum systems, its infinity

you have to subtract out a normalized infinity to yield a finite element which is true

perfect example is the Casimir effect, theres an attractive force between charged plates because virtual particles can't form in the short wavelength between, so the outside vacuum becomes stronger by comparison

It's a quantum force that emerges because there's literally less of nothing

which implies "nothing" is already starting with energy aka zero-point energy

im off da perc

[tender tulip]

please go on it and crack the hodge conjecture

[gray snow]

and smoke crak

[willow patio]

hm lemme google it and ill solve it

nah this stuff looks hard lol

im smart but not quite set theory and group theory genius yet

lol

tbh thats what i want to master next, because I want to do programming whether I can create geometries that do most of the footwork for me in calculating certain outcomes

[wide falcon]

nice

[wide falcon]

i'm still not convinced by vacuum zpe arguments

they seem to be based on some assumption that because a particle in a box has no uniform stationary state that the vacuum mustn't either

the problem with this is that the vacuum is (notionally and in effect due to hubble stuff) unbounded, and therefore supports a uniform stationary state, needn't have chaotic fluctuations per se

rather than assume there must be background fluctuations, it seems more sensible to ask "how strong are the ones in our universe?"

i say this is the path toward resolving the the vacuum catastrophe persuasively

[marsh dragon]

Wow. Physics

[zealous garden]

There's no such thing as nothing

[marsh dragon]

I just want to ask question about physics

[wide falcon]

go

ask

[gray snow]

Bro

My dj talking physik

[marsh dragon]

What is the best book for. Physics, i am accountancy but i am interest in physics/chem since its more. Imaginable and complex than accountancy brroo

[burnt dune]

can you solve any point-set problem using algebraic topology

[gray snow]

Ye bro

[burnt dune]

srsly

[gray snow]

Bro what is point set

[wide falcon]

here is how to answer that

"can point set problems encode arbitrary numbers"

if so gl with the halting problem

goedel moment

[burnt dune]

what

[gray snow]

Bro what is point set

[burnt dune]

hahaha

[gray snow]

Exblain

[wide falcon]

algebraic topology is just one halting proof in effect

[gray snow]

Set with points in it

N dim points

In set

[wide falcon]

there exists no algorithm which proves an arbitary program halts

[gray snow]

Vector space?

[wide falcon]

if you can put arbitrary program in point set problem then poof

oh and all you need for arbitrary program is be able to represent arbitrary integer

so if your point set problems can encode arbitrary integers then no algebraic topolgy won't solve them all

[gray snow]

Brooo brain cell not found problem

[burnt dune]

ur trolling me

;angry

[gray snow]

No bro

Explain point set first

[wide falcon]

depends what topic

the discipline of physics is divided broadly into topics of discrete or fluid mechanics, optics, nuclear physics, astronomy, cosmology....

quantum, materials,...

[marsh dragon]

After classical physics what next?

[gray snow]

BROOO

[wide falcon]

either more classical or you go quantum

[gray snow]

Opticks though

[wide falcon]

i honestly can't recommend texts

i didn't learn from one

[gray snow]

Wtf how you learn

If not bok

[wide falcon]

stealing math from a shitload of sources

and arguing about things with people

[marsh dragon]

Online? Khan academy

[wide falcon]

i learned qm from lectures

[gray snow]

Na bro just read veach

All physik you need

[wide falcon]

veach is basically all of science in one paper

phd completionist

[gray snow]

Ye bro it's so good

He doink 100% run on phd

Got all those achievement

I do phd Speedrun

[marsh dragon]

Yup its good but do you imagine physics like a Einstein?

[wide falcon]

sure i guess

[gray snow]

10% completion

[wide falcon]

einstein was mostly a good talker

and good writer

was able to attract enough attention to get help formalizing something a lot of people had fancied

[gray snow]

Ye bro I suck at both

But I enjoy writing

Isn't that weird

[wide falcon]

a lot of people were aware of the michelson morley result

the lorenz criterion follows pretty naturally so

idk einstein wasn't big math guy he was big lateral thinker

that's the point

[gray snow]

Oh he didn't come up with that by himself?

[wide falcon]

i mean yes and no

he writes with incredible saliency

[gray snow]

I thought he big into mathy

[wide falcon]

he totally gets why things are happening but did not often do the calculations alone

[marsh dragon]

Yup

[gray snow]

Aight

Gr is written in diff geo shit right?

Spacetime moneyfold

• diff

Broo why tf my English so bad

[marsh dragon]

Same my englisj is already bad

[zealous garden]

yeah GR is like basic diff geo afaik

[wide falcon]

it really is just a matter of putting the right physical constants on basic riemann manifolds

[gray snow]

Also explain intuition behind moneyfolds

[zealous garden]

it's super simple

[wide falcon]

oh and philosophizing about the cosmological constant which is probably zero

that part was weird

oh and mach's principle is completely mindblowing

[zealous garden]

I question the assumptions a little bit sometimes

[gray snow]

Moneyfold is surface that is locally homeomorphic with Euclid?

So locally

Some trick with open sets?

[wide falcon]

moneyfold = manifold apparently

[gray snow]

Ye bro

[zealous garden]

manifold lmfao

[wide falcon]

no it's a trick with limits and calculus

[gray snow]

What it has to do with calc?

[wide falcon]

locally planar means limit exists

[gray snow]

Ye bro

But isn't that differentiable moneyfold then

[marsh dragon]

Can you solve simple anti derivative equation using in your imagine?

[wide falcon]

sure

[marsh dragon]

How?

Without using paper

[wide falcon]

yeah that's what i say but wiki🅱️edia arti🅱️le yknow

[gray snow]

Ye bro

[wide falcon]

do you know what a low pass filter is

[gray snow]

Bro I need to grind that measure theory course

Extreme hard

Otherwise no passing grade

[gray snow]

You just cut low freq

Fourier vro

[marsh dragon]

Nope but i can learn it fast

[wide falcon]

a low pass filter is a filter which accepts a signal and gives back a signal where the higher frequences are attenuated

for a first-order low-pass filter, the attenuation varies depending how far above the cutoff frequency you are

[gray snow]

Oh wtf

It the other way around

[wide falcon]

they roll off at 6db/octave

[gray snow]

Fishbrain moment

[marsh dragon]

What is the formula. And. Equation?

[gray snow]

Fourier vro

[wide falcon]

don't worry about that

above the cutoff frequency, if you double your frequency, you get half the signal strength

below the cutoff frequency, the signal is conserved

there is some blending in between

if you lower the cutoff frequency, it makes everything quieter, but you get comparatively louder bass

integration is like having a first order low pass filter with cutoff frequency zero

it literally just applies the 6db/octave rolloff for all frequencies

so like you can figure out how signals should be shaped when you take the antideriv

[gray snow]

Bro I have no clue where this man's get all this shit

[wide falcon]

oh also i got really good at mental symbol manipulation in middle school

dsp is cool okay

[gray snow]

Na bro that's just brain cell

[wide falcon]

i wrote some filters specifically to listen to music all day and have my speakers sound good

[gray snow]

Bro that's literally just brain cell

There no learning

[wide falcon]

actually no because

i had to practice it starting with algebra courses

never did it before but i just refused to write steps

lol

[gray snow]

Why though

[wide falcon]

because i realized it'd be more useful to know how to do it on the back of an envelope or without writing

so i would just

look at the problem

come up with a sequence of calculator button presses

execute

make teacher mad but get a lot of right answer

[gray snow]

That faster in exam though

But I think high error probl

[marsh dragon]

Yup

[gray snow]

Because when shit get long enough

You forget

[marsh dragon]

Do you try usw excel for chemistry?

[gray snow]

That question of working memory

And therefore question of brain cell

[wide falcon]

maybe i don't remember

i use latex for crazy amount of shit these days

[gray snow]

Ye bro latex so good

[marsh dragon]

Ow i use it in stoichiometry

[wide falcon]

write latex document which solves the homework problems lmao

theoretically possible

[next schooner]

stoichiometry

[marsh dragon]

Do you wsnt the excel?

[next schooner]

no it's ok

[marsh dragon]

Do you try to created a problem in math?

[wide falcon]

i am trying to create a monstrous problem in math

the synthetic classification of differentiable manifolds

https://ojuea.us/connection.pdf is supporting work

it's where i figured out you can project all vectors tangent to get a matrix whose entries are partial derivatives of variables

i can increase the gobbeldygook factor further if you dare

[marsh dragon]

I trying to connect accounting(boook keeping) /chemistry/physics un s one problem

[wide falcon]

bookkeeping is just the theory of error correction via once-redundant ledgers

[marsh dragon]

Yup from recording to journal to ledger

[gray snow]

Why though

Also bro you have shed ip?

[wide falcon]

because the synthetic classification of polytopes is extensive and the corresponding classification for differentiable manifolds is nonexistent

[wide falcon]

yes i can see your ip

[gray snow]

Ok bro

But ye bro

I struggle to understand moneyfold

[wide falcon]

don't

just forget everything

a circle is a manifold

so is a square

so is a sphere

so is a tesseract

so is spacetime

[gray snow]

I know right

[wide falcon]

so is a point

so are fractals

[gray snow]

But the local Euclid space definition thing is confusion

[wide falcon]

so are most functions

[gray snow]

Wtf

[wide falcon]

er

most practical functions

[gray snow]

Function is map

[wide falcon]

almost all functions are not manifolds but

[gray snow]

How is moneyfold map

[wide falcon]

bro because

if you have manifold in 4 coords

and you pick 3

you get the fourth back

[gray snow]

Oh

Ye bro that brain cell

Nice trick

[wide falcon]

you can think of manifolds as generalizations of certain kinds of functions this way

so like if some book solves such a problem with functions

you can just be like

"why so verbose bro"

[zealous garden]

yes for some nice functions the graph is a manifold

[gray snow]

Ye bro this why I try use moneyfold

Less verbose

And if you have differential moneyfold u have some nice property

Can do limit + anal

[zealous garden]

differentiability is so dreamy

[wide falcon]

differentiable manifold be like

p d = d

yeah i'm gonna change the whole paper to use p instead rq

[gray snow]

Also bro why trying make thesis Soo difficult

This the most difficult shit I try so far

Insane difficulty bro

[bronze wedge]

measurable spaces are so much cooler than manifolds

hot take^^^

[wide falcon]

differentiable manifold bro

diffgeo gives metric and metric gives the only measure you actually need nerrrrd

[zealous garden]

Based

[odd narwhal]

let's split the difference: rectifiable sets

[deep mango]

actually true

well

integrating over non BV objects is important!

[neat lintel]

HELLO

CAN SOEMONE HELP

I WILL DIE

IF THIS DOESNT GET ANSWERED

[open aspen]

Why would you die lmao

[bright hill]

please see #❓how-to-get-help

🙂

[open aspen]

Shh darq I'm committing entrapment

[mint canopy]

Rest in peace 😌

[heavy storm]

-5

[neat lintel]

yes ty

that was right

10 hours ago

[heavy storm]

I just opened this channel

My b 💀

[gaunt latch]

I don't like proofs with verbal language

[surreal sapphire]

whats verbal language?

[gaunt latch]

usual language

[surreal sapphire]

whats the alternative?

[gaunt latch]

like the one we speak

[odd narwhal]

2 column proofs

[surreal sapphire]

shin go away

[odd narwhal]

I think that's what they mean tho

[surreal sapphire]

ok, let me look up what this is

[odd narwhal]

There's this tendency to get obsessed with rigour and write everything completely formally when you start out with maths

[gaunt latch]

I don't get obsessed

I consider it a bad practice ( you might consider it a good one )..

[odd narwhal]

I'm not talking specifically about you

But if you consider it a bad practice it is likely you have not yet seen a lot of complex proofs

[gaunt latch]

I just give my opinion

[gaunt latch]

I have seen

[odd narwhal]

Proofs in higher maths would just be completely unreadable if we did not use natural language

Some are unreadable even with natural language

If you want complete formalism, I suggest you try learning a proof assistant software like lean or coq

[gaunt latch]

I believe we can write it with something finer

I don't like natural language in the middle of math

[odd narwhal]

Translating even basic theorems into lean is a grand endeavour, and the end result is not something that's meant to be interpreted hy a human, but by a computer

We are not computers

[odd narwhal]

What would that be

[surreal sapphire]

but math is communicated in natural language most of the time

[gaunt latch]

like at least some verbal stuff can be replaced with something else

I don't have to write all that

I love symbols

[surreal sapphire]

but thats bad from the readers perspective

you want a good flow of reading

[gaunt latch]

we must agree on the thing already

[surreal sapphire]

and some symbols interrupt that for no reason

[manic ginkgo]

Ultimately you’ll have to explain what all the symbols mean and I don’t know how you’re going to do that besides natural language?

[gaunt latch]

natural language doesn't give me a good flow of reading

[surreal sapphire]

i would be interested in a proof you consider good

[gaunt latch]

i even hate using anything verbal in programming

it doesn't make anything easier to me just more effort in

[odd narwhal]

What's the most complex theorem you've seen so far (or an example of a theorem you consider highly complex)

[bronze pelican]

Quick: prove the medians of any triangle are concurrent

[odd narwhal]

I wanna get a feel for the level of maths you've encountered

[manic ginkgo]

APL’s got you covered: https://en.wikipedia.org/wiki/APL_(programming_language)

[gaunt latch]

I know APL

[gaunt latch]

a complex theorem won't give you the level of math I am encountering because there are existing theorems that everyone knows even without any specific knowledge in math and their proofs are written in long papers such as Abel–Ruffini theorem, Gorenstein–Harada theorem, Almgren's regularity theorem or even The Classification theorems out there.. I personally go with the so called Ostrowski–Hadamard gap theorem right now in complex analysis which I don't think requires a 2 column proof and I still stand on my opinion that if it wasn't that big it will look finer with more symbolism.

[odd narwhal]

I meant a theorem you've seen a proof of

[gaunt latch]

last one was a converse fabry theorem proof by some Irainian

it was like 5/6 papers ( and I am still checking its validity ) so I don't know what exactly you meant

[fading tusk]

I particularly enjoyed reading the classification of finite simple groups

[gaunt latch]

was one by contradiction at the end

[fading tusk]

Sorry I can't confirm or deny at this time

[gaunt latch]

if you want the previous one it was just Turán's theorem and its generalizations

[fading tusk]

Proof of turan can be short af

[gaunt latch]

well.. can you prove it in another way?

[fading tusk]

I have seen two proofs

[gaunt latch]

if shorter means easier.. can you prove turan's theorem with a new proof?

[fading tusk]

no

oh wait I forgot it falls to Caro-wei

proof of Robertson-Seymour 🙂

is a long one

[gaunt latch]

I won't spend my life from 1983 to 2004 proving a theorem

[fading tusk]

but u'll be a respected scholar while it happens

they'll invite u to spitball to different places

[gaunt latch]

I am not a math major

[fading tusk]

I see

well, the people involved in that proof were well regarded scholars

while they did it

[gaunt latch]

I do take the math for Engineering and CS

I totally don't need to involve myself now in long proofs journey

[fading tusk]

makes sense

[gaunt latch]

when I said I do take the math for Engineering/CS I didn't mean that I am here to learn their math.. but rather involving more math in them if possible

that's what I should be doing in my postgrad time

preparing myself for advanced research and higher studies

[fading tusk]

Oh I see

[fervent pebble]

i just found either a mildly funny troll or collatz crankery on my yt recommended 💀

[alpine kindle]

this is either very convincing fake crankery or real crankery

[storm sage]

omg

there should be a fake crank channel

[solid snow]

bruhhhhh

[storm sage]

lol

[willow patio]

i figured out the other day that multiplication is a form of addition and division is a form of subtraction

v big brainz

unless the quantity is greater or less than 1, then the roles flip obviously lo;

[storm sage]

wait what do you mean?

[willow patio]

ill do a quick little thing in ms paint and snip it over, just 1 sec

Say you just have a little equation thats T = xyz, so as time goes on, the 3d parameters of a simple shape grow

you can rewrite that in two ways, 1=(xyz)/T or 0=(xyz)-T

so rewriting a variable relation to have a constant of 0 makes time act as a divisor, and rewriting a variable relation to have a constant of 1 makes time act as a subtractor

but you get the same data points either way lol

so operations are innately related to binaries

[wooden flax]

fuck chemistry 😭

this makes 0 sense

[zealous garden]

what kinda chemistry

[proven hornet]

just do theoretical chemistry

its mostly physics

and math

[storm sage]

chemistry is great

[gaunt latch]

cope chemistry

[wooden flax]

elementary chemistry

im on electron configurations, afkaus principle, orbitial diagrams, wavelengths, etc

orbitial diagrams make 0 sense to me

[little vine]

How people figured out chemistry I will never know

[wide falcon]

needed to figure out how to feed plants without harvesting entire islands for nitrogen

etc

[zealous garden]

centuries of experiment

incredibly intelligent and brave men and women, many of whom have given their lives to create this wealth of knowledge for us

[proven hornet]

luckily as a mathematician I only have to give up my sanity

[vivid halo]

spherical harmonics

[lavish kayak]

random ass solutions to the wave equation.

Memorize em and weep

[wooden flax]

oh thats the fun part

the wave equation

why did you spherical harmonics ng

i like them

[bronze wedge]

stochastic wave equation

[wooden flax]

who

[bronze wedge]

me

[open aspen]

I really really do not want to do this DEs homework

The professor just assigns pages upon pages of raw computation

In a graduate course!

Like I think we know, at the very least, after the first homework to find eigenstuffs

But noooo

It's gonna be like 22 pages

So lame

[lavish kayak]

Good to know that dull stupid homework never ends

[wooden flax]

wtf

that sounds even worse than my chem hw

[open aspen]

It doesn't make sense

[wooden flax]

just be like "trivial by mathematica" on every problem LOL

[open aspen]

It doesn't even make sense in an undergrad linear algebra course honestly

[wooden flax]

oh this is a GRAD course???

[open aspen]

Someone sited wolfram on a few questions

Got 0 on them

Yes

[wooden flax]

holy

[open aspen]

It's so fuckijg stupid

[crystal stream]

lol

[open aspen]

Why am I spending my night calculating eigenvectors

[crystal stream]

bet you 100$ the prof. did not compute the answers manually

[open aspen]

I have better shit to do. Like watch Netflix and ignore student emails

[wooden flax]

lol

[bronze wedge]

http://simpde.infinityfreeapp.com/

SPDE numerical simulation ^^^

[open aspen]

That link

[next schooner]

cursed

[open aspen]

Is 2 of my phone lengths tall

[bronze wedge]

fixed

[next schooner]

my phone refuses to load it

oh, neat

what exactly is it?

looks like a wave equation with some noise and diffusion thrown in

[bronze wedge]

stochastic wave equation

though i guess you can choose a lot of other equations

[next schooner]

mmmh interesting

reminds me of two-species Turing patterning

diffusion-driven instability

neat

[trim sparrow]

Hey guys, i wanna learn math thoroughly, can you guys tell me every topics there are?

[bronze wedge]

you cant learn all of math

[trim sparrow]

Why?

[bronze wedge]

too broad

too many fields

[trim sparrow]

Its a hobby, i like learning, even if its too many i still wanna do it

[zealous garden]

You can probably learn a nontrivial amount of every field, depending on your definition of field

even a substantial amount depending on your habits

but not all

[trim sparrow]

Which topic do you guys think the most beautiful?

[zealous garden]

and you probably won't want to

[trim sparrow]

Ok lets start with basics first, since i dont know what my level is

[zealous garden]

what do you know

[trim sparrow]

Mostly algebra, some basic calculus

[zealous garden]

Algebra like quadratic equation or Algebra like Groups and Rings

[trim sparrow]

Polynomial is fine

[wooden flax]

cool link!

[trim sparrow]

But i like the math, where you find like sum of infinite series

[zealous garden]

I see, I think Abstract Algebra is really beautiful so far, and I enjoy Analysis very much

[wooden flax]

abstract algebra is really great

[trim sparrow]

Yeah, i like analysis too, but dont know where to start

[wooden flax]

try reading something like Pugh or Schroder

[neat lintel]

Hello.

[bronze wedge]

algebra is like what algebroids do, analysis is what analychads do

[wooden flax]

those are good intros

[wooden flax]

yeah, but i think you mixed them up

[zealous garden]

Why not both

[bronze wedge]

abbott

[wooden flax]

algebchads and analyvirgins

[bronze wedge]

esp if you are self studying

[wooden flax]

bruh what

you are the last person i would have expected to rec that

[trim sparrow]

Ok gotta read those

[serene parrot]

the books are all fine

[wooden flax]

abbot does nothing

[bronze wedge]

the person seems to be a "beginner"

schroder is fine - but its long

[wooden flax]

i was a beginner when i self studied by pugh/schroder

[wooden flax]

i mean you dont need to do like the last 2 chapters

last chapter is like applications to pde and stuff like that

[brittle socket]

Nice

[wooden flax]

my bad not last chapter

[trim sparrow]

Are there lots of problems?

[serene parrot]

yes

[wooden flax]

last 6 chapters

[bronze wedge]

strictly speaking schroder part 1 is undergrad real analysis

part 2 is like

more advanced topics

and then part 3 is applied analysis

[wooden flax]

last 6 chapters are finite element method, ODE, physics, hilbert spaces, diffgeo, measure theory

part 2 is best part no cap

[wooden flax]

exactly

so part 1 is the same lenght as abbot except covers 10x as much

[trim sparrow]

You know the book problem in Mathematical analysis 1 by W.J.Kaczor, i tried this book but i cannot do nything, i think this can tell what my level is

[wooden flax]

also last 2 parts are probably just more adv undergrad

but u know better than me

[serene parrot]

you can start from the very beginning of any introductory real analysis book

you will need some basic set theory

[bronze wedge]

advanced undergrad is the materiel, yeah, but could form part of a first y grad program

[wooden flax]

lol that is just problems

how do you learn from that

[trim sparrow]

Testing if i can do any of that

[wooden flax]

there is 0% i could have done a single prbolem from that because i wouldnt have known what a single term ment

*before i learned analysis

[trim sparrow]

Ah, good point, i dont know what that supremum mean

[serene parrot]

you can probably find some good video series on the subject

[bronze wedge]

looking through problems and seeing whether you could do any of them is a good idea

just saying

bc

even if you dont know much

there will be something you could do

[wooden flax]

vmm do you think its reasonable that you need to be able to solve these problems 100% right now if you want to learn analaysis 1 https://www.google.com/books/edition/Problems_in_Mathematical_Analysis_Real_n/eoXxBwAAQBAJ?hl=en&gbpv=1&printsec=frontcover

[trim sparrow]

Do you consider that book easy?

[wooden flax]

some you can obviously do but some use like supremum and infimum which alot of ppl who dont know analyis dont know

[wooden flax]

i dont consider it a book

at least a textbook

try an actual textbook and go from there

if schroder is too hard just do spivak or something

[serene parrot]

you must read some bit of the subject before jumping into exercises

[bronze wedge]

fair enough

but still

even if you dont know the terms

you can kind of feel whether or not you can do the exercises

[wooden flax]

yeah i agree

[bronze wedge]

there used to be this teaching method (called moore's method or smth), were grad students would be given the definitions, and have to deduce the theorems

iirc first used w/ topology

[wooden flax]

that sounds like it would be very beneficial to students

but it would take too much time

[worn garnet]

Yes it's called Moore's method

[bronze wedge]

its not that beneficial lmao

definitely has permanently scarred some grad students

[worn garnet]

Revelant dicussion here: https://www.reddit.com/r/math/comments/x23j3n/is_it_okay_to_remember_results_but_not_be_able_to/

[bronze wedge]

iirc Aumann did this w/ topology

(the same aumann who won the nobel in econ)

[worn garnet]

I remember /u/djao talking about how to properly read a math textbook and that post was an eye opener

The thing was with Moore's method it quickly got you to the dependency view of mathematics

https://www.reddit.com/r/math/comments/8tee8y/comment/e16w377/?utm_source=share&utm_medium=web2x&context=3

@bronze wedge but Moore's method does have some problems some students could not tell what was orginal mathematics and old mathematics

[open aspen]

I'd like to file an official complain against @delicate mulch

what he has done to the cats community is unacceptable

[sick burrow]

get me the fuck out of undergrad

can it be fall 2023 plz thanks

[fervent pebble]

damn that bad? 💀

[sick burrow]

Small liberal arts school

Basically no one on the campus knows math

Including most of the math majors

I was super shy freshman year and remote sophomore year so I know approximately nobody

And the only way I can do actual math is through reading courses

And then there's the fact that like 80+% of students here don't actually seem to care about their majors

[brittle socket]

[night meadow]

Why is dividing by 0.5 the same as multiplying it two times

I'm sorry if it's a dumb question

[mint canopy]

Good question

So here's an observation

If I have some number — let's call it x — and I divide it by 1, I get x

Picture that as how many 1s fit into x. Hopefully that's clear to you.

Now how many 0.5s fit into something? Since 0.5 fits into 1 twice, there'll be two 0.5s in x for every 1 in x

So the result will be 2x.

Does that kind of make intuitive sense? I think this is a good "first-principles" explanation.

[night meadow]

It makes perfect sense thank you man

[mint canopy]

Great stuff

[night meadow]

I feel dumb for realizing it now

[mint canopy]

Not dumb at all. If you get it, that's great

Now just to say a little more though

This comes up because 0.5 = 1/2.

So x / (1/2) = 2x

In general, x / (1 / n) = nx

where n is some other number

So for example, x / 0.25 = 4x. And so on.

[night meadow]

Thanks

[bright hill]

Not at all

(almost) Everything in math is obvious in hindsight

[modest harness]

Also it doesn’t make you smart to just believe in the concepts taught to you

A lot of them are non legitimate math with roots in legitimate math that makes them usable

[open aspen]

Based and dy/dx is a fraction pilled

[ancient flame]

lol

[proud olive]

How do you solve odes without treating them like fractions btw?

[sick burrow]

https://www.wolframalpha.com

[fathom swallow]

Boytjie (Plutonic Relations)

[mint canopy]

In all the typical circumstances that treating dy/dx as a fraction holds, this is actually what's going on under the hood.

[jaunty stag]

Can anyone explain me this 💀

Question: why mango is more sweeter than apple
Answer: hence, apple is more sweeter than mango

💀

[zealous garden]

Perhaps the question is wrong

[mint canopy]

Ah yes, math

[jaunty stag]

Yes, totally

[jaunty stag]

💀

[neat lintel]

Since the valence electron in rubidium is lore loosely bound it should be more reactive

[jaunty stag]

Yeah but why potassium is more reactive

It has to be rb

[neat lintel]

Francium is the most reactive metal on the periodic table but it is a laboratory-produced element so in practicality it is cesium that is the most reactive

[neat lintel]

Potassium isn't more reactive

[jaunty stag]

They both are radioactive so not stable :/
So none of them is reactive ig

Highly reactive*

[jaunty stag]

So thats wrong info?

[neat lintel]

Yes I believe so but to be sure ask your teacher

[jaunty stag]

Yeah thats the reason i was searching on google... My teacher ignored me

[neat lintel]

Why lol

[jaunty stag]

We ask her 2-3 times

[jaunty stag]

I dont know 💀

Maybe rb is an exception?

Have to read book now 😐

[neat lintel]

Ok well I've been taught that the reactivity increase because there's less pull from the nucleus on the electrons when they're further out which makes sense.

[jaunty stag]

Yep

But u cant forget the fact, that this thing is chemistry

So, anything could happen yk 💀

||unwanted exceptions||

lol

[neat lintel]

Maybe potassium is the most reactive of the frequently occuring metals in nature. I don't know how common rubidium is.

[jaunty stag]

Hmmm maybe

[neat lintel]

@jaunty stag

You can see here fluorine is highly reactive

The most reactive element actually

Potassium and rubidium are almost the same

I don't know if it is entirely right though to use electronegativity to figure out reactiveness because obviously, hydrogen is very reactive

[jaunty stag]

But we are talking about metals 💀

[jaunty stag]

Oo

[jaunty stag]

Yeah but it is chemistry lol

[jaunty stag]

Metals

[neat lintel]

Rubidium is more reactive with 99% certainty ok.

[jaunty stag]

Ok

Got it, Sir!

But i still doubt that 1%

🗿

jk

[neat lintel]

If your teacher says otherwise just debate her or him

[jaunty stag]

Hmm ...lets see....
Idk why teacher didnt even said the name of "rubidium"

[neat lintel]

What precisely did your teacher say

[jaunty stag]

Umm...
"Bla bla bla bla so fr and cesium are radioactive (didnt even told that if they are radioactive then still why not reactive) bla bla bla bla so potassium is the highly reactive as you can see(pointing the potassium in group 1)

[jaunty stag]

That bla bla part is kinda similar to this

[neat lintel]

Not all cesium isotopes are radioactive

[jaunty stag]

Havent studied radioactive chapter yet
I Just know that they are not stable

[neat lintel]

Cesium-133 is stable

[jaunty stag]

:/

[neat lintel]

All radioactive means is that it'll decay into another element until its stable and it'll give off radiation while doing so.

[jaunty stag]

Oooo

So, Radioactive Elements shows random properties or their are some principles?

[neat lintel]

What do you mean

[jaunty stag]

Thats another question

[neat lintel]

There are principles for radioactive elements yes, how long the decay takes and what kind of radiation is emitted

[jaunty stag]

I mean like radioactive elements are diff from normal elements...
So do they ALL follow some rules or each shows random properties

[jaunty stag]

Oo

[neat lintel]

They follow rules yes but they're not the same as non-radioactive elements

[jaunty stag]

Hmm

I see

Tnx for the info

[fading zealot]

tfw the pattern broke

[fading zealot]

Hmmm
What does this have to do with multiplying dice rolls

[vivid halo]

are you sure the next 3 terms in your sequence are 36, 40, 43?

[bronze pelican]

What is this

[fading zealot]

It's not

Welp, at least I have a new entry to the OEIS

[burnt dune]

yo algebraic topology actually is lit

why cant they create like

some subfield of algebra

that is algebraic topology with no topology

like yes mr atiyah i choose to be blind 🙂

idc

[open aspen]

What

[vivid halo]

homological algebra

[burnt dune]

atiyahs quote

on not studying algebraic geometry and just studying one of the two

"would you rather be blind or deaf"

its like hes saying whats the point of studying things for the sake of themselves if these things do not have relate so something bigger ig

[burnt dune]

will check that out

[fast ivy]

Algebraic K-Theory

[burnt dune]

dk what K theory is

other than vector bundles

[vivid halo]

algebraic K-theory too hard

[fast ivy]

Topological K-Theory would be studying K-groups associated to loc compact hausdorff spaces. For example, the K_0 group of a space would be the grothendieck group associated to the monoid of isomorphism classes of complex (or real) vector bundles of finite rank over your space. You can also assign other K groups to your space and these satisfy generalized cohomology properties and so on.

[burnt dune]

yooo

i am learning about loc compact hausdorff rnn lmao

like diving deeper

[fast ivy]

I think you can do top k theory over more general spaces???

but the theory I know is for loc compact spaces

The thing with algebraic k theory

Is that there are similar constructions of k groups

that work for rings

And these k groups give you information about the structure of the ring.

Found the relevant result

So like, the 0-th K group of a compact hausdorff space happens to be isomorphic to a group of idempotent operators over C(X) with a certain sum.

And turns out that this construction using idempotent operators generalizes nicely to more general rings.

[burnt dune]

yoo

[fast ivy]

And you define the 0-th K group of a ring like this.

[burnt dune]

wtf

groups are everywhere

[fast ivy]

The bigger issue is generalizing higher k groups to rings.

[vivid halo]

the bigger issue is computing anything once you have that generalization

[fast ivy]

oh yeah lmao

I forgot to say that actually computing K groups is hard

But yeah, generalizing higher k-groups to rings was a really non-trivial problem.

[burnt dune]

wdym computing shit is hard

just plug in the rule?

[fast ivy]

And appearently Quillen was the one to first give the "right" generalization.

And algebraic k theory is about that

[fast ivy]

https://youtu.be/YXcSTY7l46s

[wooden flax]

ooh ill watch this

[fast ivy]

this lecture is pretty good

it goes over topological k theory, and then gives a brief overview of what operator k theory and algebraic k theory are about.

[wooden flax]

sw33t