serious-discussion

[storm sage]

Hmm

[burnt ledge]

Lmao

[neat lintel]

This can be a gradual change.

I use capital theta when I am doing maths for fun for π/2 if that helps @storm sage

[burnt ledge]

i promise you it's useless

[neat lintel]

Just helps in writing trigonometric identities mainly easily though

[burnt ledge]

im a "piist" if you want to call me that purely because i live in a pi world

[neat lintel]

Like $\sin(\Theta) = 1$ or $\cos(\Theta) = 0$

[fathom swallow]

Nidhi

[solar hawk]

im officially a piist and amuist because of finnboltz

[long matrix]

sin 0 = 0

cos 0 = 1

[solar hawk]

sinx=x

[neat lintel]

sin(x) ≈ 0

Trust me, I am an engineer

[final igloo]

engineers dont care about sig figs

[sonic field]

sig figs don't sound like they taste good.

[neat lintel]

Amu is stupid.

[solar hawk]

amu as in the constant

or me

lol

[sonic field]

So now the real question is... is amukhl constant?

[neat lintel]

What does that even mean?

[neat lintel]

The constant.

[sonic field]

idk ask them XD

[solar hawk]

i made a new cpnstnat

amu

here

[neat lintel]

The constant is stupid.

[solar hawk]

ikr

thats why people use pi and tau

but now because of this bs

i will be pretty and use pi

only

[burnt ledge]

whats the amu constant

isnt it already atomic mass unit

[neat lintel]

A stupid constant invented by amukh1. It's equal to 2tau.

[storm sage]

That seems kinda useful to me

Ratio between a sphere's surface area and its radius squared

[burnt ledge]

Right

[solar hawk]

^

thats definitely why i made it

[burnt ledge]

Especially because it actually deals with the dimensions we live in

why do we need a "circle constant" when we live in 3 dimensions

[solar hawk]

mhm

[burnt ledge]

a sphere constant makes more sense @neat lintel

[solar hawk]

fr

oh wow he would haate this guy

https://www.youtube.com/@EpicMathTime

[neat lintel]

Circles are more fundamental than spheres.

[storm sage]

S^0 is the most fundamental space

[little vine]

Circles are spheres

[storm sage]

Almost every other space contains some copy of it

[neat lintel]

A circle is a continuous curve.

[burnt ledge]

A sphere is a continuous surface

[little vine]

Lol

[solar hawk]

so is literally every other continuous curve

[neat lintel]

Spheres are less fundamental than circles.

[little vine]

Harpz chose chaos

[burnt ledge]

Why?

[storm sage]

[citation needed]

[solar hawk]

alr guys in a couple days my website amuday will be out

[neat lintel]

Circles are easily constructed and defined.

[solar hawk]

amu manifesto soon

down with tau!

[burnt ledge]

So are spheres

[neat lintel]

They have more dimensions.

[storm sage]

Circles are a special type of sphere

[burnt ledge]

Btw spheres are the same definition as a circle

[neat lintel]

Take your 4-dimensional compass and construct a sphere.

[little vine]

Tell us about your website

[burnt ledge]

Youre just coping that you cant say a circle has the correct number of dimensions

[solar hawk]

bascially its tauday.com except with the best constant ever

[little vine]

4 ball

[burnt ledge]

Because a sphere does

[neat lintel]

It's 1-dimensional.

[solar hawk]

$\mathbb{N} = {\vartheta \vartheta^{-1}, 2 \vartheta \vartheta^{-1}, \dots }$

[fathom swallow]

amukh1 | JS fanboy

[little vine]

Nuh uh

[little vine]

I don't understand

[solar hawk]

screw the natural numbers, nows its the amu-natural numbers

[burnt ledge]

*blows a bubble*

[solar hawk]

like tell you about my actual website or the joke one im talking about rn

[burnt ledge]

and nothing else that is real is 1-dimensional

[solar hawk]

the joke one isnt real

[burnt ledge]

so spheres are better becayse they exist and are the correct number of dimensions

[little vine]

Either lol but I didn't get the joke because I haven't been chatting here

[solar hawk]

https://amukh1.dev

so basically

finn hates pi

[storm sage]

omg

[solar hawk]

hes an avid fan of https://tauday.com and basically i am pretending to make my own constant

[storm sage]

this is the perfect conversational context to bring up the glome in

[little vine]

Why does that menu rotate @solar hawk

[storm sage]

@odd brook quick

Glomify this conversation

[solar hawk]

idk thought it looked cool

it doesnt have buttons tho

[little vine]

Pi is fine

[solar hawk]

whats that mean

[solar hawk]

ye i like pi and tau

he is pusing for basically tau only idk whats up w that

[neat lintel]

I like amu

[solar hawk]

me too

[neat lintel]

I agree with Michael Hartl.

[solar hawk]

ong amu rule all of the constants

[solar hawk]

i read the article a long time ago and thought it was cool

i dont live by it tho

[little vine]

Some feedback: I'm impressed you know how to do it but it's a little irritating. But maybe someone will appreciate it

[neat lintel]

2010?

[solar hawk]

like i care more about dino chicken nuggies

[solar hawk]

im 15

[odd brook]

🪩 <- glome

[little vine]

What's your favorite constant

[solar hawk]

ill prolly make a new webs soon cuz it old

[neat lintel]

15 ???? You are sooo young

[solar hawk]

i like e

[little vine]

Correct opinion

[storm sage]

You should make little hover texts because I have no idea what these icons mean lol

[storm sage]

3

[odd brook]

3 is good

[solar hawk]

well if i were trying to get hired by a company i assume they would know

[neat lintel]

When did you read the article?

[solar hawk]

idk

definitely long ago enough i cant remember it

i watched a yt video on it

[neat lintel]

Isn't that pi ?

[solar hawk]

"pi is wrong"

[neat lintel]

That's also e

[neat lintel]

Do you mean Vihart's video?

The most beautiful equation in maths

[solar hawk]

idk

[neat lintel]

$3^{i3} = -1$

[fathom swallow]

Nidhi

[solar hawk]

lmao

[neat lintel]

Is this true?

[solar hawk]

thats so cursed

[sonic field]

omg wtf is that

[solar hawk]

e^ipi = -1

e = pi = 3

its a joke

^

[sonic field]

my eyes died jus now at that LOL

[neat lintel]

Ah come on, @solar hawk u could have told its true and it would be much more fun

[solar hawk]

i used to think physicists were called physicians

[solar hawk]

lmao

it would have been

[neat lintel]

Hilarious.

What actually is 3^3i?

[solar hawk]

a complex number

-0.988127927 - 0.153633328 i

[burnt ledge]

1 is my fav

[neat lintel]

It's equal to 27^i.

[burnt ledge]

tbf this is pretty close to -1

[storm sage]

3^(3i) = e^(i 3 log 3) = cos(3 log 3) + i sin(3 log 3)

[solar hawk]

obv

[neat lintel]

Prove Euler's Formula.

[solar hawk]

binomial theorem

[storm sage]

It's by definition

[burnt ledge]

Sorry, thats not one of the four proofs of math

[solar hawk]

whats that

[storm sage]

Dammit stupid super reacitons

[solar hawk]

there eric

oh lmao

u did the super

[neat lintel]

This is very unsatisfying.

[solar hawk]

if your grad+ shouldnt you be able to prove it

[neat lintel]

I'm only up to derivatives in calculus.

[solar hawk]

how tf r u gonna get grad+ then lol

[neat lintel]

I won't until later.

[solar hawk]

why apply now

[neat lintel]

I did?

[solar hawk]

nvm

im tripping.

someone else with ur pfp

lmao

[storm sage]

You can motivate it by Taylor expansions

But you'd need another semester of calculus

[neat lintel]

Why do the expansions for sine and cosine work?

[solar hawk]

isnt calc 1 and calc 2 yearly courses?

[storm sage]

Not in a typical uni

[solar hawk]

search taylor series proof idk

[solar hawk]

ah

i was going by my hs

calc is an hs course tho

[storm sage]

They are based on the derivatives of sine and cosine

[wet mortar]

if you want something "satisfying"

[neat lintel]

I understand the derivatives of sine and cosine well. How can you get these series from them?

[storm sage]

Do you know how to do linear approximations of functions?

[wet mortar]

it's not too hard to define sin and cos on R in terms of angles

[neat lintel]

What are those?

[storm sage]

For example if x is small, f(x) is approximately f(0) + f'(0)x

So sin x is approximately sin 0 + (cos 0)x, which is just x

[wet mortar]

and it's not too hard to show this agrees with the power series definition on R

[neat lintel]

What exactly does f'(0)x mean?

[storm sage]

f'(0) multiplied by x

[wet mortar]

so it's not so sinful to extend them to C via the power series

[solar hawk]

its the point-slope form of a line

[neat lintel]

Why do linear approximations of functions work?

[solar hawk]

f is a function

a is a point on the function

[long matrix]

finnboltz at it again

[solar hawk]

f'(a) is the derivative of f at a

[wet mortar]

and then using the power series it it's super easy to show euler's formula if you use the power series definition of exp

[solar hawk]

y - y1 = m(x-x1)

[wet mortar]

ofc you might not like that definition of exp

[storm sage]

It's the definition of the derivative

A function is differentiable if and only if this linear approximation works

[solar hawk]

y - f(a) = f'(a)(x-a)

right

[storm sage]

If there's no linear approximation, we say it's not differentiable

[solar hawk]

then y = f(a) + f'(a)(x-a)

[storm sage]

Like for example |x| is not differentiable at x=0

[solar hawk]

if a is 0

y = f(0) + f'(0)x

[wet mortar]

but there are other ones (perhaps only on R) that are nice and you can show they agree with the power series definition

[storm sage]

By "this linear approximation works" I mean the resulting error between the original function and the linear approximation goes to zero faster than x does, in the sense that the limit of error(x) / x = 0

[wet mortar]

so yeah euler's formula is somewhat interesting if approached from that angle

[neat lintel]

I don't quite understand what e is.

[long matrix]

sir gimme an example where that limit = 1

[storm sage]

[\lim_{h\to 0} \frac{f(x+h)- (f(x) + f'(x)h)}{h} = 0]

[wet mortar]

e is just exp(1)

[storm sage]

This the formal way of saying that the error goes to 0 faster than h does

[long matrix]

|x| gets u 1 right

[fathom swallow]

eulerERICteristic

[solar hawk]

e is the number such that d/dx e^x = e^x

[storm sage]

The value depends on what the linear approximation you choose is, but if the function isn't differentiable, then there's no reasonable linear approximation to choose

[wet mortar]

the exponential function on R can be defined as the unique Lie group homomorphism f from R to R^+ with f'(0)=1

[long matrix]

thonk

ig.

[wet mortar]

this is perhaps a more "moral" definition

[long matrix]

do we have some structures where there are multiple valid approximations

[wet mortar]

than the power series

[neat lintel]

So, the slope of the tangent line to the graph of e^x is e^x?

[solar hawk]

uh

the slope of the tangent line of e^x at a is e^a

[neat lintel]

How can you show that e is the sum of the reciprocals of the factorials?

[long matrix]

by utilising math exchange

[solar hawk]

idk

i just know it true

its just the definition

of e

there is no show

[little vine]

Sounds like a job for stack exchange

[solar hawk]

like i dont show amu = 2tau, i define it to be so

[neat lintel]

Why should these definitions be equivalent?

[solar hawk]

oh ye its easier to prove the first one i told u

[solar hawk]

d/dx e^x = e^x is prolly easier than this

go try it out ok

[wet mortar]

it's not obvious

[solar hawk]

come back in 6 hrs if u couldnt

[wet mortar]

it takes work

[neat lintel]

I don't know much about infinite series.

[solar hawk]

then learn it

https://tutorial.math.lamar.edu/classes/calcii/seriesintro.aspx

[potent mason]

How to study Physics Electricity, particularly AC circiuts and all of dat things?

[storm sage]

Hmmm I don't know of any such structures

They would have to be weird though

[long matrix]

[storm sage]

A space that can't tell apart linear functions is.....

[long matrix]

non euclidean

[sonic field]

it probably would be a good idea to start in an introductory physics textbook, I think Halladay is a pretty good one. If you're looking for more of a focus on actual Electricity and Magnetism, Griffiths is a good introductory book VERY readable. Some of the more standard circuit books are out there, like Nilsson could be approachable if you're looking for circuit theory.

[little vine]

What's the top space where there can be multiple limits?

[sonic field]

another textbook I found that explains the concepts well is Young and Freedman university physics.

Are you currently taking a physics class?

[neat lintel]

I don't think I'm ready to learn series in calculus.

[sonic field]

https://tenor.com/view/jump-water-fall-swim-boat-gif-21380412

[long matrix]

this certainly happens with indistinguishable points

i think non-hausdorff is sufficient though maybe

line with 2 origins satisfies that

[little vine]

Hmm ok

[storm sage]

Unironically the best circuits textbook I've read is allaboutcircuits.com

[long matrix]

circus

[storm sage]

https://www.allaboutcircuits.com/textbook/ @potent mason you might find this helpful :)

[storm sage]

Not sure if it's sufficient but it's definitely necessary

[sonic field]

saving this so I can pass it along to others. Thank you!

[long matrix]

yeah im using words stupidly

[storm sage]

Np! Thank the creators of this website, it's really great

[storm sage]

I feel like it should be sufficient if your space is first-countable. If x, y don't have any disjoint open neighborhoods, then you can have a sequence hitting all the intersections of the open neighborhoods or something

Don't quote me on that, my general topology is still kinda bad

[long matrix]

ive only seen the defn of first-countable once

oh god its convoluted

[storm sage]

Oh it's just saying that around every point, you only need countably many things to characterize the neighborhoods

Often you need this condition when working with sequences because you only get countably many elements

Every metric space is first-countable, so it doesn't really matter when starting out

But eventually, topologists like to move from sequences to a more general notion called nets which basically sidesteps this issue of countability :)

[long matrix]

point set

[storm sage]

Uh

Okay then

This is useful in analysis too, if that makes you feel better

[long matrix]

im not an analysis person lol

so when i see sequences...

[long matrix]

I'm trying to understand this intuition along with wiki's defn but well

I can get this but well it doesnt really mean much to me

[storm sage]

Yeah I think the best way to understand it is to think of a space which isn't first-countable and then see what breaks in it. I gotta do something else rn though, but I'll come back to this later if you're up for it.

[long matrix]

waw

[alpine comet]

After a course on point-set topo, I must say the notion of neighbourhood is still one that causes me most trouble

Especially if it's local compactness. Most intuition goes right out of window

[jagged forge]

Maybe I’m just a victim of the Dunning Kruger effect, but I sort of felt like the basics in topology like open sets, neighborhoods, and compactness were pretty intuitive

I mean I guess it gets weird with some of the weird topological spaces and what neighborhoods look like there

[neat lintel]

Its great tbh

[storm sage]

They're intuitive for me for R^n

Not necessarily other topological spaces

[little vine]

Metric spaces you can lean super heavy into the metric

[burnt ledge]

is a topology induced by a metric always T2

[wet berry]

If the metric is non discrete I think so

[burnt ledge]

doesnt discrete netric induce discrete topology is T2?

[deep mango]

Yeah, in fact every metric topology is T6.

Most importantly they're "normal" which says not only can any 2 points be separated by open sets, but any 2 disjoint closed sets can be separated by open sets.

[burnt ledge]

Ohhh is it called normal because topologys induced by a norm are that

that would be quite awesome if thats why

otherwse it would just be fine

Pretty cool tho tq for answer

[wet mortar]

no

[burnt ledge]

oh.

but at least it is the case that they are

[storm sage]

No, mathematicians are just bad at naming stuff

[burnt ledge]

yhhh

it would be especially infuriating tho if like. norm =/> normal. At least with the way things are at the moment we have sanity, and norm => metric => normal topology

[loud snow]

Not true

Naming becomes harder to do

[storm sage]

Okay but "regular" and "normal"? lol

[loud snow]

What is your education level in math/ whats one thing you are currently studying?

[storm sage]

Honestly people make fun of the T axioms but I prefer T3 and T4 to regular and normal

[storm sage]

Is this related to the current convo or the start of a new convo

[wet mortar]

tfw people only name hausdorff

[loud snow]

Current convo

[wet mortar]

kolmogorov and frechet malding

[loud snow]

But its because im curious

[storm sage]

I'm an undergraduate. I'm currently learning differential topology and algebraic topology.

[loud snow]

Oh great

The craziest name I could think of in AT?

Actually the names of spectral sequences I never learned differences between them

I think I only learned what Serre’s one is

The name isn’t enlightening at all though

But idk what other name I would give to those concepts

Or something like homotopy for example, I dont know if thats considered a bad name or not

[storm sage]

homotopy is a good name imo

It makes sense

Similar shape

[loud snow]

Is that what it means?

Homo means similar and topy is deformation?

Nah i made that up

Naming is just harder and the convention of using peoples names in definitions feels antiquated.

But I like it personally but it makes math way too inclusive and it’s impossible to change this anyways

[burnt ledge]

its called Hausdorff because the points can be hausd orff into disjoint open sets

[wet mortar]

so true bestie

[burnt ledge]

i read that in a book once and its so fun

[little vine]

This is funny

Every dwarf has their own little house

[storm sage]

homo means same and top means shape

I guess top means more like place

But I think it's analogous

[loud snow]

How do people find out connections between applied and pure math

Or is it applied math people searching for things?

The most recent thing that comes to mind that I thought was cool was something PCA adjacent called UMAP where David Spivak wrote something about fuzzy simplcial sets that is being used to address issues with the idea

I dont know of any examples of pure people going out of their way for the applied people though

Does anyone have any?

[weary terrace]

I would say that all math is pure math first

If you happened to find some application for it beyond, "just because," then it becomes applied

So if you're saying an applied mathematician's work is helping pure mathematicians

I would assume that simply means their application is also on the forefront of pure math

Pure mathematicians figure things out and then applications are sometimes discovered way later

But all of the framework is laid out because the pure mathematicians figured that out just because they wanted to

There was some example of physicists retrofitting a fleshed out mathematical framework that fit their problem i can't remember the exact story

But basically pure mathematicians worked out all the properties of a certain system and many years later a physical application for this Pure Math construct was discovered

In other words the pure mathematicians help out the applied people by working out all the details to all the questions and scenarios that nobody else ever wondered about

And then applied fields often have the generations of groundwork mathematics established for them as a result

[loud snow]

This isnt how things go though.

Its not that pure mathematicians figure out every single detail that the applied mathematicians start cherry picking. The example I gave is an example of an invented applied math concept but to help prove a certain aspect of it pure math was being applied

[weary terrace]

But how can you say applied math is not a subset of.pure math you know

[loud snow]

?

[neat lintel]

man ppl arguing about pure vs applied

[loud snow]

I wasnt talking about that though?

[neat lintel]

we don't have those in my uni

It's just the math major

[loud snow]

No one is arguing that? Why dont you read my original post?

[weary terrace]

Its the same at many places for undergrad

But you specialize if you study further or in your career

And maybe just have a preference lol

[loud snow]

There are many classic examples like Euler Lagrange equations for principle of least action or Einstein developing Brownian Motion

[weary terrace]

I dodged all the applied courses

[river moon]

I guess you can count the creation of distribution theory and generalized functions theory as consequence of the fact that physicists were using dirac delta function when it wasn't a function in the first place and there was no theory about it

[loud snow]

Oh damn thats a good example

I forgot about this and I never learned much about what distributions were formally, only in passing. It somehow was mentioned in a differential topology class but I forgot context. I think it had something to do with vertical and horizontal decomposition of tangent spaces

[weary terrace]

I think there are probably some good examples we may take for granted

Especially if you stretch it across history

[loud snow]

Yeah I dont think that is worthwhile though

Like focusing on modern math 1800s+?

[flat harbor]

in a historical context splitting hairs between pure and applied is really just a waste of time

[loud snow]

Yeah that was not the intention

The point is that there are somewhat more clear delineations now even though its fuzzy

And the example I gave its obvious who was pure or applied

The umap thing is really cool since the development is as recent as 2020

[flat harbor]

the specific instances where one field inspires another definitely exists

but thats just how acad works?

[loud snow]

The umap thing is coolest imo since it uses category language to help show an equivalence between different metric realizations

[loud snow]

Yeah its hard to see that sometimes

[flat harbor]

like i get ct is this woaah abstractions silly thing and every time its used in a paper it gets added to a reddit post rundown

[loud snow]

Yeah I know how buzzywordy it can be

[neat lintel]

Like 'vibrations' and 'consciousness' are New Age hippie buzzwords.

[alpine comet]

don't forget "toxins, impurities, energy"

[loud snow]

a lot of math couldnt be done without language of categories. Its used in papers very often

[flat harbor]

but if u dont give any context at all for what pure and applied means then it might as well as mean nothing

[loud snow]

You could also make your own interpretations?

[neat lintel]

One YouTube channel called 'Spirit Science' mentioned 'vibrations of consciousness'. What does that even mean?

[flat harbor]

thats... not how communication works lmao

[loud snow]

Like a nearest neighbor generalization on manifolds is arguably applied math

[flat harbor]

i push this vibe actly

[loud snow]

This is how all communication works?

[flat harbor]

for just talking in everyday life

i dont want to clarify about every little detail

but when ure discussing stuff like science and shit then at least try lmao

[jagged forge]

We’re all connnected through the quantum consciousness guys

[loud snow]

You dont need and you never do?

[loud snow]

Thats a weird attitude to have I wont lie

Not everything has clear delineations in math or science

[alpine comet]

let's be honest, if you pull out a random math paper, chances are there won't be any category theory

[loud snow]

If its in geometry then it will?

[flat harbor]

yea and u avoid using those terms

thats standard practice in any field

[loud snow]

No you dont lol?

There are tons of newer math ideas with lots of interpretations

An example is mirror symmetry

[alpine comet]

then that's super specific, lol. Cat theory was created for alg topo, geometry benefited from it naturally

[loud snow]

If you ask 3 profs what it is they can give you 3 different perspectives

[flat harbor]

listen mate u asked a question about whether theres "connections between applied and pure math"

[loud snow]

No it is t super specific?

[jagged forge]

My first introduction to category theory was actually when learning about the dual vector space not being naturally isomorphic

[loud snow]

Most of algebraic geometry relies on category language so what you are saying is very unfounded

There is also plenty of overlap between fields

[alpine comet]

Did I make myself clear? I said cat theory was created for it, hence why it's so common

[flat harbor]

and i think its a nothing burger cause the line that splits pure and applied is one out of convenience

it doesnt say anything about the qualities of the field

[loud snow]

Do you think my question was to do this though?

Do you know what my question was?

[loud snow]

Then you should retract the any random math paper statement

[weary terrace]

They never mentioned category theory a single time i never heard of it from any professor or grad student or otherwise throughout my whole math major

I'm sure its incredibly important and useful and ubiquitous but it doesnt seem necessary for a lot of significant results

[alpine comet]

what? no, my point stands. if you take a random math paper, chances are it's not gonna be about alg geometry.

And cat theory is not commonly seen outside alg geometry

[flat harbor]

honestly idk what im even arguing against at this point if u wanted more examples like umap then cheers fam

[weary terrace]

I went to school about 7 years ago it seems category theory is more popular recently

To be talked about

[loud snow]

Its the opposite. Transparent Element gave an example im looking for

Please try to understand or clarify if you don’t understand what I was saying. I would be glad to help and answer questions

[loud snow]

First time it showed up for me was in grad algebra class when talking about homology

The professor did ANT

[flat harbor]

sorry i didnt invest time into reading ur textwall fam. didnt rly think it was that important

[loud snow]

Most of my school was NT, Dynamical Systems, and math physcis

[loud snow]

If you dont have anything constructive please dont respond next time

[loud snow]

It doesnt show up in a lot of math but for a good chunk of other math its used in the definition for every object

[weary terrace]

I'm curious about it because it sounds very uhhh

Generally applicable

[loud snow]

The language of category theory is meant for that which is great

But when you want to define certain objects CT is the only language you can use versus ZFC set theory language

Typical example being the definition for a scheme in AG

[flat harbor]

lmfao then how about this one, the entire field of real analysis was a pure field developed for describing functions

symplectic geometry was developed for classical mechanics

[weary terrace]

This is like honestly the type of thing i immediately think when i hear "what have pure mathematicians done?"

Uhhh they fucking figured out how to do everything related to numbers in your field haha

[flat harbor]

yea like a large amnt of abstraction is an abstraction of "something"

so ud expect a large amnt of them to start from some "applied field"

[loud snow]

The story is more complicated than that but I was also aiming for more recent examples. The example transparent element gave was good, but I am curious about modern day things

[weary terrace]

You should ask a professor

If youre in school

[loud snow]

Well im not

[flat harbor]

modern day? like 21st century stuff?

[loud snow]

Or 20th

[weary terrace]

They'll have the years of experience in the relevant fields to give you great examples

[flat harbor]

nobody knows how the dependencies are for contemporary acad its all fucked up

[loud snow]

Yeah I have a feeling some people do but its really hard to keep track of

And there doesnt seem to be any consistent tools for doing it either

[alpine comet]

Creation of knot theory was from the effort to classify knots a very, very long time ago. Most foundational papers in this field are in 20th century

[weary terrace]

No academia is a mess

[loud snow]

It would be cool if academia had more documentation on this for the amount of work they do

[alpine comet]

Many of prominent researchers whose names are with essential tools are still alive and working

[loud snow]

You are joking right?

[weary terrace]

If the classes i have seen as a tutor are any indication there is no order or accountability to half of what is being done in higher ed

Math at least you can usually grade objectively xD

[flat harbor]

examples from what i know is that "very real physics" was the backbone for developing gauge theory

[loud snow]

This becomes less and less true

[flat harbor]

every field related to computers wuld fit ur bill as well

[alpine comet]

For example, in a very recent development, Lisa Piccirillo used something to prove that Conway knot is not slice, called Rasmussen's s-invariant

[weary terrace]

I did get some courses with projects at upper level where i was graded subjectively I can't lie

[alpine comet]

And sure enough, Rasmussen is alive and well, just created this tool maybe 10-20-ish years ago. He's teaching in UK, Oxford iirc

[flat harbor]

but again finding examples where u can historically track "this inspired that" runs very short and frays all over the place the more u get to modern examples

i think itd be harder to find fields or concepts that abstractise a single "thing"

[loud snow]

This isn’t exactly what I asked but its close

Not about inspiration but more about directly helping another field

[alpine comet]

Another example maybe with Pachter and Sturmfels. They are mathematicians, but went out to help biologists.

[flat harbor]

ok but like what does that mean

do u mean linked by citations

[alpine comet]

Almost every developments we have in the study of RNA can be traced back of many of their papers back in 1970s

they really made the effort to create math models for it

[loud snow]

Yeah thats the closest

[alpine comet]

Or don't ask me. Ask Edward Witten.

[loud snow]

Like I imagine if there are important conversations that happen between two academics in different fields and then one decides to change projects and start going another way

Maybe not as dramatic but something similar

[flat harbor]

in that case u rly wuld have to ask acads in the field

[loud snow]

I think there was some lady that stopped being math professor to study neurology and wrote an influential paper recently

[alpine comet]

Tbh, I would cite my own works because they are probably the closest things I can find atm 😄 but I am not that pompous

[loud snow]

Yeah ill have an opportunity next year

[flat harbor]

id imagine everyone has at least one or two memorable interactions they can talk abt with a "im not sure if this is what u asked for but"

[loud snow]

Yeah right

If you are still in school id ask you to ask one of your professors and report to me

Isnt that serious tho

[wet mortar]

tfw rasmussen

also no, cambridge

[alpine comet]

smh, not like I care about UK anyway

[wet mortar]

my rasmussen impression goes crazy

[neat ruin]

Was 20x3 bru😭

[wispy crypt]

i have an issue

i have coaching and school

in a board year

[neat lintel]

What does that mean?

[wispy crypt]

like boards?

uhh

they're like

the main exams you have in school whcih actually matter

but not for college applications

[neat lintel]

I hate exams

[wispy crypt]

yeah most people do

i try to concnentrate on school so i get good baord marks

so i do really bad in coaching

[neat lintel]

What is coaching?

[sly flint]

To do good in coaching+school, you must have good retaining capacity. So you don't have to study again and just review notes.

[neat lintel]

What is coaching?

[wispy crypt]

yeah thats the thing...
i dont

i dont know whcih to contentrate on though

im in 10th

[sly flint]

Institutions where people go to study for olympiads and mostly entrance exams like JEE or NEET at the not so small cost of 500,000Rs< for 4-3 years.

[torn willow]

My personal experience is your time should be spent on JEE/NEET

Board should be studied 1 day before the relevant exam

Board is like JEE \union irrelevant crap

[wispy crypt]

uhh its icse so

[torn willow]

Skipping irrelevant crap can still get you like 90

[sly flint]

NCERT based exams are pretty elementary so don't worry about them. Schools often make their tests difficult than the actual board paper.

[torn willow]

Ah my condolences

[sly flint]

Dorime~

[wispy crypt]

its kidna hard to get above 90 wihtou8thj studying

[torn willow]

My thing applies to CBSE only, ig

[wispy crypt]

in isce

[torn willow]

ICSE is a completely different can of worms

[wispy crypt]

wchih makes yopur enlgihs decent

shoud i switch to cbse in 11th

[torn willow]

Yeah

CBSE is much much easier

And less effort

[sly flint]

Definitely.

[torn willow]

Plus people only look at your raw marks, ig. It's easier to score in CBSE

[neat lintel]

I would have to break pots in zelda for decades to get that amount of rupees

[wispy crypt]

ok it aint thats much

its like a fourth of hwo much i pay for school

[torn willow]

It is a significant amount

[sly flint]

Plus foreign colleges don't really care about which board you come from, cbse, icse or ib. Just be at the top 5-10% of your class.

[torn willow]

Yeah ICSE is like hard mode with no benefits

[sly flint]

And have a good profile, bag some olympiads. Take the SAT.

[torn willow]

Something like 1L people get 490+ in CBSE iirc

[neat lintel]

Oh god more college apps stuff. I hate that crap it's so unfair

[sly flint]

Yeah.

[torn willow]

https://timesofindia.indiatimes.com/education/news/cbse-class-x-results-2-3-lakh-get-90-95-percenters-double/articleshow/69209440.cms
Ok, 50k is 475

[wispy crypt]

i kinda like icse tho

like

i mean

0 offense

[torn willow]

Do you want to learn or do you want to get into a good college without overstressing yourself

[wispy crypt]

but the people in my coahcing are a bit
hwo do you say it
rowdy
no offense

[wispy crypt]

learn

[sly flint]

People being people. There are good CBSE schools too y'know.
I've switched from ICSE to IGCSE and ultimately landed at CBSE.

[wispy crypt]

whcih would you suggest

[sly flint]

Are you aiming for JEE/NEET?

If yes, then CBSE.

[wispy crypt]

ig so

id think we habve the money for mit or anything

its just

idek

[sly flint]

People from CBSE have also gotten into MIT.
There was some kid in allen who got letters from MIT, oxford, and some other uni I can't remember.

[wispy crypt]

wait

are you in allen

[sly flint]

Currently? Yes.

[wispy crypt]

us

[torn willow]

Yeah one of my classmates got into MIT

[wispy crypt]

what did he do to get lettters form mit

how geiNus brewh

[torn willow]

Jee rank < 10

Olympiad silver medalist

[sly flint]

God dayum.

[wispy crypt]

FR

wait

alr

[sly flint]

Just do well in whatever you try.

[wispy crypt]

wait

ok

this may be too personal

but whcih center do you go to

[torn willow]

That will totally doxx lmao

[wispy crypt]

fine wtv

[sly flint]

I'm in [redacted]? Which state are you in?

[wispy crypt]

haryana

nvm then

[sly flint]

Yeah.

[tender holly]

Hey, can anyone suggest a difficult math problem related to a parabola ax^2+b

[rocky shuttle]

Compute an arc length parametrization of the parabola

[zealous garden]

I was just thinking about Arc length parameterization

[static loom]

compute the difference in height between the focus and where a line of slope 1 is tangent

[neat lintel]

Is tau better than pi?

[rocky shuttle]

Take the worst of both worlds: pau

[neat lintel]

Is pau 3tau/4?

[neat lintel]

Which is equal to 3tau/4.

[rocky shuttle]

No, it's 1 pau

[static loom]

I prefer ti, sqrt(pi*tau)

I mean, for one circles are geometrical so we should be taking the geometric mean

plus it has the feature of being equal to sqrt(2pi^2)=sqrt(2)pi is beautiful how it combines the diagonal of a unit square length

I mean wow

amazing

unifying squares and circles as one

[raven plaza]

Surely π+e

[deep mango]

2pi comes up a lot more often in math than pi does, but changing standards is only ever worth it if the change makes a big difference. having 2's in some places is not a big inconvenience for just about anyone who regularly uses pi

[neat lintel]

It's not that much work.

[deep mango]

so "better" but not better enough

[zealous garden]

Tau is infinitely better than Pi

Because Tau day is in the summer

[rocky shuttle]

spring > summer

[deep mango]

Surely having it in March is better so that people can celebrate it in school

[zealous garden]

Nein

[rocky shuttle]

Ja

[deep mango]

If it were in the summer, when would you get together with other math people to celebrate it

[zealous garden]

Summer is better than spring, spring is the worst season

[static loom]

funny I was just reading about a compromise for some old networking standard where they proposed 32 bytes or 64 bytes, and the committee compromised on 48 bytes lmao

[deep mango]

You're both nutters, fall is the best season

[static loom]

I prefer 'autumn'

[deep mango]

Spring is second best and summer is worst

[static loom]

fall sounds disasterous

[zealous garden]

Fall is better than summer, but winter is best

[deep mango]

Wow

[zealous garden]

Having it in summer is better

[neat lintel]

Not where I live.

[zealous garden]

Because it promotes seeking knowledge yourself, and year round learning to help combat the common atrophy of knowledge during summer months in children

[zealous garden]

That's what you get for choosing the wrong hemisphere to spawn in

[rocky shuttle]

What if I'm on the equator

[zealous garden]

Then you win

[neat lintel]

Do Flat-Earthers deny the existence of the Equator?

[rocky shuttle]

[neat lintel]

Why do they believe Earth is flat?

[rocky shuttle]

They were not taught Riemannian geometry in school

[zealous garden]

I need to learn Riemannian and PseudoRiemannian geometry

God told me to

[neat lintel]

If a Flat-Earther ever tells you the ocean would fall off if Earth were spherical, ask them 'But where would it fall to?'.

[static loom]

flat earthers don't exist

[neat lintel]

They do.

[static loom]

nope

[zealous garden]

Flat earth denier?

Based

[static loom]

😉

[neat lintel]

That's a perfect way to mislead someone into thinking you're a flerf. Look up 'Myth of the Flat Earth'.

[deep mango]

I didn't like the idea of flat earth before

But now that I know they're called flerfs

I think ill look into it more seriously

[static loom]

lol

lets become flerffers

so flerffin' cool

[neat lintel]

Why don't you seriously look into why people think insects aren't animals?

[deep mango]

Okay

[static loom]

we already know they're not

[deep mango]

Let's start with a simpler question

[static loom]

ultra was just showing us some diagrams earlier

[neat lintel]

Insects are animals.

[deep mango]

Are sponges really animals?

I mean come on

[static loom]

https://cdn.discordapp.com/attachments/487651208048410627/1132294249749155940/Screenshot_20230721_225200.jpg

refute this wise guy

[deep mango]

I guess I could believe it

[neat lintel]

That's not an animal, that's a robot made to look like an animal.

[static loom]

exactly

[neat lintel]

It's not an insect.

[static loom]

like you said, it's not an animal, that's a flerffing robot

[neat lintel]

But why do people think insects aren't animals?

[static loom]

nobody thinks that

this is another strawman for the intellectually lazy to procrastinate attacking

find real enemies (not me)

[neat lintel]

Many people do.

[static loom]

name one

[neat lintel]

You'll find some here: https://www.reddit.com/r/polls/comments/u72xa6/are_insects_animals/

[static loom]

they're trollin

[neat lintel]

They aren't. They genuinely think insects aren't animals.

[static loom]

then go ask them, what are you doin here asking me

[neat lintel]

The post is closed.

[static loom]

make a new post

there's many of them

[neat lintel]

I'll do that.

[static loom]

cool

good luck

[neat lintel]

Why do people think spiders are insects?

[static loom]

dumb

obviously spiders are arachnids like octopuses cause they have 8 legs

[neat lintel]

An octopus is a cephalopod mollusc, not an arthropod like an arachnid.

[static loom]

oh? regardless :2

[little vine]

I bet spider taste like crab but I'm too grossed out to find out

[neat lintel]

They're both arthropods.

[zealous garden]

So they probably do then?

[little vine]

You know those 17 year locusts

I bet you could fry those up

They have those dehydrated shrimps

At the grocery store

[static loom]

oh throw them in ramen

[little vine]

Ewww mang

Waiter there's a fly in my soup

[static loom]

thats fly soup

[little vine]

waiter there are not enough flies in my soup

[tepid light]

fly soup

[stuck crown]

Good day

[split pawn]

hi meir

[stuck crown]

Hi muhammad

[neat lintel]

Hi

[stuck crown]

No

[split pawn]

Hiiiya meir

[stuck crown]

You go back

[neat lintel]

Me ?

[split pawn]

Yes

[stuck crown]

Who else

[neat lintel]

I didn't even do anything

[stuck crown]

[tepid light]

good day

[stuck crown]

Well anyway

[split pawn]

yepyep

Im here

So, you had some rest?

[stuck crown]

I woke up from my nap

Yes

[split pawn]

I didnt have any

[stuck crown]

Why not

[split pawn]

Was engaged in this biology discussion with someone

who thinks cladistics is everything

[stuck crown]

Oh

[split pawn]

"invertebrate" doesnt make sense

[stuck crown]

[split pawn]

and "tau" is better than pi

[stuck crown]

oh

that guy

[split pawn]

Yeaa

Oh hes here

shhhhh

[stuck crown]

Um

[neat lintel]

The word 'invertebrate' doesn't have any justification to exist.

[stuck crown]

shut up

and go to regular discussion

[neat lintel]

Hello, inarthropod. What do you have in common with a jellyfish, you ask? Well, you both lack jointed legs and a chitinous exoskeleton.

[tepid light]

finnboltz

[split pawn]

Thats his message for everyone

[stuck crown]

My legs are jointed

[split pawn]

Ig Ill muffle da voice meir

[stuck crown]

Yes

[neat lintel]

They aren't segmented, though, in the same way arthropod legs are.

[split pawn]

yeah

[neat lintel]

Isn't 'inarthropod' a silly word?

[split pawn]

So ig meir this channel has been affected too

[stuck crown]

This channel has been tainted

breached

[split pawn]

Thats because YOU created it, not the scientific community.

[split pawn]

yesh

Now what do we do

[stuck crown]

We need a password on Discussion 2

[split pawn]

We need to construct a hazmat only area

[stuck crown]

Hm

[split pawn]

And the hazmats are the ones we wear at the 100pc mortality hospital

[stuck crown]

We could go to a restricted channel if I was active role

[split pawn]

So that no one else gets that

Yeah, sad.

Actually

[neat lintel]

There's no such thing as an 'invertebrate'.

[split pawn]

We'll move to

[tepid light]

yeeee pull up w da hazmat suit

[split pawn]

yeh

[neat lintel]

Do all inarthropods need to do so?

[split pawn]

<@&268886789983436800> check his message log, why is he deleting and repeat pinging me with his message. I received the information once, and I need not reply.

@neat lintel

This behaviour is annoying

[neat lintel]

As annoying as the word 'invertebrate'.

[split pawn]

You're blocked.

[neon tundra]

24h mute, stop being annoying

[fierce ether]

Asking for a reference... Does anyone know what $\mathbb{Z}_n^{\times}$ means?

[fathom swallow]

pilgrim

[fierce ether]

It is a kind of group, but I don't know what group exactly.

Also, $\mathbb{Z}_0^{\times}$ is supposed to have order 2. I suppose this means it has 2 elements.

[fathom swallow]

pilgrim

[fierce ether]

I am studying this in the context of Euler's totient function.

[mint canopy]

It's the group of units of Z_n

[fierce ether]

Thanks. What is Z_n?

[mint canopy]

Where did you see this written?

[fierce ether]

I am doing a summer project formalizing Euler's totient function in Agda. So I have to learn a bit of its background. This is where I first see it mentioned:

[mint canopy]

OK

Z_n is the ring of integers modulo n

It's also more often written Z/nZ

[fierce ether]

OK, thank you.

Aaaaah, this clears it up. Thanks!

[mint canopy]

You probably won't need any more information on ring theory to get this done

But that being said, you may indeed need to pick up a book on number theory

Some books write U(n) instead of Z_n^\times, so perhaps you've seen that

But most if not all use the notation Z_n or Z/nZ

[fierce ether]

Hmmm, but the way Z/nZ is defined, I don't see how Z/0Z has 2 elements, as modulo 0 is not well-defined.

[mint canopy]

Well, writing Z_0 is very unusual, but as it happens it is totally well-defined.

Z_0 is, by the typical definition of modulo and of quotient rings, just Z.

What definition did you have in mind?

Oh but I see another issue

Z_0 does not have two elements

[fierce ether]

OK, thanks, I inferred the definition from n >= 2.

[mint canopy]

Z_0^\times does

[fierce ether]

Yes, I mixed up these.

Thanks.

[quick beacon]

@hollow hatch if you're still around:

I'll do just one of the two terms.

2021 is 5 mod 7. We use mod 7 here because we're interested in the divisibility of the result mod 7.

2022 is 0 mod 6. We use mod 6 here because when multiplying 5 under mod 7, you require 6 multiplications to return to 5. 5 -> 25 = 4 -> 20 = 6 -> 30 = 2 -> 10 = 3 -> 15 = 1 -> 5 (this is what I was talking about earlier about the multiplicative group of Z/7Z).

So we arrive at 2021^2022 = 5^0 mod 7 = 1.

You can do something similar with the second term, then finally after adding you just have to do one more exponent.

Sorry about the delay, I had to take care of irl stuff.

[hollow hatch]

It's i already figured it out my teacher explained it to me. Thanks she didn't use this method it's a lot easier

Thanks

[serene pulsar]

more studying 💪

I have basically 2 days left to go

[oblique beacon]

What's the study.

[serene pulsar]

Today I'm on the Level 6 Exam review, and almost done with it. It's the final exam review that would place me in Calc 1 when I enter college, which is what I want so badly.

I think I started at Level 3 maybe 2.5 weeks ago?

When I started I didn't know basic things, like how to subtract/divide fractions, simple trig stuff, etc.

But now I'm doing a lot of trig and it's not that bad, and a lot of other harder stuff like logarithms.

I wish I had learned this stuff in high school honestly because I'd probably be flying through it now

but I am optimistic and enjoying the process

[marble delta]

Is it just me or does anyone else like discords old username system better

[neat lintel]

dude

are you living under a rock? literally everyone hated this change

it's just been a while so the outrage has died down

[split pawn]

Hes been living under a metamorphic rock

[vernal token]

I didn't change my username

[gaunt quest]

stay strong 💪

[vernal token]

I just click the notification away everytime I log in

[oblique beacon]

Lol I'm glad you're enjoying the process because I'm going through hell rn.

[serene pulsar]

😔

[mental stratus]

https://tenor.com/view/yay-gif-24728828

enjoying it matters the most, you'll get through it trust

[serene pulsar]

thank you 😄

[oblique beacon]

What he said

[serene pulsar]

my fiancé is bringing me home sweet treats from a bakery, sugar and dough will be the perfect math fuel

vegan chocolate macadamia cookie, key lime bar, and an eclair 😋

[neat lintel]

lucky

[serene pulsar]

I am very lucky. I definitely need it after all this studying

[neat lintel]

I don’t think I’m gonna get the chance to eat my dinner until tmr tbh. The pork’s been brining for a good amount of time, but I’m still making the marinade that ima put it in afterward

Lmk how ur goodies go

[serene pulsar]

I will, and you too. That sounds really good

[oblique beacon]

Key lime bar? I thought only lemon bars existed.

[proven plinth]

bruhhh

but good thing you know what a fridge is

[neat lintel]

It’s cuz i didn’t start around or before 10AM

[proven plinth]

lately I've only been eating light stuff

cuz of the heat

[neat lintel]

That’s reasonable

I haven’t been eating much

I think I’ve had about 600 calories today and i honestly dgaf

I sleep in the next 3-5 hours too

[proven plinth]

I didn't breakfast, didn't really eat lunch, but ate 2 pastry thingies bread cheese and popcorn at dinner, hell nah that ain't healthy lol

[neat lintel]

I’m still alive and weightlifting while I do that 🤷

As long as I don’t feel like i need to go to the hospital it’s wtv

Nice dinner choice

[proven plinth]

thanks, sorta ate what I could get

[proven plinth]

600 calories ain't much tho

[neat lintel]

Yeah ik

[proven plinth]

unless you forgot a digit

[neat lintel]

If I forgot a digit, I would need to rethink my dating life

[proven plinth]

ah nvm I'm tired, I didn't read the text above

lul

idk, average calory intake should be at around 3200

how is one supposed to achieve that

[neat lintel]

3200 is a lot unless you’re active at the gym

[proven plinth]

ok maybe google is shitting at me

[neat lintel]

If you’re pretty sedentary and you want to stay around the same weight i don’t recommend going that far above 2000

Unless you have a really fast metabolism

[proven plinth]

eating and drinking when being hungry and thirsty is mostly fine I guess

assuming you have a healthy hunger sensation

[neat lintel]

My meal today has been one slice of pizza, one thingy of cheesey bread, and a quarter of a tostada

They are all leftovers

Me making food is declaring I don’t wanna eat pizza a third day in a row

[proven plinth]

that's good

there's awful sugar days, but I sometimes just can't help it, some days I ago I started eating like cake followed up with energy thruout the day an occasional cacao, other sweety drinks, a damn pudding and other stuff I can't remember

[neat lintel]

Everyone has awful sugar days. It’s when you have them too often that it’s cause for concern

One sugar day spaced far apart from the last sugar day is a part of living a happy life

[jagged forge]

if u have too many bad sugar days u might get type 2 diabetes like me

though that’s years of bad eating tbh

[serene pulsar]

I never thought I would get this problem, I had to study so much haha https://imgur.com/a/46af6la

I didn't even know what a unit circle was

This has been the hardest problem yet, but now I think I've got it down

[jagged forge]

The unit circle… enemy of high school and college students everywhere

[serene pulsar]

I learned a neat trick from a reddit comment about using your palm (facing you) to calculate the coordinates (cosine/sine) easily

that helped a lot honestly

It's silly tricks like that that carry me

I need to be able to see a pattern myself to learn something

[orchid zealot]

I would be most pleased if thou wouldst demonstrate this for me.

[serene pulsar]

Oh yeah let me get back on my PC real quick. I was taking a study break to lie down lol

https://www.reddit.com/r/math/comments/842i0w/comment/dvmmct4/

here it is

Comment copy and pasted in case anyone doesn't want to visit the link:

Hold your left hand out in front of you, palm facing you. Your pinky is 0 degrees and thumb is 90. You other fingers represent 30 45 and 60 degrees. You count sin starting from your pinky and cos from your thumb. The numer of finger you count is the radical and it's always over 2. Thus;
Sin 30 = from pinky 1 finger away =1/2
Cos 45 = from thumb 2 fingers away = sqrt(2)/2```

[serene pulsar]

I tried a bit of each of the treats. The eclair wasn't the best eclair I had, but it was huge and still yummy. The keylime bar was too strong imo. The tiramisu was awesome, and the vegan chocolate nut cookie was the best treat.

[neat lintel]

Treat feedbacks r what I live for

Now that u said key lime bar is too strong I wanna try it

I like lemon/lime

[serene pulsar]

I love lemon/lime and strong flavors, but boy was it powerful. I think if there was a bit more crust it'd be easier to eat.

[deep mango]

tiramisu is hands down the best dessert

[neat lintel]

hi

[deep mango]

and i will not take any dissent on this

[neat lintel]

I'm new

[deep mango]

hello siddyboy

[neat lintel]

Can anybody tell me what can we do here?

[neat lintel]

hi ryc

[deep mango]

the discussion channels / chill are just for random discussions, sometimes involving math, sometimes not so much

there's a help section above where you can ask questions or help others, see #❓how-to-get-help for instructions

below, there are topic channels for particular kinds of math, including channels for undergraduate / graduate level math classes

[neat lintel]

ok thnx

[deep mango]

enjoy yourself

[neat lintel]

okayy

[serene pulsar]

This was my first time trying it and it was great

[neat lintel]

Malnutrition -> Brain damage

[deep mango]

i have had many tiramisus in many forms across several nations

[woven whale]

panna Cotta>>>>

[deep mango]

a good tiramisu captures the perfect mix of the warmth of a fuzzy, disembodied nostalgia and the chilly shivers of culinary sublimity

[jagged forge]

That sentence alone is a culinary masterpiece

[deep mango]

a good panna cotta, on the other hand, is just bearably edible enough to allow the diner to eat it without vomiting

🤢

[serene pulsar]

woah

I've always wanted to try it after seeing it on Bob's Burgers funny enough haha. I've never seen it illustrated or IRL before that.

Only ever heard of it and bad descriptions of it lol.

[little vine]

It's p good. Lemme see @nimble crest wax poetic about cheesecake next

I'm ryc, I'm from nyc. Our food is better than yours. Cope.

[deep mango]

wrong ryc

[deep mango]

umm, well i have a lot of opinions about cheesecake

but they're more vulgar

most importantly, it's not a fucking cake

except for burnt basque cheesecake or those japanese cheescakes, which are cakes

i think cheesecake is really good but A. easy to fuck up and B. overrated (i previously overrated it as well)

[jagged forge]

I’m diabetic and I wish I still could eat multiple slices of cheesecake

[little vine]

Sorry

I don't actually think you're a food snob

[jagged forge]

No I definitely am not

[little vine]

Not you

[jagged forge]

Oh

[little vine]

Ryc

Ahahaha

[deep mango]

im a food snob

[jagged forge]

I was like what do u have against me lol

[little vine]

Oh

[deep mango]

thats a point of pride

[little vine]

You do seem like an authority on the matter

[jagged forge]

How would you classify cheesecake if it ain’t a cake

[deep mango]

it's a tart

[little vine]

Based opinion

I agree

[jagged forge]

Google agrees with you

[little vine]

It's sorta a custard right

I haven't made it in a hot minute but don't you use a shit ton of eggs

[long matrix]

ur a tart

[serene pulsar]

Welp I'm going to bed for tonight. I'll have all day tomorrow and the next day to study, and then the exam. I have 5 more questions on the review to learn and then I'm going to measure myself by taking the review while timed, with just a calculator. Hopefully that test goes well and I can review any questions I get wrong/have forgotten.

I think it's going to be tedious though because to review I basically have to press "get similar question" on all, but they only let you do that every 5 seconds so I have to wait in between to refresh the exam or just click retry as I go. I'm steering away from the latter because if I see my previous answers at all I'm sure it'll influence my results.

[quasi jetty]

Please read #❓how-to-get-help

[meager torrent]

Hi everyone,
I hope that I am asking on the correct channel.
How can I learn mathematical thinking beyond solving math exercises? I want to understand and achieve a high mastery in Calculus I, II, III, linear algebra and analysis in the following academic year. So far (end of 2nd year) I have learnt some parts of Calculus I, II, and III, but not as rigorously, because I am an economics student. Next year I will learn them more thoroughly in an econometrics/statistics department. So far I got ~ 3.0/4.0 GPA from my math courses and 3.6/4.0 from my stats/econometrics courses.
Do you know maybe any courses that could help? Or are there any learning techniques that you use and you found them helpful?

[neat lintel]

What is the severity of malnutrition necessary for the brain to have noticeable (and irreversible) impacts? I am perfectly healthy atm. The closest things I got r serious cases of malnutrition need to occur for at least 3 months, and in extreme cases of anorexia brain damage may occur

Long story short I am not worried about my brain. Especially when I know I have access to more food that I’m not afraid to eat the moment I understand my body needs the vitamins and minerals

[serene pulsar]

Being short on calories for a day definitely doesn't cause malnutrition lmao.

[neat lintel]

it might cause you to be hungry though

[serene pulsar]

I have found a lot more help in reddit comments and this server than in any of the educational videos they provide on the review lol.

My learning style is so different from how they expect me to learn, probably because I'm autistic. They seem to just want me to memorize things, but I can't memorize things. I need to be able to derive them myself, and then I'll understand.

Like I had no clue why a reference angle of 30 degrees would have sides 2, 1, and sqrt(3), but it's obvious now when I think of it in terms of sine and the unit circle. If the sine that correlates to 30 degrees on the unit circle is 1/2, then of course the hypotenuse is 2 and the opposite side is 1, and then I can figure out radical 3 from there.

I can draw the whole unit circle now from "memory" after only learning it yesterday, but that's only because I found a pattern that works for me. I know how to get all the degrees, so I can just calculate the radians which are otherwise confusing to me in their pattern, and I can easily get the coordinates with that palm trick (which I don't even need anymore cause I learned the pattern).

When I initially saw it I was so daunted because the video expected me to just memorize it all lol.

Without telling me why it is like it is.

Anyway, back to studying 💪

[desert crest]

hey

[cold rivet]

is there a name for this rule

like

if i divide any nonimaginary positive number by 2 or divide it by 2 i will eventually get

like 2-4 or like 4-8 or 8-16

it will always end up between all of those

[mental stratus]

nonimaginary positive number?

[cold rivet]

yes

[mental stratus]

do you mean positive reals?

[cold rivet]

yea

[mental stratus]

[cold rivet]

agreed

but like

does someone understand what i mean?

like if it was with 3 then it woukd be 3-9 9-27

they would always end up in these “hoops”

i call it hoop theory

lets goo no other math concept is called that

im gonna study it and write a book

[solar hawk]

Wat

[solid snow]

you've just described exponentiating by 2

[cold rivet]

yes well sort of

if i multiply or divide a number a certain amount of times (by 2) it will always end up in certain hoops