serious-discussion

[ocean harbor]

https://cdn.discordapp.com/emojis/1048660781123780749.gif?v=1&size=48&quality=lossless

here's another one im current working

[long matrix]

kawaii

[ocean harbor]

without pen

[rocky shuttle]

Did you also draw the background here?

[ocean harbor]

I don't have any suggestions about background so I added a math background with glow

looks good

[wanton coyote]

With finger?

[ocean harbor]

ye index finger

[opal marsh]

Drew that with just finger is indeed IMPRESSIVE🤩🤩🤩

Nice job!🧡

[ocean harbor]

thanks

[latent edge]

I see demons, I'm satisfied

[limber stratus]

In your opinon whats the hardest calc?

[ocean harbor]

optimizations

[limber stratus]

I mean 1,2 or 3

[ocean harbor]

most people say calculus 3 the easiest

but perhaps calc 2 is harder

[vast wraith]

it’s so extremely weird to me how standarized these things are over there

[limber stratus]

Okay! I was thinkin about jobs for fall and wanted to feel out the waters with calc

Was thinking about tutoring at like kumon or somethin

[dire stump]

violent kumon flashbacks

[neat lintel]

react what you think the best variable is

[limber stratus]

wait why

[dire stump]

i just remember my parents making me go and hating it

but at the same time i'm grateful because it made me really good at math for my age and it's probably part of why i started to love it and became a math major

[surreal bison]

yeah i stopped going to kumon when i got better at mathematics than the head of the center

that indeed made it hard when neither of us could figure out the questions

[neat lintel]

participate pls i wanna see

[lunar python]

kumon cooked

[latent edge]

stop using the fucking word "cooked"

[limber stratus]

Would it be a bad gig for a college person

[latent edge]

none. all are easy

[tardy summit]

For me calc 1 was the hardest not because of the material but because it's all new

[dire stump]

based

[static loom]

thats so raw

[long matrix]

yall cooked

medium rare

[deep mango]

Youre burnt to a crisp

Im gonna roast you

[static loom]

let him cook!

[neat lintel]

Hello people. Can i partition a disconnected graph into two sets of vertices such that every vertex in one set is joined to every vertex of the other set?

[static loom]

take a graph that's just two vertices with no edges

good luck

[neat lintel]

Fuck me

My argument relied on it not being true

[static loom]

in a more general sense, it sounds like the kind of thing that would be true iff it was a union of two bipartite graphs

but I'm thinking that's not really true didn't think it through at all

[neat lintel]

I'm trying to create a proof to prove that if a graph G is disconnected, then it's complement is connected

The complement can only be connected when the previous statement is true, right ?

At least intuitively

Sorry, mistake

[static loom]

I'm thinking if G is the union of A and B, then since there are no connections between the vertices of A and B that it means in the complement every vertex of A connects to every vertex of B and vice versa, so if you want to get from some vertex a in A to b in B, they're already connected and if you want to get to some vertex a to a' both in A, since b in B is connected to every vertex in A, a - b - a' connects them

[neat lintel]

And that is the only case we need to deal with, right? Because what i'm thinking is that every other partition (A, B) of the vertex set of G will have at least two vertices, one in A and another in B, such that they are non-adjacent and thus their complement will be adjacent, right?

I just need to show the case that would make the complement of G disconnected is actually impossible

Does it make actual sense?

Because it feel like i'm filling too much of the proof with intuition

[neat lintel]

And that is what i think i thought, more or less. Just that we didn't learn about paths still

Can understand it without using paths though

[static loom]

I didn't think I said anything about paths

[neat lintel]

Fair enough

That is essentially my argument then

[static loom]

I pretty much gave a full proof so I'm a bit confused by what you're doing

[neat lintel]

Is the union of A and B the set of vertices of G?

[static loom]

yeah, specifically A is a completely connected component, it's a subgraph of G that's NOT connected to B

I feel like my terminology might be weird in my last statement there. A is just a connected graph disjoint from B and the union of A and B make G. B need not be conected though

[neat lintel]

Does A really need to be connected though?

[static loom]

I'm choosing it for convenience

[neat lintel]

I see

[static loom]

G can be decomposed into some finite disjoint union of connected graphs

[neat lintel]

Is that a theorem?

[static loom]

what is your definition of disconnected graph

[neat lintel]

A non-connected graph. And a connected graph is a graph such that every one of its partitions (X, Y) has an edge ending in a vertex of X and a vertex of Y

[static loom]

cool so then a disconnected graph has a partition of (X,Y) so that there is not an edge from a vertex of X to Y, right?

[neat lintel]

Indeed

[static loom]

let's pretend we called those partitions A and B instead of X and Y

now since a graph has finitely many vertices, and since a partition must have at least 1 vertex, the size of these graphs is strictly less than the starting graph

and so we can do a little induction and keep going down until we have only connected graphs

and this is the finite union we're talking about here

[neat lintel]

Makes sense

[static loom]

maybe I shouldn't have said this, I was just trying to relate it back to what we were calling them in our problem

but whatever ok cool

idk if this helps, but if your graph G decomposes into a bunch of graphs, adding more edges within each of those connected components to make them complete graphs will only take away from the eventual complement so won't hurt your end result of trying to prove the complement is connected

specifically because then the complement would be a complete n-partite graph, with n the number of components of G

if that helps to draw out an example and think about proving that a complete n-partite graph is completely connected

that will always be a subgraph of the complement of your graph, since your original graph is a subgraph of the complete graphs (thereby adding in more edges in the complement)

[neat lintel]

So the argument is: Well, since adding the missing edges between those connected graphs gives us a complete n-partite graph, our complement will have to be connected?

That's pretty neat

@static loom Thanks a lot for the help

[static loom]

yeah you're welcome

[surreal bison]

that's cooked

[surreal bison]

you think stochastic calculus is easy? interesting.

what about the umbral calculus

[neat lintel]

Ur username is inappropriate

[surreal bison]

or like those functional calculus shenanigans

[neat lintel]

How is that @neat lintel ?

My nick is because of the god, it's not supposed to be wordplay

[latent edge]

umbral calculus is fun

I've been putting in some gucci stuff to NT

beautiful art

[latent edge]

stochastic calculus is boring

sorry

stochastic just makes me think of stats

I don't like stats

[surreal bison]

deltoid

it's deep analysis

just

no numbers

[latent edge]

I'm good then

that's what I usually deal with number theory

[surreal bison]

look just imagine some loglogs

[latent edge]

I'm good -> that is fine with me

not like "no thanks"

[surreal bison]

good!

[latent edge]

[latent edge]

ghost ping

[ocean harbor]

https://media.discordapp.net/attachments/1182503419529941164/1226585413011902655/1218065854873341962.gif

[latent edge]

are you serious

[vast surge]

No I'm zorn's lemon

[latent edge]

https://tenor.com/view/slow-loop-koharu-minagi-pout-pouting-pouting-anime-gif-24517204

[modest cove]

guys is the stewart calculus book good?

for multivariable calculus?

and differential equations calc 4

[empty mirage]

Maximally sour lemons

[long matrix]

deltoid

[rocky galleon]

Only one way to find out brother

[lime cedar]

i have a question about adobe, can i ask here? or no

[north topaz]

just ask

[lime cedar]

I'm trying to combine pdf files into 1 pdf but adobe doesn't show the combined pdf

howwwwwwwwww do i fix this

[ocean harbor]

cant you use something else

adobe sucks

[flat harbor]

theres literally online tools everywhere

[north topaz]

https://www.ilovepdf.com/, if you can't be bothered to find one yourself

[ocean harbor]

https://tenor.com/view/calculus-cat-cat-math-studying-cat-gif-23164559

[tacit magnet]

His face 😭

[vernal token]

Why is the girl reading it out loud

[latent edge]

I would be terrified as well

It's not Rudin

[tacit magnet]

[ocean harbor]

[icy void]

Why should i not major in mathematics

What r downsides of math major

[sonic sentinel]

rubber duck strategy

[steep nexus]

im pretty sure the mental reasons are number 1

[neat lintel]

You're gonna be poor most likely

And it's quite stressful, even worse when you get to the shit teachers that gatekeep courses you gotta do

[old oak]

Because you ask the same question repeatedly and clearly ignore any responses, that's not a good trait in a mathematician.

[neat lintel]

And i tell you, shitty teachers take quite a toll on you

But it's pretty fun, you should try it

And change majors if you dislike what you get

[old oak]

I wonder if they're some kind of bot actually

[neat lintel]

Maybe

Some people are just trolls

[old oak]

They ask the exact same question in multiple channels every few days and don't engage with the replies at all

Not sure what the point of such a bot would be, but it's weird behavior

[neat lintel]

Maybe they just don't know much english

Makes it harder to interact

[ebon pine]

Hi, I've got a question : Can the sun live safety without planets ?

[static loom]

lol

[ebon pine]

In my opinion, I don't think so. The sun is exerting a force to the planets but that's vice versa

[static loom]

it would die of loneliness 😭

[ebon pine]

Once there is no planets, the sun will wander in the space

Or maybe even collapse with other stars and then self destroy

[tawdry pecan]

it wanders regardless

[ebon pine]

Also, the wormhole of our system is a lot affected by the planets. If they disappear, the sun will die faster

That's a theory I don't know about this one

[vast wraith]

[flat harbor]

maybe elitism is the answer after all

we make ppl cool fancy videos and they go and do this

[fiery rock]

Wsg math people

How does one use geogebra

Ion understand it

[rocky shuttle]

Tinker around

[open mauve]

use it

be Pythagora

annihilate anyone who have discovered irrational numbers

because it irritates you

[scarlet lantern]

Good question. There is typically a cloud of dust around young stars. As the grains of dust orbit the star they can smash together and fuse, building up like a rolling snowball. It is believed that planets form this way. Over millions and billions of years they grow from the size of a human hair to huge rocks to an entire world, sometimes picking up ice or gas as they go. As they grow the planets get pushed away and may settle into a stable orbit, forming a solar system. In theory it is possible that a star could never form any planets because this process never starts or starts and gets interrupted, but I do not believe there are any confirmed observations of planet-less stars (caveat: I’m the furthest thing from an astronomer, so I couldn’t say for sure). One reason for this is it’s difficult to even prove this — absence of evidence is not evidence of absence. There are examples of rapidly moving stars we think are lonely, free to wander through the universe without being kept in place by orbiting planets. One such example is Scholz’ star, which is believed to have flown past our own sun about 70K years ago

[latent zodiac]

the cat's expression proves it wants to read spivak.

[jagged forge]

dang they named a star after peter scholze

he is a star after all

[scarlet lantern]

Ironically he's a particularly metal rich star, which tend to have more planets

[jagged forge]

guess it’s just greedy and hogged all the matter for itself

[north topaz]

Wtf you have 408 games????

That's an insane amount of money on just games

Steam

[jagged forge]

the joy of adulthood, buying games in the hopes of finding them fun again

and then never playing them

[north topaz]

......

[bronze wedge]

this is so real

[latent edge]

This is so real

[jagged forge]

most of the time i'm either working, programming, or doing math

[latent edge]

That's me as well

[jagged forge]

it's not as fun as games can be but it gives me a nonzero reward

[latent edge]

Adult life is 🗿

I'm thankfully finding some time for math and music

[jagged forge]

yeah

[latent edge]

My time would be limited if I find a job I think but I don't imagine it changing

[jagged forge]

does school actually take up that much of your time tho

i get the impression u just ace everything

[latent edge]

I ace everything and just sit in silence because I don't enjoy what I do anymore

Sometimes it takes my time yeah but I kind of feel good finishing the work regardless of the grade

You can have my sweet 4.0 GPA or whatever you guys call it I don't give a shit about it

[visual breach]

Woah, genius

[misty trail]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

[visual breach]

This is bad attitude of me, sorry

[open mauve]

games are too boring nowadays

[woven basalt]

give them to me then

oh okay

[north topaz]

if you are 16 or older, god save your soul

it's super hard to tell satire apart from truth

fair

[ebon pine]

Yes, but maybe the mass of the force of gravity on the sun could make it stable, so that even if there is no more planets to exert a force on him, the MilkWay will do the work for them

[tulip void]

if you're re learning math how difficult and long would it take to 100% and 100% understand algebra 1 geometry algebra 2 trig precalculus, differential calculus, integral calculus, calculus ab, calculus bc, multivariable calculus, differential equations, linear algebra progressing from algebra 1 to higher levels of math

[open mauve]

it's online lol

[surreal bison]

This is the way

[woven basalt]

yea just gimme your id then

[surreal bison]

I got honors for getting above a 3.75. This surprised me.

I still don't know what my GPA is

[woven basalt]

💀

[rocky galleon]

Not if i rizz up his grandmas gyatt first🙄

[vast wraith]

i refuse to believe this means anything

[rustic aspen]

You better give my chem book back

Its literally missing

And i have chem subject tomorrow

[olive yoke]

no, kitten.

[rustic aspen]

D daddy??

[sterile juniper]

Hi discussion 2

Wasup

Im immigrant from discussion 1

[rustic aspen]

Me 2

[olive yoke]

Yes my kitten, what is it

[rustic aspen]

Discussion 1 is war

[rustic aspen]

My chem book went missing for 4 days

And i have chem book tomorrow

What should i do

[olive yoke]

Chem test tomorrow?

[rustic aspen]

Yes yes

I need to rewrite 10 sheets

[olive yoke]

Do you know about what topics?

[rustic aspen]

Ik

[olive yoke]

Then use google

And try to learn as much as you can

[rustic aspen]

Wow youre so helpfull

Thats not the point daddy

[olive yoke]

?

[rustic aspen]

I have a lot of chem assignment

I have finished it

BUT I HAVENT SUBMITTED

[olive yoke]

Do it then

[rustic aspen]

Too lazy

[olive yoke]

Dang, if you don’t do it I will break up with you

🤷‍♂️

[queen sierra]

If I have my exam paper I did recently in hand is there a way to make it become a pdf so I can use my iPad?

[floral horizon]

if there's a printer you can use, i guess you can scan it right?

[sterile juniper]

Here's nuke war shelters

[rustic aspen]

Noo 😭😭😭

[olive yoke]

Your choice kitten😘

Do your homework

I need to do mine too now

[rustic aspen]

Okay daddy

❤

[olive yoke]

I would love you even if you were a worm 🪱

[olive yoke]

Talk to you later kitty cat

😏

[rustic aspen]

Bye bye 😚❤

[neat lintel]

wtf

rizzamatics?

[sleek wing]

nonceamatics

[olive yoke]

Quantum Rizzics

[neat lintel]

erm what the summation

[olive yoke]

No

It’s private

[sterile juniper]

rizza

rizza x radius²

[neat lintel]

april fools reference?

!worms

[quasi jetty]

[neat lintel]

@olive yoke pp

[olive yoke]

I didn’t kniw that

@neat lintel what’s wring with you buddy

wrong*

[neat lintel]

yeah for april fools this year

ppl could become worming

[olive yoke]

oh

[neat lintel]

and have "worm" in their name

and a little worm badge

it was really weird

[sterile juniper]

Potassium 40

[tranquil needle]

global worming am i right

[neat lintel]

K-40 stupid

[olive yoke]

yeah sounds weird

[sterile juniper]

Tungsten

W?

[tranquil needle]

noe weirder than we are slowed light

[neat lintel]

lol

[olive yoke]

…

[neat lintel]

did u crack jee mains

[tranquil needle]

hell naw bro

im in 9th

[neat lintel]

man prepare from now on

[tranquil needle]

ofc bro

[neat lintel]

if you don't get iit there is a new rule that you have to get fucked by modi ji

[tranquil needle]

shi

[neat lintel]

and have to shout yes daddy

hard

[tranquil needle]

imma have to fail then

[neat lintel]

🤨

modisexual?

ig

[tranquil needle]

jk im no melodi

[neat lintel]

all jokes aside don't ruin ur life at 11th class i did and want to kill my self every day

[tranquil needle]

bro my awesome sense of humur will save me

[neat lintel]

It won't for me man I got addicted to drugs

shit changed me

I was in top 2000 of the country

now I'm not even passing baord exams

life's shit bro just giving u heads up

[tranquil needle]

dw bro

when imma be rich

ill gist u a yacht

[neat lintel]

dw?

nah les buy modi and get fucked hard by him

[tranquil needle]

yep

always plan A

but jokes aside, im thinking about colleges abroad

[neat lintel]

ye man

try to get 90% above and academic achievements

imma hook you up incase if ur still here 4 years later

[tranquil needle]

i just dont know how to go about EC's

[neat lintel]

don't worry about it

[tranquil needle]

Im getting A*'s tho

[neat lintel]

grind hard for 4 years

[tranquil needle]

yep

[neat lintel]

try to get other achievements

like school captain

spirts

Olympiada

[tranquil needle]

i qualified for F1 in schools national

I got gold in Cambridge sci comp

[neat lintel]

Holy shit

your gonna get it my dud

[tranquil needle]

hopefully bro

with gods grace

[neat lintel]

k man I have to study good luck

[tranquil needle]

bro u motivated me

im ging too

my man

[tranquil needle]

thnx

[dapper badge]

This is a bit late, but would you still be down to start reading this together?

[bronze pelican]

Yes

[dapper badge]

Yay

[woven basalt]

nah

i lost it

sorry 😭

[clear fox]

Anyone got any non-math related hobbies?

[vocal scroll]

I'd like to learn an instrument at some point

[vast surge]

I try to boardgame when I have the time. (I don't often have the time)

[proud kettle]

do you know what instrument you might would like trying out?

[ocean harbor]

I play geometry dash

[quasi orchid]

Mm

[wanton bough]

Volleyball and running

[quasi orchid]

what tha pfp

anime?

[ocean harbor]

danganronpa v3

[quasi orchid]

game?

anime?

[ocean harbor]

both

it has a game and series

https://cdn.discordapp.com/emojis/1155009924141678602.gif?size=240&quality=lossless

[quasi orchid]

okay

charac?

[ocean harbor]

kokichi ouma

https://cdn.discordapp.com/emojis/1112022027847606383.gif?size=48&quality=lossless&name=catcombing

[quasi orchid]

Okay thanks

[vocal scroll]

No

[dense hornet]

I build high power rockets in my free time 🚀

[tranquil needle]

I wanna start learning how to code

[static loom]

I have an ASMR channel with over 1 million subscribers

[tranquil needle]

give mane

name

[static loom]

I also am a liar

[static loom]

https://tenor.com/view/viralhog-legendary-beautiful-king-mane-gif-12328907

[jolly linden]

Hello!

I’m almost done with my Philosophy bachelor’s with a specialization in Formal philosophical Logic and causal modeling

How hard is it to go from here to a master’s degree in mathematical logic and set theory?

If very hard, can I get a PHD in philosophy and then pursue a PHD in mathematics?

Keep in mind, money is not an issue in my case. And I’ve done 2 conference presentations so far which have both been in formal logic.

Thank you very greatly ahead of time. If you have any book recommendations for the intersection between mathematics and philosophy as well, I’ll be immensely grateful if not indescribably grateful🙏

Furthermore, I’m very well acquainted with set theory at my level!

[compact gulch]

ídk, but i wish you good luck

[jagged pendant]

bro

is just spamming this everywhere

[clear fox]

Math isn’t just logic

So probably a bad idea

The logic part might be easy

[plain goblet]

Depends how much math you have done prior to this

[clear fox]

But you should probably try looking up some grad level set theory problems before a commitment

[plain goblet]

Finding a student in what you are trying to get into is your best bet

He will have all the answers and the textbooks as examples too

[fair mural]

i play a lot of hollow knight

[ebon pine]

I am living

[lunar python]

hOLLOW KNIGHT

[ocean harbor]

wtf you're back

[proud kettle]

I play too many instruments

[south thicket]

Hello

[mortal valve]

i'm learning spanish

está divertido

[vernal token]

Does spending time on this discord server count?

[clear fox]

Estoy haciendo español 1 en mi escuela

Está divertido tambíen

[vernal token]

You mean at your uni?

[clear fox]

No, mi escuela (high school)

[vernal token]

.. you go to high school? I thought you were a grad student

[clear fox]

I self studied a lot

[solid yarrow]

lol

[vernal token]

How did you have the time?

[solid yarrow]

CJ be cracking

Any advice on self-study?

I suck at it a lot

[clear fox]

I have like no other hobbies

[clear fox]

What level are you at?

[solid yarrow]

currently sitting in my 2nd semester lol

but i need tips for semester break :3

wanna study ca

[clear fox]

ca?

[solid yarrow]

complex analysis

[vernal token]

I mean didn't you have a lot of exams and everything?

School till 5pm and stuff

[clear fox]

I’m in the US

[vernal token]

Yeah

[clear fox]

I just looked up like lecture notes online

Faculty of Khan has a pretty good playlist

[solid yarrow]

But... like what did you do, when you got stuck on problems?

Because talking in Discord is... difficult

Like you'd not really have somebody to talk to, would you?

[clear fox]

https://youtube.com/playlist?list=PLdgVBOaXkb9CNMqbsL9GTWwU542DiRrPB&si=P_NnM5KmfSWAT7gN

[clear fox]

Uh

[solid yarrow]

I got a book about ca, that's the thing

Only cost me a few bucks

[clear fox]

Usually books are kinda hard by themselves

I needed some video help or just discord stuff

[solid yarrow]

Though I still think a book is prob. the best source to learn it.

[clear fox]

Yeah they have a lot of information

[solid yarrow]

But you'd usually need a couple of books

[clear fox]

But technically I’m not qualified to talk about grad level math stuff

[solid yarrow]

Change my mind. But trying to learn stuff from one book is a bad approach. Like sure stick mainly to one book. But if you get stuck on a proof etc., search for it in your other books

The more angles you look at a problem/ theorem, the more you really understand the problem.

[clear fox]

If you can understand and learn from the books than that’s good, but for me, personally, I couldn’t do that

[solid yarrow]

That's one reason why I hate my scripts in anal and linalg. Like... we only have one way.

Kinda sucks.

[clear fox]

And it’s kinda weird to ask your parents for like 7 math books

[clear fox]

Yeah

[solid yarrow]

piracy

[clear fox]

For linear algebra I liked khan academy

[solid yarrow]

Yeah... I'm still in search of a good linalg book.

But atleast for now... to no avail.

Like most topics my script covers aren't covered inside books I have.

Kinda sucks...

[clear fox]

For analysis

There was a really good book by Cummings

But it was introducing real analysis

So like εδ proofs and ε-N proofs

Pretty cheap only like $20

[jolly linden]

“Tell me you know nothing about formal logic, without telling me you know nothing about formal logic”

No thanks

[old sequoia]

maths is about creativity too

isnt just logic

[mortal valve]

muy bien mucho gusto, ¿tienes el sentimiento que te terminas aprendiendo el idioma?

[mortal valve]

jaja

[livid crane]

Do yall suggest books by Chris McMullen or Dover books

[north topaz]

el curso español 1 me da la impresión de que no aprendes mucho, en otras palabras te enseña español muy muy básico

[mortal valve]

todos cursos español 1 en america están mismos?

whoops

¿todos las cursos de español 1 en america "son iguales"?

[north topaz]

probablemente no

[mortal valve]

así

[clear fox]

¿Porque estamos hablando español en un servior de íngles?

[north topaz]

ya que empezaste con español jajaja

anyways shall we switch back to English

[celest latch]

@scarlet dew you here?

[scarlet dew]

Yea

Come at the other one

[celest latch]

Which one?

[scarlet dew]

Wait

[celest latch]

Mention me there

[scarlet dew]

K

[twilit monolith]

El pana intentando aprender modismos de todos los países

[static loom]

que triste

[pulsar pagoda]

basado discussy 2

y no me invitaron

[static loom]

deberiamos pingearte? ||pienso que "pingear" no es una palabra que significa "to ping" lol||

[pulsar pagoda]

si eso significa es un anglicismo

pero hay otra palabra en espa;ol

q puede prestarse para malinterpretaciones

https://www.youtube.com/watch?v=NJYoqCDKoT4

borges basado

[static loom]

que raro, tengo que leer sus libros en... espanol lol

[pulsar pagoda]

Discussy en español though...

Tendríamos q proponerlo en meta suggestions

[harsh peak]

1 + 1 = 3,4,5,6,7,8,9,10 + accidente = 0

[mortal valve]

😂 solo español es bueno

[twilit monolith]

usamos pingear no más

se entiende

[pulsar pagoda]

si

q los mods esten tan chill por usar espa;ol es super cool

asi q mejor nos comportamos para q siga asi

xD

[twilit monolith]

chaotic evil: usar spanglish

[pulsar pagoda]

hay q darle sabor a la conversacion

@storm sage verdad?

[neat lintel]

can anyone here help me with uniform circular motion? @late dawn

[storm sage]

debes usar inglés en #serious-discussion

[storm sage]

Try asking in a help channel #❓how-to-get-help , or in the physics server discord.gg/physics

[vast wraith]

i am weighing my options: (1) stay up until 3 AM so that i can read the new chapter in this gay webtoon the instant it drops, or (2) sleep early so that i can go to these lectures on the occasion of the abel prize, including of course the prize winner’s

tough choice tbh

[old oak]

gay stuff wins every time

unless it's gay lectures as well, it's no contest

[woven sparrow]

https://tenor.com/view/among-us-twerk-gif-20973689

[vast wraith]

monke brain do be pushing 1 but i am also somewhat successfully shilling 2 by arithmetical considerations and consulting with frens

[ocean harbor]

https://cdn.discordapp.com/attachments/937568987565404170/1241587158226305165/caption.gif

[woven sparrow]

DONT

[ocean harbor]

https://tenor.com/view/geometry-dash-wave-okay-and-okay-and-gif-13011678769021441085

[vast wraith]

horrible

[south arch]

anybody here who reads math textbooks for fun, do you guys take notes or do practice problems as well or do yall just read the text raw?

i am curious how different peoples' answers are

[ocean harbor]

I use textbooks only for practice

[neat lintel]

who up integrating they functions?

[weary willow]

me

[south arch]

fair enough

[clear fox]

Do you guys think I should dual enroll diff equs or linear algebra first (assuming I already took calc 3)

[south arch]

linear

[wet mortar]

what the hell is the bold

[split oak]

What is a 1-form? And how is the Lie algebra of real numbers defined?

[fresh comet]

actually, I'm curious; in what way is f(x)dx a linear functional?

idk any Lie theory, so that's the only thing I can ask

[neat lintel]

Ad is G -> Aut(G), Ad is G -> GL(g), and ad is g -> gl(g)

silly notation

[wet mortar]

oh the conjugation action

[neat lintel]

conjugation and all its derivatives :3

[neat lintel]

the answer depends on how much handwaving and definition skipping i'm allowed to get away with

:3

[fresh comet]

hm, what if we like

don't do any handwaving

would I get decimated

[latent edge]

that's dumb

unless I'm missing something

[fresh comet]

<@&268886789983436800>

[terse comet]

what

[wet mortar]

[plain island]

https://tenor.com/view/frozen-elsa-smile-happy-gif-16227182

[fresh comet]

deleted already

[wet mortar]

booba

[terse comet]

damn and i missed them?

so sad

[visual breach]

Just realized Complex geometry can be very complex

It both has algebraic geometric structure and smooth structure given by R-extension

juggling the two effects would be ugh

[raven plaza]

Analytic structure?

[brazen mulch]

greet discussy

[neat lintel]

hi

[brittle socket]

Some old screenshots

[velvet dagger]

This is so brilliant I even had to go back and figure out what I meant

[brittle socket]

[velvet dagger]

Sometimes I'm just on another level fr

Just like you

[brittle socket]

[velvet dagger]

When I mow you

You're on a lower level

[velvet dagger]

Lamo

[brazen mulch]

loma

[static loom]

i thought you were mowing him cause he's grass lol

[velvet dagger]

Yeah

It was such a brilliant line I needed to think for a second to realize what I was saying

(Mostly that I think of grass as the new pfp and pfps are how I know people, so I didn't even pay attention to whom I was replying)

[timid helm]

y'all

L1={(c^i)(b^k)(a^k)|i,k>=0}
L3={(a^i)(b^i)(c^k)|i,k>=0}
what is the intersection of L1 and L3

i've been trying to solve this for two days

idk how to intersect correctly

[pearl moth]

where a,b,c are arbitrary integers?

well, we don't need to know that, we'll just treat them as members of some unspecified group i guess

although if that group is not commutative, i'd expect that the intersection would be extremely small....

because c comes frist in L1 and a comes first in L3, so the only elements that would be in the intersection would be those where the number of occurrences of a and c are zero, which means the identity is the only element that survives

if the group is commutative, though, the problem is a bit harder

[timid helm]

i'm gonna be honest idk what that means

[pearl moth]

nevermind, i decided to take an AA approach

acutally doesn't have to be a group, a monoid is enough here

could be strings

[timid helm]

so only b remains?

but if a is zero then b has to be zero aswell

[pearl moth]

except there are no elements in L1 that have b's without a's and no elements in L3 that have b's without c's so if you can't have any a's or c's you can't have any b's either

but again i stress thuis only applies if the algebra containing a,b, and c is a noncommutative monoid

if that structure is commutative then this argument doesn't necessarily work

are these regular languages?

[timid helm]

wait L3 can have c's without b's

[pearl moth]

regular languages are usually monoids and are not necessarily commutative

oh my bad, i misread the specification

[timid helm]

i think so

[visual breach]

Is this languages

[timid helm]

yes

[visual breach]

Set theoretical intersection could work

[pearl moth]

the key here is still that languages aren't commutative

all the strings in L1 have c's first, then b's then a's

all the srings in L3 have a's first, then b's, then c's

the intersection contains all strings consisting solely of zero or more c's

you can't have any a's or b's, because they're in reversed order betyween the two, and always occur in equal numbers (aaabbb in L3, bbbaaa in L1)

[timid helm]

so something like {c^n|n>=0}?

[pearl moth]

that's my take on it

[timid helm]

ok i think i understand how it works now

but what if L3 was {(a^i)(b^i)(c^k)|i,k>0}

would there be an intersection then?

cause b and a can't be zero

[visual breach]

Then L3 would be even smaller

So intersection is smaller, and intersection needs to be included in L3

So yeah, no element in the intersection

[timid helm]

yeah i get it now

thank you sm

[pearl moth]

well the null element might be in the intersection

the empty element is an element

[timid helm]

but how can there be an empty element if i and k are greater than 0

[pearl moth]

yeah, if it's strictly greater than the null element is not in the language

[timid helm]

yeah i thought so

[vast wraith]

woops i slept through talagrand’s lecture

[old oak]

Did you at least read the gay webtoon?

[vast wraith]

yes, this morning

[old oak]

Not all bad news then

[vast wraith]

yes, now i just need to get out of bed before the sun sets again

[novel fox]

You GMT+7 or something

[vast wraith]

i made it out of bed

CEST / UTC+2

i forget how that relates to GMT

[flat harbor]

welcome to the land of the living

[vast wraith]

thanks i’ll see how long i can manage to stay

[old oak]

GMT+2 or GMT+1 depending on season, I think

[vast wraith]

oh so it’s the same as utc

no wait

[pastel tusk]

isn't GMT = UTC

[old oak]

UTC and GMT are almost the same timezone

There's some pedantic distinction, I think

[north topaz]

UTC is a time standard based on GMT

[vast wraith]

CEST is always utc+2, CET changes between utc+1 and +2

[old oak]

Ah yes

[sonic sentinel]

holy shit i got permission from one of my classmates to try to generate his face using chatgpt plus (i got it from my sister to use it for like two weeks blah blah blah)

i enetered like

a ten word description of his face

and dall e gave something that looked like it could be their brother or a future photo of the guy

like literally the only thing it got wrong was the proportions of the facial hair, that's it. face structure was correct, head hair was pretty accurate, it somehow even guessed that the face should have a unibrow (maybe cause of ethnicity)

i tried to replicate it with another classmate but it didn't work for him (tried adjusting the prompt and asking it to make changes but no success)

[jovial ember]

I think you just uncovered a plot by the government to kill all humans

Probably

[ocean harbor]

chair monkey

[sonic sentinel]

chair monke

[old oak]

Oh no, not again

[jovial ember]

Akira

[jovial ember]

Unmm…. Alshfik

[sonic sentinel]

exactly ten words

don't want to paste the exact prompt but it was: [ethnicity] teenage boy, [skull shape], with beard, low fade haircut.

[blazing pawn]

Omg which webtoon

[vast wraith]

Realta

[old oak]

White guy with haircut strikes again

[ocean harbor]

fanta :)

https://cdn.discordapp.com/emojis/1112022027847606383.gif?size=48&quality=lossless&name=catcombing

[jovial ember]

Fanta

[sonic sentinel]

he isn't white lmao

[vast wraith]

can we talk about something interesting please

like, the icosahedron

[latent edge]

rodbet based

[vast wraith]

hi hi deltoid-no-more

[latent edge]

I'm still Deltoid

Just a different name

[sonic sentinel]

these aren't real words

[vast wraith]

oh, lol

i have seen the name steiner in steiner system but i have no idea what that is

something something block design, something kitten construction

[latent edge]

Combinatorics shenanigans

[vast wraith]

(@blazing pawn you wouldn’t want to miss this)

[empty mirage]

I am currently preparing for edp

Let me make stock of the situation here: I need to revise the change of variables formula for second order linear stuff, revise characterisation, revise the fourier series, revise the fourier transform.

[sturdy gulch]

might be a bit of a skill issue on my part, but is the interpretation for the constant of integration only interpretable when we're working with the "integral as the opposite of a derivative?"

because when i try to think of the constant of integration in terms of area, it makes absolutely zero sense

what

[pastel tusk]

I swapped them around didn't I

uh

[sturdy gulch]

yeah 💀

yeah no i know but im asking how to interpret it

[pastel tusk]

constant only applies to antiderivativw, it cancels out when you subtract in fundamental theorem of calculus

if you know that

[sturdy gulch]

no i do

oh right that's because area is relative

to a starting point

[pastel tusk]

yeah

[sturdy gulch]

so indefinite integrals are basically "what function has this as its derivative" and definite integrals are "what's the area of this function between two points using that new function"

[sturdy gulch]

im gonna definitely forget about that but

that's actually very useful to remember

[vast wraith]

what functions* plural

[sturdy gulch]

mb

[vast wraith]

[sturdy gulch]

okay wait another question

is the average value pf the derivative between two points equal to the slope between those two points?

like

how do i even explain what im asking

uh

so like say i sum up some number of y values of 2x between 0 and 2, and divide it by the number is samples i took, would the limit of that approach the average slope of x^2 + C from 0 to 2, or 2?

[lapis hull]

Well the continuous average is, because it's just $\frac1{b-a}\int_a^bf'(x) = \frac{f(b)-f(a)}{b-a}$

[fathom swallow]

Respectful sqeral

[sturdy gulch]

that's such a nice way to see the connection between integrals and derivative

but im not sure im gonna remember that 💀 i have memory loss the instant it comes to solving an integral

not that i need to tho

[lapis hull]

Well it's just the fundamental theorem of calculus

[sturdy gulch]

no i know the fundamental theorem of calculus but it just feels like such a weird connection between area and slope

[lapis hull]

Ah I see

[sturdy gulch]

maybe i should actually look for a proof of it

or is that a definition

[lapis hull]

Well I'm sure you could find some geometric hand wavy proof of it too

[lapis hull]

Again it's just FTOC

[sturdy gulch]

i was asking that question because 3b1b was using the idea of average slope between two points equalling the limit of the average of the instantaneous rates of change over the interval

which kind of makes sense ish

does this just come down to MVT

[tulip tapir]

do you understand why dividing the integral of a function over an interval by the length of the interval gives you the average value?

[sturdy gulch]

yes

mo

wait

yes

💀

mb

yeah that does make sense

[tulip tapir]

wait i may have misread

where exactly does your confusion lie?

[sturdy gulch]

i saw a proof for the FTC that uses the idea of the average value of a function on some interval, then implying equivalence of that to the instantaneous slope of its integral between those two points

or

$\frac{\int f'(x)dx)}{x_2 - x_1} = \frac{(f(x_2) - f(x_1))}{x_2 - x_1}$

[tulip tapir]

ah

[sturdy gulch]

womp

[tulip tapir]

yes MVT should be a good motivator

[sturdy gulch]

its not editing right

[tulip tapir]

lol

all good

[sturdy gulch]

wtf 😭

[fathom swallow]

Serphic

[sturdy gulch]

okay it is no longer scuffed

wait nevermind I FORGOT TO DEFINE THE INTEGRAL

[tulip tapir]

its fine

[sturdy gulch]

yknow what fuck that you get what i mean

[tulip tapir]

what are you confused about?

[sturdy gulch]

good question

my brain's just not connecting the ideas

idk what im lost on but something just doesnt make sense 😭

[tulip tapir]

are you convinced of the fundamental theorem of calculus?

[sturdy gulch]

kind of?

like ive been working with it and its obvious it works but it's a weird connection with area and slope that i dont really find intuitive yet

[tulip tapir]

so the way i try to think of it

imagine you have f defined from [a, b], and F the function which computes the area under its curve from a to x, with x insnide [a, b]

[sturdy gulch]

mhm

[tulip tapir]

a question you may want to ask is, whats the difference between F(x) and F(x+h)? now, if f was constant, at least within the interval [x, x+h], you'd just have f(x)*h

because you just cleanly take that next rectangle

but if f was sloped at that point, you'd have some error

[sturdy gulch]

mhm

[tulip tapir]

but as you bring x+h close to x, that error becomes small, and you should begin to see something which mirrors the definition of derivative for F

specifically, the limit as h goes to zero of F(x+h)-F(x) is the same as taking that limit with f(x)*h

then you can divide by h

the important part is that MVT ensures that, for every h, there is something between x and x+h such that this equality holds

and these "somethings" will approach x by the squeeze theorem

[sturdy gulch]

ohh

[tulip tapir]

its. hard to visualize the "slope" of the area function F

since we are speaking of it as an area, not a curve

but the slope is just the rate of change at that point

and if f(x) was negative, the (signed) area would surely be getting smaller

so you should feel like the "slope of the area" is connected with the original function – it just happens as we showed earlier that they are indeed equal

[flat cloud]

is a double major on software engineering and applied maths overkill?

I spoke with a counselor and he thought there was enough overlap to the point a math minor would be more practical

[tulip tapir]

not necessarily

surely if there was enough overlap, that would make finishing the second major easier

[flat cloud]

of course, but by overkill I mean that it's too redundant, and I could use the opportunity to gain different skills

but I believe applied maths would give me an advanced understanding of logic no?

[tulip tapir]

i think thats something you can figure out

you can start taking classes and see if you want to keep going and finish out the major

[tulip tapir]

uh not sure what you mean

[flat cloud]

stuff like problem solving, identifying patterns, and well being a logical thinker

[tulip tapir]

ah

yeah math does help with that (pure math most of all 😉 )

[flat cloud]

I do have to eventually choose between pure maths or applied maths

both are very interesting and the same ammount of extra classes

[tulip tapir]

i will vote for pure math if that means anything, i think that will be far more beneficial if you care about the problem-solving, rigorous way of thinking that math provides

but i would just start taking core classes and see if you want to take more

often times ppl set their mind on a secondary major but don't really care for it, but still slog through to get the requirements

but if you like it, you can just keep doing it

[dire stump]

hello, current double major in cs and math here

not sure if i'd call it overkill

and while they might overlap in stuff like gen-eds and there probably isn't any math in your cs classes that you're not already doing in your math classes, i wouldn't call it extensive overlap

like comparing that to the analysis and algebra and topology courses and stuff that math majors take isn't really comparable

and especially with how the cs/swe job market is looking rn i'd say the math major is actually more of a selling point

there's already plenty of people who know how to code, not all of them have the analytical reasoning skills necessary

[brazen mulch]

is this a conflict of interes-

[flat cloud]

@dire stump would you say studying each field significantly improved your skills in the other? and was a major the best option or a minor would've had the same effect?

I hope I can slip a psychology minor somewhere during my career

it was my first interest entering and it'd be sad if it went nowhere

[plucky tide]

3^2x−10(3 ^x+1)+3^ 4=0 this is a basic question can it be solve using the factor method?

[neat lintel]

!help

[quasi jetty]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[split oak]

Yes

[vapid laurel]

hello guys, do you think if it's lame for schools to care about being late?

[static loom]

it's lame that my boss cares if I'm late to work too

[visual breach]

We cattle life

[rocky galleon]

Super lame like its not that deep🙄

[long matrix]

if youre late today, youll be late tomorrow, then ull be late to work in 10 years, and then if everyone is late the economy fucks up, the stock market crashes, the government will collapse and the earth will explode.
So dont be late.

[brazen mulch]

"if youre late today, youll be late tomorrow"

leap of logic: failed

[raven plaza]

Yes but would you rather your children go to a school that cares about them being late or doesn't

[pseudo prism]

I've stumbled across some mathematical research papers in my self studies but they always seem to go over my head. Could someone recommend some of the prerequisite courses for understanding some of the latest (or even basic) papers? (For reference, I started researching this one topic for fun and putting my results in a document, it was titled, "Lattice Points under Functions." In the very unprofessional "paper", I just try to make a concrete formula for the number of lattice points under a linear function from an interval, pretty basic, I know. )

[rocky galleon]

Oh!

[long matrix]

if you drive them there i bet not

[vast wraith]

good good

[raven plaza]

Skill Issue, simply live in a city where cars are redundant

[pearl moth]

cardundant

[old oak]

OK, but what are the bad points

[long matrix]

u

[old oak]

I aim to please

[sharp berry]

anyone help with trionometry

[balmy hare]

hello guys

stfu

[pastel tusk]

?

[ocean harbor]

https://tenor.com/view/gd-geometry-dash-sakupen-circles-stfu-stfu-i'm-playing-gd-gif-2682408120184002311

[vast wraith]

it’s another day of not being out the door and heading to campus before almost 3 pm

[next schooner]

A majority of research mathematics papers are going to be presenting cutting edge results in their specific subfields. If you want to be able to read papers from that subfield, then you're gonna need to work through at least an undergraduate course and ideally a graduate course in said subfield.

It varies but many students spend the first 6-12 months of their PhD studies learning how to properly read and understand research papers

[glossy zephyr]

Goku?

[proven knoll]

,av harryzebeast

[fathom swallow]

harryzebeast's Avatar

Click here to view the image.

[proven knoll]

Goku

[vast wraith]

suddenly i feel less bad for struggling with this, as an undergrad

[north topaz]

oh come on like even at masters' your supervisor is supposed to guide you through the process

give you assignments and prod you along so that you can publish something of your own work

so if you're already starting at undergrad you're not a typical undergrad student

also worth noting that for the US, a 'PhD program' is in reality an integrated masters' and PhD

I heard at some unis you can drop out midway and get a masters' degree

[vast wraith]

i was certainly overly ambitious in my bachelor thesis, did not end up with a good final product, but i learnt a lot in the process 🙏

[north topaz]

cool

[vast wraith]

i was also horrible at remembering to ask my supervisor for advice… it was mostly me just rambling about what i’d been reading and trying to make sense of, and her helping me select what to focus in on

…which i did not listen to, since i’m an idiot

[north topaz]

@neat lintel what the hell

you must be a big fan of Young Sheldon

howdy

[neat lintel]

Big fan? You realize you are talking to the one and only Sheldon Lee Cooper?

The math in this server is to easy, even Georgie could do it.

[north topaz]

One day I'll find a Paige on this server who shall make you feel inferior

[proven knoll]

Dr. Cooper

[ocean harbor]

Dr. Goober

[proven knoll]

[livid spoke]

Idk but I seriously need an advice. I have a assignment / like a home exam to be turned in tomorrow. I have an exam next week as well. I cannot decide. I am done almost with the assignment but I feel insecure. It has a fail rate of 90% and I am doing reexamination btw. And I have now studied a lot for the exam but I need to study a lot more in order to pass or get a little higher but moments like this indecision takes over me.

[ocean harbor]

if you're mainly prepared for an exam then you should be fine unless you want to review some stuff

also I'm curious what kind of assessment you're doing

[livid spoke]

I have not really prepared well. This whole half semester has been "Hell" so I didn't really have this flow of learning. But the past couple of days I have covered most of it but I know damn well I need to spend more times on it. The other assignment it CS theory related.

[ocean harbor]

oof that sounds stressful as hell

never heard something about cs theory

[latent edge]

Counter strike theory is cool

[glossy zephyr]

Goku

[livid spoke]

Computer science theory stuff I mean

[glass peak]

Gla1ve?

[marsh wyvern]

how do i put undergraduate role?

[fresh comet]

go to id:customize

[loud snow]

What is the asignment

[severe swallow]

anybody know if the latex compiler has randomness in its algorith

istg it's the only thing where I sometimes change literally nothing and warnings start appearing and disappearing after recompiling

[loud snow]

What warnings

[woven sparrow]

https://tenor.com/view/nephew-roommate-father-brother-cousin-gif-11282634

[jovial ember]

Thanks bro

[shrewd moon]

good morning folks going to study geometry, trig, calc, and the rest

[solar hawk]

Hi

Hi bb

[latent zodiac]

lemme latex

[craggy parcel]

no

[latent zodiac]

ok ill just sen ss

[solar hawk]

Oke

[solar hawk]

How do I grow my beard?

[craggy parcel]

rudin typeset spotted

[craggy parcel]

uhh just give it time

[latent zodiac]

also the fact that it literally says "principles of mathematical analysis" but sure

[solar hawk]

That’s hot

[craggy parcel]

yeah okay i didnt see it

[latent zodiac]

exactly bro

[solar hawk]

I like how Rudin kept going with the

Metric space topology stuff

[latent zodiac]

i remember darq saying chapter 4 makes chapter 2 click

[solar hawk]

When I moved to Abbott - I lost that

[latent zodiac]

and when i read chapter 4 i understood what he was talking about

[solar hawk]

He sticks hella to the reals???

[latent zodiac]

and omg the practice problems on this section are really nice

[solar hawk]

Metric spaces is literally an “extra” topic at the end

[latent zodiac]

i feel rudin deals with complex in the shittiest way possible

almost as if it was on purpose

[solar hawk]

Thankfully I bought a book that COMPLETELY focuses on metric spaces thank god

[latent zodiac]

what??

[solar hawk]

What

[latent zodiac]

like

a point set topo book?

[solar hawk]

It’s literally called metric spaces

Or smthn

[latent zodiac]

hmm that sounds interesting

[solar hawk]

No we’re using ITM for that

[latent zodiac]

i wanna get to ITM

but i wanna finish rudin first since it feels wrong

[solar hawk]

I think you only need upto continuity for the first 4 chapters or smthn

I’m jus gonna do it lol

[latent zodiac]

yes slay

[craggy parcel]

yeah youre supposed to know baby rudin and intro group theory i think

[solar hawk]

We’re only going to need upto the first 4 chapters stuff so

There should not be any group theory

Or the group theory will just be easy

[craggy parcel]

im learning about matrices today 🔥

[solar hawk]

Nice

Wait what

For the first time?

[latent zodiac]

amukh what book did u use for linalg

just curious

[solar hawk]

Bronson

[craggy parcel]

the matrix group

[solar hawk]

• Axler

[latent zodiac]

like hte burner?

[solar hawk]

The what

What’s a burner

[craggy parcel]

i wanna get to tensor and exterior algebra in df but im like

running out of time

[solar hawk]

I wanna learn dg

[latent zodiac]

bunsen burner

wtf is dg

[steady rapids]

differential geometry im assuming

[latent zodiac]

oh u right

[solar hawk]

Yea

[latent zodiac]

i wanna get to algebraic topo and measure theroy first

[solar hawk]

Oh

Why

[latent zodiac]

and then ill stop spamming analysis and learn some abs alg

[latent zodiac]

cuz interesting

me gusta

[solar hawk]

Ok

[steady rapids]

For some reason smooth manifolds and topics therein has always fascinated me so much more than any other field

something about the field is so appealing to me

just super fun to learn about.

[solar hawk]

Frrr

[latent zodiac]

mfw shawty a smooth manifold 😝 😝 😝 😝 😝

[solar hawk]

I wanna read ISM

[latent zodiac]

RM?

[solar hawk]

no

[latent zodiac]

after i mean

[steady rapids]

Whats that

[solar hawk]

Maybe

[latent zodiac]

lee wrote a book on reimann manifolds

[solar hawk]

Idk

Prolly

[steady rapids]

yall gotta quit the acronyms lmao

[solar hawk]

lol

[latent zodiac]

its not "intro to" so i assume you need ITM and ISM

[steady rapids]

Intro to Riem Geometry is great textbook

[solar hawk]

Huh

It is IRM

[steady rapids]

Yea something like ethat

[solar hawk]

it’s not an entry level book I assume

[steady rapids]

it is an entry level book imo

as long as you know enough about smooth manifolds

[latent zodiac]

yeah its gtm

[solar hawk]

But it’s still intro to RM as it prolly doesn’t include Riemann manifolds in the pre req

[solar hawk]

How’s that entry level

[latent zodiac]

it assumes you have read lee's other books lol

[steady rapids]

just know the basics about smooth manifolds and youll be fine

[solar hawk]

Yea

[solar hawk]

Ig

[steady rapids]

you dont have to be a super expert on them

[solar hawk]

Idk

[latent zodiac]

wish lee would turn me into a smooth manifold 😓

[solar hawk]

Ok makes sense

[solar hawk]

HUH

[latent zodiac]

amukh are you still planning to read baby spivak?

[steady rapids]

just know about tangent spaces and how to compute local information, local frames, local coordinate systems, how to compute differentials, and youll be fine

[latent zodiac]

i have my copy on my desk cuz im all preped and shit for summer 😭

[solar hawk]

Huh*

[craggy parcel]

pause

[solar hawk]

Calc on manifolds

[steady rapids]

which is like the first 25% ish of intro to smooth manifolds

[solar hawk]

I plan to read COM

[latent zodiac]

🤨

[solar hawk]

LOL VRUH

[steady rapids]

another great textbook is intro to smooth optimization by Nicolas Boumal

[solar hawk]

zzz

[steady rapids]

its probably my fave textbook of all time

[latent zodiac]

i will prob use analysis on manifolds since its my undertanding that the two books cover the same material and munkres doesnt skimp on the explainations lol

[steady rapids]

in some ways, better than Lee's book as an entry-level book

[latent zodiac]

will basic real analysis be enough for lee's books

or do i need to learn some grou theory beforehand