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🧵 /mg/ maths general

Anonymous No. 16562509

[math]/\mathfrak{mg}/[/math]

Deutsche Mathematik edition
Talk maths, formerly >>16534183

Anonymous No. 16562601

the most beautiful math ever produced is by weierstrass and his analysis school and 30 students who revolutionized all mathematics

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accumulatorNetwork.pdf

Anonymous No. 16562704

Abstract erosion by a load traversing a routed network on a directed graph with applications to processes and games

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Pilot-Preras-2-35....jpg

Anonymous No. 16563103

anyone here do math in cursive? I find it very difficult to take nice looking notes because different lecturers force you to take different notes and often they're very non linear and you often have to go back and cross something out because they made a mistake or you did
i can't really figure out how to do proper spacing either, especially when there's multiple exponents and stacked fractions
i dont know why but it really bothers me, i dont have ocd but it make me anxious somehow
i've been using graph ruled a4 notebooks and gel pens but they're pretty bad for the angle i'm using and i really dont enjoy pencils so i'll probably switch to a fountain pen
i'm curious if there's anyone who has a legit though out formatting style with proper spacing etc.

Anonymous No. 16563111

>>16563103
I do have ocd, I just write whatever without much thought and then turn it into LaTeX, improving your tools won't change anything, you actually have to put in some work studying penmanship for things to look decent (at least 6-7 months), but is it really worth it?

Anonymous No. 16563116

>>16563111
i think you write posts without much thought either but since you appear to have not read my post i was strictly referring to formatting
>improving your tools won't change anything, you actually have to put in some work studying penmanship for things to look decent (at least 6-7 months)
that's just your dogshit opinion you can be entitled to as a flaming retard with OCD rotten brain but it's wholly unrelated to my post

Anonymous No. 16563123

>>16563116
Yeah you're right I don't really put much thought when answering to retards in this shithole and also yeah you nailed it I barely read your post. I thought you were whinning about not being able to format your notes properly, my opinion is that that is a waste of time, but whatever you do you.

Anonymous No. 16563178

How do I stop being bad at math? I can barely understand high school level math and everything beyond that is incomprehensible to me.

Anonymous No. 16563195

>>16563178
what about it do you not understand?

Anonymous No. 16563201

>>16563103
i dont write in cursive i write in retarded half-cursive because i never learned real cursive

i like using graph ruled notebooks and my fountain pen, occasionally i fuck up and smear the fountain pen but the tactile feedback from writing with a decent one is unparalleled, good experience. gel pens are decent

my formatting changes based on whether or not im loaded on stimulants. on stimulants i get the ability to write even better organized and spaced notes on completely unlined paper. i usually measure spacing in terms of writing eq'ns with the line of the graph going through them and then writing exponents or subscript shite on the lines above and below where i wrote the equation, if that makes sense. pretty hard to commit to specific spacing for notes tho

the formatting pisses me off regularly but ultimately it doesnt matter that much; i seldom even go back and look at my own notes, i just take the notes to keep myself busy while listening to a lecture

Anonymous No. 16563236

>>16563195
I can grasp the basics of those concepts but I struggle with developing a deeper understanding of them. I alao have a hard time utilizing them when I try to solve math problems

Anonymous No. 16563262

How do I fraud my way through a math PhD
I don't know how I got here or why the hell I'm here, but somehow I am a fully funded math PhD student.
I don't even know what a Lagrange multiplier is I had to ask deepseek

Anonymous No. 16563290

>>16563236
BHAHAHAHHAA
Tell me more

Anonymous No. 16563538

>>16563262
What does your position require you to research?

Anonymous No. 16563543

>>16563236
What concepts?

Anonymous No. 16564330

After studying Analysis and Topology, how much Category Theory do I need to learn to study the dual notions of Oralysis and Bottomology?

Anonymous No. 16564924

>>16562601
>beautiful
>math
when will this meme end?

Anonymous No. 16564932

>>16564924
what are you doing here, midwit?

Anonymous No. 16564935

>>16564932
>midwit
midwits latch onto the idea that math is "beautiful" because that's the same word every other normie uses. then you look at what they think is "beautiful" and find out their taste is garbage.

Anonymous No. 16564942

>>16564924
>>16564935
holy shit you are ELITE and may I say BASED

Anonymous No. 16564950

>>16564935
sublime
you happy?

Anonymous No. 16564956

>>16564950
even worse.
how about "interesting." that's all it is. no more circlejerking over math

Anonymous No. 16564962

>>16564956
There are many interesting things out there that carry no aesthetic value. Female hyenas having massive clitori is interesting, but it’s neither beautiful nor sublime.

Anonymous No. 16564969

>>16564935
Personally I find all math that I don't understand but want to understand beautiful. Then when I properly understand it it's no longer beautiful and I move on to the next thing.

Anonymous No. 16565001

Why do computer scientists prefer to talk about directed sets rather than chains when it comes to partial orders/preorders?
I'm not well-versed in CS but from the little bit I've seen in introductory texts to program semantics it would seem that most of the given examples for DCPOs would also apply to chain complete orders and I feel like the theory of those is way easier? Maybe that's naive of me but for example I still don't fully comprehend the fixed point theorem for DCPOs and would have no idea how to come up with that on my own while the one for chain complete orders is quite intuitive and straightforward.

Anonymous No. 16565009

>>16563543
simple stuff like calculus

Anonymous No. 16565013

>>16565009
Name a specific concept you lack the intuition/deeper understanding of.

Anonymous No. 16565029

>>16565013
Differential

Anonymous No. 16565068

>>16565029
Pretty sure that's not a concept in calculus. Don't you mean the derivative?

Anonymous No. 16565076

With roughly one month and a half at my disposal to study differential geometry and Riemannian geometry, what are some good textbooks I could use if I want to study everything in this time frame?
Also, should I skip topological manifolds?

Anonymous No. 16565167

>>16565001
What’s a directed set? If that’s the same as a word (a function from a subset of the naturals to some set), then it’s simply because that’s how computer memory is set up.

Anonymous No. 16565189

>>16565076
Perhaps Differential Geometry and Its Applications by John Oprea?
>>16565167
NTA, but I understand that directed set means the set with preorder (relation that's both reflexive and transitive) where any two elements have an upper bound: https://en.wikipedia.org/wiki/Directed_set
(It's generalization of a sequence.)

Anonymous No. 16565209

>>16565189
>(It's generalization of a sequence.)
A net (a function from any directed set) is a generalization of a sequence (a function from the naturals directed by the usual order).

Anonymous No. 16565437

Greetings mathematicians!

Can anyone give to me a homeomorphism between [math](-\infty, a][/math] and [math](a, b][/math]
and a homeomorphism between [math](a, b][/math] and [math][a, b)[/math]?

Anonymous No. 16565454

>>16565437
Dear Anonymous

I'm sorry, but your questions (especially the second) are far too trivial. This thread is not about solving your homework. (Have you ever heard about exponential function and 1-x function)?

Anonymous No. 16565552

>>16565189
Ah, so directed sets are natural generalizations of chains from tosets to posets. My guess is that CS guys would need this for various data structures like trees?

Anonymous No. 16565745

The FUCK do I do with a BS in math. I only did this shit cause it was easy.
Now my lame ass parents are taking about how I need a job so I can get a wife.
Women don't even like asian guys, I just want to play video games.

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Anonymous No. 16565747

image:
17-gon

source(image):
https://www.wolframalpha.com/input?i=PolarPlot%5BSec%5Bt-%282*Pi%29%2F17*Round%5B%2817*t%29%2F%282*Pi%29%5D%5D%2C%7Bt%2C0%2C2*Pi%7D%5D

quote:
"If you had to choose a few words or symbols to encapsulate your legacy, what would you pick? Johann Carl Friedrich Gauss (1777–1855) left behind a trophy case stocked with mathematical achievements to choose from, but above all, he wanted a "regular heptadecagon" etched on his headstone. The highly symmetrical 17-sided shape starred in a proof that Gauss considered one of his greatest contributions to math."

source(quote):
https://www.scientificamerican.com/article/why-this-great-mathematician-wanted-a-heptadecagon-on-his-tombstone

Anonymous No. 16565902

>>16565437
First, create the homeomorphism between (a,b] and [a,b). That should be easy enough: create a continuous bijection within [a, b] such that f(a) = b and f(b) = a.
Then, ask yourself which property of this set could be exploited to create a homeomorphism to an infinite interval. Tip: use the distance between x and something, and put it in the denominator.

Anonymous No. 16566257

>>16565745
based

Anonymous No. 16566546

I'm struggling to understand why unsoundness doesn't imply inconsistency.
For some statement P which is independent of PA but proven by True Arithmetic, isn't the proof of P contained in the standard natural numbers which appear in all models of arithmetic, including non-standard ones?

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Anonymous No. 16566646

>>16565747

image:
2.125-gon
or 17/8-gon
(unfortunately, the tips are missing)

source(image):
https://www.wolframalpha.com/input?i=PolarPlot%5BSec%5Bt-%282*Pi%29%2F%2817%2F8%29*Round%5B%28%2817%2F8%29*t%29%2F%282*Pi%29%5D%5D%2C%7Bt%2C0%2C8*2*Pi%7D%5D

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22over7-gon.gif

Anonymous No. 16566665

image:
22/7-gon
(unfortunately, the tips are missing)

source(image):
https://www.wolframalpha.com/input?i=PolarPlot%5BSec%5Bt-%282*Pi%29%2F%2822%2F7%29*Round%5B%28%2822%2F7%29*t%29%2F%282*Pi%29%5D%5D%2C%7Bt%2C0%2C7*2*Pi%7D%5D

note:
22/7 ~ pi

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Anonymous No. 16566714

image:
pentagon
or 5-gon

source(image):
https://www.wolframalpha.com/input?i=PolarPlot%5BSec%5Bt-%282*Pi%29%2F5*Round%5B%285*t%29%2F%282*Pi%29%5D%5D%2C%7Bt%2C0%2C2*Pi%7D%5D

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Anonymous No. 16566731

>>16566714

image:
pentagram
or 5/2-gon

source(image):
https://www.wolframalpha.com/input?i=PolarPlot%5BSec%5Bt-%282*Pi%29%2F%285%2F2%29*Round%5B%28%285%2F2%29*t%29%2F%282*Pi%29%5D%5D%2C%7Bt%2C0%2C2*2*Pi%7D%5D

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Anonymous No. 16566754

how the FUCK do i become a professional MATHMAN i already have a bachelors but i want to pivot to math, but i'm POOR and OLD

Anonymous No. 16567239

What is stratification

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Anonymous No. 16567429

>>16566714
Does D*v Z*kh**m still work at The Pentagon?

Anonymous No. 16567447

>>16565068
>the derivative
is a ratio
of two differentials

Anonymous No. 16567454

>>16566731
a pentagram?
why that reminds me of
Satan's chosen jeople

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Anonymous No. 16567491

omg
a 6/5-gon
or 1.2-gon

https://www.wolframalpha.com/input?i=PolarPlot%5BSec%5Bt-%282*Pi%29%2F%286%2F5%29*Round%5B%28%286%2F5%29*t%29%2F%282*Pi%29%5D%5D%2C%7Bt%2C0%2C5*2*Pi%7D%5D

note the central hexagram

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Anonymous No. 16567672

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1-7th of 22-7ths-....gif

Anonymous No. 16567696

>>16566665

image:
1/7 of 22/7-gon

source(image):
https://www.wolframalpha.com/input?i=PolarPlot%5BSec%5Bt-%282*Pi%29%2F%2822%2F7%29*Round%5B%28%2822%2F7%29*t%29%2F%282*Pi%29%5D%5D%2C%7Bt%2C6*Pi%2C8*Pi%7D%5D

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1-8th of 17-8ths-....gif

Anonymous No. 16567712

>>16566646

image:
1/8 of 17/8-gon

source(image):
https://www.wolframalpha.com/input?i=PolarPlot%5BSec%5Bt-%282*Pi%29%2F%2817%2F8%29*Round%5B%28%2817%2F8%29*t%29%2F%282*Pi%29%5D%5D%2C%7Bt%2C7*Pi%2C9*Pi%7D%5D

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3 revolutions of ....gif

Anonymous No. 16567904

>>16567696

image:
3 revolutions of a pi-gon

source(image):
https://www.wolframalpha.com/input?i=PolarPlot%5BSec%5Bt-%282*Pi%29%2FPi*Round%5B%28Pi*t%29%2F%282*Pi%29%5D%5D%2C%7Bt%2C0%2C3*2*Pi%7D%5D

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19-7ths-gon.gif

Anonymous No. 16567964

image:
19/7-gon
(unfortunately, the tips are missing)

source(image):
https://www.wolframalpha.com/input?i=PolarPlot%5BSec%5Bt-%282*Pi%29%2F%2819%2F7%29*Round%5B%28%2819%2F7%29*t%29%2F%282*Pi%29%5D%5D%2C%7Bt%2C0%2C7*2*Pi%7D%5D

note:
19/7 ~ e

Anonymous No. 16568140

Guys, PLEASE help me.
I have the opportunity to enter grad school. I was a good student overall, but only God knows how I got my C in Abstract Algebra.
I'm undecided between going for Riemannian Geometry and Model Theory. What should I do? Which of these is least likely to require me to understand fields and Galois theory?

Anonymous No. 16568152

>>16568140
Learn fields and galois theory.

Anonymous No. 16568626

What are some statements independent of ZFC that are resolved by positive set theory (in particular, [math]\mathsf{GPK}^+_\infty[/math])?

Anonymous No. 16568690

i'm moving out
of TFBT = this f*ck*ng bait thread

Anonymous No. 16568704

Does anyone have the trivium by Verbitsky?
I can't seem to find the combined pdf of the questions.

Anonymous No. 16568817

>>16568152
Yeah, I'll obviously have to learn it at some point if not just so I can feel less like a fraud. But I'm fucked if it shows up right as I start my program.

Anonymous No. 16568818

>>16568140
NOT Model Theory.

Anonymous No. 16568886

>>16568140
>Riemannian geometry
modern Riemannian geometry requires good knowledge of Lie theory and understanding of category theory, so good luck with that if you struggled with finite groups.

Anonymous No. 16568999

>>16568886
I didn't struggle with groups. My problem was when halfway through the year the professor had to go home due to health issues and we got a new one to teach us the fields, extensions and Galois theory part.

Anonymous No. 16569273

What are some good, non-introductory, logic textbooks that, preferably, also talk about Gödel incompleteness theorems?

Anonymous No. 16569408

>>16568999
If you do go to grad school, you’ll realize that if you want to actually learn any subject, you do it yourself. Professors are all lazy cunts anyways, even if there are some needles in the shitstack.

Anonymous No. 16569416

>>16569408
Big true. The only grad level math courses I've taken are electives in analysis and measure (information theorist EE here).

Even then, there was an absolute fuckton of self-teaching required to understand what was going on in the course (and that's just a reality of the material, my professor was pretty great). The biggest thing courses do is provide you a clear structure for your self-teaching.

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Anonymous No. 16569576

Redpill me on obscure categories and their relation with other categories. I'll start. The category of pointed sets consists of sets with a single distinguished element and a morphism between such sets, ie a function that satisfies f(e_1) = e_2, where e_1 and e_2 are the respective distinguished elements.

This category lets one talk of kernels and related objects such as exact sequences in an algebra-free context. Examples of non-algebraic structures where this might show up are manifolds on which a frame has been fixed, so that the diffeomorphisms are restricted to those that are "inertial with respect to the frame".

Anonymous No. 16569590

I might add that such “pointed manifolds” correspond to the choice of the Levi-Civita connection, which makes the torsion vanish.

Anonymous No. 16569760

whats the type of math that will allow me to make cool stuff with computer graphics?

t. retard

Anonymous No. 16569867

>>16568704
>>16562509
Anyone has the PDF?

Anonymous No. 16569925

>>16569760
Linear algebra

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🗑️ Anonymous No. 16570145

AI can't into order of quantifiers.

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Anonymous No. 16570178

>>16569273
Ebbinghaus-Flum-Thomas
>>16562704
More like: Abstract erosion from a load crossing over your moms pussy

Anonymous No. 16570180

>>16570178
*traversing

Anonymous No. 16570218

>>16569760
3d vectors and matrix, are involved, doing calculations with these, if you boil it down, cgi is a bunch of points in 3d space affected by other points and vectors , not sure what the matrix are for, I guess resterizing the whole mess
t not a /sci/ chad

Anonymous No. 16570234

>>16570218
>not sure what the matrix are for, I guess resterizing the whole mess
How did you even find your way to this thread?

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Anonymous No. 16570377

>>16563103
>anyone here do math in cursive?
Your red pen reminds me of my TWSBI clear plastic converter pen, and those do come with italic nibs. I really miss that pen, I broke it a long time ago and I never bothered to buy another.

Cursive should be avoided in general. It's just a sloppier version of Chancery Italic, which is made anachronistic by the fact that we do not write with utensils with italic nibs (i.e. you are not an italian scribe employed by the vatican writing with a quill carved out of a feather). Our "nibs" are a fine hair-width now, in the form of a pencil tip or a piece of chalk, etc.

To expound more on cursive being retarded. Handwriting where the ideal is the nib never leaving the page is like typing where your fingers never leave the keyboard. Silly. If "swipe type" didn't automatically typeset your writing properly, then it would look similar to this retard shit:
>iuytdfghjikooiuytrerfghn'uytb nmnbvcxdsadrftgrerfv bvgfrde
This is the same exact problem, I am not joking, with cursive.
And then even in isolation, the letters turn into random glyphs of their own with no rhyme or reason discernable, especially if you're a second grader. Imagine torturing a kid with memorizing picrel and being told to write in this ugly script instead of exposing him to the actual roots of European culture and the actual method of handwriting as it was developed. Couldn't be me.

It's illegible and is self-defeating in purpose. Also, two things: 1) it makes you gay. Imagine what it does to your personality if the way you write might as well look like you dot your "i"s with hearts and punctuate your periods by drawing little daisies. Writing in cursive is the equivalent of speaking with a gay lisp. 2) if the goal is "economy of movement" and faster writing to capture lecture notes, then you should actually be using the journalism technique of "shorthand". We don't do this because this is a COPE. It is NOT done because of speed. It's done because people are GAY

Anonymous No. 16570392

>>16570377
>Cursive should be avoided in general
stopped reading past this

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Anonymous No. 16570395

>>16570377
However, if just for the sake of better style, the beauty of Chancery Italic is that it can be learned in 6 or 7 minutes unlike the other anon's suggestion of 6-7 months of practice. All that's left to do is to write normally, in print, but when you would write in symbols, make them special by using the italic form. Even without an italic nib, it's distinguishable and looks correct.

Anonymous No. 16570404

>>16570392
Cursive is just a late degenerate form of traditional penmanship.

Anonymous No. 16570410

>>16570395
>autistic enough to write simplified chinese
>too autistic to make it legible or make sense

Anonymous No. 16570423

>>16570410
As far as writing with a mouse in ms paint is concerned, it serves its function as sample text, Would you have preferred Brazilian Portuguese?

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🗑️ Anonymous No. 16570434

>>16570395
>png file with transparency
Dear Anon, this is how your image looks like on my browser. You had one job.

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Anonymous No. 16570442

>Cursive is just a late degenerate form of traditional penmanship.

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1738256980818820.jpg

Anonymous No. 16570446

>>16570395
>png file with transparency
Dear Anon, this is how your image looks like on my browser. Sincerely, you had one job.

Anonymous No. 16570447

>>16570446
Maybe stop complaining to others if the problem is with your own theming?

Anonymous No. 16570450

also ich find ja unvollstaendigkeit muss unvollstaendig sein, sonst waer sie ja universell und somit widerspruechlich; die metawerkzeug ausrede glaub ich nich, weil's kein system gibt das von aussen vollstaendig analysiert werden kann. sprich, entweder unvollstaendigkeit funktioniert nur so wie das axiom der wahl, oder unvollstaendigkeit muss wissen wenn wir mit unvollstaendigeit ueber unvollstaendigeit reden, und das klingt alles nich so als waer das vollstaendig. also, find ich jetz so.

Anonymous No. 16570487

>>16570377
>GAY

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Anonymous No. 16570501

Math anons please help, I am doing an independent study in a grad school level topic in my undergrad because it was offered to me by my favorite professor. It seemed like a good idea because if he is offering it it means he thinks I’m capable. Every single problem from the book that I do I either don’t know where to start or I just completely miss the mark. Is this normal for this level content? I feel like I am learning a lot, I know much more about the topic than I used to, but aren’t I supposed to be getting some questions right first try? Or is it that with this high level stuff you just learn by being wrong all the time? I imagine my professor is frustrated that I’m a midwit.

Anonymous No. 16570563

>>16570501
>aren’t I supposed to be getting some questions right first try?
not if you're jumping years ahead and aren't absolutely hardcore engaged out of interested, no.
as in, i think excepting "just because" was a mistake

Anonymous No. 16570588

>>16567727
No I will not "formalize it in lean" and no, I will not try to make the paper "more rigorous". Frankly I'm done thinking about this dumbfuck problem, so do it yourself.

Anonymous No. 16570694

>>16570501
>I know a lot more about the topic than I used to
Sounds like it's a success.
What topic?

Anonymous No. 16570706

>>16570563
So isn’t that kind of fucked then? Professor must have way overshot my abilities. It’s like going up to a primary schooler and asking if they want to take a bench pressing class for adults, then when the primary schooler gets their chest caved in they “shouldn’t have just accepted the class”. I thought, with my professor telling me over and over that he thinks I should do it, that I should therefore do it. If you’re like “heh, obviously you shouldn’t have done that” is my professor just fucking with me? Also FWIW I think I miscommunicated, to me that sentence did not mean I did it “just cause” I do have a very good interest in what we are talking about and thought I could do it. I gave it deep consideration. I just chose wrong anyways I guess.

Anonymous No. 16570721

>>16570694
Eh, I was avoiding “doxxing” myself if my professor lurks here but it probably doesn’t matter, it’s Lie Algebras. I’m comfortable enough with all the definitions and concepts it’s built on, but then when it comes to the proofs I’m just dead in the water.

Anonymous No. 16570760

>>16570721
>if my professor lurks here but it probably doesn’t matter, it’s Lie Algebras
you realize that this is not some superduper niche thing, right?

Anonymous No. 16570825

>>16570760
Being specifically someone posting at the times I am, with the exact problem I am, with specifically this exact independent study that I started just now, in this semester. Tell me how many people you think fit that description reasonably, right this second. Also, nothing I said even slightly implied that I think it’s some “super duper niche thing”. I should have expected /sci to be illiterate.

Anonymous No. 16570844

Does anyone have that meme that's like "This is nonsense made up by lunatics. We've been had!" It's just some graphs (can't remember what they were off the top of my head since this is like three or four years ago now), and it appears as if it was made in MS Paint.

Anonymous No. 16571040

>>16570825
You’re paranoid. Plenty of undergrads doing research projects. And expecting a professor to browse 4chinz… That’s a tall order.

Anonymous No. 16571169

>>16570234
amazing and informative insight your knowledge shines through

Anonymous No. 16571323

>>16570392
Me too.

Anonymous No. 16571437

>>16569576
>non-algebraic structures
which immediately get algebraized

You can also do galois theory with them.
Start with monic polynomial.
vectorize coeffs.
let this be your base point in C^n
closed loops starting and ending at base point induce permutations on roots

Anonymous No. 16571452

How are people like Tao and Schulz supposedly among the smartest humans who've ever lived, yet they have not amassed wealth and resources or other markers of success in our society. Maybe this is the wrong thread to ask in, I'd just like to know what is their metric, or possibly optimized/parabolized breakpoint for material success vs intellectual pursuit as a function of FUN maximization. I only thought of this because Tao's wife is unattractive, but there are smart sexy girls like the Deepseek engineer, so he doesn't need to stoop so low.

Anonymous No. 16571517

>>16571452
maybe because they're real people who live in the real world and not a set of numbers in some imaginary 5 dimensional metric space that exists only in your incel fantasies?

Anonymous No. 16571809

>>16571437
This is something akin to roots of semisimple Lie algebras or am I thinking in the wrong direction?

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Anonymous No. 16571844

>>16570844

Anonymous No. 16571859

>>16571844
Genuinely funny

Anonymous No. 16571920

>>16571809
I'll give a small example
p(x) = x^2-b
r1 = sqrt(b)
r2 = -sqrt(b)

base point (0,-b) in C^2 corresponds to our p(x)
vary vector (0,-b) over some path in C^2 back to (0,-b)
If b winds around 0 an odd number of times then r1 and r2 swap due to the sqrt branch

performing one loop then another is just composition of induced permutations

We can guarantee no winding in innermost radicals (in the formulas for the roots) by restricting to composing commutators of loops.
We can guarantee no winding in second innermost radicals (in the formulas for the roots) by restricting to composing commutators of commutators of loops.
...
https://en.wikipedia.org/wiki/Commutator_subgroup#Derived_series

S1 through S4 will eventually terminate (meaning the formulas for the roots have finitely many nested radicals)
We see the group S5 does not terminate. It gets stuck at A5 in general. This is pretty much Abel Ruffini.

Anonymous No. 16572085

>>16570844
>>16571844
>>16571859
You are sub 80 IQ monkeys. Go back to plebbit faggots.

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Anonymous No. 16572245

>>16571844
Here u go

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Anonymous No. 16572465

Am I just retarded or who is it that Riemann got this equation? because I just keep on getting the bottom and these don't look like the same thing to me.

Anonymous No. 16572536

>>16572465
Substitute [math]x = ny [/math]


[eqn]n^{-s} \int_0^\infty x^{s-1} e^{-x} dx\\
= n^{-s} \int_0^\infty n^{s-1} y^{s-1} e^{-ny} n dy \\
= \int_0^\infty y^{s-1} e^{-ny} dy [/eqn]

Anonymous No. 16572542

>>16572536
I thought there might be a substitution necessary but I suck at math so I didn't see it. How do you even see substitutions like that? there should be a book purely on substitutions honestly, I would read that.

Anyway, thanks a zillion.

Anonymous No. 16572545

>>16563178
you literally just need to have a working memory and the ability to recognize patterns which is innate in all humans
how can you be bad @ math

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Anonymous No. 16572611

There was a person here a while back who asked this exact question. I'm reading Category Theory In Context by Riehl and noticed this and thought they might find it interesting if they read the thread.

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Anonymous No. 16572614

>>16572611
Here's the lemma.

Anonymous No. 16572657

what math do I need to know to understand neural networks? i'm a college freshman who has taken up to integral calculus

Anonymous No. 16572665

>>16572657
Some basic calculus based probability theory, a good bit of linear algebra, some basics of graph theory. That's pretty much it for the simpler parts of neural networks.

Anonymous No. 16572671

>>16571517
I don't understand your answer.

Anonymous No. 16572675

>>16572611
Wait, I don't get the fifth one. Isn't the order-reversal morphism (going from leq to geq) an isomorphism too? Or is that only true for tosets?

Anonymous No. 16572693

>>16572671
your ideas about "success" or "fun maximization" have nothing to do with the real world or real every day people's motivations.

Anonymous No. 16572860

>>16572675
Example (v) isn't talking about isomorphisms in the category of posets, but about the isomorphisms in a fixed poset (viewed as a thin category)

Anonymous No. 16572953

>>16571452
They have a blast doing math, my guy. That's the simple answer.

Anonymous No. 16573146

>ywn intuitively understand stationary sets

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Anonymous No. 16573318

I'm trying to get through this and I keep getting filtered, any tips?

Anonymous No. 16573331

>>16573146
A stationary set is a sponge.

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Anonymous No. 16573652

Can a Maths senpai help a kouhai out?
>>16573621
>>16573643

Anonymous No. 16573657

>>16573318
Can you describe what parts have gotten you so far? Also, what is your stats/math background? Is it the general concepts that are tripping you up or the mathematical mechanics?

Anonymous No. 16573749

What's a strategy for showing that an element does not belong to an inductively defined set?
For example if one were to define the even naturals inductively as 0 is even and if n is even then so is n + 2, how would one show that 1 isn't even?

Anonymous No. 16573762

>>16562509
Is it too informal/juvenile to use tcolorboxes in an undergrad thesis to denote between Definitions/Theorems/Lemmas etc...

Anonymous No. 16573786

>>16573749
your definition isn't strong enough to prove that.
you need
"0 is even and for n > 0, n is even if and only if there exists even m >= 0 such that n = m + 2."

your definition isn't strong enough because it doesn't say that ONLY 0, 0 + 2, 0 + 2 + 2,... are even.

Anonymous No. 16573852

how can i self learn a higher lvl math text book by myself most effectively? ?

Anonymous No. 16573937

>>16562509
Does anyone have the trivium PDF by Verbitsky?
The website by him is down.

Anonymous No. 16573953

is structure and interpretation of classical mechanics a good into to calculus based CM if I already have a trig based overview of basic physics?

Anonymous No. 16573959

>>16573318
They were never good at writing a rigorous mathy book which just makes it that much worse when they start using more abstract math concepts. If you are struggling you need to put it away and just study more pure math for a bit. Least Squares Regression uses elements of calculus and statistics but it is primarily an application of Linear Algebra. Hence the frequent use of matrix equations.

Anonymous No. 16573978

Any good books on three dimensional projective geometry?

Anonymous No. 16573980

>>16573318
Read the og: The Nature of Statistical Learning by Vapnik.

Anonymous No. 16574175

>>16573953
sir, this is the mathematics general

Anonymous No. 16574198

Is there a proof of four-colour theorem that doesn't require a shit-ton of computer calculations? (Or a proof that's impossible to prove a four-colour theorem without a shit-ton of computer calculations?)

Anonymous No. 16574200

>>16574198
Yeah, you do the calculations yourself.

Anonymous No. 16574201

>>16574198
go ahead and find it. I believe in you, anon.

Anonymous No. 16574371

>>16574175
but it has lots of math in it tho

Anonymous No. 16574503

>>16574371
Your mom has lots of BBC in her but she isn’t BBC herself.

Anonymous No. 16574609

>>16574503
Mutt's law remains undefeated.

Anonymous No. 16574787

It's been years since I've done some math. What are some fun topics one can dive into? I have a degree in math so any suggestion is welcomed, I don't care how advanced.

Anonymous No. 16574798

>>16574787
Dessins are pretty entertaining as a new challenge.

Anonymous No. 16574809

>>16574798
https://en.wikipedia.org/wiki/Dessin_d%27enfant
this what you mean?

Anonymous No. 16574940

>>16573749
>>16573786
To define a set inductively usually means to define it as the *least* set closed under some rules.
The even naturals are indeed the least subset of N that contains 0 and is closed under addition by 2.
But many other subsets of N are closed in that sense and a lot of them will also contain 1 (for example N itself is closed under both rules and contains 1).
So you absolutely have to use the fact that the evens are not just closed under your two rules but are actually the least closed set if you wish to prove that 1 is not even.
A common way to proceed is to prove the equivalent statement that every even number is not equal to 1. This can be proven inductively (not using induction on the naturals, but using the induction principle arising from the inductive definition of the evens): Since the evens are the least subset of N containing 0 and closed under addition by 2, it is sufficient to prove that the set of naturals not equal to 1 is also closed under both these rules. Then the evens are a subset of the naturals not equal to 1, hence every even number is not equal to 1, so 1 is not even.
But the set of naturals not equal to 1 immediately contains 0 since 0 is not equal to 1 and it is also immediately closed under addition by 2 since n + 2 cannot be equal to 1, so we are done here.

Anonymous No. 16574941

>>16574940
Something somewhat related to what the other anon said: Defined this way you can also prove (again inductively) that every even number is either 0 or arises from addition by 2 of some other even number. The converse of that statement is immediate, so the even numbers are *exactly* those naturals that are either 0 or of the form e + 2 with e again being an even number.
The upshot to all this is that this is essentially a corollary of Lambek's lemma applied to the posetal category of subsets of N with endofunctor/monotone function given by taking subsets of N to their image under addition by 2 and also appending a 0 to that image. The even numbers are then the initial algebra/prefixed point of this functor/function, which by Lambek's lemma turns out to be an actual fixed point, which here ends up being the statement that n is even iff it's equal to 0 or of the form e + 2 with e again being even.

Anonymous No. 16574944

>>16574809
Yep. Absolutely magnificent little thingies. Their scope is frankly unbelievable.

Anonymous No. 16575016

>>16574787
If you like probability, PGMs are super cool and can handle a ton of different topics in both probability theory and statistics.

Anonymous No. 16575096

>>16574198
Nope, I'm working on it.
Gotta be more general than tait's conjecture.
https://en.wikipedia.org/wiki/Cauchy%E2%80%93Binet_formula
https://en.wikipedia.org/wiki/Kirchhoff%27s_theorem
https://en.wikipedia.org/wiki/FKT_algorithm

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Anonymous No. 16575448

>>16573852
Here’s how I read my textbooks. I’m an engineer.
>Start by reading the book, actually reading it.
>When you encounter something you don’t know, take the time to understand what its saying and understand what it means.
>if they show proofs, try doing the proofs yourself.
>re-read the part you originally got stuck on and refine your understanding on that part (sentence, definition, example, etc) until you are confident you understand the concept.
>repeat until you’ve read the whole book.

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Anonymous No. 16575770

What is the most efficient and performant way to calculate the inverse of x-sin(x) without using a naĂŻve algorithm like Newton's method?

Anonymous No. 16575788

>>16575770
By the way, the (x,y) points are ((Ď€/2)-1,Ď€/2) and (Ď„-(Ď€/2)+1,Ď„-(Ď€/2)) where the curve touches the line.

Anonymous No. 16575792

Forcing feels like witchcraft. how did that jew cohen even come up with it...

Anonymous No. 16575812

anyone using AI/LLMs to help with math? Or are they not good enough at the upper level math subjects? I know wolfram exists but never used it.

Anonymous No. 16575848

>>16575812
LLM's don't follow logical rules. They are interpolation systems, not directly constrained by mathematical logic. If you need "close but you'll never know if it's right," an LLM is probably not a bad first pass. If you actually need to be certain it is correct and logically consistent, LLM's will not help you. They can't even know how many of each particular letter are in any given word without having to conjure up some human written Python code to check.

🗑️ Anonymous No. 16575856

>>16575770
Some partial but loose approximations I've found for small parts: [math]\sqrt[3]{6x}; \left(\frac{\pi}{2}\right)^{-1} + \sqrt{2x - \pi + 3}; \frac{3\pi}{2} + 1 - \sqrt{3 + 3\pi - 2x}[/math]

Anonymous No. 16575871

>>16575770
Some partial but loose approximations I've found for small parts:
[math]\sqrt[3]{6x}; \frac{\pi}{2} - 1 + \sqrt{2x - \pi + 3}; \frac{3\pi}{2} + 1 - \sqrt{3 + 3\pi - 2x}[/math]
Had to delete my previous post because of a LaTeX conversion error, AI mistaked -1 for ^{-1}.
>>16575812
They usually suck, which is why I still need human assistance.

Anonymous No. 16576089

>>16574503
leave mom and jamal out of this and just answer my question nerd

Anonymous No. 16576115

>>16575812
It is interesting to see deepseek think.
You can learn from the AI. At the very least it definitely can solve book problems and be your answer key when self studying.
>>16575848
retard
deepseek is solving putnam problems in 10 minutes
I trust its logic more than any random undergrad.

Anonymous No. 16576166

>>16575812
Trying to get an LLM to talk about math is easily the most disappointing thing I've ever done with one. They're dumb as fuck and the only other place I've noticed the hallucination problem as badly as mathematics is in translation
They're not even reliable at regurgitating standard things that are probably in their training data several dozen times in different books and posts

Anonymous No. 16576172

>>16576166
Example problem to give LLM so I can see what you mean?

Anonymous No. 16576185

>>16571452
Terence Tao makes well over half a million dollars a year just in base salary from UCLA. Sure, he could make a lot more by quitting and diddling derivatives in some quant shop, but there's no way you can say he isn't a financially successful person

Anonymous No. 16576192

>>16575770
[math]f^{-1}(x)-a= \lim\limits_{n \rightarrow \infty} \dfrac{nD_{z=a}^n[log(f(z)-x)]}{D_{z=a}^{n}[log(f(z)-x)]}[/math]

Anonymous No. 16576195

>>16576192
should be n+1 on the bottom D

Anonymous No. 16576225

>>16571452
you sound ugly

Anonymous No. 16576233

>>16576115
saaar sukdeep will solve everything ples invest

Anonymous No. 16576291

>>16576172
Prove R(3,4)<=9. A basic problem in graph theory with widely published solutions that are definitely in their training data but none of the scamgpt models are able to solve it. Deepseek r1 was able to solve it though.

Anonymous No. 16576293

>>16576172
Ask any of the llms to produce or reproduce any proof that every vector space having a basis implies the axiom of choice. Its a standard proof yet none of the llms are able to reproduce it.