/sci/ - Science & Math

First for wageslaving in McDonalds with physics PhDs.

>>11882271
>Elliptic curves

2nd for allah's mathematician

0-3 — Study
4-7 — Clean room
8-9 — Convert to Islam

>>11882285
Based

>>11882271
Aluffi or Lang for Algebra?

>>11882340
Both are memes
Lang is a good meme, Aluffi is a bad meme

>>11882341
Examples of a mediocre meme?

>>11882345
Dummit/Foote

>>11882306
>Elliptic curves
roll

>>11882341
>Lang is a good meme
I'll add it to my next springer link order

>>11882376
Don't forget this one.

Are there any common alternatives to ZFC?

>>11882386
ZF

>>11882386
https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Bernays%E2%80%93G%C3%B6del_set_theory

>>11882386
A good number of mathematicians technically work over Grothendieck-Tarski.
No one gives a shit, tho.

>>11882386
New Foundations

Did Wildberger's proof of the Goldbach conjecture stand the test of time?

>>11882386
ZF+AD if you are a sadist. ZF+V=L if you have no love or beauty in your heart. ZFC+countably many Woodin Cardinals with a measurable above them all if you like cabals. ZF+MM if you are based. KPinf if you took the higherrecursiontheorypill.
>>11882458
I can count one hand the number of set theorists that work with NF.

>>11882458
>>11882500
What context does one even use NF in?

How much do textbook publishers care about people violating DRM protected files? I might have a textbook from a smallish publisher that I want to upload to libgen, but I'm concerned about getting fucked

>>11882531
You might want to ask the libgen forums about this, since they're the specialists.

>>11882512
The big outstanding problem is whether NF is consistent. Considering how old NF is, like 60 or 70 years, and how active set theory is, it is amazing how that is still open. The ones who get into NF really care about this question and logic. One person who does NF has flat out told me that NF would be a terrible theory for which to embed mathematics.

>>11882546
After looking at the axioms for two minutes, it seems inconsistent.
What's the specialist consensus btw?

>>11882554
They don't know. One person purports to have a proof but it is so insanely complicated that no one has settled on whether it is correct. He is a bona fide set theorist at an institution, not a crank or anything. One story I heard, is that the guy got a famous set theorists to look at the proof a while back and he found an error. The error is supposed fixed but he has sort of exhausted his goodwill. Another persons comment on the proof is that it has an exposition problem, the guy writes really strange. The fact is, there so few people who care about NF that it is hard to get people to review it.

>>11882571
That's sad.

>>11882571
Is NF just an elaborate troll?

>>11882384
What is a sigmoid colon?

>>11882531
Shouldn't there be a process to make it basically untraceable to you?

>>11882531
>How much do textbook publishers care about people violating DRM protected files?
DRM is intended to keep dumbass normies from emailing textbooks to their friends or googling "stewartz calculus newest edtion". Libgen isn't going anywhere, and publishing companies know there's really nothing they can do about it.
>but I'm concerned about getting fucked
If anyone tries to do something they're just going to go after libgen itself, not an individual uploader, and how would they find you anyway? They're not going to send some NSA crack team to trace a PDF on libgen back through a proxy to you and then sue you based on the grounds of an IP address.

>>11882631
Why? Are you allergic to other entities or existences?

>>11882640
???

>>11882460
>this number, which incidentally can't be written down, can't be written as a sum of two primes, because we can't write down one of them
This doesn't even make the really stupid kind of sense, what the fuck Wildberger.

>>11882613
It is an exceedingly weird theory. I've never actually read about it on my own, only seen a bunch of talks. It is a stratified typed theory of sets, for which, in some sense, you can ignore the type system. The idea is that If you have a formula F with typed variables x, you can replace all instances of x with x^+, the next type, call that new formula F^+. Then you can prove that F holds iff F^+ holds. It honestly really confuses me, and really I just don't care. Many set theorists don't care for this sort of axiomatic/logical analysis. Sure axioms come up in mainstream set theory, but not like this. For instance, you may construct a class of models or be looking at combinatorial principles, and notice that some property always holds. In that case you would see what you could prove from that property, what is its consistency strength, when does it break, etc. In my opinion, if this guys proof is not correct, a(n) (in)consistency proof of NF will come from people interested in logic primarily, not necessarily set theorists.

>>11882644
If you don't want people in your personal space then why live?

>t.innocent q-bit

>>11882653
I thought he was a good mathematician? Why does he write like a schizo here?

>>11882653
>z is the biggest number we can write down
>okay now consider n = 2z
norman pls

>>11882340
Do yourself a favor and develop a Foote fetish.

>>11882660
Avoiding some countries retarded piracy laws is not wanting human contact to you, what?

Brainlet here. What do you call the point on this graph where red becomes green at 12?

>>11882764
An inflection point.

>>11882726
Avoiding <some_humans> in favor of others? So privacy is like a pre-consent filter for prudes? Fascinating.

>>11882794
Go away weirdo

Dude what?

>>11882881
>is on 4chan
>turns 360
>¿¿¿
>back where I started

Pic relates.

>>11882884
Funnel requires two points of balance for any future or current convergence to connect.

Pic relatives.

Topologists be like

If category theory is so fundamental, why can't you formalize probability theory with it?

>>11882987
https://golem.ph.utexas.edu/category/2020/06/categorical_probability_and_st.html

Literally a one second search shows that people do this.

>>11882928
That is the most complex orgy arrangement I've ever seen. And it allows for complete cohesion and zero-incidence concerns for pre-approved applicants?

Amazing. Keep it up, whoever is on top of me!

>>11882653
>This doesn't even make the really stupid kind of sense
But it does. The guy *literally* believes in finitely many numbers which exist=can be written down.

>>11882928
thats a really hot diagram dude, where'd you find it

>>11883039
It's certainly not how any normal person thinks about mathematics. But he's also technically not wrong. Just by finiteness of our existence there are plenty of strongly inaccessible objects. Indeed, the set of computable numbers is countable! What a mess.
Fortunately we have generalization and abstraction frameworks for mathematics which escape this problem. Something can exist without one being able to write it down.

>>11882764
the red-green point

>>11882386
You can find a list of set theories e.g. here

https://en.wikipedia.org/wiki/List_of_first-order_theories#Set_theories

I'd say it's even a scratch to say that ZFC is "used". It's studied by set theories for sure.
But in practice, any predicate (class) that's not evidently inconsistent will be by freely used by mathematicians :P

>>11883100
>But he's also technically not wrong.
Exactly. He is just basing his claim on an extremely strong premise, namely the finiteness of the integers.

>Something can exist without one being able to write it down.
Unless you are Wildberger that is true.

I think *something* can be said for his approach, as it is closer to a "computerized mathematics", where every object is explicitly computable. But on the other hand, computers, right now, are coping pretty well with abstract objects, which rely on notions of "infinity".

>>11883051
https://www.irif.fr/~mellies/papers/segal-lics-2010.pdf

>abelian sandpile
>chip firing game

Was he right to refuse the Millennium prize? I mean you just don't do that it would be like Terrence Tao refusing the Fields.

>>11883352
Perelman also declined the Fields. He was trying his best to avoid fame but obviously , since you're posting about him, it didn't work.

>>11883356
>He was trying his best to avoid fame but obviously , since you're posting about him, it didn't work.
That's not the reason why he declined both prizes. Sure he didn't seek glory but he also published outside academia. His few published statements are also a bit uncanny because Perelman didn't want to be compared to a mathematical hero.

Let [math]G[/math] be a group, [math]H \subseteq G[/math] a subgroup. Is it possible that [math]gHg^{-1} \subsetneq H[/math] for some element g? (obviously i have infinite groups in mind here)

>>11883371
Yes.

>>11883371
Colette poster, I'm extremely disappointed, I can't believe you forgot the definition of normal subgroup.

>>11883371
Yes. Let [math] G = S_3, H = \langle (12) \rangle \text{ and } g = (13) [/math]

>>11882285
I like you a lot

>>11882997
This is not a peer reviewed publication but rather a seminar by a small group of autists forcefully re-interpreting and formalizing a single aspect of probability theory to match their category ideology while disregarding a lot of semantics of the original models.

>>11883467
the truth is the most painful weapon

>>11882764
the zero of a function

>>11883467
>peer reviewed
Who cares? Was Pythagoras' work peer reviewed? Was the disquisitiones arithmeticae peer reviewed?
Now fuck off

>>11883374
>>11883394
>>11883446
thank you but I wanted to ask:
is it possible that [math]gHg^{-1}[/math] is a *proper* subset of [math]H[/math]?

How does one think like an analyst? I can't even solve a single of baby rudin's problems, even though I have read 7 chapters.

>>11883371
the state of animeposters

>>11883543
I sympathize with you but it's really not that hard. Just think about it.

>>11883541
I think so. Set [math]G[/math] as the set of all permutations of integers, and [math]H[/math] as the set of all permutations of natural numbers (i.e. permutations of integers which fix the negative numbers). Set [math]g(n) = n+1[/math] (maybe n-1). Then [math]g H g^{-1}[/math] should be the permutations which fix the nonpositive numbers.
Unless I fucked up, quite possible. Not checking tho.

>>11883216
Yes, precisely. It's funny too because he doesn't even work in a semicomputable mathematics, he works in a purely computable one where all processes must terminate. Like I think of algebraic numbers as fully computable since it is easy to write an algorithm which outputs the first n digits. But that's not enough for Wildberger.
I also appreciate your point that computers can handle infinite objects well. There's kind of a question of representation here: of course, there is a finite amount of matter in the universe, so a computer can be of bounded size, and thus there are finitely many configurations of rules to set forth for a program. Some of these rules may tackle a very very large proportion of mathematical objects, but there are also a vast ocean of objects which no human or computer will be able to grasp individually. But we're not throwing them out. Meanwhile, wildberger is playing in the tide pool to the side of the ocean where he can see and touch everything clearly. Maybe it makes sense but it's boring.

https://youtu.be/QVKj3LADCnA

>>11883617
>>11883541
To add to this, it's not possible when H is finite.

>>11883647
https://www.khanacademy.org/math/linear-algebra

I read in this book
https://www.barnesandnoble.com/w/quantum-computing-for-everyone-chris-bernhardt/1129557017

That you can get started quantum computing and learning quantum physics, before you learn classical mechanics, if you can wrap your head around linear algebra. Is this true?

https://docs.microsoft.com/en-us/quantum/overview/algebra-for-quantum-computing

>>11883363
But he quite literally is a mathematical hero, to basically every smooth geometer... Is it just autism?

>>11883714
>to basically every smooth geometer
All 5 of them.

It's so fucking hard to get into spectral sequences. It's just a wild forest of indices and objects
AAAAAHH

>>11883617
>>11883666
this is exactly what i was looking for, thank you

>>11883722
Worry not, anon. It's just r horizontal and r-1 vertical steps, and either left&up or right&down.

>>11883543
Through practice. There are also a few tricks.
1. Sometimes you can't prove something but you can prove it easily with an error of epsilon. Prove it that way and see if continuity will let you push epsilon to 0.
2. Know the various definitions and equivalences for open, closed, compact, etc and know the theorems about continuous functions on compact sets. They are extraordinarily useful and work just about anywhere if you use them correctly. Specifically, there is often a delicate balance between whether you should approach question involving compact spaces through the lens of converging subsequences, or through the lens of open covers, or just using a pre-made theorem you have already. Try all of them (starting with premade theorems)
3. Oftentimes you run into nasty expressions with big fractions, with trig functions, etc etc. If all you need to do is show that said expression is less than something, then don't work with that expression, work with a simpler expression which is greater than it. Use things like sin(x) < x for x > 0. Use common finite and infinite series formulas, like the geometric one. Sometimes it won't work but the whole point of this is experimentation and finding that balance.

Idk if this too elementary for /mg/, I just wanted to share how satisfying it is to just sit down and try to work out most of the theorems in elementary arithmetic simply from the axioms
a+0=a
a+S(b)=S(a+b)
a*0=0
a*S(b)=a*b+a
and induction
I did just that and derived theorems like a*b=b*a. a*(b*c)=(a*b)*c, a+b=b+a and it's very satisfying to see it work out so nicely (I have never seen the proofs before). You should try it.
>>11883722
I know that feel bro.

>>11883721
Precisely. What does he think? He's going to be treated like some kind of deity?
Sounds to me like he just is scared of socializing.

https://libgen.is/book/index.php?md5=26CE0F0057C1FFF647491C51560DC5F2

nooooo

>why yes, I am a field of characteristic 1. How could you tell?

>>11883467
>This is not a peer reviewed publication
OH NO! How dare people publish anything without jumping through the hoops of a retarded publishing process, which has not all that much evidence in favor of it actually preventing fraud or errors.
Imagine what if people just published things and let other people in the field judge it.

>>11883773
>https://en.wikipedia.org/wiki/Field_with_one_element
This is quite possibly the stupidest wikipedia page I've ever read, and I have no idea how so many people I genuinely respect actually participated in this.

>>11883570
I kneel.

>>11883784
OHNONONONO quick my fellow algebraists, how do we hide this so that the analysts and geometers will not mock us relentlessly for the next decades??

https://web.mit.edu/18.06/www/Fall18/

I'm too brainlet, never gunna make it

>>11883807
It doesn't bother me. I don't speak monkey, so I can¨t understand what they are saying.

>>11883822
Make what exactly?

>>11883823
Big braindom

>>11883823
You know, elliptic curves...

>>11883824
You can extend your cranial capacity by shooting your head with a shotgun.

>>11883826
I know and I don't care.

>>11883829
>He'll never see the beauty of a nice elliptic curve

not gunna make it

>>11883831
>muh beauty
Cringe.

>>11883832
baka desu ne

>>11883831
>the beauty of a nice elliptic curve
>beauty
>a fucking 2-torus which is also the zeroes of an irreducible smooth cubic
It really isn't all that you're making it out to be.

>>11883835
>this is your brain on topology

>>11883784
"field with one element" as a mathematical object doesn't actually exist. You just study how geometry over a field with one element would behave by taking results about fields with n elements and extrapolating

>>11883855
Yes, we aren't talking about geometers studying objects that they can't construct or even prove exist, or synthetic differential geometers having to use intuitionist logic because their definitions produce classical contradictions.
We're talking about "if we could properly formulate the notion of square circle, this could lead to a proof of the Riemann conjecture."

>>11882928

it's a coffee cup which is equivalent to a donut

>>11883647
Strang a shit
>>11883700
I have no idea but Through the Looking Glass has a video on exactly that

hello mathlet here, i'm trying to undo years of being in the "i'm just not good at math" camp, is pic related a decent intro to foundational literature?

For background, I'm a linguistics undergrad and i'm really interested in mathematical linguistics and formal languages but realize i kinda lack the basic skills to support those interests. Mathematical ling is mostly made up of set theory and formal logic, and seeing how the first 3 books in this image have to do with that I figured it would be a fun starting point.

Thanks for any help!

>>11884122

I never come to 4chan anymore but just dropped in randomly today. I am a 5th year math PhD student and I only know of a couple of these. It seems like one of those meme-y flowcharts the Internet likes so much. The choices seem a bit repetitive in some ways too.

I suggest asking some linguistics professors what they think you should read. Usually a math department has a logician or two, worth emailing them as well.

>>11884136

meme book images are generally bullshit

Fellow category/algebra trannies, does anyone know if [math] K_0(\mathbb{Z}) [/math] is known? Because the monoid of isomorphism classes of finite finitely generated [math] \mathbb{Z}[/math]-modules contains [math] \mathbb{N}[/math], an element for each finitely generated group, and?

I'm sure there's ton of literature on it, but are there any particular books you guys recommend for Galois theory?

>>11882635
You're a retard who doesn't understand drm.
>anon orders a textbook using his real ip and credit card tied to his real name
>this information is tied to a number in their database
>same number is also encoded in the pdf via some steganographic means
>pdf is uploaded unprocessed to file sharing service
>publisher downloads file, checks special number, immediately gets anon's info
This process is so simple that nearly every printer these days encodes this information in every single print job via semi-invisible dots.
Now, I'm not saying they do this, but it's extremely simple and pretending that the (((publishers))) wouldn't bust it out just to be petty cunts is ignorant of the history of copyright fuckery.

Are all applied math courses just plug and chug 'methods' based stuff?

>>11884122
u cannot learn math above 25

>>11884190
Isn't that just [math]\mathbb{Z}[/math]? You add the inverses and you even get the tensor product act as your multiplication. Or, this is a vague memory from a few years ago. I could be wrong.

>>11884211
24

>>11884211
>undergrad
he's got a few years left then

>>11884211
>>11884216
>>11884219
Epic meme, fellow redditors!
Upvotes for all!

>>11884211
t.

>>11884209
In undergrad? Yes.
In grad? No.

>>11883747
Cute.
>>11884190
The integers form a PID, so every finitely generated projective module over them is free (source: https://math.stackexchange.com/questions/162945/submodule-of-free-module-over-a-p-i-d-is-free-even-when-the-module-is-not-finit )
This implies that [math]K_0 ( \mathbb{Z} ) = \mathbb{Z}[/math] as the other anon pointed out, doesn't it?
>>11884209
No, just the shitty ones.

>>11883638
>there is a finite amount of matter in the universe

Please stop this, nowhere has it been confirmed that the universe is finite.

>>11884239
Wrong link, my bad.
https://math.stackexchange.com/questions/147754/finitely-generated-projective-module

>>11884240
Care to provide a proof?

What is the comfiest field of mathematics for self study?
(I know up to and including Laplace transforms if it matters)

>>11884268
Sounds like a good time to get into algebra.

>>11884268
Read Thread Pic
>pic related :D

>>11884264
1.0...1, 1.0...2, 1.0...3, ... 1.9...

As you can see, within 1 unit of matter there is an infinite amount of matter

>>11884264
The burden of proof is on you to show it's finite. I remain agnostic until I see evidence one way or the other.

>>11884302
Do you subscribe to Leibniz's theory of monads?

>>11884313
I'm not super into philosophy or metaphysics. This is a scientific question.

>>11884268
>up to

¿What does all math «up to» Laplace transforms consist of?

>>11884333
>¿

>>11884327
Science is inherently philosophical.

>>11883236
thanks, thats going into my porn folder

>>11884333
Laplace transforms and Heaviside functions are usually the second to last topic covered in a first course on ODEs.

Do you guys think it might actually be possible to mathematically show that the universe has a finite amount of energy since otherwise some kind of Eilenberg-Mazur swindle or Riemann rearrangement could be done to produce infinite energy?

>>11884368
no

>>11884369
FUCK.

What's with all the math mental masturbation? It's literally just numbers.

>>11884389
It literally isn't.

>>11884361
:(

>>11883543
This book, develop set theory, logic and induction methods for analytics functions.

Best book for learning analyst tools.

It's on libgen.is

>>11884216
I don't think so. The [math]\mathbb{Z}^n[/math] gives [math] \mathbb{N}[/math] in the monoid, which becomes [math] \mathbb{Z}[/math] when you take the group completion, but you have to add all the finite groups, which are all finitely generated [math] \mathbb{Z}[/math]-modules?

>>11884190
K_0 is Z, and I believe it is not known what it is for higher. In fact, I think K_0 is R for a PID. Been a while though.

>>11884445
You do remember you want the modules to be projective and f.g.? An abelian group is projective iff it is a direct summand of a direct sum of copies of the integers -> a f.g. projective abelian group is simply a sum of finite copies of Z.

>>11884457
>projective
Oh yeah I forgot about that, that was my error. Thank you.

>>11884196
Aluffi is good if you just want a short intro, plus you already have all the necessary background material there. I also liked Morandi, which is a bit more complete (and obviously, focused) so gives a better overall understanding. If you're not planning on going past the basics of a first course, I'd probably just recommend for you to google the lecture notes of a good course at a good uni

>>11884454
>K_0 is R for a PID
You mean Z? Every finitely generated projective module over a local ring or PID is free?

>>11884462
Thanks. I'll check out Morandi.

>>11884459
You're welcome.

>>11884470
Shut up, tranny.

>>11884480
OK. Have a nice weekend.

>>11884470
You're cute.

In an attempt to improve my posture, I've been thinking of using some sort of platform upon which to rest books and notebooks as I write or read, but I ask if this isn't faggotry on my part. I've already done something similar with my computer, it now stands on top of a wooden platform of sorts and it's much more comfortable to use it for extended periods of time, but to solve the book/notebook problem I'd have to use an inclined platform, and the only things I can think of either aren't sturdy enough or seem exaggerated(the first thing that came to mind were those supports used by musicians to put their sheet music on).
Any suggestions?

>>11884493
you mean one of these things?

>>11884493
Monks knew how to do it.

>>11884465
just dug up some notes, there's the following:
>[math]K_0(\mathbb F)=\mathbb Z[/math] for any field since all modules are free
>[math]K_0(R)=\mathbb Z[/math] for any PID [math]R[/math], since the submodules of free modules are free (in the case [math]R=\mathbb Z[/math], free abelian subgroups are free), so any finitely generated projective module is free of finite rank.
>[math]K_0(R)=\mathbb Z^n[/math] where [math]R [/math] is a semi-simple ring, [math]n[/math] being the number of simple module modules; this is the case since every R-module is then a direct sum of simple R-modules, and simple R-modules are projective.
>[math]K_0(R/I)=K_0(R)[/math] for nilpotent ideals [math]I[/math].
>If [math]R[/math] is 1-dimensional Noetherian ring, then [math]K_0(R)=\mathbb Z\oplus \text{Pic}(R)[/math], the Picard group being the isomorphism classes of rank 1 finitely generated projective modules.

>>11884504
Love Noetherinian rings, lads.

>>11884506
This is like saying "I love not being stabbed in the dick"
Nobody loves Noetherianity, it's just the default non-suffering state of existence.

>>11884502
Don't mind me, just posting the greatest clergy mathematician of all time.

Why do people even study mathematics when everything can be summed up as just an array of numbers? Just study arrays lmao

>>11884538
>Just study arrays lmao
That's ... what we do

>>11884538
I study noetherian arrays ONLY

Is there a different way to prove the distributive law for the Boolean ring defined by [math](\mathcal{P}(x),\Delta,\cap)[/math] other than using the characteristic function [math]\chi(x)_A= \begin{cases} 1, x \in A \\ 0, x \notin A \end{cases} [/math]?

>>11884493
Well the downside of that is tendency of raising shoulders instead, if you have shoulder issues then id not recommend it

>>11884628
Delete your post nigger. Stop fucking your LaTeX up.

>>11884501
That's a dream come true, although I'm not sure what to call it. I searched amazon for "inclined book support" and got a bunch of gym benches.

>>11884502
That looks comfy, although I'm trying to keep my back upright, as opposed to him(even if his back is straight)

>>11884628
Sure.
[math]A \cap (B \Delta C) = A \cap (B - C \cup C - B) = [A \cap (B-C)] \cup [A \cap (C-B)] = [(A \cap B) - C] \cup [(A \cap C) - B] = [(A \cap B) - (A \cap C)] \cup [(A \cap C) - (A \cap B)] = (A \cap B) \Delta (A \cap C)[/math]
Justifying the individual steps exercise reader.

>>11884652
Thanks, animeposter.

Very basic question about logic here. Please don't hurt me.

I understand that in propositional logic, you have syllogisms like
>All men mortal
>Socrates is a man
>Therefore Socrates is mortal

I also understand that in predicate logic you have to quantify your variables and have with propositions like
>For every x, if x is a man, x is mortal
>x = Socrates
>Therefore Socrates is a man

But how exactly does second-order logic extend this? What extra features are present in second-order logic and what is their purpose? I thought first-order logic was "sufficiently expressive" like set theory.

https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/index.htm

>>11884508
so if you were given a polynomial ring on infinitely many variables, were you just stabbed in the dick?

Is the idea of a unit even defined in a ring without identity?

>>11884808
No.

>>11884508
how would you describe the "being a field and thus modules are vector spaces again :)" property ? also just the default non-suffering state of existence ?

>>11884772
whats the problem

>>11884772
>interactive java aplets ("Mathlets")
Listen, I'm not laughing because it's funny, I'm laughing because I'm retarded.

>>11884849
That didn't elude me

>>11884853
Kek.

>>11884849
my sides

https://youtu.be/IMj5dgGWxSM

I may as well be watching this, I'd learn a bit more.

Fuck.

https://youtu.be/ObPg3ki9GOI

I CAN'T TAKE IT AHHHHHHHHHHHHHHHHHHH

>>11884808
Yes, if you mean a rng, which is a ring which doesn't necessarily have an identity, but which could have one.

See also: Nonassociative algebras may be taken to include associative ones.

>>11884883
Leibniz > Newton

>>11884883
>the birth of calculus (1986)
Wait... it's that modern?! I thought it was centuries old.

>>11884899
https://plato.stanford.edu/entries/descartes/
https://en.wikipedia.org/wiki/Descartes%27_theorem

damn bro, dem circles be kissin

>>11884873
>just attend the Polytechnique
I fucking wish

>>11884883
for me, its cavalieri

>>11884924
https://youtu.be/sG_6nlMZ8f4

for me it's these guys on youtube.

Guys, I just saw Grant (3blue1brow) in a gay bar.

>>11884939
this

>>11884501
Just saw this on Amazon, it comes as a double support(as in you can put a book in the "first" and another on top, with the second part being an extension of the first height wise) that can be disassembled into two, I do wonder if it'll make a positive difference though

>>11884941
did you suck his dick

>>11884798
Yes

https://en.wikipedia.org/wiki/Henry_Perigal
https://youtu.be/AzmUCL1OHhs

>>11884209
No
t. applied math student

https://youtu.be/WqzK3UAXaHs

You can learn math at literally any age. You just shouldn't expect to make any original result if you're older than 24 and not a grad student already.

>>11885069
>tfw will be 24 and one month when I start my PhD

Can anyone recommend a good book on stochastic processes? Or just random walks.

>>11885079
Unironically the Dover book on it.

How should I approach the issue of not understanding some concepts as I read a textbook? Just get on with it and hope to get it in the future? It's very frustrating.

How do you guys study along a textbook? I'm liking the Cornell method, but one page is not enough for all the notes I take. Do I just keep making notes, then summarize after the section? Or do I do one page of notes, summarize, then start a new page?

>>11885097
Ask /mg/.

>>11885097
>>11885097
If you're like me everything is way too hard or way too easy.

I think the most comprehensive system in place for people like us as far as undergraduate texts are concerned is khan academy's system where you take quizzes and master material and it tracks what you have and haven't done and shows you areas and topics you haven't covered. It's a mixture of structure and freedom to explore that I really enjoy.

The only issue is you have to invest enough time to know what you don't know, so you can know things you don't know yet. That's where it just gets annoying and unfun. Plus you can lose your account and there goes everything.

Ultimately I'm just trying to learn calc online and left defeated. Truly the king of brainlets.

>>11885107
I open the book and read
when I find an exercise, I think about it, unless it's very boring. If it's too complicated to do mentally I write it down.

A couple days later I sit down with a notepad and rebuild as much of it as I can.

Notes have always been a complete waste of time for me personally. Maybe it's different for other people.

>>11885097
"fuck it" is not a particularly good way to approach "I have a problem".
Obviously understanding doesn't have to be immediately perfect (nor can it be) but moving forward when you're totally lost is just going to make you even more lost.
If you don't get a concept, reread the sections until you do. Draw/compute some examples. If the explanation in the book is cancer (happens often, the majority of textbooks are bad) and you've been stuck for a while, go find a different source and read its explanation, or ask a real person if you can.

>>11885116
I wish there was a software like math trainer that just shot questions at you with resources to solve them with progressive difficulty. Like a game. That sort of software is really fun. I wish math trainer wasn't just limited to mental math.

>>11885119
>when I find an exercise, I think about it, unless it's very boring. If it's too complicated to do mentally I write it down.
Based

>>11885119
I think you're gunna hurt your brain if you do nothing but study all day everyday.

>>11884808
I mean, you could be a loser and define a pseudo inverse of [math]x[/math] to be a [math]y[/math] such that [math]x = xyx[/math] and [math]y = yxy[/math]

What does /sci/ thinks about this guide?

>>11885164
I will have to check it out more.

>>11885153
You make von Neumann sad by saying that.

Can anyone recommend me a map for studying set/model/proof theory?

>>11882340
idk the rest, I like Aluffi

>>11882386
von Neumann-Bernays-Gödel, Morse-Kelly, Kripte-Plantek and Quine

>>11882500
What is AD? Determinacy?

>>11883855
Let G = {e} you define e+e=e and e*e=e. Obviously (G,+) and (G,·) are abelian groups and it is clear that it also distributes, therefore it is a field

>>11884268
I've never had more fun than doing synthetic geometry. I know it ends, and quite soon, but hey it was fun

>>11884941
idk why but I could believe it

>>11885107
I take notes of anything I read and it has worked so far for me

>>11885164
this has already been posted

>>11885164
>No algebra
>No topology
>No linear algebra

>>11885164
Wrong file.

>>11885164
Superfluous. Enderton's Elements of Set Theory is a much more difficult and involved book than "Principles of Mathematics," "Foundations of Analysis," and (probably) "Basic Mathematics."

The only two books you need to read here are "Book of Proof" and "Elements of Set Theory."

>>11884394
it's literally all about arrays of numbers.

>>11885124
NGMI

>>11883855
if youre not an autist about defining a field its pretty straight forward

>>11885183
I dont think he would mind

>>11885205
If you need to study all day rather than do actual research or creative work you're very much NGMI by any historically founded metric of success in science and math.

>>11885186
>Let G = {e} you define e+e=e and e*e=e. Obviously (G,+) and (G,·) are abelian groups and it is clear that it also distributes, therefore it is a field
You can do this if you want but it's about as productive as letting 1 be prime. It provides no benefit in any way, the only effect is that it forces you to hedge 99% of your theorems with "for all fields except this one shitty one" instead of just saying "for all fields"

Threadly reminder to spend quarantine time together with your physicists friends

>>11885259
What if I don't have friends, physishit or normal?

>>11885229
I don't know any field theorem that fails on the trivial field. Also 1 is not prime because of the concept of unit and the unique decomposition property. The fact that this field is "non-productive" doesn't imply it doesn't exist as other people suggested. Also it is useful for category theory

>>11885196
I like this map

>>11885186
https://www.math.wisc.edu/~miller/old/m771-10/kunen770.pdf

>>11885266
>I don't know any field theorem that fails on the trivial field.
Fucking everything falls apart over the trivial field, what are you talking about.
The entire theory of field extensions collapses because you have no usable vector spaces (hence no concept of dimension) and no irreducible polynomials either (because you don't have a legitimate polynomial ring).
Also you've now invented a field of characteristic 1, so you do appear to believe that 1 is a prime.

>>11885226
Seethe.

>>11885358
ok, but its got uses in a different aspect of math
so i dont care

>>11885376
>go full retard
>start pretending you were trolling once you can't respond
it's all so tiresome

>>11885266
This really reminds me of the "But do you really need reflexivity when defining an equivalence relation" thing.
Bro you use non-triviality all the time.

>Professor/book unironically uses [math]\nu[/math]

>>11885186
Yes AD is the axiom of determinancy.
>>11885196
I made that image about two years ago, and I have learned a lot since then. If I were to remake it today, I would probably add a bridge between Enderton's Elements of set theory and Kunen's Set theory. Enderton is great, I used it in my undergrad set theory course, but it leaves a lot to be wanting in terms of the model theoretic aspects of set theory. For that I recommend Roitman's set theory book, which are more like course notes. Roitman's book develops a fairly comprehensive theory about when sets satisfy certain axioms. Also the last two chapters of Roitman are a fantastic survey of advanced set theory. Covering things like, constructibility, combinatorial set theory, measurable cardinals, cardinal characteristics, and stationary sets. What she does really well is given the reader a glimpse of powerful theorems and show you how to use them. Of course, she hasn't developed the theory to prove them, she really is just whetting the appetite. The problems are pretty easy, but if you look at the problems as more of putting a shit ton of examples in your back pocket to come back to, they work well. I would probably add a bridge between Kunen and Kanamori's book too. Kunen doesn't really talk about large cardinals, and Kanamori rockets you into the theory. I have just starting reading some chapters from Schindler's Set theory book and so far it seems like a nice balance, but his exercises are either stupid easy or painfully hard. If you couldn't tell, model theory is not really my area. Hopefully someone who knows more model theory can add some books on other research areas of model theory, rather than just stability theory.

>>11884995
love this one

>>11885384
i was a different anon, and im not trolling you retard
different areas of math can have differing and even contradictory conventions
are you new?
>>11885266
isnt me

Im getting filtered by logic bros.. fuck this

>>11885733
Are you a woman lmao

>>11885965

>>11885733
Are you a libtard?
I heard they get destroyed by logic all the time.

>>11885498
>physics class on waves and optics
>professor uses [math]v[/math] for velocity and [math]\nu[/math] for frequency
Hey, at least I'm not solely responsible for my brainlet status.

>>11883100
>Something can exist without one being able to write it down.
only classical logicians say this

Can i become a banker by having a PhD in math?!
bank manager is the highest paid job in my country, so i wonder if it's possible for a mathematician who works in finance sector to climb up the ladder and become the manager.
Is "being good at math" the most important factor to reach this goal, or are there far more important things like connection, social status, etc...?!

>>11885186
>Let G = {e} you define e+e=e and e*e=e. Obviously (G,+) and (G,·) are abelian groups and it is clear that it also distributes, therefore it is a field
Aren't field supposed to have at least two elements?

>>11882386
https://en.wikipedia.org/wiki/Tarski–Grothendieck_set_theory

>he thinks adult education has anything at all to do with his intelligence
ishygddt

>>11886386
ngmi

>>11882271
I have a CLOSED loop rehab band (O shaped). However, its too loose. How can i tie it to make a new tighter loop of desired smaller circumference? I mean knot, not including getting specified length in the method.

>>11886464
>rehab band
I am not familiar with that diff from terminology. Can you print me to a definition?

>>11886446
do you understand the idea of accumulated marginal advantage? think about that for the rest of the morning/night for me and then never post in this thread again.

>>11886494
Its basically an Array. Array of numbers. Other name is a resistance band.

>>11886508
>do you understand the idea of accumulated marginal advantage?
Meaningless Buzzword.
ngmi

any recommendations for stochastic differential equations and stochastics in general?

>>11885988
L O N D O N

>>11886551
its literally the same as someone who drives a faster vehicle with a larger amount of fuel beginning a marathon race hours before another care you fucking brainlet nigger. There is no way in any world that a stupid person will compete with a genius especially given the latter begins mathematical training at an earlier stage in life. This is so obvious to anyone who has ever dealt with virtuosos and collegiate athletes who begin training during childhood and also outperform other high level performers and athletes that also began at an earlier age. You are talking to me as if I don't study math, this is wrong! I study every single day, but I have no designs to be a mathematician as I simply cannot compete with those that are naturally talented and have been studying for a decade longer than I have. Instead I choose to do work in a field where I am naturally talented and have been doing work to build the necessary skills for research for longer than others. If you cannot understand this or refuse to do so you are either very stupid or mentally deranged.

>>11886566
I'd recommend killing yourself instead of doing that.

>>11886668
bad experience?

>>11886658
>Schizo ranting
Ngmi

>>11886658
math is not a sport . it doesn't matter how good you are at it as long as you are able to get results . it's mostly luck

>>11886658
also you are very bitter and pissed off. what's the harm in letting people try? (i'm >>11886733)

>>11886566
>>11886566
lets not let our eyes of the prize here fellas

>>11886566
>>11886825
why dont you just look for one of the 1000 math stack exchange questions that are identical to yours

>>11886737
>you are very bitter and pissed off

>>11886835
i want to see what yall think

>>11886891
i think that it doesn't really matter where you start . just try a bunch of books that get recommended (elsewhere because I don't think anyone here is very interested in stochastic anything) and find the one that's not so hard that you don't understand while not so easy that you find it boring

>>11884122
pick one book at random and work through it, just do a lot of exercises and a lot of proofs its all about doing

>>11886566
>>11886891
The Dover one (unironically).

Any good texts on sieve theory?

>>11885079
>>11886566
Is it worth getting into stochastics? Are there any important problems, or at least interesting? And what about applications?
t. soon to be grad math student

>>11886940
Yes, yes, and yes.

>>11886959
Do you mind extending your thought a little bit?

>>11886967
stochastics has infinity applications biological math is closely related, lots of optimization stuff, lots of operations research and econometrics stuff

>>11886996
like it might surprise yall mathheads but this kind of commercially viable stuff is actually the topic of tons of research

>>11886996
>applications
>infinity

>>11887012
Yes.

Explain the birch swinnerton dyer conjecture to me like I'm retarded.

>>11887177
nah if you're retarded there's no point in explaining

>>11887186
Then explain it to me like I'm beginning grad school.

>>11887191
Elliptic curves rational points funny patterns.

>>11887191
if you're beginning grad school you can just read the statement on wikipedia

>>11887192
Develop please
>>11887195
Yeah but I'd really like someone to spoonfeed me.

>>11882275
this will be me in a while
I'm going to submit another paper but now I have no university affiliation and I'm considering just writing down the restaurant's name to at least get a laugh from someone

>>11886377
Yes. No (second is xor not ir).

Found out my math degree with a stats and actuarial concentration will take five years to finish.

Five. Years.

I'd be 43 and just getting started in the job market. Tell me, /sci/: is it worth it?

>>11887404
Yes.

>>11882386
Elementary theory of the category of sets, or even better, just forget about set theory and use type theory.

>>11887404
>2020
>unironically being 38 years old
Yikes, bro. This is a zoomer board.

>>11887404
Depends on your goals in life. What do you want that money for - why does the "job market" matter to you?

You can learn tensorflow in 5 months and then get some job that will probably earn you about the same as the job you get right out of your degree. Imho (with emphasis on h), we study to learn. You only go 100 years to live, better learn some pretty math, and fuck some fit girls.

>>11887474
>Left
Soul
>Right
Soulless

>>11887460

>>11887536

>>11887404
If it's your calling you'll figure it out

>>11882275
NOOOOOO WHAT ARE YOU DOING!!!!???? YOU CAN'T JUST STUDY PURE MATHEMATICS. WHAT ABOUT YOUR WIFE AND CHILDREN AND CONSOOOOMING?? HOW WILL GET THE LATEST ITODDLER PHONE AND LAMBO TO IMPRESS THE GOY?? NOOOOOOOOOO

>>11887536

>>11887404
Im turning 25 and have 3 more years of uni ahead but I really enjoy my area of study. People like you give me hope- you are considering this at that age. I already feel too late and that i wasted my prominent years on stuff i didnt care about. Just do what you enjoy doing if you can.

>>11887569
Have sex.

>>11887602
I'm 24 and I'll get my bachelor's next year.

>>11887609
>>11887602
Keep plugging away.

What's the GMI age for the first published paper?
First paper published by 22, 5 papers by 24?

>>11887664
>5 papers in 2 years
I smell a combinatoritard

>>11887740
There's nothing wrong with combinatorics.

>>11887609
I'm 24 and I got my masters already.

>>11887749
Congrats. Are you doing a PhD?

>>11887749
I am 23 and would have my Masters soon if I ever started with my Thesis instead of dicking around on the Internet LMAO

>>11887749
So... standard track?

>>11887806
What if I told you that CS was applied mathematics?

>>11887749
I'm 19 lmao.

>>11887747
ok now count nothing in 6 different ways, you fucking number monkey

Love Dedekind cuts, lads.

>>11882386
homotopy type theory

>>11887740
oh my, looks like I was found out
Combinatorial geometry to be precise though.

>>11887837
Ok.
Nothing, zero, nada, zilch, smallest non-negative amount, [math] \emptyset [/math]

>>11887602
>Just do what you enjoy doing if you can
This. If you actually manage to make some contributions, let those be a side product of doing what you enjoy. No giving up yet.

>>11888111
HOLY CHECKED

>>11888111
Based and digitspilled.

>>11888125
>>11888129
Hate to admit it, but those digits are my greatest achievement this week.

>>11888131
It's not much, but it's honest work.

>>11888139
Yep. At least the post was sincere. Have some godly LaTexing background music to accompany all your Greek letters. https://www.youtube.com/watch?v=i-3h9TQ312c

>>11887771
>>11887792
yes and yes

>>11888165
I call and raise you this https://youtu.be/02pg9V1ENL8

>>11887177
https://www.youtube.com/watch?v=2gbQWIzb6Dg

>>11887569
Imagine making these memes lol. Is it just like one miserable guy who takes photos of himself getting triggered for ideas

>>11888266
>Is it just like one miserable guy who takes photos of himself getting triggered for ideas
Unironically, yes.

>>11888238
That was nice! Have you learned anything cool lately?

>>11888302
Hume's reconciliation of freewill and determinism.

>>11888302
I've spent a week starting to learn Japanese if that counts as cool!

>>11888312
That's pretty cool.

>>11888313
I guess that counts.

>>11888317
>I guess

>>11888325
Sorry I'm getting drunk and stupid and can't express myseld.

>>11888333
Holy digits.

>>11888333
It's okay those digits can excuse any mistake

>>11888336
>>11888337
Lol I wonder if I hit 11888555 as well.

>>11887740
seethe

I likw thewe threads! Good night /mh/

>>11888555
Night, lad.

>>11888341
>>11888555
Oh fuck off

does the incompleteness theorem imply intuitionism?

does the incompleteness theorem imply intuitionism is true?

Is there some name for a set which is the closure of an open set?

>>11888555
>>11888341
WHAT

>>11888571
no, but kinda
>>11888587
a closed set

>>11888637
>mfw anon claims that [math]\{ 0 \} \in \mathbb{R}[/math] can be written as the closure of an open set

>>11888651
>{0}∈R can be written as the closure of an open set
This but unironically.

>>11888657
Closure of what open set?

>>11888667
{0} in the discrete topology

>>11888571
A better question is why do the incompleteness theorems bring out the pseuds? It is a very simple theorem about a certain class of first order theories. Only retards and cranks try and extract something philosophical out of it.

>>11888753
Math is inherently philosophical.

>>11884122
Do we have something like this for physics?

what is the eromanga sensei of mathematics?

>>11888889
Off by one.

>>11888914
this is /mg/, not /csg/

>>11888558
Thanks.

>>11888568
>>11888624
Magic.

Good morning, /mg/.

>>11889094
Morning, lad.

>>11889105
Thank you, friend.

Is the finance career route pure hype?
I need some applied fluff to finish my masters degree and I can take it all in finance classes.

I guess, making good money would be nice, but do they really earn more than engineers/programmers?
I am not talking about the top guys at Renaissance Tech.
I'm talking about average dudes with no exceptional talents or intelligence who work for normal investment banks. Cause that would be me in the future.

My dream job is to work with either with machine learning or physics/engineering.

New thread
>>11889375