/sci/ - Science & Math

first for engineering

is there a maximum angular velocity like how theres a maximum velocity?

>>11502149
that image is extremely lame, sorry math guys

"is honestly maybe ready to try dating again"

if you presented this sentence to an old man who was trying to retain the last bit of virility he possessed, all the remaining testosterone would flee his testicles as rapidly as possible

>>11502166
Our times are different, we weren't shaped by wars or ignorant parents, we were shaped by the internet, by loneliness, our mental health is fucked up, our social interactions have drastically fallen, this is the age of depression, times have changed, old man.

dating is for normies online gfs and stem qt cuddlebuddies are for autisms

>>11502192
Protip: they don't give a fuck about consumers, that's why almost all of their books are available online, they facilitate piracy because they know no one in their right minds will pay 70 bucks for a poorly printed, poorly binded book.

Their market is libraries and autistic collectors, so they charge as high as they want because both of those have the money to spend

>>11502205
>they facilitate piracy
What? I thought someone(possibly an entire department collaborating with each other) with extensive institutional access just ran a bot that scraped and uploaded literally everything.

>>11502192
For springer I'm using sci-hub, every book there has DOI i just put it in there and boom, works for every book new or old.

>>11502209
yes of course, how do you think sci-hub works?

>Think about, when your a prof at a uni you basically sit around all, not doing shit except arcane math that only you and your buddies can actually evaluate the value of, so you spew a bunch of bullshit and people will nod along, then you get funding and grad students to bully. You control the lives of undergrads and they bend to your will. Free donuts or pizza at colloquium talks. Frankly, being a mathematician is already the perfect crime.
Enjoyed this post in the last thread kek

>>11502161
>is there a maximum angular velocity
For a given size wheel, it can't turn faster than would make part of it exceed the speed of light.

>>11502361
Side fact: that also means the ratio of circumference to diameter isn't pi for rotating objects.

>>11502356
What is service? You still have to do annoying administrative tasks and serve on committees drafting documents and other bullshit.
>tfw sitting on budget commitee

God dammit I hate math pseuds. This image just makes it that much worse. Congrats.

>>11502179
Speak for yourself bro my parents are hella ignorant.

>>11502149
/sci/ anons I have a question. I have a friend who's doing an MMath (4 year) at Cambridge University and is about to graduate in a few months. He's one of the smartest people I know.
He's landed a job of 65K pounds as an analyst for a very famous American investment bank in London. Now I do know that 300k starting for math majors is a meme, but isn't 65k pounds too low, that too for a Cambridge grad? Or are the salary trends of USA and UK too different?

>>11502604
it's probably like 90K after bonus if he's an investment banking analyst
https://news.efinancialcareers.com/ca-en/277526/banking-salaries-and-bonuses

Yes UK is lower
Other work roles besides investment banking like in the IT side, risk, whatever, tend to be lower too

How would the sheer amount of work be if I try to do a Physics/MechE/EE Major with two minors in Math and Computer Science respectively?

>>11502356
They left out the part where you torture yourself for 20 years hoping for the slim chance to be rewarded with this.

>>11502192
this but unironically

Let [math]\Sigma_3[/math] be the symmetric group of 3 letters. Then [math]\Omega ((B\Sigma_3) ^\land_3) [/math], the loop space of the Bousfield-Kan 3-completion of the classifying space, should be homotopy equivalent to [math]S^3 \{3\}[/math]. Why is that? The only result stating anything similar I have managed to find is that if we have a finite 2-perfect group [math]G[/math] containing the dihedral group [math]D_{2^n}[/math] as a Sylow 2-subgroup, then [math] \Omega (BG^\land _2) \simeq S^3 \{2^{n+1} \}[/math].

>>11502813
Use the fibre square lemma.

>>11502813
Not [math]\Omega (B ^\land_2)[/math] but [math]\Omega (B ^\land_2) \langle 1 \rangle[/math].

>>11502817
I can't see it. I've tried to fit the 3-sphere into the picture for a week now.

>>11502632
Ok I guess I made a mistake. I stand corrected. Thanks

>>11502886
Not necessarily. I know [math]\pi_3 ((B\Sigma_3) ^\land_3) \cong \mathbb{Z}_3 \cong \pi_3 ((S^3) ^\land _3[/math], and that lower homotopy groups of [math](B\Sigma_3) ^\land_3[/math] are trivial. I also know that the cohomology rings of the loop spade and the fibre are isomorphic as algebras over [math]\mathbb{F}_3[/math]. How to make the pieces fit is what I can't see.

>>11502604
65k is almost twice the average salary.
In the US, 90k is about what you'd expect which is almost twice the average, as well.

>>11502149
>considered going tradcath
lol

Rate these books, which are worth reading? Am i missing important and interesting books? I will start a undergrad this year.

Lara Alcock - How to Study for a Mathematics Degree
Kevin Houston - How to Think Like a Mathematician
Richard Earl - Towards Higher Mathematics
R P Feyman, Lectures in Physics
T W Körner, The Pleasures of Counting
Clegg, Brian A Brief History of Infinity
Hofstadter, Douglas Gödel, Escher, Bach.

>>11503165
No need for thefirst three, they're pseud trash

Lectures in physics is a high level book

Fourth and fifith are more pseud trash

Sixth is philosophy

https://faculty.washington.edu/jathreya/
>I share in Federico Ardila-Mantilla's axioms:

>Axiom 1
>Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
>Axiom 2
>Everyone can have joyful, meaningful, and empowering mathematical experiences.
>Axiom 3
>Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
>Axiom 4
>Every student deserves to be treated with dignity and respect.

>>11503173
why are they pseud trash?

>>11503200
>>11503173
And What books would you recommend?

>>11502813
>>11502833
Okay, so I found a reference for this. Actually two. Please ignore.

>>11503221
What kind of book do you need?

>>11503254
Also, what is your background knowledge in maths/science?

>Get to a math problem
>paralyzed by fear
>No matter how easy the question is

Solutions?

>>11503263
Stop masturbating so much.

>>11503263
do more problems
solving math problems is the point of math

>>11503275
But what if you do pointless topology?

If I have a Poisson manifold with a Riemannian metric, the Poisson 2-vector gives me a canonical tangent plane at every point, and the tangent plane thus has a sectional curvature.
Does anyone have any papers deriving neat properties of the Poisson structure from this? I tried googling about Riemannian poisson manifolds, but it seems to be going in another direction.

>>11503257
>>11503254
Im this anon >>11503165
My background knowledge is european Highschool math Level. I have compiled books and resources for the first abstract Algebra and real analysis course.
I think im looking for stuff that broadens my Horizon when it comes to math, stuff that helps with "thinking" like a mathematician, interesting insights, history, stuff for more pleasure reading instead of rigorous text books, something that makes me more well rounded and helps with my Studies

https://www.youtube.com/watch?v=OZQlZ3kIgOI
>We have given and discovered a groundbreaking function which gives sequence or say progression of prime.

>>11503298
Read Neuromancer and go do drugs at raves. Oh wait, that is how you become a philosopher.

>>11503298
https://www.amazon.com/Mathematics-Its-History-Undergraduate-Texts/dp/144196052X/ref=sr_1_5?keywords=john+stillwell&qid=1585228967&sr=8-5
https://www.amazon.com/Elements-Mathematics-Euclid-John-Stillwell-ebook/dp/B018WO3570/ref=sr_1_6?keywords=john+stillwell&qid=1585228967&sr=8-6
https://usamo.files.wordpress.com/2017/08/napkin-2017-08-15.pdf

might be suitable for you

>>11503323
>John Stillwell
Who is that man and why should I care for his books?

>>11502149
Ok anons, now that I don't have to waste my time in my shitty pure maths Master's I want to learn numerical analysis. Any tips on how to do it besides reading textbooks? I'm already familiar with the topic and like it, it's just a matter of knowing what to do and not being a useless waste of space (the actual problem, really).

>>11502188
>stem qt cuddlebuddies are for autisms
Why did cuddling with my friend feel good in the moment but feels now like a massive fucking mistake? I'm scared anon.

>>11503323
Also, you cannot learn to think like a mathematician without solving LOTS of problems. I recommend Andreescu's "Putnam and Beyond", it starts at an elementary level, covers a wide variety of topics and has hints/solutions to all of the problems.

>>11503340
I will never understand how people follow that path, numerical analysis is by far the most boring subject in math imho

>>11503334
He's a very good expositor of mathematics. Why don't you find out for yourself?

btw, the wiki probably has some books that may be of interest to you: https://4chan-science.fandom.com/wiki/Mathematics

>>11502705
Isn't this kind of overkill counterproductive?

>>11502705
It would be trivial and left to you as an exercise.

>>11503323
>https://usamo.files.wordpress.com/2017/08/napkin-2017-08-15.pdf
What's that? At first I thought it was a history book on advanced topics such as rings, quantum theory etc which would be pretty nice, but it looks like it's a very small overview on those subjects, which would honestly be quite a waste of time to read.

Can I use the Hubbard-Douady to estimate distance to a M-Set using a different function than the [math]z_{n+1} = z_n^2 +c [\math] ?

I want to use [math]z_{n+1} = r*z_n*(1-z_n)[\math], but I can't manage to calculate the derivative correctly.

Image related.

>>11503198
Fake and gay except for 3.

>>11503263
Complete and absolutely fuck up your Master's.

Work with physicists fag, come out and play!
WORK WITH PHYSICISTS FAG, COME OUT AND PLAY!!!!

>>11503349
I like it. It has programming, practical applications, nice theory behind it, etc...

>>11503361
What is your definition of a "waste of time to read"? Of course it's not going to give you a deep understanding of all the topics, but you asked for something that will "broaden your horizons", which I assumed to mean will give you a taste of a lot of different topics that you may encounter in your further studies but will not be truly challenging reading or go into much depth.

Threadly reminder to work with biologists, they need you
https://en.wikipedia.org/wiki/Hardy%E2%80%93Weinberg_principle

>>11503386
>Applied math that aren't physics
Into the trash it goes

>>11503323
Thank you, ill look into them. Do you think the books in my first Post are Bad? I just copied them from Oxford/cambridge reading list for Future students and i thought theyd give decent reccomendations

>>11503397
Feynman lectures are good as a supplement to a standard education in physics. I have no idea about the other ones.

Imagine studying graduate level math instead of learning Japanese...

>>11503409
>Learning a language for 5+ years that's only spoken on a very small island completely isolated from the rest of the world and where the population completely despises the presence of foreigners and its society is so fucked up that young people don't even wanna have sex or relationships anymore.
Buy hey, at least you'll be able to watch your cartoons and read your comics in the original languages, I'm sure it'll be worth it considering the deep philosophical implications of those works can't be translated well into english.

>>11503420

I probably make more as a freelance translator than any of you unemployable math autists, and you obviously don't know anything about Japan or translation theory so maybe you should stop posting.

imagine studying japanese and not studying grad level math instead of learning french and reading EGA

>>11503432
You realize barely anyone will hire you for traslation without a degree, right? And if you go for a degree it's +4years, so 9 years until you are capable of working with it.

Math degree + master + PhD takes 10 years at most and I really doubt you earn more than a mathematician with a PhD.

>>11503409
why not both?

>>11503437
Je suis apprended le français, je suis un noveau, ces't un plus belle langue.

>>11503451
You realize how time consuming graduate level math is? Unless you're a genius I doubt you'll have the time to consistently study japanese, a very hard language.

>>11503455
No it's fucking not. The spelling is all retarded and gay, and it sounds fucking ugly. It's even worse than English. Si lo que quieres es un idioma bello, aprende castellano. Eta kriston Chad izan nahi baduzu, ikasi euskera.

God hate fucking hate autistic faggots
>inb4 autistic smug reply

Why do british phd programs usually take 3 years while us programs take 5?

>>11503473
Pero yo onions un estudiante avanzado de castellano, aunque no penso que seas tan bonito, el frances es mucho mejor, mon ami.

>>11503483
good, don't

>>11503443

I have a degree, what are you talking about? You can pass JLPT N1 in 4 years if you study hard and that allows you to earn 10million plus yen a year in Japan or really as much as you want if you move to the US and have specialist knowledge like law or medicine.

But anyway I am bored of translation and started to learn programming now.

>>11503485
Strange, brazilian programs takes 4 years

>>11503496
Oh boy, you just gave up your bait right? Posting a chinese notebook claiming it's japanese holy kek

>>11503500
No

Fuck off

Shut up

>>11503487
*pienso and *sea. Unless you were calling me ugly. In which case y-you too. Y el francés da asquete.

>>11503500

Idiot.

>>11503524
It's the same book

>>11503524
It's not The same book

>>11503595

Fuck you.

Here is the proof I bought it in a Japanese bookshop, 円 is the symbol for yen.

>>11503611
Did you know you can buy books written in a language that is not the same as the language of the country where the book is sold?

>>11503620

Ok here is the author of the book:

https://www.fit.ac.jp/~shibata/

Now you tell my why a Japanese researcher would write a book in Chinese?

>>11503640
Because the yellow folk are dumb.

>>11503657

Average IQ of 105 and significantly less crime than whitoid societies would beg to differ.

>>11503674
Your mom begs black men to dick her.

>>11503496
you can see, for example, the り on the cover, which is not a chinese symbol
softbank is a japanese corporation
it's a japanese book

>>11503679
There's no 'ri' on the cover anywhere, only chinese diagrams.
Softbank can be a japanese editor, but that doesn't mean all their books are in japanese

>>11503455
quoi?

>>11503720
Dire-je quelque chose erreur? Je suis un noveau en le français

>>11503715
look on the green rectangle
then look to the right
look at the blue square
there's your ri

>>11503720
Don't be a cunt and just correct her outright.

>>11503165
I disagree with >>11503173, it's not really pseud trash, more just basic advice that you'd already get if you took an intro to proof course, along with some stuff about time management and what not. Really, thinking like a mathematician requires experience. A decent intro to proofs book is Mathematical Proofs: A Transition to Advanced Mathematics. You'll get the same experience as the books you mentioned and more with it.

>>11503777
>Mathematical Proofs: A Transition to Advanced Mathematics.
Is that Chartrand's book? If it isn't, then Chartrand's book is better, it's the best intro to proofs

>>11503785
It is indeed Chartrand's book, yes

Extemely important, make sure to answer:
https://www.strawpoll.me/19623913
Also, they need to have actual names.

>>11502149
shia does wear some good outfits but thats mostly just cause hes got a farmer build and is an 8.5+

>>11503838
Please name 21-25 (co)homology theories to prove you're not bullshitting.

>>11503863
Singular, Simplicial, Cech, Alexander-Spanier, Group, Tate, Galois, Equivariant, Symplectic, Poisson, Floer, Morse, Poisson, Sheaf, de Rham, Cyclic, Hochschild, Borel-Moore, Étale, l-adic, motivic.

>>11503877
>Poisson twice
Swap with Lie Algebra.
Add in Dolbeaut and Elliptic in case you'll complain about one of them.

>>11503838
who cares about this soulless garbage tho

>>11503715
3色刷り you illiterate

>>11502149
this image is pathetic. its clearly written by an alcoholic redditor trying to justify his unhealthy habit. why would you use this image.

>>11503293
It sounds like you get an integrable tangent subbundle that you can polarize against, which is central in geometric quantization; it allows us to quantize a prequantum bundle. This is why a classification of Poisson structures is so sought after.
Perhaps this article https://aip.scitation.org/doi/abs/10.1063/1.529446 would be of interest to you.
>>11503409
中出しOKだし
>>11503838
Using Brown representability I can name as many as [math]|\pi_0 {\bf hSpec}|[/math] lol.

>>11503899
It's kind of funny how cohomology seems like a mysterious thing when you're an undergrad, but there are probably quite a few people here who can name more than me.)
>>11503915
>actual
>names
Thanks for the paper tho.

>>11503838
>singular
>simplicial
>cellular
>borel
>etale
>hochschild
>cyclic
>galois
>sheaf
>cech
>alexander-spanier
>functor
>group
Probably 11-15. Too lazy to count those.

>>11503920
>never got what the fuck cohomology was
>eventually just absorb it
>now i act like i know what cohomology is
if someone actually asked me what cohomology is supposed to be, philosophically, i doubt i could tell them

>>11503950
It's just the dual measure of n-holes.

>>11503960
but that's how i think of it and that's how i would explain it
i'm looking for the philosophical side of the question, why bother with the dual situation?

>>11503968
>why bother with the dual situation
Because it's easier to multiply.

Can somebody please help me?
I need to find the 55th permutation of a sequence, knowing that the 1st one is "aaabcc". What is bugging me are the repeating elements. If all of them were unique, I could solve this.

>just use brute force lmao
That's not the point, I know what the solution is, but I need an efficient way to get to it.

>>11503968
Think about the diagonal map of a space and forget the nasty technical details for a moment. Taking the hole approach, this gives you a coassociative coproduct, but if you dualise the whole thing you get an associative product. You will then end up having a nice graded ring and so on. Rings are much easier to deal with than corings, at least to me. That's one reason.

>>11503977
>coassociative coproduct
I'm just learning about this, care to explain what you mean by this?

>>11503973
Oh, that's very clear and concise. Thank you.
>>11503977
And that expands on it well. Thanks.

>>11503915
How long did you take to learn jap yukari-sama?

>>11503976
>55th permutation of a sequence
What the fuck do you mean 55th.
What ordering?

>>11503979
Okay. Let [math]\mu \colon R\otimes R \to R[/math] be the multiplication of a ring. Then the associativity can be expressed as [math]\mu \circ ( \mu \otimes 1_R) = \mu \circ ( 1_R \otimes \mu)[/math] (just plug stuff in if you doubt me. Now, let's dualise this. A coproduct of a coring would be a morphism [math]\Delta \colon C \to C\otimes C[/math], and coassociativity means [math](\Delta \otimes 1_C) \circ \Delta = (1_C \otimes \Delta) \circ \Delta[/math]. Basically just flip everything around. Then, you can try to formulate units for rings this way. This gives you counits for corings. You can probably guess that cocommutativity is applying the twist after the coproduct, where commutativity is twisting before taking the product. I'm actually writing this while taking a shit, so you get to fill in the details of the corings yourself, as it is time to leave my meditation chamber.

>>11503984
No problem.

>>11503990
lexical order i think
"cbacaa" is the solution

[math]e[/math] is just a meme. it's not a real number of any sort. don't get fooled guys.

>>11503997
>it's not a real number
True. It is a letter.

>>11503976
>>11503994
Ah, then it's just modulos.
Compute how many start with a. These are the first n permutations. If n<50, you know that your desired permutation starts with a. Otherwise, check how many n' start with b, and if n+n'<50, you know it starts with b, but otherwise with c.
And so on for the following digits.

>>11504001
I swapped both inequalities and wrote 50 instead of 55, but whatever,

Yukari if you're so smart can you answer a simple optimization/nonsmooth analysis question?

>>11503986
3 minutes.
>>11504038
I can try I guess?

>>11504071
I need to describe solution maps for optimization of functions [math]f(x,t)[/math], convex in [math]x[/math], under time-varying constraints [math]g(x,t) \le 0[/math], also convex in [math]x[/math] and with bounded derivative in [math]t[/math].
There is a theorem by Rockafellar that describes solution maps for static constraint case. The rate of change of the optimum is determined by the convexity modulus of the cost function.
When the constraint is dynamic, everything is way more tricky.
It seems there needs to be a part of the optimum dynamics that comes from the rate of change of the constraint.

>>11503165
All crap. Read https://web.evanchen.cc/napkin.html instead

>>11503198
I even disagree with 3. Some math is just useless

>>11503361
"very small overview"? It covers all of undergrad plus more. What do you feel it doesn't include?

>>11504084
>describe
Oof.
Did you try splitting up its behavior into when the maximization point is below [math]g(x, t)=0[/math] and when it's strictly above? If the former, it just follows the point along. If the latter, it moves along [math]g(x, t) = 0[/math] in a way that might be fucked up because of the nonsmoothness.

>>11504084
If I understood you correctly you wish to optimize, for each [math]t[/math], [math]f_t = f(\cdot, t)[/math] on the zero locus [math]\Sigma_t = g^{-1}_t(0) \subset E[/math], right? Assuming time-independence, Rockefeller allows you to use variational methods to optimize [math]f[/math] on a dense subset, which necessarily intersects the zero locus transversally. This then allows you to study optimizers as the joint kernel of a bilinear form [math]q_f = \langle \partial f(x) \cdot,\cdot\rangle[/math] on the tangent space [math]T_x \Sigma_0[/math]. The idea is that optimizers satisfy [math]v\in \bigcap_u \operatorname{ker}q_f(u,\cdot)[/math].
Now for the time-dependent case, my first thought is this: we wish to find the regularity conditions on [math]f,g[/math] necessary for the existence of a bounded linear operator [math]\alpha_t[/math] (the time-evolution operator) on the Banach algebra [math]\mathcal{A}[/math] of convex functions such that [math]\alpha_t(g_0(x)) = g(x,t)[/math], then you may apply this operator to [math]\partial f[/math] to find the bilinear form [math]q_{f,t} = \langle \alpha_t(\partial f(x))\cdot,\cdot\rangle[/math] on [math]T_x\Sigma_t[/math], since [math]\Sigma_t = g^{-1}_t(0) = (\alpha_t g_0)^{-1}(0)[/math]. This then allows you to apply Rockefeller at each [math]t[/math] and your solutions will evolve along with [math]\alpha_t[/math]. In particular if we have a C^*-structure on [math]\mathcal{A}[/math] then it'd be even better if we can find unitaries [math]U_t[/math] such that [math]\alpha_t(g)= U_t^\dagger g U_t[/math], since in this case we can just evolve optimizers [math]v_0 \mapsto v_t = (dU_t) v_0[/math] like a propagator.
This is just a formal idea ofc, it's an interesting problem.

>>11503409
>learning language to consume media
>>11503432
You don't need to know Japanese to translate. Use google and context. Retard.
>>11503500
I like you. I can't believe this guy is serious.
>>11503437
You don't need to learn French to read EGA. Just the basics of math terminology and google is enough. It's translated now anyways so it doesn't matter.

>>11504123
Yeah, but it doesn't cover any subject with the depth it needs, it just gives you an overview of important topics inside a certain subject

>>11504139

I'd like to see you translate a complex legal document with "google and context", fucking idiot.

>>11504134
ayyyy gurl. I have a question. Do you know of any good lecture notes/texts written on tqft from a physical point of view? I can put up with some mathematics, but a physical exposition is definitely preferable. I generally prefer to think in terms of local coordinates, but do know the 'coordinate free' language. Any recommendations?

>>11504152
Look at Dijkgraaf-Witten's original 1990 paper.

>>11504149
Sorry I'm not interested in complex legal documents.

>>11503747 Oui, il y avait une erreur dans la première phrase. <<C'est>> s'écrit comme ça. Par ailleurs, il faut avoir au moins un verbe conjugué dans chaque phrase graphique (Phrase qui commence avec une majuscule et finit avec un période). Alors >Dire-je quelque chose erreur? doit avoir un verbe conjugué, mais <<dire>> est à l'infinitif. Il faut donc le changer à <<dis>> ou <<dit>>. Also that last part of the sentence weirds me out. I don't quite know exactly why it doesn't work, but instead of that I would write << Dis-je quelque chose de mal? >>

Je vous suggère de consulter ces ressources: https://la-conjugaison.nouvelobs.com/du/verbe/dire.php (conjugaison des verbes et règles de grammaire), https://bonpatron.com/en/ (vérificateur de grammaire) et https://www.linguee.com/english-french (C'est un traducteur qui peut traduire des mots/phrases complexes et qui donne des contextes différents)

>>11504168
Thank you very much, I love french so much, it's a really beautiful language, my objective is to reach a level where I can read Récoltes et Semailles by Grothendieck and the classic A La Recherche du Temps Perdu by Proust.

>>11504159
I was hoping for something a touch more pedagogical, with perhaps some calculations relevant (quasi-relevant even) to experimental consideration.

>>11504134
Calm down a bit with your abstract nonsense. This is a real problem that needs a real working solution.

You can't express the solutions maps anyways.
What you can do though, is to express their rate of change bound.
In the static case, you have something like [math] \left\lVert \mathcal D x^*(t) \right\rVert \le \frac 1 m \left\lVert \frac{\partial}{\partial t} \nabla f \right\rVert [/math]

>>11504202
Oops, guess I forgot non-linear Schroedinger problems are too abstract. Sorry.
>their rate of change bound
Yes, then you (formally) take [math]\partial f = \sup \partial x^*[/math] of the subdifferentials in the supremum of the [math]E^*[/math] norm. Use this to study the variations of [math]f[/math] like you would in finite-dimensional calculus on manifolds.

>>11504221
You're such a cunt, geez, no wonder no one likes you here

>>11504168
« and ». If you use GNU/Linux you may type those with the compose key

>>11504238
he's literally just another NPD tranny. 4chins is full of them, best you learn to ignore them if you don't like them.

>>11504240
Yeah, I know, I'm just to lazy to search it out all the time or memorize the numpad code

>>11504198
Search around arxiv for review articles on studying the QHE as a statistical Abliean Chern-Simons theory. E.g. https://arxiv.org/abs/1712.03595..
>>11504238
>randomly calls dismisses my concrete idea "abstract nonsense"
You reap what you sow, little boy.

>>11504251
Thought so, which is why I offered a simpler solution. ;)

Should I strenghten my calculus basis by reading Apostol's I and II before tackling Real and Complex Analysis? Or can I just go straight to Analysis? I studied Calculus through Stewart and still remember most things.

>>11502424
Thanks Miles.

>>11504499
you should stop posting

>>11503367
Can anyone answer my question ? :(

>>11504499
Can anyone that's not a cunt answer my question ? :(

>>11504609
Depends on your analysis books. If they're on the easier/introductory side, you're good to go. Otherwise it might not be a bad idea.

>>11504609
No. This is /sci/. It is on you.

>>11503165
>Alcock
heh

H-hey brahs, w-we're all gonna make it, r-right? Then why do I keep failing? Why do I feel like dying?

I think I might not make it.

>>11503397
oh oops, I forgot to link you to the most recent version of the napkin. this >>11504105 anon linked it, read that instead

>>11503367
>>11504523
After about 30 minutes of tracking this shit down I think you can provided you define the appropriate maps
https://books.google.com/books?id=ZOfUsvemJDMC&pg=PA506&lpg=PA506&dq=douady+rabbit+external+ray&source=bl&ots=7kD1T8kwni&sig=ACfU3U0Uy0-YNKUtDK-HwP9Ln1mEl5Cf4Q&hl=en&ppis=_e&sa=X&ved=2ahUKEwjZ9JndobnoAhUPj54KHTj4DTIQ6AEwEHoECAkQAQ#v=onepage&q=douady%20rabbit%20external%20ray&f=false

>>11504680
>906 pages
Is someone supposed to read that befote starting college? That's impossible, it would take at the very least an entire year to read everything and do the exercises.

>>11504609
if you are reasonably comfortable with delta epsilon proofs then just go straight into analysis. A lot of analysis books will cover the stuff you may have forgotten from calculus but in more depth, and they are usually self-contained.

>>11504701
Not all before college

i know this might be retarded, but how did they graph accurately/use the coordinates system before computers? did they ever solve things graphically?

>>11502149

A question on how to use mathematical language when speaking to the general public.

>Let's say that we are talking about infections of covid-19.
>Let's say there are 300 documented infections
>Person A, incorrectly states that there are 200 documented infections

Is person A incorrect by 1/3 or incorrect by 1/2?

Obviously, a 50% increase of 200 is 300, but 200/300 is 2/3.

So what is the answer? How much are they "off" by?

>>11504739
/r/askmath

>>11502149
>read on reddit
crossposters need to be purged

>>11503198
What is this fucking "empowerment" bullshit that appear here and there ? I don't even understand this fuckery. Is it because I am a CIS hetero-normed binary white patriarch ?

>>11504071
Yukari is best 2hu and deserves to be put in a wedding dress

>>11504499
Yes.

Small brain engineer here, I just found a bunch of old coins, which had me thinking:
Is there a way to make a set of coins bigger than one that have a mass that lets you know the numbee of all the coins you have by weighing them all at once?
I imagine it would have something to do with primes but that's as far as I got.

>>11504238
I like him. He dabs on you insufferable pedantic midwits hard and isn't afraid of anything.

Noob here. Let's say I have a spacecraft that can travel at the speed of light and I decide to go to Proxima Centauri which is about 4.3 LY away if I'm not mistaken. That trip should last about 4.3 years for someone who's already at Proxima Centauri and is waiting for me to arrive. But how much time would that trip last for me?

hey /sci im searching for an article that proves mathematicly how to move faster than the speed of light using gravitons and antigravitons, can't find it on google.

>>11505039
Sure, for some weights probably. Probs not all though

what area of math is concerned with probability in 2 dimensions. for example, I want to calculate the average position that an object will land onto an asymmetrical shape (such as a scalene triangle)

>>11505086
you would experience 0 change in the space ship, lightspeed experiences past and present at once, in a sense, youre stationary in time and the world moves around you, in general, and when you get to relativistic speeds, a discrepancy forms between you and the outside (which you experience as going fast relative to you)

>>11505223
calculus, statistics

>>11504680
>>11504701
Napkin is mostly a meme, it has some stuff that could spark your curiosity for some areas in maths but it's really biased toward the author's view of the topic, he's some former olympiad champion who now does research in combinatorics

>>11502705
Just do physics and math, drop CS and EE you can learn whatever you want about those fields in your free time. not physics, not math, learn it in your free time. if you can do the former the latter should be trivial.

>>11505379
Just skip the stuff you don't care about? I only read the sections on algebraic topology, category theory, and algebraic geometry. They were so useful I recommend it to anyone. Maybe the easy stuff is poorly done but I doubt it.

>Book recommendation

>>11504912

That's literally what this thread is.

>>11505313
could you elaborate perhaps? I understand how both would relate, but, for example, how would one go about calculating the "average position" in xy coordinates on a scalene triangle?

>>11504221
Useless. But thanks for the effort

"hey kid you got any uppers?"

>>11504678
Some of us were not meant for this world. It's only natural.

>>11503382
>nice theory
*800 pages of convergence proofs*

>>11505859
>*800 pages of convergence proofs*
Thanks, I really needed to get that coom out of my system.
>tfw post-nut realisation that no one's answered your question

>>11505796
Damn, I would love to party with Paul.

I had a random idea about emulating Turing machines with Transformations on a set.
Imagine I very broadly have a set of transformations [math] (T_i)_{i \in I}[/math] where [math] T_i: P(\mathbb{R}^d) \rightarrow P(\mathbb{R}^d)[/math].
For example take the Steiner symmetrizations (symmetric decreasing rearrangements) in all directions.
Then I could use this as a sort of computing machine... A set is an input and then each set corrseponds to a specific symmtrizatiom which is applied next.
Basically I have a function
[math] F: P(\mathbb{R}) \rightarrow I[/math] which assigns each set a subsequent transformation.
The question is how I can show that such a system is Turing complete. Or in general, does anyone find this interesting too?
You would sort of have... a super continuous input and output in the form of a set.

wow this thread is really garbage

What is a good book on probability theory? I already know about basic measure theory and I already had a course about probability so I would like something not too slow.

>>11506105
y-you too

What's the difference between topological algebra and algebraic topology?

>>11506211
the former is a certain kind of mathematical object, the latter is a field of study

How to become an expert in hyperbolic geometry?

>>11506243
Wear googles with fisheye lens

>>11502813
anime and maths.

cringe.

>>11506243
Depends on what you want to study exactly. I'm not an expert by any means, but maybe I can help if you tell me what's your goal. Hyperbolic geometry is very wide and you can do a lot of things with it.

Cute animals and maths. I like these curfew life.

>>11505105
Which weights would that be? I haven't been able to find any.

>>11506768
Well, firstly it would depend on which country's coins you're using. The important thing here though is that the collective weight is an addition of the individual weights, not a multiplication. So while your intuition about primes being necessary is correct, since no prime-like system exists under addition, this wouldn't work in general. If you wanted to find out which weights would work, then again I'd point you to the first sentence.

>>11506768
1 2 4 8 16 ...

>>11506849
I am talking about a newly created set of coins, so I'm not seeing how the country matters here. To rephrase my problem: For which masses of the items C1 to Cn of a set of n items is it possible to know how many items of each type you have by knowing only the sum of the masses of all items you have?
Upon some further thinking it seems impossible using rational weighs, so any real world application is out the window anyway if that's true.
>>11506884
How so? Two coins weighing 1 are not differentiable from one coin weighing 2.

>>11505039
You can do it, but not IRL, since you need irrational coin weights to make it work. Specifically you'd need weights linearly independent over Q (hence Z), since any nontrivial solution to a1w1+a2w2+...anwn = 0 would tell you that there's some combination of coins that's equivalent to some different combination of coins.

>>11506906
one coin weighs 1
second coin weighs 2
third coin weighs 4
etc

>>11507422
you are extremely retarded
please stop posting until you get that sorted out

>>11506571
I appreciate this post and the anon who made it.

>>11503263
raise your self esteem

[math]\text{Reductio ad absurdum}[/math] is now banned. How much of mathematics survives?

>>11508173
Well, my supervisor said I seemed like I was losing my mind working non-stop in captivity and told me to go outside. Then I went to buy a bunny. With this bunny, I will work even harder.

>>11508451
Just be constructive, bro :^)

hello gays. i'm not trying to troll you, but I'm just curious to know... what are you planning to do after getting the math degree? which jobs are you going to qualify to? there isn't place in academia for all of you, i guess

>>11508603
this is a forbidden question

>>11508451

AC is banned - bye bye basis, bye bye functional analysis and more

>>11508603

How to estimate [math]3!^{3!^{3!^{3!^{3!^3!}}}}[/math] ?

>>11508603
Research or warehouse. Those are my plans.

>>11508651
Just say it's big.

>>11508658
I know. I've got a monograph on big numbers (tetrations, Knuth's up-arrow notation, Steinhaus-Moser notation, Ackermann, TREE() etc.) This number is listed as "very big" with no estimation given.

>>11508710
Okay, so you have an estimation. Note the following:
>number
It is finite, and so you have the infinity as a strict upper bound.
>very big
It is therefore bigger than big. An estimate would then be big < your number < infinity.

>>11508720
>completely useless and completely correct answer
spoken like a true mathematician

How can you check if a mathematician does "good math"™?
I mean, in another discipline I'd take look at their Google scholar, see if the person has a high h-index and highly cited papers. In math, though, many academics seem to not have google scholar...

>>11508731
What for?

>>11508720
>infinity as a strict upper bound
That's a pretty shitty upper bound anon, did you try [math]n+1[/math]?

>>11508751
for many reasons. For example to see if he might be a good advisor

>>11508835
I only proved the existence of an upper bound.

I read through Tao's measure theory book and the only thing I got out of it was "your function needs to be supported on a moderately well behaved set to integrate it". Why is everyone always telling me I needed this to do statistics? It's nice to know there was a rigorous, formal theory underpinning ideas like probability distributions but I wasn't really worried about that in the first place.

>>11508603
There's a place in academia for me, just not for all these other chumps.

>>11508965
Taos book is shit. To understand what a randol variable is you ned to know what a measurable function is.

Is there a function which composed with itself gives sine? ([math]f(f(x))=sin(x)[/math])

>>11509444
Probably, yeah.
[math]\sin x[/math] solves the ODE [math]D^2 g = -g[/math] with conditions [math]f(0)=0[/math] and [math]f( \pi /2) = 1[/math], so [math]f \circ f =g[/math] also solves some ODE with conditions, and then you throw Picard at it.

>>11509466
Huge mess of a post but whatever, figure it out on your own.

>>11509466
wow, just so dumb

>>11509444
>>11509466
Never mind, found it.
https://math.stackexchange.com/questions/3143402/how-to-find-functional-square-root-of-sinx
>>11509506
K.

>>11508731
>>11508874
The best way to find potential supervisors is to tell your undergrad profs your goals and ask for recommendations. They know their colleagues and their work personally and are much more qualified than you to judge what'd be a good place for you.

But if you really can't do this, for example if nobody at your campus works anywhere near what you want to do, then there's a few things you could think about:
>citations are not a good metric in math. even top-tier math papers are a slow burn to build up many references, and many quality papers don't get a ton of them ever.
>where do they publish? It's not too hard to get a rough picture of which journals are top-quality, mid-quality, no-name, etc. (and this is a question you can ask literally any prof on your campus and they can answer by heart), and somebody with e.g. multiple annals papers is probably pretty good
>are they _still_ publishing in good journals recently? there's a demographic of older mathematicians who did brilliant work 25 years ago, got their tenure, and then piddled around ever since. if he hasn't done anything noteworthy in a decade he probably doesn't have many great ideas left especially kicking around waiting for a thesis.
>where did they do their PhD/with whom? This might seem like an elitist metric, but it's too accurate to simply ignore. Not very many really good researchers come from middling schools and literally who advisors, sadly.
>are they tenured? tenure's a pretty good sign they're not utter donkey dicks, and you're taking a bigger gamble on an associate prof (or god forbid an assistant). It's generally not a good idea unless there's a really strong reason to specifically choose them

>>11509466
i don't think it's that simple, because when you differentiate [math]f \circ f[/math] you get expressions like [math]f' \circ f[/math], and I don't remember much from ODEs but I don't think existence theorems cover that stuff

>>11509577
thank you!

>>11509546
Kek, that user856 answer is great

>>11508637
>bye bye basis, bye bye functional analysis and more

If you ban blind people from dart, it's not "bye bye dart."
Everything that's good about those subjects doesn't need to pick a basis for those vector spaces for which one can provably not write down a basis.

>>11509776
you are a fucking moron

Hey, I took a break from math for a while now, and I'm thinking of starting up a thread as a "reading club" for a particular book to get back into it while learning with some other anons. In fact, I did this around November of 2018 for Atiyah/Macdonald's comm alg and it wasn't very successful, but a lot of people said they would have participated if it weren't for their midterms. Now that there's a bit more of free time so I see an opportunity. Let me know if you're interested. I was planning on doing one of the following books:

> Morandi's Field and Galois theory
> Bosch's Commutative algebra and algebraic geometry (first half, maybe second)
> Shafarevich Basic algebraic geometry 1

Let me know if you have other interesting suggestions, preferably algebraic and not too advanced (so as to keep the thread somewhat accessible)

>>11510014
I am interested, but I know from experience that people (including the initiator) have always jumped off after a month or so. The quarantine might be a reason why you have an advantage, but people will find excuses nonetheless. And be aware that they are, indeed, excuses, it's not because they suddenly find they don't have the time.

Anyway, from your list I'd be more interested in the first, but I have no strong feelings.

Where or how would you want to perform it?

>>11510068
I'd make a thread that lasts as long as it does, then renew from then on. It's hard to say how since everyone reads at their own pace but the idea would be for anons to upload their solutions to exercises, ask questions about theorems/proofs they dont understand and others might help explain, and progress slowly through the book. I'm open to ideas however

>>11508267
>Just be confident bro!
T-thanks Chad, I-I'll try.

Suppose we have a polynomial [math]f(x)=x^2+ax+b[/math], with roots [math]\alpha,\beta[/math]. I want to find the polynomial with roots [math]\alpha^2,\beta^2[/math]. I can do this in one of two ways.

First, I know that [math]f(x)=x^2+ax+b=(x-\alpha)(x-\beta)=x^2-(\alpha+\beta)x+\alpha\beta[/math], so that [math]-a = \alpha+\beta, b=\alpha\beta[/math]. Hence [math]\alpha^2+\beta^2= (\alpha+\beta)^2-2\alpha\beta=a^2-2b[/math].

Hence the polynomial that we're looking for, [math]g(x)=(x-\alpha^2)(x-\beta^2)=x^2-(\alpha^2+\beta^2)x+\alpha^2\beta^2[/math], can be written [math]g(x)=x^2+(2b-a^2)x+b^2[/math].

However, we can try something else. We can look at the substitution [math]x\mapsto \sqrt y[/math]. We then get [math] y+a\sqrt y + b=0[/math] as our polynomial. Rewritting and squaring, we get [math](y+b)^2=a^2 y\implies y^2 +(2b-a^2)y+b^2=0[/math].

So we see that the latter substitution has cleverly given us the desired polynomial.

Now I want to find the polynomial with roots [math]\alpha^3,\beta^3[/math]. I can attempt and easily get the solution by doing the first method. However, is there a way to do it with a substitution like in the second method? From what I've tried, there is no easy way to simplify the equation one gets with cube roots if we do the obvious attempt at a substitution. Is there a more systematic method of doing this?

>>11502161
Objects can't be rigid in special relativity, so if a wheel were spinning at relativistic speeds then it wouldn't be meaningful to quote a single angular velocity.

>But I could do it! With my knowledge of mathematics, I could commit enough perfect crimes to get that money! And I will!
Why aren't more mathematicians out there committing perfect crimes? Has anyone tried this? I'm gonna try this.

>>11510387
This wasn't funny the first time anon.

>>11510250
you have [math]x^{2/3} + ax^{1/3} + b = 0[/math] and you want to get rid of the 1/3's.
A quick answer is: let [math]\omega[/math] be the third root of unity, i.e. [math]\omega := \frac{-1 + i\sqrt{3}}{2}[/math], then make use of the following identity:
[math](a+b+c)(a+b\omega+c\omega^2)(a+b\omega^2+c\omega^4) = a^3+b^3+c^3-3abc[/math]
putting [math]x^{2/3}, ax^{1/3}, b[/math] as a, b, c into this gives you [math]0 = x^2+ a^3x-3abx + b^3[/math].
If you know a bit of Galois theory, you can view this trick as a standard operation: there is an extension [math]\mathbb{Q}(x^{1/3}) / \mathbb{Q}(x)[/math], you have an element [math]x^{2/3} + ax^{1/3} + b[/math] of the larger field, then you take its norm.

>>11504238
I like him too. He is the living proof that someone with an EE degree can know a lot about math & physics.

Prove what you think is a new theorem. Not an Earth-shattering one, just prove something. The date at which the theorem was actually produced (you probably aren't up to date) tells you how far along you are.

>>11510422
You first, loser.

for a limit in analysis, if its going from n to infinity can i just freely switch that out to be the equivalent to limit as 1/n approaches 0? It seems trivial but would I need to quote a lemma if I put that down?

>>11510422
>prove some technical lemma
>random guy on overflow goes "this was actually proven in Bourbaki Vol. 53 Sec. 24 Lem. 33.3452"
>mfw

>>11510422
436343733263745843532213564343 * 34347552343246574632355457685325 + 17^3 = 14987339217924131880581509431668276350703333802430930734371388

I manually verified it and I'm sure nobody wrote it down before me.

>>11510404
Why not just set [math]z = x^\frac{1}{3}[/math], substitute, and solve [math]z^2 + a z + b = 0[/math] and finally resubstitute?

>>11510520
>tfw will never be as Chad as that kid or this poster

Hey Faggots,
My name is Superalgebra, and I hate every single one of you. All of you are fat, retarded, no-lifes who spend every second of their day looking at stupid ass pictures. You are everything bad in the world. Honestly, have any of you ever helped explain theoretical guage fields in physics that exhibit supersymmetry? I mean, I guess it’s fun making fun of people because of your own insecurities, but you all take to a whole new level. This is even worse than Becchi, Rouet, Stora, Tyutin quantization of guage symmetry being different in grading than the standard correspondance Lie Superalgebra in theoretical physics to bosons being even and fermions being odd.
Don’t be a stranger. Just hit me with your best quark. I’m pretty much the reason for Vertex Operated Algebras show a need for the extension of General Relativity due to the emergence of graviscalar particles because of the metric tensor. I wasn't captain of the football team (I was too busy solving M-theory for that), and never starter on my basketball team (who needs basketball when I can solve Lagrangian mechanics?). What math do you play, other than “2+2=KFC”? I also get straight A’s, and have a banging hot Penrose–Hawking singularity (It just blew me; Shit was SO cash). You are all faggots who should just kill yourselves. Thanks for listening.
Pic Related: It’s me and my variations.

>>11510624
This is a SCIENCE board. Jokes are not SCIENCE. This is the cancer that is killing /sci/

>>11510648
What joke? Jokes are supposed to be funny

How many irreducible reps are there of the complex Lie group/Lie algebra E6?

I can't even seem to find a resource to learn the theory.

Is it 51840 since that's the dimension of its Weyl group?

>>11510533
yes you can do this of course, but I think the anon who asked originally wanted to avoid computing roots explicitly

https://www.youtube.com/watch?v=lJhmJJ_q6Go

>>11510661
I can't find the answer either.

For me, it's the Grassmanian.

What's the difference between Theorem, Lemma and Corolary? Are there other variations that I'm not aware of?

>>11502149
I'm losing my fucking mind here so I could use some help. I'm trying to program an object that reflects off of other objects but can not remember how to fucking do trig at all. The object has its speed in the x direction and speed in the y direction stored. My two main questions are how do I get a vector from that and what the fuck does d and n mean in r=d−2(d⋅n)n.

>>11510923
Just use the Clifford algebra LMAO

>>11510926
That looks even more like gibberish.

>>11510926
Please just answer my questions I've been trying to figure this out for hours and cant find anything on this in plain english.

>>11510941
LMAO just compute the reflection isometry associated to the surface the object is bouncing off and apply it to the velocity vector.

I'm reading into the axiom of choice and honestly it all seems pretty good to me

>>11511172
>contradiction? You mean exhaustion on the base possibilities of [math]P[/math] being true or not
Also, induction proofs are usually long.

>>11502149
0.999 = 1

Did you need third removed for A implies B if and only if not B implies not A?

>>11511172
>>11511229
transfinite induction is gigachad tier

Does anyone else notice that we have to be incredibly business-savvy so as to have the financial resources to convince the educational system that we have the intellectual resources to become business-savvy?

>>11502154
First for this doomer is worse off

1. Alcoholic
2. Vaping is worse than smoking (especially in the coronavirus era).
3. Too stupid to see the vanity or his actions

I'm confused by profinite integers. I get how normal integers appear, but what about numbers that are in certain Zp but not others?
For example, what does sqrt(2) look like as a profinite integer? If we index by p, then the fourth entry will be how sqrt(2) appears in Z7 which is easy (3+7+2*7^2+6*7^3+...) but what about the first entry? (sqrt(2) not in Z2, ramified) or third entry? (sqrt(2) not in Z5).
Any help appreciated.

>>11510904
A lemma is a statement that helps you prove a theorem, a corollary is something that follows immediately from a theorem or a lemma.

>>11511254
(A => B) => ((not B) => (not A))
is constructively true. In fact it's a special case of
(A => B) => ((B => C) => (A => C)

The Brouwer–Heyting–Kolmogorov style functional proof p of this is very easy:
[math] p(f) := g \mapsto ( a \mapsto g(f(a)) ) [/math]
where f:A->B, g:B->C, a:A.

In words
>given a reason f to believe that A implies, B, then given a reason g that B implies C, then the following is the case: given a reason that A holds, you can conclude that B holds (via f) and, in turn, that C holds (via g).

Replace =>C with =>False to get the claim about negation.

The other direction can't constructively be true. No matter how many reasons to believe about some negations and implications between negations being true, you can't ever find a reason to believe =>B (unless you take double negation as an axiom)

>>11511254
(A => B) => ((not B) => (not A))
is constructively true. In fact it's a special case of
(A => B) => ((B => C) => (A => C))

The Brouwer–Heyting–Kolmogorov style functional proof p of this is very easy:
p(f):=g(ag(f(a)))
where f:A->B, g:B->C, a:A.

In words
>given a reason f to believe that A implies B, then given a reason g that B implies C, then the following is the case: given a reason that A holds, you can conclude that B holds (via f) and, in turn, that C holds (via g).

Replace =>C with =>False to get the claim about negation.

The other direction can't constructively be true. No matter how many reasons to believe about some negations and implications between negations being true, you can't ever find a reason to believe =>B (unless you take double negation as an axiom)

>>11511254
(A => B) => ((not B) => (not A))
is constructively true. In fact it's a special case of
(A => B) => ((B => C) => (A => C))

The Brouwer–Heyting–Kolmogorov style functional proof p of this is very easy:

p(f) := g \mapsto ( a \mapsto g(f(a)) )

where f:A->B, g:B->C, a:A.

In words
>given a reason f to believe that A implies B, then given a reason g that B implies C, then the following is the case: given a reason that A holds, you can conclude that B holds (via f) and, in turn, that C holds (via g).

Replace =>C with =>False to get the claim about negation.

The other direction can't constructively be true. No matter how many reasons to believe about some negations and implications between negations being true, you can't ever find a reason to believe =>B (unless you take double negation as an axiom)

>>11511789
why do you think there should be something like sqrt(2) among the profinite integers? i think there's no such element, precisely for the reason you stated

>>11510904
All are theorems.
The words Lemma and Corollary are used for particular theorems in the context of a mathematical text. They just help organizing the text. Think of them as foreplay and the cigarette after, with fucking being the main event you're all about.

>>11511864
The galois group G of the maximal non-ramified extension K of Qp is canonically isomophic to the profinite integers. If we look at Q7 then K contains sqrt(2) and there should be some element in profinite integers corresponding to this?

>>11511900
by Qp you mean p-adic numbers?
first of all, Q7 contains sqrt(2) already
second, how does "a field extension contains sqrt(2)" imply "something isomorphic to galois group contains sqrt(2)"

>>11511952
You're right. Thank you. sqrt(5) in K (but not Qp) means that 2 is in G which is obvious?

How do you define a polyhedron?

>>11502149
I will never be good at maths. I will know brief parts of many areas, I will be better than the average person, but I will never be truly good at maths.

ahh so satisfying to be able to use latex now after taking the 5 minutes it took to learn it. was retarded to not do it earlier

[eqn]\left(\int_0^\infty e^{{-\alpha x}^2}\mathrm{d}x=\frac{1}{2}\sqrt{\int_{-\infty}^\infty \left(e^{{\alpha x}^2}\mathrm{d}x\right)}\int_{-\infty}^\infty e^{{\alpha y}^2}\mathrm{d}y=\frac{1}{2}\sqrt{\frac{\pi}{\alpha}}\right)[/eqn]

[eqn]\sum_{k=0}^\infty a_0q^k=\lim_{n\rightarrow\infty}\sum_{k=0}^n a_0q^k=\lim_{n\rightarrow\infty}a_0\frac{1-q^{n+1}}{1-q}=\frac{a_0}{1-q}[/eqn]

>>11511994
:something something utter lack of assumptions of convergence:

>>11511828
Thanks, lad.

>>11512002
>"convergence assumptions"? never heard of them.

Apparently I have some free time right now.
Give me something to learn and point me to a comfy resource for learning it.

>>11512170
Erdmann and Wildons Intro to Lie algebras is the most comfy math book I've ever read

>>11511963
We don't. Plato didn't define polyhedron and we're following suit.

What's a Calabi-Yau manifold?

>>11512286

>>11512286
>Calabi-Yau
(After reading Wikipedia article) I have no damnest clue.

>>11510904
There's also proposition, which is a lesser theorem. But be careful, since lemmas can become theorems in retrospect.

>>11512288
>>11512291
It used to be shitposted like crazy in here

>>11512184

>>11512344
imagine actually doing any exercise that begins with the word "check"

>>11512344
>her
The men are exempt from this trivial shit, naturally.

>>11512407
You don't have to skip them. You can do them in your head in less than 2 minutes.

>>11512414
Naïve Lie theory.

>>11512420
>prove the Jacobi identity in your head
Nigga are you serious.

>>11503198
https://www.ams.org/publications/journals/notices/201610/rnoti-p1164.pdf
>Todos Cuentan: Cultivating Diversity in Combinatorics
What does one call this disease of intellect?

>>11512420
>You can do them in your head in less than 2 minutes.
The fact that a jacobi identity works always amounts to nothing more than just writing out a gigantic pile of bullshit and then noticing it all cancels
you're not keeping track of a 12-term expression in your head

>>11512423
>>11512430
In the context of this exercise it is merely the composition of linear maps.

>>11512442
You're not very bright, are you

>>11512445
Please do elaborate.

>>11512442
>linear maps
Jacobi works for any associative ring with [math][a, b]=ab-ba[/math], lad.

>>11512456
It seems you can't read, so there is literally no point in attempting to discuss anything with you.

>>11512447
Which particular Jacobi identity you are checking (barring the abelian one, before some smarmy autist points it out) makes absolutely no difference to the fact that proving they hold fundamentally involves expanding some huge ugly mess of an expression. The proof for a commutator bracket is EXACTLY just "write out a dozen expressions and cancel them all".

>>11512425
Leftism.

>>11512467
The absolute illiteracy in this thread.

>>11512467
>huge ugly mess of an expression
It's actually not that bad, about 4 lines.
Substantially better than polarization.
>an entire page and a half of calculations

>>11512425
I'm 99% sure this dude wrote his own Wikipedia article considering it's all in broken-ass English full of typos and how fellatory it is compared to a normal academic wikipedia entry.

>>11512480
He looks like the type of guy who would drop a soap in prison showers and tell you to pick it up.

>>11512482
*orients your matroid*

>>11512482
does he really anon?

>>11512480
Why does he even have a Wiki article? Dios mío el cringe.

>>11512480
>I'm 99% sure this dude wrote his own Wikipedia article considering it's all in broken-ass English full of typos and how fellatory it is compared to a normal academic wikipedia entry.
Nah, after checking one of his papers it's clear he has a good grasp of English. Also, after looking over his cv, if he was going to write his own wiki, he would've added a lot more shit to it. As for the tone, to that I'd point out that there are far worse examples out there, and most likely what happened is someone decided just to haphazardly copy tidbits from articles without really proofreading them.

>>11512538
>t. Federico

>>11512538
Looking through the edit history, it looks like it's actually not him. Most of the page was written by a guy named Cjardon-UIC, and if you click on him it turns out he's a student editor from a mathematical writing class at UIC. Apparently UIC is handing out credits for writing shitty wikipedia articles about mathematicians now.

>>11512480
>>11512538
Federico Ardila here. Thanks for warning me about these issues with the wikipedia page. I tried to fix some of them. Anything I missed?

>>11512620
There's this photo of a really unsettling guy with a creepy smile. You should change that.

>>11512618
The absolute state of American universities.

>>11512629
Thanks for the feedback.
I would swap it for this: http://math.sfsu.edu/federico/ image , but I have no idea how to mess with image copyright in wikipedia.

why don't i understand geometry

i literally have no insight into any of these things

my only hope is reasoning via contrapositive and reverse engineering solutions over and over. i.e. this would be true if this was true, which would be true if this was true, and so on until i find something in my notes

>>11512781
what kind of geometry do you mean

>>11512851
just like basic euclidean geometry, but more specifically synthetic geometry. how do you reason with definitions that encompass infinite sets of objects without computations? it just seems so bizarre

>>11510404
Thanks a lot. I see that part about Galois theory - where does the "norm" come into this? I seem to recognize the right hand side of the identity