/sci/ - Science & Math

>/mg/
>posts physics shit
let's just start over

>>12554735
Reminder to work with physicists

>>12554738
physicists don't want my help, plus I don't care about the universe

>>12554752
Then why do you study math? I have discovered something which the ancients knew as basic fact and yet we have never produced a proof...
Theorem:
>All mathematical concepts originate in physical experience

>>12554710
He's the one who made that famous meme list about subjects to study, you idiot.

I'm about to end this whole man's career
>let

>>12554876
Obviously. I said he never posted on /mg/ himself, like retard-kun claimed.

>>12554916
Gosh, you're such an idiot.

What's a good textbook for mathematical logic with a specific focus on CS?

>>12554976
> I was here when Misha was still posting
Anon literally thought Verbitsky himself posted here. He's wrong and retarded.

>>12555031
Yeah, because you're Verbitsky himself to know which threads he posted on, huh retard? I didn't know 4chan wasn't anonymous and you could see where people posted. Go fuck yourself, idiot.

>some 2018 newfag gatekeeping and talking about trannies
tells you about the state of /mg/

>>12554756
>No proof
>Math general
The absolute state

how do I show that an element of a ring is irreducible?

>>12555076
you prove that the element satisfies the condition in definition irreducibility

>>12555076
Would it lead to a contradiction if you assumed it is reducible? Show us the problem.

>>12555050
It's called a "conjecture", you absolute twerp.

>>12555037
People asked anon why he think Verbitsky posted here and he pointed to the chart spam. I said I personally know the person who posted them. That means it was not Verbitsky. Didn't expect I'd have to interact with such low IQ imbeciles as you on /mg/ out of all places.

>>12555037
Do you also think Scholze and Mochizuko posted on /mg/?
God what a retard.

Hello. My name is Ed Witten. Nice to meet you all.
Check out my website:
https://www.ias.edu/sns/witten

https://www.youtube.com/watch?v=vfGHbIBgkgs
Wtf is this real I'm literally shaking please tlel me mario didnt say the f word

>>12555171
>>12555184
The difference is that Verbitsky is some literal nobody.

>>12555156
Oh mt God, you're so fucking dumb, please never come back here again, dumb newfag.
>>12555171
That person even said that Verbitsky himself posted that chart on /sci/, but because one of his retarded dumb friends spams that chart he seems to think that it's impossible to Verbitsky to have ever posted here, what an utter fucking imbecile. This is why I hate newfags.

>>12555200
>Verbitsky himself posted that chart on /sci/
He didn't.
>it's impossible to Verbitsky to have ever posted here
It's not impossible. He could come here and post right now. But inferring from someone posting the chart to that person being Verbitsky himself is plain retarded. Get a brain.

>>12555200
You're actually retarded

>>12555204
Just because your retarded friend spams the chart here, doesn't mean Verbitsky himself never posted it here, you can't know because you're not him. Just accept defeat, dumb newfag, I'm tired of trying to knock sense into your molecular brain. Be humble, sit the fuck down and lurk more.
>>12555208
Yes, you are.

Just ignore the retard.

>>12555245
Yes, I will. Tired of trying to put some sense into those dumbfuck newfags every single time and we're not even in summer vacations yet.

>>12555251
I've posted here for longer than you and can attest to the fact that you're a retard who doesn't have a clue what you're talking about.

Is there a list anywhere of recommended exercises from Hatcher? I don't want to do all of them but I don't trust my judgement in picking a good variety.

>>12555340
>but I don't trust my judgement in picking a good variety
Then you don't have experience enough in high level math and self-studying to be tackling Hatcher right now.

>>12555344
>Then you don't have experience enough in high level math
Ive taken point-set topology and commutative algebra, including homological algebra. Also measure analysis, pde theory, etc. I want to get into geometry though.
>and self-studying
Never done it before, so you might be right there.

>>12555344
>>12555357
Also algebraic topology from Munkres, when I mean Hatcher I mean mainly chapters 3 and 4

>>12555340
>I don’t want to do all of them
Why not?

>>12555135
Mathematically speaking, I have a conjecture which states you should kill yourself.

How do I self study math?

Is the analytic number theorist anon here?
What book(s) do you recommend to get a good fundamental grasp of the subject? Nothing advanced or too extensive, just the main basic content.

>>12554756
>All mathematical concepts originate in physical experience
Complex numbers were developed while attempting to find a general solution of cubic equations. As abstract as fuck.

>>12555815
Hmm
I think I need to amend the conjecture then, but in a way it still holds. Cubes came from natural phenomenon.

>>12555754
Apostol's books are good.

>>12555842
People invented structures where you can divide by zero, supposedly because it makes a bunch of constructions and definitions more compact and unified.
Where is division by zero happening in the physical world? It's nothing more than writting aesthetics and abstract curiosity.

I want to make quantum computer games.
I don't know anything about quantum or computers.
help me please.

Is topology related to the concept of inheritance? Like genetics?

>>12555881
So that's where I'd ammend the theory. It's not that all math comes directly from a natural source, but that each mathematical object has a universally useful setting that it falls into, and that we tend to discover mathematical objects in a way that coincides with how we think.

>>12555998
>Is topology related to the concept of inheritance?
No. Subspaces don't inherit all properties.

>>12555995
So, quantum can actually be simulated with regular computers depending how much quantum you want. What do you want the game to be about?

>>12556024
I feel like this is a very bad answer. Can't you try a little harder? I can already come up with some trivial examples. like a recursive class of sets. But think about quotient or product grou

ps. I got inspired by realizing that a table is literally a proto chair, a chair is just an L table. And this relates to genetics because animals are 4 legged and table like but humans sprouted a head, for which the chair rest is made. And there is the term "genus" in topology. So different topological genuses correspond to different stages of evolution, somehow

>>12556031
>>12556034
Yes. You are absolutely correct. All animals have 4 legs but only humans have heads. I wonder if this bio-topological inheritance is related also to your relatives dying and you getting stuff.

>>12556046
Maybe its whole sets of slightly varied topologies, all intersecting and unioning.

>>12556028
>What do you want the game to be about?
Open world, gathering, farming, building, and adventuring.

>>12556057
Holy shit, someone get Miyamoto on the phone!

>>12556057
I guess you could use quantum graphic systems and use a novel monitor, to make it look more realistic. You can copy quantum effects and their simple functions for known quantum phenomenon, like double slit and quantum optics and maybe some chemistry. But for simulating physics as a whole, you could make miniature quantum isomorphisms of larger physical bodies. But its generally imperceptable at human timescales.

>>12556046
https://en.wikipedia.org/wiki/Genus_(mathematics)
>implying that this isnt mitosis
And when the organism gets large it forms many-celled tubes and gets to another layer of genus

Genuses are analogous to polar coordinates and a linear branchial generalization of genus is analogous to euclidean

How do we differentiate the gamma function?

>>12556178
More importantly, how do we decide the order for the train we are running on the anime tranny?

>>12556178
normally we don't care about the derivative of the gamma function, and we work with the logarithmic derivatives instead, which give you the polygamma functions [math]\psi^{(s)}(z)[/math] where [math]\psi(z)=\psi^{(0)}(z)[/math] is the usual digamma function

the basic philosophy behind this is that the gamma function is the generalisation of the factorial to the complex plane, so you'd expect that the logarithmic derivative of the gamma function is more important since that brings the multiplicative behaviour over into additive behaviour, and you wind up with simple series and integral expressions for the digamma function, for example

>>12556224
smallest to biggest, in terms of girth

If I have a monomorphism [math]a[/math] and I know it's bijective, does this means that the inverse is also a monomorphism?

>>12556461
wait I meant homomorphism

>>12556461
on its image, why wouldn't it be?

Pssssst..... I am a ring, such that there is a unique ring homomorphism from me to every other ring. Which ring am I?

So who the fuck is the phd tranny that lurks here?

I’m trying to learn some linear algebra since I’m taking it this upcoming semester. Does anyone have a nice explanation for determinants? Shilov’s book is okay so far but I feel like I don’t understand. Picrel is drawing how I sort of conceptualize their construction.

>>12554735
physicists are the one driving maths, they are the mathematicians of the renaissance.

>>12556950
Phtsicist belive all math is calculus and linear algebra with some notation changes.

>>12556923
if you want to remember what's the formula for 3x3 determinants then look at this picture
https://en.wikipedia.org/wiki/Rule_of_Sarrus
but there's not much meaning to it, it's just how things work in the particular case of 3x3 determinants
the important thing is what the determinant does (how det changes when you swap rows, add rows, multiply row by a number)
also the interpretation "det = signed volume of a parallelohedron"
and in fact from those properties you can work backwards to obtain the formula of the nxn determinant
that should all come up in your book sooner or later

>>12556923
Hoffman and Kunze’s Linear Algebra book has the best coverage of Determinants and Grasmann rings

Good morning, /mg/!
>Hilbert's 17th problem in free skew fields
https://arxiv.org/pdf/2101.02314.pdf


>>12556461
If you are talking about a homomorphism, then yes.To get [math]f^{-1}(xy) = f^{-1}(x) f^{-1}(y)[/math], let [math]x = f(a), y = f(b)[/math] (bijection so this is OK). Then [math]f^{-1}(xy) = f^{-1}( f(a) f(b)) = f^{-1}f(ab) = ab = f^{-1}(x) f^{-1}(y)[/math]. This is enough for groups, for rings you need to do the sum your self, as well as multiplicative identity. For modules, pretty much the same and so on.

>>12556875
[math]\mathbb{Z}[/math]

>>12556887
Some mentally ill attention whore who is not even a PhD yet.

>>12557368
wow
just wow
i have not expected this level of transphobia from an anime poster

>>12557380
I've lived with that poster for 28 years. I know what I'm saying.

From wikipedia,

>In mathematics and physics, a topological soliton or a topological defect is a solution of a system of partial differential equations or of a quantum field theory homotopically distinct from the vacuum solution.

Where do I find a resource that explains this mathematically without heavily depending on physical prerequisites?

>>12557410
You can't, really. What a soliton is doesn't have a proper mathematical definition yet. This is partly because solitons have a bunch of special properties which exist in classical solitons but not in QFT solitons (the particle-like behaviour is actually much stronger in the classical solitons which you observe in fluids and optical fibres and so on).
You may find Richard Palais' notes useful, which goes into the theory of loop groups somewhat, or Fadeev and Takhtajan's book Hamiltonian Methods in (something something) Solitons interesting - personally I found the second one rather boring, but it's as boring as it is independent of any major physical understanding, so it has that going for it.
But in general, you shouldn't expect too much here. It's not well understood at all. For example, the KP hierarchy comes up in the solution to the Schottky problem in algebraic geometry and I think is the only known solution, but this is very interesting because the KP hierarchy is actually a very natural physical set of PDEs which describe the nonlinear motion of shallow inviscid fluids. It's not at all clear why such a connection between an eminently physical phenomenon and a very abstract problem in a very abstract field exists.
Having said that, most physicists dismiss this and consider it very boring when I point this out, so you can decide for yourself whether that is actually interesting.

>>12557436
For more on connections with algebraic geometry, Sato, Jimbo, and Date have a book simply titled "Solitons". It's blue, and very thin.

>>12557436
>>12557441
oops, I should point out that "soliton" used in this sense is distinct from "soliton" used to mean "topological defect" in QFT
For QFT solitons, I don't know so many mathematical books. They're also much more boring so I kinda don't care about them. But there's Solitons and Instantons by Rajamaran, which doesn't require heaps of physical theory, and there's also one by this Eastern European guy whose name I can't remember, but he did a course at Oxford a while ago: Solitons, Twistors, and something something. It deals with Yang-Mills theory, Inverse Scattering, Twistors, I think topological solitons as well, and you'll know you have the right book when you see this proof which uses notation for some curves in the first chapter or so that looks like [math]C\cup C_k[/math] which made me giggle

>>12557436
come to think of it, Olver's book Lie Groups and Applications to Differential Equations also has a chapter which deals with completely integrable systems, solitons, and bihamiltonian systems (if a system is bihamiltonian it's pretty much always going to admit soliton solutions) but again, these are more for classical solitons, not topological defects

>>12557436
>>12557441
>>12557456
>>12557480
Thank you, I will definitely dig into this. Under what term do cosmic strings* fall, solitons or QFT topological defects? And by "loop groups" do you mean the homotopy groups?

* https://en.wikipedia.org/wiki/Topological_defect#Symmetry_breakdown

>>12557502
>cosmic strings
those are QFT "solitons"
Classical solitons have much stronger properties. These are the solitons which actually behave as particles: you can have [math]n[/math]-soliton solutions which look like [math]n[/math] solitary wave solutions at infinity, and which interact by passing through each other and emerging asymptotically unchanged up to phase shift - QFT solitons typically lack this, because it's a very hard property to preserve when you require the solitons to also behave relativistically.
The only relativistic equation I know of which admits solitons which satisfy the stronger "classical" soliton conditions is the sine-Gordon equation. So typically in QFT when people talk about "solitons" they mean "topological defect" but abuse the term soliton because I think they just think it sounds cooler.
The difference is a topological soliton has not been shown to admit [math]n[/math]-soliton solutions at all, and so even the question of whether arbitrarily many topological defects can interact and emerge identically up to phase shift is moot. It typically lacks the richer mathematical structure of the classical solitons.
>by "loop groups" do you mean the homotopy groups
No, I mean things which are called loop groups. They are groups of smooth maps of a circle into a compact Lie group.

>>12557502
>loop groups
Palais may be a good start https://arxiv.org/pdf/dg-ga/9708004.pdf
also Graeme Segal and friends write about them a bit

>>12557509
>>12557511
The Palais notes look great, I often run into trouble learning from physics books because they refuse to simply give the mathematical rundown. Biting my tongue everytime I see tensor fields.

Which of the resources mentioned above could lead me to understanding cosmic strings and their gravitational interactions? I originally wanted to learn general theory before delving into the cosmic strings, but knowing there is a split complicates things as my time is finite. I should make time for reading about the cuck curves, though.

>>12557548
If time is an issue and you only need one then try Rajamaran, but not knowing exactly what you need to know I can only guess

>>12557557
>but not knowing exactly what you need to know I can only guess
I understand. It's not that I'm on a deadline, it's just that I'm looking for research opportunities and don't want to spend a lot of time here if I find nothing promising. Therefore I don't want to dedicate too much time to the solitons and defects before understanding more, even if they look very interesting. Thanks for your posts!

Is it possible to learn algebraic topology, quantum field theory and foundations at a research level? Of course, I would make one of them as my main area and the other more of hobbies, would that be feasible or am I being unrealistic?

>>12557883
why don't you learn one first

>>12557886
But I am, I'm currently studying algebraic topology.

>>12557883
I don't think so. To be at the cutting edge of QFT would require you to basically drop everything else.

>>12557898
What about Quantum Gravity or general relativity?

>>12557902
The things you are mentioning are pretty far apart. Maybe tell us a bit more about what you're looking to achieve by learning about these fields?

>>12557906
I'm just looking at cool fields of physics to specialize in, although physics is not my area. In math I'm interested in foundations and algebraic topology and I plan to make my career around the latter.

>>12557908
>I'm just looking at cool fields of physics to specialize in, although physics is not my area.
Physics has some neat fields but you should be warned that you won't find the mathematical rigour you are used to as a mathematician there. If you can look past that, there are interesting geometrically flavoured results in general relativity. Seeing as you're interested in algebraic topology and foundations you might be more interested in an area that is more dependent on category theory and/or algebraic geometry, though. Might make your life easier as well if there is a connection to the other areas you're working on.

>In math I'm interested in foundations and algebraic topology and I plan to make my career around the latter.
You could also look at homotopy type theory which does both. I'd treat that as a side venture though, there aren't any positions for it and people have labeled it a meme.

>>12557902
Have you considered Quantum Topos Theory?
You like foundations, you like algebraic topology, and you're studying physics for the sake of studying physics. It's a match made in heaven.

>>12556991
Hardly. Many great theoretical physicsists recognize the math they use/develop to explain the physical world is often *underdeveloped* as a mathematical theory. Feynman's operational calculus is a notable example that underpins QED. I had an advisor in undergrad who was a former physics phd student who quit to go work in math because he couldn't handle the lack of mathematical rigor. He now works on rigorous framework for Feynman's operational calculus. Man was the best mathematician I ever met. Systematic, serious, and unwilling to accept subpar work. Wish I could be more like him sometimes.

>>12557908
The iconic Yukariposter did condensed matter physics which is physics only if you insist it is that, as it was so algebro-topological otherwise. Also, HoTT mentioned by the other anon could be your thing. However...

>>12557955
>there aren't any positions for it
https://golem.ph.utexas.edu/category/2021/01/postdoctoral_position_in_hott.html

>>12557902
>general relativity
mathematically solid but research is very slow
>quantum gravity
in gridlock
>>12557908
if you'll let me give you some advice which will serve you well in the long term even if it may cause you grief in the short term, don't rush into what seems like an exciting area of research
you will be much better served in the long run by mastering the basic foundations of physics and knowing them very well
if you want to go into physics just because a field seems cool but you don't have enough general knowledge, what is likely to happen is you fail to see simple solutions to problems you could have figured out by analogous things you'd have come across with a good general knowledge of the basics, and you'll also frequently fail to see opportunities to generalise, or to take your work further, or make adjustments and corrections or advancements in theory
in other words, don't rush, and let the ideas come to you naturally as you master the core areas of physics, and this way you will come out a much better rounded researcher
i'm aware that you're not a physicist, but mathematicians are notoriously bad at seeing simple solutions to physical problems and rushing off into research too quickly normally won't end well
that said, high energy physics is the only area in which algebraic topology could plausibly be useful

Interesting, I'll try to learn more about Homotopy Type Theory and Quantum Topos Theory.

what area in mathematics is related to this problem?

Should I use Harvard's Math 55 curriculum as a guide to self-study baby rudin? I think I'm ready for Rudin since I've used Tao as an intro to Calculus.

>>12558394
Graphs.

>>12558421
what kind of graphs?

>>12556875
The trivial ring.

>>12558394
>>12558421
but really though like integer grids, linear equations, piecewise mapping, parameterisation?
what am I looking for?

>>12558710
Tropical algebra

>>12558420
Apparently you don't even know what Math 55 actually is...

>>12558733
I know 55a is Abstract Algebra, but isn't 55b Analysis or something? Not him btw

>>12558733
I know enough that it is divided into Algebra and Analysis and that the topics move fast.

>>12558527
There is no homomorphism {0}->Z because we want f(0)=0 and f(1)=1 but 1!=0 in Z.

>>12559180
Ring homomorphisms need not take 1 to 1.

>>12559407
I believe you're talking about rng homomorphisms?

>>12558710
integer programming

Do smart people on here study maths? Or do you only need to hear/read it one time and understand it perfectly forever? Is it true that only brainlets study for maths?

This has been a good episode of mg so far.

I got a neat book of math in german to help me study, it only cost 3 bucks at the used book store. I'm trying to make sense of a passage which seems to mean:
>Given a "Quadrate" with two non overlapping quadrats "eingeschlossen" within it, then their perimeters will sum to equal or less than the outer perimeter
But this seems nonsensical. If the quadrats don't have to be inscribed, they can be each half the size of the outer one and have an extra middle line of perimeter. And if they have to be inscribed, how do you inscribe two quadrilaterals into another one without letting them intersect?

>>12555031
what is that guy even doing at impa

>>12559868
>This has been a good episode of mg so far.
>math in german
>german
Why are germans trying to subvert /mg/ into being even worse?
>>12559910
There's lots of people in IMPA who are into complex geometry and symplectic geometry, what's weird about Verbitsky being there, dimwit?

>>12557388
I think you say this kind of thing of yourself here mostly because you don't want anons hating you for drawing so much attention etc.
Can't blame you though, at least it shows humility.

Just out of curiosity, are you 5 or 6 years into your PhD or did you spend more time before starting it at the 'usual age'?
I started mine 4 years late. Could be worse, I guess.

It’s been a couple months since I’ve been on this general, gotta say I really like p-adics

>>12559633
No, you're talking about unital ring homomorphisms. Check your unit privilege.

>>12560004
What do you like about them

>>12559958
Or maybe it's just one of those negative-without-any-actual-reason-days. I'm second year. I guess I'm 3 years late or something. Graduated from high school in 2011, started uni in 2013, got my master's degree in 2018, started postgrad stuff in 2019. What is your area? You wouldn't happen to be that number theorist or even geometer (?) who seemed quite worried about things last spring? How far are you in your studies?

>>12560091
>You wouldn't happen to be that number theorist or even geometer (?) who seemed quite worried about things last spring?
Hmm maybe not? Not sure what exatcly that was.

>How far are you in your studies?
I'm still going to do my qualifying exam.
Honestly, I don't know how far I'm going to get. I'm the type of person that has a very messy, foggy and faulty mind in short time intervals. I'm also kinda bad at socializing and maneuvering through conversations.The only reason I got here is because I'm relentless, somehow I managed to put enough things together eventually, because basically all my worth comes from this journey and because liking it. I can't say I'm ridiculously pationate about math, most of the time I'm dragging myself, but there are cool moments of appreciation.

>>12557967
Feynmans rules are just the chain rule and product rule lmao. I also work with that shit and believe me physicists get scared with anything more complex and that's why a lot of theories require patchwork.

What about a vector space with each field associated to distinct coordinates being distinct

>>12560275
You can't speak of linearity if you do that, since your fields are going to be distinct.
You can dance with multilinearity, which essentially is just dealing with the tensor product of all these fields over the ring of integers (or a common prime field if they have the same characteristic).

>>12560312
Why can[t you do linearity? T(A+B) and just transfer the basis independently?

>>12560342
It's not going to be a vector space. If so, what would be the field of scalars?
You could make a module over the product of fields but that's kinda lame.

>>12558732
>>12559643
do these deal with some idea similar to subcoverings in particular

>>12560365
What is a product of fields? How would I take a product of R and a field that was not its subset or poset

>everyone's posting in the meme thread when there's a perfectly decent /mg/ up
You guys suck, I'm leaving /mg/.

>>12560404
In what way is this not a perfectly decent mg thread and it came first?

>>12560185
>Hmm maybe not? Not sure what exatcly that was.
If you were either of those, you would have recognised yourself.
>I'm still going to do my qualifying exam.
What will that be like? Is it some final thing before you are done, or is this the one you must pass or else you lose your position (I'm not too familiar with the system on the other side of the ocean)?
>I'm the type of person that has a very messy, foggy and faulty mind in short time intervals. I'm also kinda bad at socializing and maneuvering through conversations
Extremely relatable. Are you also bad with all sorts of bureaucracy? You should probably try to practice some networking if you are planning to stay in academia.
>The only reason I got here is because I'm relentless, somehow I managed to put enough things together eventually, because basically all my worth comes from this journey and because liking it
Also relatable. Hard work takes the worker surprisingly far, but then comes the bitter moment when some child prodigy goes beyond our level and we just have to swallow it. It seems like you too see your value determined by your achievements, and so hitting a wall and getting stuck most likely hurts you a lot. I'd encourage you to remember you are worth more than your career, but that would be just empty words because I can't make myself believe that.
>I can't say I'm ridiculously pationate about math, most of the time I'm dragging myself, but there are cool moments of appreciation.
I guess this is the most reasonable approach. Sure, there are people who live to do maths, I'm not denying their existence, but most people who are "super passionate" and call everything beautiful are closer to r*ddit tier OMG I LUV SCIENZ!!! than actual practicioners in my eyes. To find those things to appreciate is to not dislike it, and that should be enough to carry the searcher from one cool thing to the next one. We will make it, anon!

>>12560404
>You guys suck, I'm leaving /mg/.
See you tomorrow, honey.

>>12560388
The cartesian product of fields will form a commutative ring with unity, but it's not a field. So it's a module over itself but not a vector space.

>>12560445
>Cartesian product of fields
What hapens to the operators?

>>12560450
Call the product R. In this context, the relevant morphisms (for vector spaces those are linear operators) are the R-linear maps between R-modules. It's the same definition: If M and N are R-modules, then a R-linear map between them is a function f : M -> N with f(m+n) = f(m)+f(n) and f(rm) = rf(m) for all m, n in M and r in R.
To make R be a vector space you would need a field of scalars k being a subfield of all the fields used to construct R. There is such a k if those fields have the same characteristic, otherwise there isn't.

>>12560275
Let's call that structure a wektor spaze. If we would have a finite dimensional wektor spaze [math]W = k_1 \oplus k_2 \oplus \cdots \oplus k_n[/math] with distinct fields [math]k_i[/math], then we would have two possibilities:
(1) After reindexing them, there would be a ring homomorphism [math]k_1 \to k_i[/math] for every [math]1 \le i \le n[/math]. This would make every single one of those fields a vector space over the first field, and so the wektor spaze would actually just be a [math]k_1[/math]-space.
(2) There would be some index [math]j[/math] such that no morphism [math]k_1 \to k_j[/math] exists. Then we could split the indices into two sets: those for which the morphism does exist and those for which it doesn't. The first set would give a [math]k_1[/math]-space, and then we could repeat this procedure for the other set to tidy our wektor spaze a bit. However, this would not be a vector space. You'd have to take the direct product of those fields to get a ring (not a field), and this would be a module over that ring. This thing I described would let you eliminate some of the fields, but I'm not sure if it would be canonical, and will not even attempt to think about it as it is almost 3AM.

Good night /mg/.

>>12560473
>wektor spaze
Cute

>>12560440
>If you were either of those, you would have recognised yourself
I have interest in number theory and geometry, but I think you mentioned an event unknown to me.
>is this the one you must pass or else you lose your position
Yeah. I need to pass in order to officially dive in research.
>Extremely relatable
I think most people relate to the foggy mind thing specifically, but I'm closer to a serious case. You can see here how often I misspell words, it's mainly because of it. But I trust you relate a lot with having (or having had) socializing issues.
I don't have much trouble with bureaucracy, I guess, but I get stressed sometimes. Especially when it's nonsensical/inconvenient bullshit.
>You should probably try to practice some networking if you are planning to stay in academia
Definitely. What is most painful is that I have to play a character to get good results, which is something artificial and rather distasteful imo. It's not so bad when put like "play until you become" I guess, but has its cost. It's a game I have to play anyway.
>I'd encourage you to remember you are worth more than your career
I became more convinced that I can find worth elsewhere in these last few years. I feel a bit more safe knowing that I can have a good enough plan B. Some people get so trapped in their ambitions that when everything fails they essentially die inside, we all know what some of them do... By the way, you mentioned in the other thread that you don't want a position in academia. Did your opinion change? What sort of possibility are you imagining?
>We will make it, anon!
I hope so. :3

>>12560473
So much text to say almost nothing.

>ITT
When autists realize no number, not even 0, can replace a vagina[s warmth

Is the algebraic geometry study group still going on discord?
I didn't get in there

>>12559910
Running from Putin.

>>12560604
I studied the topological structure of your mom last night buddy

>>12560604
the real tragedy is that no number can replace the warmth of a tranny's boypussy

tfw quit math and moved to biostatistics and feel the happiest i've ever been

theorems for this feel?

>>12560494
no u

>>12560572
>Yeah. I need to pass in order to officially dive in research.
In that case, good luck!
>>12560572
>You can see here how often I misspell words
I thought you were just drunk. But yeah, now I see it in a different light. Do you know any cause for it?
>But I trust you relate a lot with having (or having had) socializing issues.
Oh yes. Autism, insecurity and shyness.
>I don't have much trouble with bureaucracy
Good because you will probably have to fill a myriad of forms WHEN (not if) you have passed your exam and get started with stuff.
>It's a game I have to play anyway
I'm not sure if it's that bloody in maths as it would be in, say, economics, but in some fields the contest for the professor's seat is a real game of thrones. Nevertheless, it will require a lot of theatre to move forward. Not a surprise, though. Our social life is a collection of rituals, and increasingly so the more exclusive things get.
>I became more convinced that I can find worth elsewhere in these last few years
Good! Then I believe you will not crumble under pressure. I can tell you already that you will be stuck, you will pursue bad ideas, you will see weeks and months go to waste, all that when you do research. If your worth was completely determined by your progress, that would be when you'd feel very very very bad.
>Did your opinion change? What sort of possibility are you imagining?
Nope. I just don't think I have anything to offer to that world. I don't want to take resources away from people more competent than myself, nor do I want to live far away from my loved ones. No back up plan, though. I don't know. I have 1½ years of funding left to change my mind or figure stuff out.

>>12560582
Trying to explain why not while also trying not to fall asleep, yet you are correct.

>>12561187
Nicorette-Pall Mall thm:
>100% of smokers die

>>12560012
Today I will remind them
https://math.mit.edu/~poonen/papers/ring.pdf

>>12561271
Get married with your boyfriend and have him support you financially like girls should

>>12561296
That is probably a legally valid option, but I would have nothing to offer him in return. I would grow old and ugly without giving him kids, should he change his mind and want those. I'd just be a parasite.

>that guy who decided he's an "algebraist" after the first period of his first year of undergrad after being reality checked by intro analysis

>>12561318
just learn to cook, EZ

>>12561335
Many such cases!

>>12561357
I sort of know how to already, but not meat other than chicken. Stupid vegetarian diet. No one around to eat my meat cookings, so no chance to practice, either. Anyhow, I guess this is a bit off topic, so soon someone will be furious and post an angry post!

>>12558710
Integer programming.
Diophantine equations.

>>12559669
Everyone studies.

Quick /mg/ post all the (co)homology theories you know! Googling is cheating. I'll start with the easy ones:
>Singular
>Simplicial
>Cellular
>Cubical
>Morse
>Discrete Morse
>Persistent
>Cech
>De Rham
>Dolbeault
>Real/complex K-theory

>>12561335
>tfw this was me
I didn't really find analysis hard just boring. You quickly realise you need everything though. I wish I'd taken complex analysis.

>>12561461
singular
simplicial
and that's all

>>12561461
>Quick /mg/ post all the (co)homology theories you know!
This is like the 50th time you're posting this.

>>12561335
lmao this is so true

>>12560028

dude have you been taking the meds?

what's the most /x/ research field one can pick up?

>>12561624
Lie Groups

how do i find my area of interest?

>>12561624
Rep theory

>>12561871
un-fucking-real

>>12561871

yep, it's schizotime

>>12555076
>Proof: SageMath. QED

>>12555188
Fibrations are so fucking lit

>>12562026
The best time

>>12561285
God that's awful. Was that written by an undergrad?

>>12561624
diagrammatic algebra

>>12561461
>singular
>simplicial
>de Rham
>Cech
>group
>étale
>flat

what was the first paper you read?

>>12561461
Singular, simplicial, cellular, Alexander-Spanier, Bredon, sheaf, group (if applicable), étale, Čech, de Rham, equivariant, topological K-theories, Tate, Hochschild, cyclic, and that one mentioned in Brown's book on group cohomology which I can't remember the name of.

>>12562492
How in the fuck would I be able to remember that?

>>12562492
Valuations and local uniformization by Vaquié, it’s a survey of the theory of valuation rings and how valuation theory was used by Zariski to prove that resolution of singularities exists for surfaces

>>12562492
i write papers, not read them

>>12562253
Why the unitphobia?

>>12562689
John Baez got canceled on twitter over this and left last year

>>12562722
>using twatter
YIKES!

All mathematics (and therefore all physics) are derived from axioms, out of which we can't prove and need to accept through faith that they're real. Why is it so inconceivable that the existence of the universe derived from an axiom as well? That axiom being of course God.

>>12562750
I use twitter but I mostly follow japanese people to practice my japanese.

>>12562722
What a piggot oinkery.

>>12562823
Seems like you're restricting "mathematics" to that which is axiomizable by covertly defining it, mathematics.
In any case, mathematics is not "derived from axioms", but the axiomizable part of math is, well, axiomizable, and in many ways. Math is rarely done from the axioms, though.

>>12562722
Did he apologize later? If he did he's a cuck.

>>12562838
Do you think this is in anyway not more cringe? Lmao

>>12562823
Hi Peterson.

>>12562838
I can accept this.

>>12562889
It's ok, I don't care what your definition of cringe is honestly.

All mathematics (and therefore all physics) are derived from "Schizophrenia is a psychiatric disorder characterized by continuous or relapsing episodes of psychosis.[5] Major symptoms include hallucinations (typically hearing voices), delusions, and disorganized thinking.[7] Other symptoms include social withdrawal, decreased emotional expression, and apathy.[5][13] Symptoms typically come on gradually, begin in young adulthood, and in many cases never resolve.[3][7]"

>>12562823
No one said you had to believe the axioms were real in order to do math or physics.

>>12562939
I just realized that sprinkling fake citations in your post is a great way to make it look more credible.
That is, studies have shown that adding citations leading to nowhere will increase the perceived validity of the claims.[3]

>>12562823
Are boolean operations axioms?

>>12562961
Also, using statistics to justify your claims makes them more convincing 63% of the time.

>>12559633
>rng
TIL. In my country what you call rng is called ring and what you call ring is called ring-with-identity.

>>12562823
I am unsure on this point honestly. Is the fact that we cant help but experience things an axiom or is it some other kind of fundamental principle?

Why do we restrict ourselves to 2-D euclidean notation?

>>12561871
Imagine applying this beyond geometry to things like notation itself

>>12561461
Compactly supported, perverse/intersection, etale, Hochschild

What the heck is a pivot and is it actually important? How is every leading entry in a row reduced echelon matrix not a pivot?
This seems like one if those things that doesn't matter.

>>12562823
Physics is derived from experiments. Physical theories have two purposes: explain results of past experiments and predict results of future experiments.

Noob question. Is learning things about math, without proving it, learning math?

>>12561271
>Do you know any cause for it?
I suspect of two, maybe a combination of them:
1. Terrible sleep timings during my teens; and
2. I have a chronic disease that has mind fog as a possible symptom.
I have always been frequently absent-minded, but my cognitive performance definitely slowly went down during my late teens.

>I just don't think I have anything to offer to that world
Hm I think you're being rather pessimistic. Maybe being in such a top uni makes you quite intimidated by peers and such, but you'd probably be a big fish in a lot of other places.

>>12563419
If you can think like Poincaré, sort of yes. At least his ideas were great.

>>12563419
Yes. You will styart to prove things yourself from whatever baisis you learn

2*10^2 th post

>>12563443
>1. Terrible sleep timings during my teens; and
Well this you can't retroactively fix but
>2. I have a chronic disease that has mind fog as a possible symptom.
Have you shown your head to a doctor?
>I have always been frequently absent-minded, but my cognitive performance definitely slowly went down during my late teens.
How did you eat during those times? I noticed a huge loss of brainpower every time anorexia hit, and I'm not sure if the damage done by that is correctly amendable. That's why I'm asking.
>Hm I think you're being rather pessimistic. Maybe being in such a top uni makes you quite intimidated by peers and such, but you'd probably be a big fish in a lot of other places.
That is a good guess, but I'm not in a top uni. I don't know. Just an incredible feeling of inadequacy and inferiority. Maybe I'm a bit pessimistic, or maybe I am the one who has a realistic perspective on my abilities. Anyhow, good night!

>>12563479
Based.

>>12557410
Instantons are classified by the cohomology of certain sheaves on the moduli space of fields in the field theory.
>>12557436
>It's not at all clear why
It is clear. It's because these models are integrable and admit Lax pairs as operators on a Hilbert [math]D[/math]-module of a nCFT, which satisfy certain quantum flatness conditions. You can then begin to point-count stable curves in its moduli space via Gromov-Witten/quantum cohomology and reproduce the correlators/conserved quantities of your system.
>>12557970
I am now doing holography and HMS.

>>12556950
They haven't been driving that much math for a long time. For the past 150 years or more, it was rather the case that math was find more and more applications in physics via Lie Groups, Topology, Complex Analysis, etc. which started to be developed independently of physics.

>>12563661
>It is clear.
>posts abstract nonsense which has nothing to do with the actual behaviour of solitons as they appear in reality
You can just simplify everything you said to "because the system has infinitely many conserved quantities" i.e. is completely integrable, which is what you get from a Lax pair, but this itself does not actually distinguish a solitary wave from a classical soliton.
Besides which you said absolutely nothing about why the KP hierarchy should be a physical description of nonlinear flow of shallow fluids, you just said something relating to algebraic geometry alone and established no connection to what I was talking about at all.

>>12563737
t. seething midwit

>>12556178
[math] \Gamma(x) = \int_0^{\infty} z^{x-1} e^z dz [/math]
so you can follow the Liebnitz integral.
[math]\frac{d}{dt} \int_{a}^{b} f(x,t) dx = \int_{a}^{b} f_t(x,t) dx [/math]
Derivative of the integrand is just
[math] z^{x-1}\ln(z) e^z [/math]
So
[math] \Gamma'(x) = \int_0^{\infty} \int_0^{\infty} z^{x-1} e^z \ln(z) dz [/math]

>>12563737
>can just simplify everything you said
>as they appear in reality
>why the KP hierarchy should be a physical description of nonlinear flow of shallow fluids
...

>>12563739
yeah, seriously. if you're going to call yukari out you should call him out for being an unpassing tranny fudgepacker.

>>12563739
What are you just convinced by anything someone posts with abstract crap in it? Quantum flatness conditions have nothing to do with the KP hierarchy appearing as a physical description of shallow fluids. So as I said, it is not clear why the physics of shallow fluids should be connected to the Schottky problem. Think instead of believing anything that sounds "advanced".

>>12563784
Don't worry, the yukari poster doesn't actually know physics.

>>12555815
where did the cubic equations come from?

>>12561613
Say it with me:
Meds are for feds

>>12563851
>Implying knowing physics is a bad thing
I guess you don't want to discover new math

>>12564177
https://youtu.be/gwFvNYSCmhM

>>12564188
I fail to see a legitimate analogy.

>>12563134
>TIL.
Go back.

>>12556923
determinates are weird and not as important as they seem. theoretically they are important in establishing things like a formula for a matrix inverse, but practically they aren't used because their computational complexity sucks.

conceptually, when you solve an invertible system of linear equations, this is a factor that pops out. do gauss-jordon elimination for 1x1, 2x2, and 3x3 (a real wrist breaker, takes a page or two) to start to see the origin of such a factor. actually being able to articulate the pattern is much more difficult, but you can see the start of something that turns out to be the determinate.

the proper setting for determinates is geometric/exterior algebra. the best approach IMHO is to define a class of multilinear functions with properties satisfying a what (signed) volume function would act like (i.e. switching columns switches sign of function), and then proving that there is only one function that satisfies said properties, e.g. the determinate.

once again, theoretically they are invaluable, but practically useless beyond 3x3 matrices. determinates are one of the most difficult, and most superficial, details of basic linear algebra

ok serious question
are quantum computers ever gonna be real? if yes then how long will it take?

>>12564516

>travel

If tinder wasn't enough this puts the final nail in the coffin: she fucks non- white guys

>>12564745
The nose ring was a dead giveaway

>>12564745
>she fucks non-white guys
how is that a bad thing? she knows she deserves more than a white incel

>>12564781
yeah, she deserves a beating

>>12564795
poor seething incel
trump getting banned from everywhere must have taken a toll on you

>>12563661
holy shit i actually understand everything in this post. have i made it?

>>12563661
Nice. How's your territorial expansion going over there? Did you get your dose of anti-de S*itter stuff or is it still involved?

So say I make a random squiggle in space, say a 2d plane. How do we find it's taylor or fourier parametrization/function

>>12564516
Make an aws account and go to braket. You have access to quantum computers and simulations.

Is Automata Theory a good career path?

>>12565301
> Automata Theory
CSlet detected.

suppose i need to be able to calculate these limits easily within three weeks, what sources would you recommend me to study from?

>>12565402
Are you suppose to know Hebrew as well?

>>12554994
Shore or Rautenberg
but get Hodges' shorter model theory too

>>12554726
Are you interested in physics? If no, why not? Do you consider physical studies and the study of math to be "adjacent" in the sense that the two are closely related? Or perhaps you see them as two entirely distinct subjects with little in common?

>>12565090
Sure did, got most of QG (covariant phase space) and susyST (Fukaya [math]D^\ast\text{Coh}(X)[/math]) as well under me. Once all the structure is in place, holography is just quantum duality plus some shift in interpretation. I'm now trying to categorify this notion via https://arxiv.org/abs/2005.14178

>take course in uni
>after a year forget it
>repeat for 3 years
I looked at some exams of courses I used to have, and while I did excellent in them at the time I remember essentially nothing now. The same is true for many theorems, they just tend to slip out of mind. Often the proofs are forgotten, but sometimes the statement of the theorem itself.

I don't know if anyone else feels this way. I just wanted to vent a bit.

>>12565402
substitute x = 0.000001
that should give you a good idea

>>12565570
Just subspecialize in a field and maybe use another field as a hobby. Mathematicians don’t and can’t know all of mathematics

>>12565570
if you're forgetting most theorems then you didn't understand them to begin with, the ones you understand should become intuitive to you through practice.

>>12565672
Define understand.

>>12565641
This is right
>>12565672
This is wrong

>>12565509
I see. Is that related to your LGBTQFT stuff, though? How's the work progressing? Did you get your degree already, by the way?

Rotations of a sphere (as in: pick arbitrary line through center of sphere, rotate the sphere around this line, by an arbitrary angle) form a group
Can you see it in your mind that two such rotations combined are equal to a certain single rotation?

>>12565570
same

>>12565714
>Is that related
Of course, we can gauge higher-categorical symmetries [math]G\in {\bf Grpd}_n[/math] in a TQFT [math]Z:{\bf Bord}_{d+1} \rightarrow {\bf Vect}_\mathbb{C}[/math] just the same via the delooping [math]B:{\bf Grpd}_n \rightarrow {\bf CW}_\ast[/math]. Holography then comes from the correspondence between Levin-Wen models on [math]{\bf Rep}_n(G\rtimes \mathbb{Z}/2^F)[/math] and DW-like TQFT [math]\widehat{\Omega}^{\text{Spin}}(B(G\rtimes\mathbb{Z}/2^F))[/math], which is a form of higher Fourier-Mukai transform.

>>12565807
i say rotato
you say rotato

>>12565402

you're jewish just ask one of your uncles

>>12565829
and the sequel

What is this phenomena that instead of studying harder kids who get btfo by analysis just turn into wildberger drones?

>>12565845
wtf no i will not learn about new concepts
+-*/ for life

>>12565845
Fuck, that's me. Why am I so fucked up?

>>12565824
Good, you haven't completely changed. I must admit I don't know enough of those things to make any interesting or even content filled comment, but it's nice to see you didn't abandon your main thing even if AdS went to the trash can.

>>12565845
I know enough analysis to realize Wildberger is right about everything.
>>12565853
reddit
>>12565986
Go study kid.

>>12564745
zoomers are literally obsessed with interracial sex

>>12566459
Is it interracial if your bf has brown eyes?

>>12563499
>Have you shown your head to a doctor?
I tend to think (or I want to) that it's a waste of time rn, since I'm not rich, my insurance doesn't give me access to enough good doctors where I live and I had too many bad experiences with them. But maybe I should...
>How did you eat during those times?
My meals are kinda standard (still far from perfect though, I still need more diverse nutrients I think). The only difference was that I'd miss meals, sometimes even a whole day worth because I'd be sleeping. That made me lose some body mass, but not much. Maybe it had some impact in my health, but I bet it wasn't as much...

>>12565570
Can relate.
Maybe reading/tackling related problems from time to time is good to keep some of your knowledge in check.

Food lol

>>12565807
Yeah? This is utterly trivial to visualize, at least if you're not female-brained.

>>12565807
I can't. How do you visualize it?

>>12561461
Quick /mg/ post all the (co)homology theories you know!

None, I don't need them

>>12554752
>I don't care about the universe
mathchads RISE UP

Hi /mg/!

Spooky!
>A partial converse ghost lemma for the derived category of a commutative noetherian ring
https://arxiv.org/pdf/2101.02829.pdf
Maybe useful for someone
>The Eigenvalues of Random Matrices
https://arxiv.org/pdf/2101.02928.pdf
There was talk of Feynman diagrams earlier
>Learning scattering amplitudes by heart
https://arxiv.org/pdf/2101.02884.pdf

>>12565807
No. I've never had spatial reasoning of any sort.

>>12567285
>I tend to think (or I want to) that it's a waste of time rn, since I'm not rich, my insurance doesn't give me access to enough good doctors where I live and I had too many bad experiences with them. But maybe I should...
It could very well be something like AD(H)D or something related to your thyroid. If you were European, I'd tell you to go check it just in case, but the Burgeristani medicare thing is quite different, so I don't know if you should do anything other than wait for an insurance better than that. Your meals don't sound too bad, so it's probably not those. The brain fog after one day is pretty non-existent, but the brain fog after 4 days of not eating is already quite something.

>>12568060
BASED!

>>12568131
>BASED!
I know, moreover I'm defending my dissertation next month.

>>12568134
Is it on (co)homophobia? If it's online, I'll come and watch.

>>12568150
>homology
n-no, but is surprisingly connected with the OP

>>12568160
I will find you and attend your defence. I will track you down and then I will write a long analysis on how well you did to post in one of these threads.

>>12568172
:3

>>12568177

Suppose you got to calculate

floor(n * sqrt(2))

using a computer with n being a integer that might have THOUSANDS of digits.
This means that the multiplication would need thousands of digits exact accuracy which is not possible with floating point arithmetic.
So, we gotta play with integers.

A solution would be to calculate the continued fraction of sqrt(2) up to a certain depth, and do
(numerator * n) // denominator

Are the above correct? If yes, up to what depth do we need to calculate the continued fraction?

>>12568470
i would deal with it this way:
floor(n sqrt(2))=k iff
[math]k \leq n \sqrt{2} < k+1[/math] which is equivalent to
[math]k^2 \leq 2n^2 \leq (k+1)^2 [/math] and now all your calculations are in integers

>>12568059
Pick a start and an end. Draw an equatorial line connecting them. One rotation can do that
And two rotations can thus do it as well

>>12568470
>>12568493
If you do the search naively, your algorithm will be quadratic or worse.

>>12568498
but there are multiple rotations which "move a point X to point Y"

>>12568498
no, it's not that simple. >>12568537 is right

>>12568493
write k*sqrt(2)=sqrt(2n^2)

now write a program that adds up consecutive odd integers 1+3+5+... and has a counter of number of odd integers that it added so far of numbers that it added so far. Make it stop when is surpasses 2n^2, the number on you counter-1 is your answer.

>>12568470
Btw it's not correct, since you can have
a*n = m + ε
approx = m - δ
(or vice versa)
for some integer m and arbitrarily small ε and δ

In such a case
floor(a*n) = m
floor(approx) = m - 1

Or (if vice versa)
floor(a*n) = m - 1
floor(approx) = m


There must be a way though...

>>12568537
>>12568540
I said pick an equatorial line, that gives you one rotation from the normal, periodicity doesnt matter

Although...
There are spiral rotations that can slowly increase in latitude and match up....

>>12568791
Nevermind there are probably not spiral rotations after all

>>12568788
https://en.wikipedia.org/wiki/Continued_fraction#Some_useful_theorems

This must be somehiw relevant

>>12568791
let R1 be a rotation which brings the north pole N to a point X.
let R2 be a rotation which brings X to some other point Y.
let R be the rotation which brings N to Y "along the equatorial line"
R1 composed with R2 is not equal to R in general. think about it, try it on some easy examples if you don't believe.

Bros, am I seriously retarded if I think all I'll ever do is read Girard (in French when possible obv), and supplement with whatever background literature necessary to understand what he's on about/who's the target of the insult this time?

>>12568820
But what does {R1 composed with R2} mean? The way I was taking it is that to find the composition you just find the necessary rotation that equals it, and it should be unique

>>12568838
Yes its retarded to have narrow goals and narrow life

What are some interesting physics/engineering problems/tasks that are based in complex analysis? Feeling computational and like spiceing it up today, nothing too advanced though

Press S to spit on Tarski and his """results""".

>>12568847
I already got the brainworm, I can't read without nitpicking the logical arguments or the definitions. Can I hope to become like the cool guys at INRIA and CNRS this way?
>>12568890
S

>>12568842
>ut what does {R1 composed with R2} mean?
the rotation R1 followed by the rotation R2. it's another single rotation along a single axis, how do you find it/visualize it?

>>12568890
Why exactly? I remember the philosophy course in HS where we encountered his Convention T, and the book used "the cat is on the mat" as an example, and the picture had a cute fluffy cat. I wish journals had such imagery, as well. Hand drawn stuff.

>>12568907
>single rotation along single axis
But on a sphere there are multiple axes

>>12568945
Hahahahahah kittiessss

>>12568965
every rotation in R^3 fixes a single line, that's the axis

>>12568972
Oh I see. Right so 2 rotations is equal to 1 rotation

>>12568945
assuming it's meaningful to write whatever the fuck he wants in logical symbols because he wrote the same thing in a natural language

>>12568979
and the question is how to find or visualize this rotation

>>12568991
I'm not a logician and it's been like 6 years since I had a course on logic, so this may be a silly question, but what exactly is wrong in having the natural language as a meta language. Sure, it's not logically closed, but it's the language the logicians use naturally. What is the benefit of freeing ourselves from the shackles of our mother tongues?

>>12569016
The problem isn't in the language of choice, it's equating truisms with meaningful statements, and axiomatizing away the circularity doesn't help either. The language just enables unreadable multilayer garbage, obscured by pleonasms.

>>12569092
Put like that, I guess I'll just
>>12568890
S
Thanks!

>>12568788
>>12568804
I showed you how to solve it, here
>>12568638
But I'm gonna write it down clearer now,
you want to find
[eqn]\lfloor n\sqrt2\rfloor[/eqn] as this anon said
>>12568493
this is the same as finding k such that [eqn]k^2\leq 2n^2\leq (k+1)^2[/eqn] but [eqn]1+3+\dots +2k-1=k^2[/eqn]
so your program needs to add consecutive odd integers until theirs sum is greater then 2n^2. The number of those integers -1 is your answer.

>>12568904
>Can I hope to become like the cool guys at INRIA and CNRS this way?

Names please?

>>12569142
e.g. I was looking at what galinette (inria team) guys put out, it's pretty cool desu

>>12568638
>>12569125
thats the slowest solution possible, good luck doing that with n=10^12

>>12569155
Also wherever Bertot works (at inria)

>>12568890
You again? Go be cringe somewhere else.

>>12565638
1. that would give you a wrong idea in case of a oscillating function
2. as for intuition, it sucks it's like saying to substitute every function to their taylor expansion truncated to the first term.

>>12569155
You're welcome.

>>12569170
Anon, it's meaningless to axiomatize your mother having the property of not being a whore, it's not true irregardless of convention T.

>>12569195
what did you do?

>>12569201
Be at the right place at the right time.

>>12569220
That would only be possible if the right place is my home, and the right time is when I'm beating off to mongol anitranny legs on mg.

>>12569237
>when I'm beating off to mongol anitranny legs on mg.
I didn't know that mg was short for mgtow.

>>12569170
Have sex.

>>12568788
I found out:
https://www.sfu.ca/~vjungic/tbrown/tom-27.pdf
(Lemma 1)

If a is irrational such that 0 < a < 1
then floor(k * a) = floor(numerator / denominator * n) = (numerator * n) // denominator

For sqrt(2), we can just do:

floor(k * sqrt(2))
= floor(k + k * (sqrt(2) - 1))
= k + floor(k * (sqrt(2) - 1))

and apply the Lemma.

>>12568493
>>12569125
Thank you for the help frens

New >>12570175