/sci/ - Science & Math

first for trace formula
https://en.wikipedia.org/wiki/Arthur%E2%80%93Selberg_trace_formula

I think it's time to seriously entertain the idea of founding a math convent/commune.

>>9687048
>math
not well defined.

>>9687055
That could be one of our commune's first tasks: a proper definition for mathematics.
I am going to start looking for a location for our cloister.

>>9687063
my house. my mom can provide snacks.

>>9687048
I would join one if it was composed of normal people and not melodramatic anime roleplayers

>>9687070
I can try to be normal for you anon.

What’s a good classical mechanics book from a mathematicians perspective?

>inb4 ‘spivak’s calc and H&K’s LA

>>9687129
Arnold

>>9687129
>What’s a good classical mechanics book from a mathematicians perspective?

>>9687129
https://www.amazon.com/Physics-Mathematicians-Mechanics-Michael-Spivak/dp/0914098322

>>9687129
Clifford Truesdell's.

>>9687131
>>9687151
These textbooks are aimed at physishits.

>>9687178
>These textbooks are aimed at physishits.
Yes, including Spivak's, in spite of the title.

>>9687146
This is physishit rummage as well.

I'm unironically starting to enjoy the typewriter font. I used to hate it.

>>9687129
I don't like any book on the subject, but the less awful would be Jose and maybe Fasano.
They don't look like math at all. At most they have a shitty introduction to differential geometry without proofs. They are ugly. And fat. And boring.

All classical mechanics books for mathematicians are basically a more rigorous approach of the same topics. The problem here is not that they are aimed for physicists, but that they are books about fucking physics which is much different from math, but you retards dont understand this. Arnold is the best one.

>>9687040
how do I learn how to read an understand those diagrams?

>>9687245
Read some intro to category theory text for example. You don't have to get too far into the text.

>>9687255
I did, but it still doesn't make any sense.

>>9687242
Arnol'd is nice with is geometrical approach, but it is dumb. I see him spending a lot of pages on mathematics which is not mathematics, just too many silly examples. It is a picture book for children. If you know some basic geometry it would take nothing more than 25 pages to prove 'important' classical results of lagrangian/hamiltonian mechanics and give few examples.

>>9687267
Then you can simply give up.

I need some advice, my college has some system where when you enroll, you're allowed to retake 4 classes that you got a D or lower in and replace the grade. Once you graduate though, you can't use these forms anymore.

So now I'm in a situation where if I pass a class I'm in now, I'll graduate and won't be able to use the 2 forms I have left, so I'll have a D and an F in my gpa forever.

BUT, if I fail this class on purpose, I can use one form to replace that F, and my other form to replace my older F.


TL;DR: If I fail a class on purpose, I can raise my gpa by about .5 points. As it stands, my gpa is too shit for grad school, but the .5 boost would put me in the "maybe" range. Should I fail a class on purpose, even if it means going to scool for another year and doing two semesters with one class each?

>>9687272
Why do you need proofs? The results are in other books and are not important for the developement of the concepts in mechanics. What is importabt is the proper definition and picture of the concepts used to model, which a lot of physics books give no importance. The idea of applying math is using the results, however, the problem with physics texts are that they try to reduce everything to linear algebra + calc, without showing what is happening, but if you already know about basic subjects, arnold gives you the proper motivation. Proofs are important if with them you learn how to solve problems, and the yist of each subject, but with classical mechanics you need different set of habilities, except you want to prove shit in symplectic geometry.

>>9687279
If it's less than 3.0 i'd say just finish it, if not, talk to the teacher and ask him for advice (unless he's a shitty teacher) so you don't feel so bad about failing, I'd also recommend spending some time working instead of jumping straight to grad school, since money is nice and it gives you some time to know where you are heading and get ready, best of luck anon.

>>9687302
Failing the class would take me from 2.0 to 2.6 for my 2-year gpa, and my 60-hour gpa from like 1.8 to 2.4.

It doesn't put me over 3.0, but it shifts my bad grades back so if I get good math GRE scores I can make a case for having had a bad start, but turning myself around I think.

I also legitimately have no idea what I'm even supposed to do with just a B.S. in Math. I don't want to be like an accountant.

>>9687309
Sorry I'm dumb, it takes my 2-year gpa from 2.00 to 2.48, and my 60 hour from 2.29 to 2.64, which is dangerously close to 3.0.

>>9687129
You won't find the "mathematician's perspective" on the subject in any mechanics book, since the mathematical perspective is that it's just an application of differential geometry and deserves a chapter or two in a good differential geometry book.

>>9687279
I don't know how it works where you are, but where I am you don't graduate automatically once you meet the requirements. You have to apply for it.
Can you not take an extra year before claiming your degree?

If the course you're talking about is an upper-level course I would be very hesitant to do this, because (to me) somebody with a low GPA because of early courses is still a less scary candidate than somebody who failed measure theory.

>>9687361

I applied for my degree a while ago because I only just realized this was happening today. I guess maybe I could cancel applying for it?

The class I fail now would have its grade completely replaced once I filed this form and took it again. It's just the second real analysis course in the undergrad sequence, I don't think it's anything that big.

My bad grades aren't all early on though, I did bad in a few physics classes I had to take for the "related field" requirements of my degree, doing these two one-class semesters would just be kind of like a push-up bra for my 2-year/60 hour gpa.

>>9687292
>Why do you need proofs?
Get the fuck out retard.

>>9687368
>The class I fail now would have its grade completely replaced
It will completely replace the grade, but I would be rather surprised if they actually expunge the course itself from your transcript. It will probably be sitting there with some kind of X next to it (I have also retaken courses I failed, and this is what my official transcripts look like).

Also, real analysis as about as fundamental a course as you can get (assuming you are applying to math grad schools). I wouldn't say it's not that big.

>>9687395
>missing the point
Do you prove every result from calc when you are reading a differential equations textbooks?

>>9687400
Don't ask stupid questions.

>>9687396
Yeah hell, I dunno. I sent a message to the math advisor but I'm not expecting a lot. I just hope I hear something before my final.

>>9687403
Lol, read any graduate text, you are going to be surprised.

>>9687430
>you are going to be surprised
Doubtful.

>>9687129
>>9687131
>>9687146
>>9687151
>>9687178
>>9687230
>>9687344
Refer to >>>/toy/ for physics discussion threads.

>>9687055
>>9687063
>a proper definition for mathematics
Look into the board known as >>>/lit/ and keep such trash contained exclusively to that place.

>>9688031
What's wrong with having a definition for mathematics?

>>9688035
In what way is this even a response to my post? It doesn't matter whether or not there is anything "wrong" with it when it doesn't belong in these threads. Keep philosophy contained to >>>/lit/.

>>9688043
>It doesn't matter whether or not there is anything "wrong" with it when it doesn't belong in these threads.
Why not?

>>9688050
Read the next sentence.

>mfw /sqt/ has better math discussion than /mg/

>>9688054
>Read the next sentence.
In what way is this even a response to my post?

>>9688055
I wonder why that is.

>proof by induction

>>9688198
Literally this. Induction doesn't necessarily work every single time.

>>9688280
>Induction doesn't necessarily work every single time.
what did he mean by this?

can someone explain what is [math]1_{[0, x]}(|T|)[/math]? i mean how do you apply the indicator function to the operator

Are there pics of anime girls doing mathematics?

>>9688398
Yes.

Proof: You just posted such an Image.

>>9688404
>mathematicians' sense of humor
I want moar

>>9688398
Haven't seen a single one yet. There are drawings though.
>>9688404
Where? She's just writing down some numbers. Seems like economics or engineering.

>>9688405
Its just my autism speaking.

>>9688406
She is looking at examples of the Risch Algorithm.
Engineers write weird letters everywhere and economists write weird words that I don't understand.

>>9688406
>Haven't seen a single one yet. There are drawings though.
pics is commonly used a shortening for the word "picture", the Internet tells me that the definition of picture is the following:

picture
ˈpJktʃə/Submit
noun
1.
a painting or drawing.
"draw a picture of a tree"
synonyms: painting, drawing, sketch, print, canvas, delineation, cartoon, portrait, portrayal, illustration, artist's impression, artwork, depiction, likeness, representation, image, icon
"one of his pictures stood on an easel in the centre of the room"
2.
an impression of something formed from a description.
"a full picture of the disaster had not yet emerged"
synonyms: concept, idea, impression, mental picture, view, (mental) image, vision, visualization, notion, theory, abstraction
"they have a picture of the sort of person the child should be"

>>9688412
>Risch Algorithm
As I expected, nothing to do with mathematics.
>>9688414
I'm using the word "pictures" in a different sense here.

>>9688405
Some of the previous /mg/ threads have such Images, look in the archives.

>>9688406
Post some of those drawings then.

>>9688416
>I'm using the word "pictures" in a different sense here.
Yes, although I doubt it is wise to use words and change their definitions from what they are commonly defined as, that makes communications hared.

>>9688416
>mathematics.
Defined as?

>>9688418
Can you look them for me and post here? Thanks in advance mate.

>>9688420
Someone already posted one. The rest can be found in the same thread that one was from.

>>9688424
>change their definitions
I reject the notion of words having definitions.
>Defined as?
Ask the guys over at >>>/lit/. They specialize in that sort of stuff.

>>9688430
Stop badmouthing /lit/. They have higher IQ than people at /sci/.

>>9688430
>I reject the notion of words having definitions.
I agree that words have precise definitions, after all in my mind reject is a synonym for accept.
´
>Ask the guys over at >>>/lit/. They specialize in that sort of stuff.
They don't know. They circle jerk over some weird books that they ""enjoy"" because they do not understand them.

>>9688432
If the average /sci/ poster has an IQ of over 140 then I will have to kill myself, because most people here are absolute retarded and there is no hope for the world.

>>9688432
>badmouthing /lit/
I don't recall doing anything of the sort. I'm just redirecting him to people with more expertise in word games and defining non-mathematical things.
>>9688433
>They don't know.
Try finding people who know then, and be sure to do that beyond the premises of a thread about math.

>>9688442
>be sure to do that beyond the premises of a thread about math
If a biologist can tell me biology is, then why can't a mathematician tell me what math is?

>>9688043
The philosophy of mathematics should be discussed on both boards.

>>9688445
You never asked about what math is (you don't need a mathematician to tell you that, just pick up any text on the subject). You asked for a definition.
>>9688446
>philosophy of mathematics
This is something beyond mathematics. I guess you can make a separate thread on this board if you can convince enough people that it is somehow science.

>>9688430
>I reject the notion of words having definitions.
I see you had a good time yesterday.

>>9688446
Neil deGrasse Tyson already proved that "Philosophy of Mathematics" and "Philosophy of Science" are futile and only "Philosophers of Mathematics/Science" care about them. The average scientist doesn't give a fuck.

>>9688449
I don't understand the greater context of your post. What are you trying to convey?

>>9688450
>Neil deGrasse Tyson
I chuckled.

>>9688449
Some people here really need girlfriends.

>>9688451
I was implying you got super high yesterday and you're still coming down.

>>9688457
I don't partake in such activities.

Hey fellas, can you answer my thread? Thanks.

>>9688316

>>9688456
If (hypothetical) girlfriends needed """""us""""" that may change, but I am using math to cope with tfw nogf.

>>9688461
Ask on >>>/lit/ this is thread about mathematics, not about books.

>>9688464
Women need men, in the end all women wants to settle down with a good man and build a family.

Also, even though some deny it, all men dream of having kids and teaching their knowledge about the world to their children and see them growing into successful persons.

>>9688470
Then I neither man nor woman.

>>9688474
Yeah, you're problably just a child mentally.

>>9688470
>with a good man
I suspect the Problem lies there.

>Also, even though some deny it, all men dream of having kids and teaching their knowledge about the world to their children and see them growing into successful persons.
Of course and I would want to do that, but some things have to happen before that.

>>9688392
Pointwise.

>>9688456
Take that back right now!

>>9688432
>pic
Although the board ranking seems plausible I doubt the given scores are representative of their respective boards.

>>9688406
How is >>9688398 any different from >>9688418 in the mathematical sense?

>>9688627
Is that a genuine question? Are you not capable of thought?

>>9687292
>Why do you need proofs?
See >>9687395

> What is important is the proper definition and picture of the concepts used to model, which a lot of physics books give no importance.
> the problem with physics texts are that they try to reduce everything to linear algebra + calc
Those books are shittier than shit. Like how they distinguish between velocity and acceleration by looking at the "measure units". It is kindergarten tier, but even children would be disgusted by it.

> Proofs are important if with them you learn how to solve problems
There is no conditional. You can't not understand the proofs, AND examples/exercises are essential part of the subject. They are just written to fill the pages, and even fail to explain the math. It's embarrasing.

>>9688648
>velocity and acceleration
Refer to >>>/toy/ for the physishit threads.

>>9688648
You can go to any calc, ode and differential geometry text for proofs.

>>9688643
It is a genuine question. During my five years in university I have seen some shit. In the end, it is simply just giving meaning to some symbols and then looking at their relations, just like that picture with the anime bitch solving that integral. One field may be more abstract than the other, but not much really changes when one goes from hs to uni.

>>9688650
You think physics is a toy? Poor mathematicians, can't even comprehend anything beyond their abstract numbers.

>>9688650
I will stop after this post, you are right.

>>9688653
Yes, that is the only reasonable thing to do. But I didn't ask for that. I was just claiming that physics books are ugly and fat, because they try to explain math but they don't, and just waste pages. As Arnol'd's book. Hence it would be better a paper of 25 pages with references to real math.

>>9688664
>numbers
There are no ``numbers" in mathematics.

So did Mochijitsu finally prove his Corollary 3.12 which """"""follows from the definitions above"""""""?

>>9688665
Arnold tried to give a pure geometric picture to motivate the modeld. Its a text for graduates, you are suppsed to know the math to some extent. It's like reading his ODE as an introductory piece.

>>9688673
Oh yeah, they're all 'imaginary' right? I forgot mathematicians are literal autists who just 'imagine' numbers

>>9688659
>One field may be more abstract than the other
It's clear that your five years in university weren't spent in a math department if you still think about a piece of math being "more abstract" than another piece of math. And so it's clear that your opinion on the matter is worthless.
The main difference between the two images is that one depicts mathematics and the other doesn't.

>>9688683
>imaginary
Sounds like something physishits would be deeply interested in. Have you tried asking them about this in their threads over at >>>/toy/?

>>9688685
Indeed they were in the math dept. It seems you have no actual reason to call one of them mathematics and the other something else, as you have only tried to attack me instead of my claim.

>>9688692
>Indeed they were in the math dept.
In that case they weren't well spent. Although that's understandable given your situation. Clearly, you have to be mentally challenged if five years weren't enough for you to understand the difference between engineering and something you (allegedly) studied.
>no actual reason
They are exactly the same reasons one wouldn't call biology or philosophy mathematics. Even someone such as yourself should be able to see this quite easily.

>>9688728
I stick to my claim that you have nothing to counter my claim with. Thank you for proving my point.

>>9688731
I've countered your "claim" (if one can even call it that) about three times at this point. You seem to be pretty shit at counting for an engineering student.

>>9688738
Where? I have seen no counter-arguments.

>>9688680
Arnold is shit for physishits. Only Truesdell's approach to classical mechanics can be said to be properly "mathematical", meaning everything is proven from first principles. Directing someone to a differential equations textbooks won't help you with jack shit, because the proofs therein are not concerned with w h y the fuck certain equations and definitions involved in physical phenomena take the forms that they do, all that shit being left unexplained or being dependant on some weird form of begging the question ("""""""""physical intuition""""""""" and whatnot).
Not so with Truesdell's rational mechanics textbooks. He is a good mathematician. He defines the basic structures and makes inferences about their properties, where the knowledge being built just so happens to correspond to some shit in physics too. But you can treat it as 'pure' math.

inb4
>math is not well defined

>>9688676
No.

>>9688740
>Only Truesdell's approach to classical mechanics can be said to be properly "mathematical",
Why would a non-physishit care about "classical mechanics" regardless of the approach?

>>9688692
No proofs = no maths.

>>9688746
For the same reason one would care about say the classification of simple groups.

>>9688739
That's a common issue among people with your disability. Try asking your caretaker for help.

>>9688748
Applying proved results is math. Hs books come with proofs in civilized counties.

>>9688754
Not an argument.

>>9688752
That reason being?

>>9688756
>Applying proved results is math
Only when applied to building more math.
No proofs = no maths.

Listen up, boys. I'm doing an independent study next semester and my professor has left it up to me to choose between commutative algebra and algebraic geometry as the topic. Which of you have researched these topics? Which would be more fun to choose?

>>9688760
And solving integrals is not building more math? What about when one solves textbook problems? Or does some pre-existing proofs on his own?

>>9688759
Not privy to non-mathematicians.
(Kindly fuck off.)

>>9688761
Flip a coin if you can't decide between those two. Really.

>>9688770
>And solving integrals is not building more math?
Depends.
>when one solves textbook problems
Not math.
>does some pre-existing proofs
All proofs are "pre-existing".

>>9688776
If all proofs are pre-existing, then no new math can be done.

>>9688777
Doesn't matter. New is subjective.

(Can we please drop this subject? It's been what 10 months since we've started having "what is math" shitposts?)

>>9688780
Then this post has no value >>9688760

>>9688784
Replace "building" with "discovering".

>>9688771
>Not privy to non-mathematicians.
Did your employers just tell you the name of some result and forgot to brief you on its supposed importance? You should be prepared better next time if you wish to recruit more people into your physishit cult. It's a very poor attempt overall.

>>9688786
Don't change your arguments afterwards. Besides, discovering new things was supposed to be subjective.

>>9688740
>everything is proven from first principles
Have you read any upper level math text? Do you think they actually prove everything from analysis, topology and or algebra? Trusdell sounds interesting, but it seems you don't understand Arnold. Classical mechanics is physics and it is concered with models and results and how do they apply to the physical world. The power of a geometric approach is more than just an unrigorous heuristic, but it let's you make direct conections between abstract concepts and why they are used to model besides it just werks. The study of a system cannot be interpret just with math, math is extremely useful to properly formulate our thoughts, but math doesn't tell you the intuition behind modeling certain system in some way. If you just state that hamiltonian mechanics is contained in symplectic geometry, there is a lot to lose from understanding how you actually propose a hamiltionian on a system. Mechanics can be visualized to some extent so I have to agree (except you start to fuck with statistical mechanics and dynamical systems) it's not that much of a game changer, but it's important because shit like QFT has no clear visualization, and these tecnics are fundamental to understand the physics of it.

I don't fucking understand this obsession with proofs, as if the autism of all mathematicians is so big that they don't accept some result because they see no proof. In proper courses of a particular field, obviously it is important to prove shit, and work with that as these proves give a lot of insight as to how to deal with problems with thay field, but if you are not readily interested in the fundamentals, why is it so hard to quote some book and say, "this is a well known result" if the proof isn't really going to tell you that much. Should we construct Riemann summs on every fucking integral a physicists constructs? No, it's a waste of time.

>>9688740
>But you can treat it as 'pure' math.
I'd rather spend some time studying actual math instead of brainwashing myself into thinking that I'm not studying physics.

>>9688791
>Have you read any upper level math text?
Yes. TL;DR the rest, idc.

>>9688791
Refer to >>9688650

>>9688789
>your employers
I am a NEET.

>>9688791
>physics
>apply to the physical world
see >>>/sci/pg/ and or >>>/toy/physics/.

I need to work with the ring [math] \mathbb{Z}_2 \times \mathbb{Z}_2 [/math] and for computational purposes it would come in handy if it were isomorphic to a subring of [math] \mathbb{Z}_n [/math].

The ring [math] \mathbb{Z}_2 \times \mathbb{Z}_2 [/math] in the standard representation with elements
(0,0), (1,1), a=(1,0), b=(0,1)
has component-wise addition and multiplication and so (0,0)+x=x, (1,1)*x=x, x+x=0 e and then a+b=(1,1), a*a=a, b*b=b, a*b=0, etc.

If I'm not mistaken, I found that I can represent much of it with the set {0,1,3,4} and addition mod 2 and multiplication mod 6, e.g.

3*3 mod 6 = 9 mod 6 = 3
4 mod 6 = 9 mod 6 = 3
3*4 mod 6 = 12 mod 6 = 0

but noting plus 4 mod 2 can be 3, so it doesn't cut it. And indeed, I'd like to embed as subring of the ring Z_n, so the two mods shouldn't be different.

So is this possible? Is [math] \mathbb{Z}_2 \times \mathbb{Z}_2 [/math] the subring of Z_n for some n?

>>9688818
Try asking fellow subhuman physishits over at >>>/toy/.

Hell yeahh, Brazil is now on the Group 5 of the IMU, which is for the most developed countries for mathematical research.

Now we're together with Germany, Canada, China, United States, France, Israel, Italy, Japan, United Kingdom and Russia.

https://impa.br/en_US/page-noticias/brasil-e-promovido-a-elite-da-matematica-mundial/


Only Group 5 masterrace members allowed in this thread.

>>9688818
No there are only two groups of order 4.

>>9688818
If there is a ring homomorphism [math]\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z} \to \mathbb{Z}/n\mathbb{Z}[/math], then [math]n[/math] divides the characteristic of [math]\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}[/math], which is 2. So this forces [math]\mathbb{Z}/n\mathbb{Z}[/math] to be either [math]0[/math] or [math]\mathbb{Z}/2\mathbb{Z}[/math]. Clearly [math]\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}[/math] is not a subring of either of these rings.

>>9688916
I see, very cool, thanks.
For what it's worth, the comment made me look among the 2 by 2 matrices mod 2 and turns out that
a = ((1,0), (1,0))
b = ((0,0), (1,1))
seems to work.

>>9689018
>making your model more complicated

>>9687400
Why would you. You already proved them all reading your calc book

>>9688290
many things cannot be proved by induction

Is there a way to frame an ODE without explicitly setting certain variables to be independent/dependent?

e.g. if I've got a differential equation that gives me a solution of the form [math]y(x) = \pm \sqrt{f(x)}[/math], then my natural tendency would be to want to write that as [math]y^2 = f(x)[/math], which gives you some 1-D manifold on the Cartesian plane. But what can you say about the original ODE in this case? Anything?

>>9689200
Ask in >>>/toy/physics/ or >>>/sci/sqt/.

>>9689200
>knows about manifolds but doesn't knkw basic ode theory
This summs up modern mathematicians quite well.
https://en.m.wikipedia.org/wiki/Exact_differential_equation

what is ring theory?
plz explain, i am a brainlet

>>9689217
Thanks. Yes, I'm dumb.

>>9689234
A field of mathematics that studies the algebraic structures known as rings.

>>9689234
Group theory, but instead of [math] \langle S, * \rangle [/math] its [math] \langle S, +, \cdot , 0 \rangle [/math]

>>9689217
Why would a mathematician need to know "basic ode theory"? Do you expect mathematicians to know every engineering topic?

>Only 5 days until my Calculus I and Algebra I tests.
>Spent all my free time on the internet instead of studying
>Don't want to get low grades in order to get a good academic life in the future as a researcher
>I barely even know anything besides Limits and the basics of derivatives
>In Algebra I I can't prove anything, only solve simple problems

Just how fucked am I, friends?

>>9689117
So you understand the point then.

>>9689294
Stop using the Internet. Disable it if you need to and focus on studying, that helped me at least.

>>9689305
You on the other hand, did not understand the point about proofs at all.

>>9689328
Yes I do, I don't understand exactly what proofs that aren't simple derivations must be exposes in a classical mechanics text

>>9689314
If I do that, do you think I can still get a decent score on the tests? People say the Algebra Professor do easy tests, but the calculus ones have a intermediary difficulty and have no problem involving proofs.

>>9689294
if you are having that much trouble with calculus 1 then i will tell you right now, either give up or change your mindset and start actually studying.

what are some good math/phd related twitter @s?

>>9689393
I will, I will change my life completely from now on, I'll study hard every day and rise to the top. I'll take inspiration from Luffy, Souma and Goku, whose only objective is to surpass all others with pure efforts alone.

>>9689387
>If I do that, do you think I can still get a decent score on the tests?
Only one way to find that out, but if you work hard enough it should be possible.
5 days isn't much time, but if you show some discipline it should be possible.

>>9689399
Who's Luffy and Suoma?

I know Goku, but the portrayal of someone who gets ahead just by trainging, not having to participate in human politics and mind fuckers, is a fable. Nobody wins being a Goku in real life, unless you find someone who likes you and does the thinking for you.

That being said - for as long as you just enjoy doing math for yourself - sure you can just git gud and live in a happy bubble. Not sure if any of the famous mathematicans wasn't driven by fame, though.

>>9689234
The theory behind the lord of the rings.
Kys,
me.

>>9689426
Luffy is a pirate from the East Blue whose dream is to surpass all pirates and become the pirate king.

Souma is a chef whose dream is to one day surpass his father's cooking, but in other to do that he has to first defeat all the top students in Tootsuki Academy (an academy specialized in cooking).

I will follow in their steps and reach the top of mathematics with my efforts alone, I will one day reach the same level of success that Gauss, Newton, Euler, Riemann, Gödel reached. Just wait and see.

>>9689234
What I find suspicious is that you asked about ring theory, even if that exact phrases was never used in the thread. How, from reading people talk about rings, would a brainlet know there's ring theory.

(9689447)
> success that Gauss, Newton, Euler, Riemann, Gödel reached
Find the intruder.

>>9689460
Newton. Everyone else spoke German.

>>9688432
/g/ should be lower...

>>9689399
woah

>>9689460
>Find the intruder.
Riemann. The only mathematician on that list.

>>9689460
Are you suggesting Godel was not on the same level as those other names?

>>9689779
OVER THE LINE

>>9689835
How so? It's the truth.

>>9689902
If Gauss, Euler, Newton and Godel weren't mathematicians, then what the hell were they?

>>9689460
Gödel, because americunts can write the other guys' names but not his.

>>9688450
>black science man says so

>>9689947
>, because americunts can write the other guys' names
But they CAN'T, Gauß is written wrong.

>>9687267
become smarter faggot

If my scatterplot looks like this (points of observation are spread out and far away from the linear fit line), and I'm using two supposedly unrelated variables, does it mean that they are uncorrelated?
Sorry if its a stupid question, I'm retarded.

>>9689234
"how to get married to a rich dude" for women

>>9689934
gods

>>9691043
>two unrelated variables
>line of best fit might as well be the line of worst fit
>literally no trend, completely scattered points
>hurr guys are they uncorrelated?
are you unironically retarded?

>>9691043
You have to formulate a hypothesis test on the slope of the line; construct confidence intervals using bootstrap samples and see whether a slope of zero falls within it, if yes it means that you can't conclude any correlation from your experiment. But if you know from the beginning that the variables are uncorrelated then all this is futile....

>>9691019
They are removing the double-S thing in German, so Gauss is the correct modern spelling.

so i need to put together a
>math related application in C#
for my programming class

what should i make? im a brainlet undergrad so keep it simple pls

>>9691201
Classification of surfaces.

>>9691201
Depends on how much time and effort you're willing to put into it.
If those aren't obstacles to you and you want a good learning experience, try automating one of the constructive proofs of theorems in mathematical logic, e.g.
http://www.math.ku.dk/~asgert/teachingnotes/iml-completenessguide.pdf

How do I find the lowest number of isosceles triangles any other triangel can be cut into?

>>9691201
> C#
> programming
> math
Pick one.

>>9691033
>faggot
Why the homophobia?

>>9691185
>They are removing the double-S thing in German
It still exists and there are many words with have it in them.
There are even words where the ß changes the meaning look at:
Masse (the mass)
Maße (The measures)

Replacing the ss with an ß creates an ambiguous word and not just that, these things are spoken very differently.

>Gauss is the correct modern spelling.
No, that is absolutely false.
The rules of modern German say that the ß still exists and MUST be used if it can be in any way.

His name is Gauß and unless you are writing and the ß doesn't exist it is incorrect to replace the ß with an ss.

>>9691418
>The rules of modern German say that the ß still exists and MUST be used if it can be in any way.
Source for this? Oh right, [math]\not\exists[/math]

>>9691418
>The rules of modern German say that the ß still exists and MUST be used if it can be in any way.
Which dumbaß came up with that rule?

>>9691455
Why do you need a source that German spelling dictates that words must be spelled correctly?
Anyway, here are the rules:
https://www.duden.de/sprachwissen/rechtschreibregeln/doppel-s-und-scharfes-s

>>9691455
It is the correct spelling of the word, why would "spelling correctly" be dumb rule?

The rule LITERALLY just says, spell the word correctly, if you can't use ss.
I do not see why you are surprised by this.

>>9691451
>>9691462
And by the way, by "must be used", I mean must be used if the word is spelled that way.

Okay, but German isn't English, so who the fuck cares???

>>9691462
Not gonna read that because you are unable to even reply properly.

>>9691484
Read: https://www.duden.de/sprachwissen/rechtschreibregeln/doppel-s-und-scharfes-s

Its the rules for using s, ss and ß.
If the ß is not available you can use ss in its place, else you are supposed to spell it correctly.

>>9691486
See >>9691484

>>9691494
I replied properly though.

Nice dodge attempt, but at least now you know hat to spell Gauß.

>>9691497
I already did, and I still know. You on the other hand are new to this site and should just stick to lurking.

>>9691217
divide by the number of sides

>>9691504
>I already did, and I still know.
Why did you debate with me the correct spelling of Gauß, then?

>You on the other hand are new to this site and should just stick to lurking.
Yeah I will. You have probably been here already for nearly a week, maybe someday I can be as much of an oldfag as you are now.
Do you know who moot is? I hear people talking about him, but who is that guy?

>>9691516
I did not debate, debate takes two and you were the only one trying to debate.
>moot
Mod*, please learn how to spell.

>>9691522
>I did not debate
Okay, then lets call it a free lesson from me to you about the usage of the ß in the German language.

>Mod*, please learn how to spell.
Like on reddit?

>>9691525
There was no lesson on that. Only on how some losers think they should come and correct other people's "mistakes" even if such don't exist.
>reddit
Is that where you spend your time?

>>9691530
>There was no lesson on that. Only on how some losers think they should come and correct other people's "mistakes" even if such don't exist.
The claim that "They are removing the double-S thing in German" and "Gauss is the correct modern spelling" are both wrong, I already gave you a source on that.

>>9691530
>Is that where you spend your time?
The walrus beacons at midnigh, right fellow redditor, xD.

>>9691534
Which I did not click since you proved to be a failure incapable of replying to the correct poster. Your ironic reddit posting is simply cringy.

>>9691542
>Which I did not click since you proved to be a failure incapable of replying to the correct poster.
Yes, mistakes happen.

>Your ironic reddit posting is simply cringy.
If I were able to function normally I would be posting on /r/mathematics right now.

>>9691550
You are correct. Mistakes happen, and one of those mistakes was your conception. Some mistakes can still be corrected, though. Please remove yourself from this world as soon as possible.

>>9691554
I am living out of spite to the people who have wanted me to commit suicide.

If I get called a virgin for often enough I might actually find a girlfriend some time.

I also would be posting cute anime girls with every single post I make but sadly my hard drive is a bit fucked up and I don't know why xD.

>>9691033
how? I mean if I really need to, I can manage the faggot part. The smarter part I'm not sure how to do.

>>9691556
Stop watching anime. Really, stop. It is merely a waste of time.

>>9691580
I know and I have stopped watching nearly all anime years ago.
After I realized that it is literally the same few stories over and over again.

But I still am collecting a lot anime reaction pics, people usually get angry when you post them too much.

>>9691585
Are you me? I used to attach them to my posts ironically to piss people off. Especially in these threads.

>>9691588
>Are you me?
Doubtful.

>I used to attach them to my posts ironically to piss people off. Especially in these threads.
Yeah, I do that too. Often I know nothing about these girls except that they are looking smug.

>>9691593
>Often I know nothing about these girls except that they are looking smug.
I did not ask you if you knew anything about them. You crossed your boundaries. This conversation ends here.

>>9691607
Have a nice day/night.

>>9691618
I don't.

>>9691631
I am sorry to hear that.

What is commonly meant by "Have a nice day/night.", is expressing that you *wish* that someone has a good day/night.

>>9691637
>I am sorry to hear that.
Mathematicians use "we", not "I".

>>9691643
>Mathematicians use "we", not "I".
Not in conversations.

Say you have the Diophantine equation [math] x^2+1=2y^n[\math], where [math] n [\math] is odd and [math] \geq 5[\math]. By factoring in [math] \mathbb{Z}[i] [\math], you can show that [math]y[\math] is the sum of two squares, and eventually derive a contradiction by embedding into [math] \mathbb{Q}_2 [\math] and deriving a contradiction from [math] 1\pm ix=i^k(1+i)(1+2(1+i)w)^n [\math] for integers [math]k[\math] and [math]w[\math].
I'm not really seeing the details of these steps, but I'm sure they're fairly obvious. Any takers? The problem is from Cassels - Local Fields

>>9691645
A socially retarded individual like >>9691643 would not know this sadly.

i'm sure i'm shitting the bed and that this is really obvious, but if there are integers [math]x,y[/math] satisfying [math]x^2+1=2y^n[/math] for some odd integer [math]n\geq 5[/math], why does [math]y[/math] have to be the sum of two integer squares?

How to check that this [math]\liminf[/math] is locally uniform in [math]x, v \in \mathbb R^3[/math]?

[math]\liminf_{\varepsilon \sarrow 0} \frac{(x_3 + v_3) \sqrt{ (x_1 + \varepsilon v_1)^2 + (x_2 + \varepsilon v_2)^2 } - x_3 \sqrt{ x_1^2 + x_2^2 }}{\varepsilon}[/math]

>>9691484
Shoulda known better than to come between a German and his rules famalam.

>>9691185
dumb fuck

>>9688031
>Not wanting terminology properly defined.
You mustn't be a mathematician.

>>9688470
>all men dream of having kids
I understand that I'm programmed this way, but such a thought has never consciously crossed my mind. I see my friends and family who have kids and it irks me. I can't relate to kids, I have not idea how to interact with them, and they're really fucking annoying most of the time. Also, I hate having to care for things. I barely even want a gf because then it's someone I'd have to give attention to

>>9691973
I believe you have some kind of autism. There is simply nothing in this world more pure or happy than a child. The smile of a little kid is contagious and enough to make the entire day of a middle-aged man happy. Children are wonderful being exactly because they are unpredictable and we can't interact objectively with them. All men, all decent and worthy men that tries to be winners in life, want to have a family and kids, in order to see them growing and shaping their thoughts and views.

If you don't desire that, then there's something wrong with you.

>Also, I hate having to care for things. I barely even want a gf because then it's someone I'd have to give attention to
You just want to escape from your responsabilities. You, as a man, should be in a constant search for the ideal women, the one who will take care of the house while you work on your mathematical research, the one who will cook for you and the one who will take care of your children. You feel like this a chore rather than a a gift, and that's because you live in a bubble and is afraid to step out of it.

Open up your horizons mate, search for the truth and don't be afraid of responsabilities and human interactions. Take your obligations as a man seriously and, after all that, achieve true happiness.

"And ye shall know the truth, and the truth shall make you free."

>>9691715
Buмp

What are some popular subjects to research on right now ?

>>9692107
Riemann Hypothesis

>>9692107
Jacobi conjecture, 1 proof/month.

>>9692107
How to get a girlfriend.

>>9692285
source?

Solve in [math]\mathbb{R}[/math]:

[math]7x^5 + 8x + 4 = 0[/math]

>>9692299
Shimada Arisu from Girls und Panzer.

>>9692351
Japanese Anime Girls and Mathematics.

Is there a better combination in life, fellas?

>>9692337
https://en.wikipedia.org/wiki/Quintic_function#Solvable_quintics

>>9692373
yes
animeposters and nooses

>>9688855
That's great news, fellow huebro!

>>9692351
how old is she?

>>9692379
Can you solve it for me? Please?

>>9692443
I can but I don't want to.

>>9692451
Please man, I'm begging you, my calculus I test is in 4 days and that's one of the questions of last year's test. I know you have a good heart, mate, please help me with this one friend.

>>9692472
Sorry, I'm too busy researching how to get a girlfriend to do pro bono work right now.

>>9692499
Go fuck yourself then motherfucker piece of shit

>>9692526
Hello Dinesh.

Philosophy major here
Can I do complex analysis if I've never done calculus or real?

>>9692886
No. Why the hell you want to do that?

>>9692902
Why can't I do that ? I have the curiosity. I'm accustomed to math

>>9691713
>i'm sure i'm shitting the bed and that this is really obvious, but if there are integers x,y satisfying x2+1=2yn for some odd integer n≥5, why does y have to be the sum of two integer squares?
Why do you think this must be so?

>>9692107
>What are some popular subjects to research on right now ?
Langlands program

>>9692905
Because in order to understand Complex Analysis you have to understand Calculus. Analysis in general is just the rigorous study of Calculus. If you have no knowledge on it, then you'll understand absolutely nothing in Complex Analysis. Just download any book on CA and see for yourself.

>>9692905
Well yes, but complex, at least all texts I've seen, builds up from real analysis concepts. The complex plane is isomorphic to R^2 so a lot is done with this identification. The notion of the derivative of a complex function is self contained as the complex form a field and you can do division, but shjt like the cauchy rieman equations, and complex integrals are not. Just seems weird to want to jump to a more specific branch without the requirements. Also, if you don't even know calculus I would disagrr that you are accustomed to math.

>>9692919
>>9692917
At my school it has no official pre-reqs. Also some math majors are forced to start with it because they started the math track late and if they held off on complex and waited for real they would have to stay at school an extra year

I guess I have no chance though.

Just found a counterexample to Fermat's Last Theorem, what do I do now?

>>9692965
Make andrew consider sudoku.

>>9692963
You need calc at least, and the details cam be picked up. But without calc ii doubt it.

>>9692965
Now you get some influential friend in the academy, show your papers to them and ask them to publish it and give credits and recommenndations to you. Otherwise, no one will take you seriously and you'll be ignored by practically every serious researcher (see Cantor).

>>9692976
can i pick up enough of what i need in a summer?

Should I take linear algebra online? How does it compare to cal 2 in terms of difficulty?

>>9691715
nigga that looks tedious to check

>>9692337
this looks too hard to find out by hand to be on a calc test if anything. Graphing it gives that it only has one solution in R, and it doesn't look rational

I'm writing my dissertation and I have a stupid punctuation question. So, in every math text, the words are usually written "if and only if". However, the correct punctuation is "if, and only if,". What should I write?

>>9693469
iff

>>9693469
The pause, almost suspense, in the second version of yours feels gay (no homo). There is no need for it, just use 'if and only if'. What are you writing about?

>>9693486
K-theory, masters diss btw

its not that its gay or not, its that if and only if is literally gramatically incorrect

>>9693147
In some countries, calculus, linear algebra and an intro to abstract algebra (groups, rings, fields -- knowledge of which is necessary for linear algebra to a certain extent), are taught in high school. So to answer your question: it's piss easy.

>>9693490
I am not an english grammarfag, but could you explain why it is incorrect? I don't see the necessity for the commas, and as you said that would make almost any math book 'Wrong.'

>>9693467
It has an exact series solution.

>>9693496
"and only if" is a different clause that has to be separated by commas. Im not a grammar nerd either but its only reasonable

>>9693490
>if and only if is literally gramatically incorrect
Nobody cares even if this is true. The comma will just take your readers longer to parse.

>>9692919
How does his lack of knowledge of an engineering topic indicate that he isn't accustomed to math?

>>9693498
Do you have a source for this? I see 'if and only if' used in other contexts, without commas.

>>9687040
That looks like the retarded brother's drawings in that Coen brothers movie about the depressed Jewish professor

What are the best kind of windows to do category theory on?

>>9693610
The silent one in your mind.

>>9693467
The question asked how many solutions there were in that equation and the answer was 1, but I had no idea how to do that.

>>9693610
>writing on glass
Kill yourself my man.

>>9693651
>The question asked how many solutions there were in that equation
Then why didn't you ask that originally? It has at least one real solution because it's an odd degree polynomial, and since its derivative 35x^4 + 8 is strictly positive, there are no more.

>>9693651
Sign changes in the derivative you stupid nigger.

>>9693661
>>9693663
Oooh, I see, I'm sorry, I didn't study much this semester and I'm still learning things, thanks for your help.

>>9689246
and what are rings?

>>9689265
again, brainlet here, i dont understand that

>>9689443
i agree. you should definitely kys

>>9689450
i didnt hear about it in this thread

>>9691715
apply a theorem instead

>>9689294
Same.
I think I'm killing myself this year bros

>>9694092
>what are rings?
You know, like the physical ones Saturn has. They have a natural algebraic structure associated to them. We study this type of concrete stuff in the deep field known as Mathematical Physics.

>>9694162
>Mathematical Physics
This is redundant.

>>9694195
No. My advisor (he studies deep TQFT) disagrees with you and I trust him more than I trust you. So sorry, I have to disagree with you as well.

>>9694242
>I
We see you're not a mathematician.

>>9694158
We're in this together bro, 3 days to my tests and I still can't concentrate, I'm completely fucked. I can only hope now that I ace the next tests.

Ganbatte!!

@9694246
terrible bait

>>9694322
>@9694246

>>9694242
>>9694322
Kill yourself my man.

>>9694699
Why are you telling me to kill myself merely for espousing an empirical worldview?

>>9687245
>>9687267

the diagrams are analogies (isomorphisms between hypergraphs) but drawn out with arrows instead

boy is to girl as hard is to soft
boy:girl::hard:soft

boy->girl
| |
hard -> soft

now replace boy, girl, hard, soft, with "mathematical objects" and don't limit yourself to squares and voila, you can now trick people into thinking you're a genius.

>>9694974
>an empirical worldview
You seem lost. This is the math general.

>>9695094
Yes. This is a general about something deeply empirical, regardless of what thugs like Grothendieck and Deligne would have you believe.

>>9695115
>This is a general about something deeply empirical
Nope.

>>9695094
>math
This is not well-defined.

>>9695122
But Mathematical Physics is an inherently empirical activity. Are you really that delusional so as to deny such basic and self-evident facts? As my advisor likes to say, "Those who cannot know Mathematical Physics cannot know mathematics itself, for they are one manifestation of the same higher entity".

>>9695142
This is the math general faggot. Fuck off.

>>9695133
>>9695142
Kill yourself.

>>9695158
I understand. That is precisely why I'm posting here and not on the other non-empirical boards.

>>9695161
Ah, yet another victim of the Serre-Grothendieck mafia.

>9695165
Go back to China.

>>9695165
Yes, physics is not a subset of math, since physics is empirical while math is analytic, but that quote from your advisor is retarded

>>9695171
>Go back to China.
We've never been.

>>9695188
>physics is not a subset of math
To be precise, physics is a [math]subcategory[/math] of maths.

>>9695200
There's a first time for everything.

>>9695204

I'll suck your dick if you differentiate this equation for p1, help your fellow brainlet please

>>9695209
My IQ is so low that i even forgot to upload my pic, sorry

>>9695212
What have you tried?

>>9695212
You're that dumb currynigger who has an exam in 3(?) days aren't you?

>>9695214
Yes, i think it's (-a1*p1^-2)/b
>>9695215
No, it's my first time here, my class colleagues hate me and i'm white

>>9695218
>my class colleagues hate me and i'm white
Tough luck. I hate amerimutts too. Why don't you go back to the US? This thread is for Europeans only.

>>9695215
Well hello, I'm the guy who has an exam in 3 days and I'm completely fucked. Thanks for remembering me.

>>9695188
Math is physical and empirical in its deeper nature. This is clear even from the writings of the likes of Grothendieck and Serre. Grothendieck himself realized this fact and set out to destroy the ongoing empiricist program in mathematics, this is something he himself admits to doing in "Récoltes et Semailles". Please at least try to understand that. Maybe you can escape the brainwashing you have went through. My advisor was actually a m*thematician before he moved to working on TQFT and an elementary proof of the cobordism hypothesis so he knows a lot about the "other side", so to speak.
If you want to look into physics to develop your innate physical intuitions I suggest the great book "Algebraic Quantum Field Theory: The Cobordism Hypothesis" by Sakurai and Townsend.

>>9695212
-a1 /bp1^2

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

>>9696167
What does this have to do with math?

Is the dragon supposed to represent death? Is CGP grey still trying to shill imortality? Why did you post it? This isn't your blog retard.