/mg/ - Mathematics General

[Anonymous No.11867252]

Bourbaki Edition

Formerly >>11861585

[Anonymous No.11867278]

What is the most general notion of derivative?

We have many concepts extending the standard derivative from calculus. Frechet derivative, Radon Nikodym derivative, exterior derivative, connections, etc etc. Other than "operators satisfying a Leibniz rule" is there a most general kind of derivative comprising all of those?

[Anonymous No.11867292]

>>11867118

Yeah, he introduces them as different concepts and gives an exercise to show they coincide in abelian categories (along with being a cokernel), but the appendix mentions categories where they don't. I actually brought it up because the exercise comes up in the appendix.

Anyways, I'm more of a whiskey man myself. Too bad I won't be able to afford much when I'm a grad student, heh.

[Anonymous No.11867296]

>>11867278
Carlitz derivative

[Anonymous No.11867309]

Would anyone be interested in a reading group on (elementary) complex dynamics?
I was thinking about using Holly Krieger's notes for a Masters' course at Cambridge: https://www.dpmms.cam.ac.uk/~hk439/CDlecturenotes.pdf
They seem fairly short but I'm kind of lacking motivation to start and I think getting a group of people to do this together would be a good idea desu. There's also some problem sheets on her website.

[Anonymous No.11867317]

>>11867309
>Holly Krieger
Why do I recognize this name?

[Anonymous No.11867337]

>>11867317
numberphile, probably

[Anonymous No.11867360]

>>11867278
The derived category.

[Anonymous No.11867453]

Why do people do
[eqn]\frac{16660-16397}{16397} = 1.6\%[/eqn] instead of [eqn]\frac{16660}{16397} -1 = 1.6\%[/eqn]?

The second one seems a lot simpler

[Anonymous No.11867470]

Why do people do
[eqn]\frac{16660-16397}{16397} = 1.6\%[/eqn] instead of [eqn]\frac{16660}{16397} -1 = 1.6\%[/eqn]?

The second one seems a lot simpler
>it's the same equation, just separating out the subtraction of [math]\frac{16397}{16397} and simplifying it to [math]1[/math]
>~33% prone to error since less digits have to be entered
>for the same reason, a subtle error is less likely to occur. If you typo the [math]- 1[/math] as even just [math]- 2[/math], you will quickly notice the error
>looks a lot cleaner

[Anonymous No.11867475]

Why do people do
[math]\frac{16660-16397}{16397} = 1.6\%[/math] instead of [math]\frac{16660}{16397} -1 = 1.6\%[/math]?

The second one seems a lot simpler
>it's the same equation, just separating out the subtraction of [math]\frac{16397}{16397}[/math] and simplifying it to [math]1[/math]
>~33% prone to error since less digits have to be entered
>for the same reason, a subtle error is less likely to occur. If you typo the [math]- 1[/math] as even just [math]- 2[/math], you will quickly notice the error
>looks a lot cleaner

[Anonymous No.11867480]

>>11867453

[Anonymous No.11867494]

>>11867360
This has nothing to do with derivatives

[Anonymous No.11867499]

>>11867292
Yup, that's what I remembered too.
>Too bad I won't be able to afford much when I'm a grad student, heh
Minimal life style otherwise. Have this great art piece to cheer you up on your road to glory.

[Anonymous No.11867518]

>>11867252
>Bourbaki
Don't wanna talk about this guy. This faggot of a didact is one of the reasons why linear algebra and analytical geometry have been divided into separate courses, while they were being lectured as one course before. In fact, with analytical geometry one could understand concepts of linear algebra way better. But Bourbaki just thought: "Oh well, fuck it. LA is enough. So we just put analytical geometry into later semesters". What a fuckwit.

[Anonymous No.11867525]

>>11867252
>Bourbaki
Don't wanna talk about this "collective" of idiots. These faggots of didacts are one of the reasons why linear algebra and analytical geometry have been divided into separate courses, while they were being lectured as one course before. In fact, with analytical geometry and linear algebra together one could understand concepts of linear algebra way better. But they just thought: "Oh well, fuck it. LA is enough. So we just put analytical geometry into later semesters". What a bunch fuckwits.

[Anonymous No.11867572]

>>11867525
Analytical geometry has never existed. There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry. Out with them!

[Anonymous No.11867579]

>>11867278
I'd say
>operators satisfying a Leibniz rule
is already extremely general, no?

I think one could also say something where the Weyl algebra maps into.

[Anonymous No.11867583]

>>11867494
Unbased and not derived category pilled.
What, next are you gonna tell me that the derived functor isn't the functor's derivative?

[Anonymous No.11867603]

Proof that every abelian category has a single element:
Let [math]\alpha : M \rightarrow N[/math] be a morphism in the category. Then, by commutativity, [math]\alpha \circ Id_M = Id_M \circ \alpha[/math], and thus [math]N=M[/math], q.e.d.

[Anonymous No.11867613]

>>11867603
Holy based.

[Anonymous No.11867623]

>>11867603
category trannies on (even higher alert) suicide watch

[Anonymous No.11867646]

>>11867603
Ok I quit, all my knowledge disproved by one post.

[Anonymous No.11867663]

>>11867603
Wait fuck, no please, this can't be right. Someone disprove this.

[Anonymous No.11867678]

>>11867309
i'm interested in dynamical systems in general, but i barely remember anything from complex analysis, i would use this as an opportunity to relearn & review
if you are willing to take it slow (by slow I mean 1 lecture a week) i would be interested

[Anonymous No.11867686]

>>11867678
Get on it.
https://www.amazon.com/gp/product/0486613887/ref=ox_sc_saved_title_3?smid=ATVPDKIKX0DER&psc=1

[Anonymous No.11867696]

>>11867686
i've got exams until 10th july, i'll get on it after then

[Anonymous No.11867782]

>>11867678
I'm also kind of rusty on my complex analysis, but 1 lecture a week, really dude? That's literally like 3 pages of material, and would take 6 months to get through one 80 page pdf.
I'm looking to do all of it this summer and hopefully find the motivation to move on to other math stuff afterwards.

[Anonymous No.11867827]

>>11867782
Considering the amount of pictures and expository text in there 3 pages a day seems like a more plausible pace to attempt, and even that's probably being generous for time.

[Anonymous No.11867852]

>>11867827
Agreed, that sounds better. Does that mean you're willing to participate?

[Anonymous No.11867863]

I thought mandatory lockdown would be good for my math studying but it's a lot harder to not fuck around in my room as opposed to the library// also i miss being able to just have physical access to any b ook i want instead of having to use pdf so gay

[Anonymous No.11867867]

>>11867863
>PDF
NGMI

[Anonymous No.11867894]

>>11867852
I wasn't the guy you were talking to if that's what you thought, I was just making an observation.
I flipped through it because the pretty rainbow fractal pictures are neat but it seems to freely assume familiarity with Riemann surfaces and my complex anal. course didn't really cover any of that so I doubt I would really be able to follow along properly.

[Anonymous No.11867915]

>>11867894
How do I get into Riemannian geometry?

[Anonymous No.11867924]

>>11867894
Ah, I see. I knew you were a different guy since you didn't post anime, but thought you were interested. Oh well.

[Anonymous No.11867928]

>>11867894
It literally stops and gives the definition of a Riemann surface.
>>11867915
Riemann surfaces and Riemannian geometry are different things, in spite of muh Teichmuller space keeps track of complex structures AND hyperbolic metrics lmao.

[Anonymous No.11867942]

Dr. Krieger is cute.

[Anonymous No.11867963]

>>11867928
>It literally stops and gives the definition of a Riemann surface.
And then immediately carpetbombs all the important theorems needed about them without proofs in the next 2 pages.
When there are theorems without proofs on page 3 of a book it's implicit that you're supposed to know how the proof goes.

[Anonymous No.11867970]

>>11867963
The proofs are left as an exercise to the reader.

[Anonymous No.11867973]

>>11867942

>3d women

literally look like this inside

[Anonymous No.11867983]

>>11867973
As opposed to figuratively?

[Anonymous No.11867999]

>>11867963
>it's implicit that you're supposed to know how the proof goes.
No, not really. The proof of uniformization is a pain in the ass, and the rest really isn't that bad.

[Anonymous No.11868005]

>>11867999
And when I say "a pain in the ass", I mean "I don't think you actually see it in the usual one semester Riemann Surfaces course."

[Anonymous No.11868026]

>I love you anon

[Anonymous No.11868027]

>>11867942
She's astoundingly average-looking, her attractiveness is increased because you know she knows more math than you do

[Anonymous No.11868028]

Love Riemann surfaces, lads.

[Anonymous No.11868042]

>>11867973
Maybe if you cope hard enough you'll finally progress to a stage of mental illness where cartoons are a satisfactory replacement for other humans

[Anonymous No.11868045]

[Anonymous No.11868068]

>>11868045
Oh shit mathbros, we got too cocky

[Anonymous No.11868075]

post your last page of notes/scribbles /mg/ (unless ur like gay or smth lol)

[Anonymous No.11868076]

>>11867963
I'm the one who proposed this thing in the first place. I guess I'm kind of familiar with the Cambridge course on Riemann surfaces, there are some notes that Krieger links to. The course definitely only gives the statement of uniformization, and also kinda skims over quite a few other things. Pic related is the syllabus, not even sure all of this is required for complex dynamics.
At the end of the day it's your call though.

[Anonymous No.11868092]

>>11868042

>cartoons

I'm not into that, my ideal woman is just an intelligence with no physical form

[Anonymous No.11868104]

>>11868075

geometers everyone

[Anonymous No.11868106]

>>11867782
oops i mistakenly assumed that 1 chapter = 1 lecture
i would be happy to read the whole pdf over the course of 2 months or so, but not much faster since i've got other math to do as well

[Anonymous No.11868108]

>>11868092
So an e-gf that never sends nudes?

[Anonymous No.11868112]

>>11868106
>since i've got other math to do as well
Do you, though?

[Anonymous No.11868143]

>>11868075
>that much wasted space
pig disgusting

[Anonymous No.11868145]

>>11868112
bro... what are you implying...

[Anonymous No.11868162]

>>11868145
Answer the question.

[Anonymous No.11868174]

>>11868162
yes i do, dumb nigger

[Anonymous No.11868184]

>>11868075
>this is what mathfags mean when they say draw a picture
FUCKING KEK

[Anonymous No.11868185]

>>11868174
Cope.

[Anonymous No.11868186]

>>11868106
I guess 2 months is fine. I would have preferred a bit faster but we'll see how it goes once we actually get started.
I'm thinking of looking at example sheet 0 (basically warmup exercises) tomorrow, we'll see how much interest this generates and I might make a separate thread for it if there's like >3 people.

[Anonymous No.11868207]

>>11868184
kek post yours then nigga
>>11868143
I will never not do this

[Anonymous No.11868213]

>>11868207
>i embarrassed myself online so you have to do the same
No faggot lmao how do you care so little about the way you take notes that you would share that?

[Anonymous No.11868266]

>>11868026
brains can't experience true love, as they are cursed to toil in hormones and genes.

[Anonymous No.11868274]

>>11868075

[Anonymous No.11868282]

I simply cannot work with notebooks. If I don't have access to blank pages I would rather have nothing to write at.

[Anonymous No.11868302]

>>11868282
Silence, zoomer.

[Anonymous No.11868304]

>>11868075

[Anonymous No.11868369]

>>11868274
>quadratic formula numerator backwards
whY? LOL
>>11868282
Get a blank note book :)

[Anonymous No.11868376]

>>11868304
>>11868274
So, no one on /mg/ understands proportionality, shading or perspective? How does this happen with all the geometers on here?

[Anonymous No.11868378]

>>11868274
What's with the cum stain?

[Anonymous No.11868384]

DIVISORS

WHAT

ARE THEY????

[Anonymous No.11868387]

>>11868378
Sometimes I get excited during class.
(It's coffee)

[Anonymous No.11868391]

>>11868384
a is a divisor of b if there exists k such that ak = b

[Anonymous No.11868392]

>>11868384
FUCKIN TENSORS, HOW DO THEY WORK?

[Anonymous No.11868394]

WHY ARE BOOKS SO FUCKING EXPENSIVE FUCK

[Anonymous No.11868399]

>>11868392
KEK

[Anonymous No.11868405]

>>11867863
I hate PDFs as well
And printing books here is so expensive I might as well just buy them

[Anonymous No.11868415]

>>11867863
>>11868405
I wouldn't say I "hate" pdfs. Ebook access is wonderful when you just want to look up one specific thing in a book.
But for reading a whole chapter/book through I need to have a physical copy to sit down with. Thankfully 4chan hasn't shredded my attention span so badly that I can't focus on one thing for an hour, but there's no way I could do it on a computer.

[Anonymous No.11868418]

>>11868415
yes that's what i meant

[Anonymous No.11868421]

>>11868282
What do you write on usually? Straight up printer paper?
>>11868415
I feel kind of the same, but my attention span did get shredded.

[Anonymous No.11868426]

Can anyone help me formalize a notion about permutation groups? Maybe a textbook reference for this?

Basically, starting from the symmetric group [math]S_n[/math], I want to find the smallest subgroup which is able to send every integer to every other integer (from [math]1[/math] to [math]n[/math]). So I suppose something like the subgroup [math]H < S_n[/math] such that [math]\forall i \in [n],[/math] [eqn]H(\{ i \}) = [n].[/eqn] Notation: [math][n] = \{1, \ldots, n \}[/math] and by [math]H(A)[/math] I mean the image of the usual group action of permutations on integers.

I know that the alternating group satisfies this, so my intuitive feeling is that normal subgroups might be the ingredient, but I'm not sure. I also am interested in general [math]n[/math], so the fact that e.g. [math]A_4[/math] is not simple doesn't interest me too much.

[Anonymous No.11868430]

>>11868426
*the image of [math]H[/math] under the usual group action

[Anonymous No.11868432]

Can you tell what is this [math]h(u,v) = ((av+b)cos(u),(av+b)sin(u),v)[/math] without plotting it online

[Anonymous No.11868438]

>>11868426
This image is really comfy.

[Anonymous No.11868440]

>>1186842>I want to find the smallest subgroup which is able to send every integer to every other integer (from 1 to n).
The cyclic group generated by the right shift permutation.

[Anonymous No.11868446]

>>11868426
A group action with one orbit is called transitive.
What you're asking for in this particular case is just one of the cyclic groups C_n generated by any n-cycle in S_n.
By running through powers of an n-cycle you can map any one element anywhere you want, and any group with less than n elements obviously(?) can't work.

[Anonymous No.11868447]

>>11868432
[eqn]h(u,v) = ((av+b)cos(u),(av+b)sin(u),v)[/eqn]

[Anonymous No.11868448]

>>11868432
isnt it just a spiral
>>11868426
and isnt that the notion of a Transitive Group Action

[Anonymous No.11868453]

>>11868448
>bidimensional
>spiral
>>11868447
Set [math]a=1[/math] and [math]b=0[/math].
In other words, a cone, I think.

[Anonymous No.11868462]

>>11868453
*two cones branching out of [math]v = -b/a[/math] in oposite directions

[Anonymous No.11868477]

>>11868453
yeah, but any 1d parameterized input would just be a possibly degenerate spiral

[Anonymous No.11868487]

>>11868448
>>11868446
Cool, thanks, I'll look into transitive subgroups. Seems to be exactly what I want.

[Anonymous No.11868503]

>>11868453
>a cone
yeah you got it right

[Anonymous No.11868527]

>>11868376
>shading
It's a quick sketch dude, it doesn't need fucking lighting

[Anonymous No.11868551]

>>11868421
>but my attention span did get shredded
mine's fucked too but I can still sit and read for an hour or so if I push myself before my ability to focus is totally shot. On a laptop I can barely get through a paragraph before I reflexively tab out to check something

[Anonymous No.11868595]

How deep into algebra do I to be need to start to understand Noether's work?

[Anonymous No.11868596]

>>11868595
like a week

[Anonymous No.11868764]

What prerequisites are there to Lang's Algebra, other than some kind of Intro to Proofs?

[Anonymous No.11868771]

>>11868764
Isn't that book a rather advanced abstract algebra text? Intro to proofs is so essential it shouldn't even be mentioned

[Anonymous No.11868786]

>>11868764
>What prerequisites are there to Lang's Algebra
The entirety of established math.

[Anonymous No.11868789]

>>11868771
I know, I'm thinking in terms of minimum requirements

[Anonymous No.11868801]

>>11868764
Basic axiomatic set theory.

[Anonymous No.11868807]

>>11868764
homotopy type theory

[Anonymous No.11868816]

>>11868807
>>>/g/

[Anonymous No.11868819]

>>11868816
Bold of you to assume I'm not already on there.

[Anonymous No.11868822]

>>11868816
>set theroids seething

[Anonymous No.11868824]

>>11868816
>>>>/g/
>>>/g/

[Anonymous No.11868835]

>>11868824
>>>>>/g/
>>>>/g/
>>>/g/
.
.
.

[Anonymous No.11868903]

>>11868764
I suggest at least a "first course" level of exposure to algebra. A good book for this is Gallian's Contemporary Abstract Algebra

[Anonymous No.11868905]

What's the best book on Category theory for someone just starting undergrad (Calculus)

[Anonymous No.11868912]

>>11868905
Topoi: The Categorical Analysis of Logic (Goldblatt)
But honestly it doesn't make sense for you to learn category theory if you are just starting calculus. If you have some experience with proofs already, Axler's Linear Algebra Done Right or Hubbard&Hubbard's Vector Calculus, Linear Algebra and Differential Forms are both good places to start.

[Anonymous No.11868919]

>>11868912
>But honestly it doesn't make sense for you to learn category theory if you are just starting calculus. If you have some experience with proofs already, Axler's Linear Algebra Done Right or Hubbard&Hubbard's Vector Calculus, Linear Algebra and Differential Forms are both good places to start.
nah

[Anonymous No.11868922]

>>11868919
Based.

[Anonymous No.11868928]

>>11868919
up to you bro. make sure to order hrt pills and a dilator if you have made up your mind

[Anonymous No.11869019]

>>11868905
None. Don't learn category theory until you need it. It's like reading a dictionary of philosophical terms instead of learning philosophy by reading philosophers. Everything will seem unmotivated and abstract. All the examples will be things you've never heard of.
A good intro is through Hatcher's Algebraic Topology, as AT was where category theory was invented. Otherwise you could learn about it from the perspective of algebraic geometry. If you're just starting calculus (lmao @ 'merica) then you don't have the prereqs for either of these subjects however.

[Anonymous No.11869025]

>>11868905
pic related

[Anonymous No.11869031]

>>11868905
>>11868919

[Anonymous No.11869184]

>>11868928
>make sure to order hrt pills and a dilator if you have made up your mind
Don't worry, wayy ahead of you on that

[Anonymous No.11869194]

>>11869184
/sci/ was right again

[Anonymous No.11869231]

>>11868426
The subgroup you're looking for is simply the cyclic group generated by the cycle
(1 2 3 4 ... n)

[Anonymous No.11869524]

>>11868075
all my scribbles are on my chalkboard because i hate pen and paper

[Anonymous No.11869576]

How hard is it to get a post-doc position? Or should I just go into coding (again)?

[Anonymous No.11869703]

Is it worth it to learn all trigonometrical identities and functions?

[Anonymous No.11869706]

>>11869703
it's worth to understand them well enough that you're able to derive them from the unit circle

[Anonymous No.11869783]

>>11868905
https://www.youtube.com/watch?v=hEW42ARKNoE

[Anonymous No.11869864]

>>11868905

[Anonymous No.11869908]

>>11869576
(Disclaimer, only speaking from secondhand experience here) not that much harder if your PhD wasn't total garbo. Pretty much anyone who wants one gets a postdoc. Real professorships are where things start getting fiercely competitive.

[Anonymous No.11869942]

>>11867278
connections win I think, if you have a vector bundle then you can give it a connection but not the other types of derivatives, if that vector bundle is flat then the exterior derivative works as a connection, if your flat vector bundle is a vector space then its the frechet derivative

radon nikodym doesn't really count as a derivative it's just a name for a function you get associated to a measure absolutely cts wrt another.

[Anonymous No.11869950]

>>11867360
kek

[Anonymous No.11869970]

>>11867278
An array of numbers, duh.

[Anonymous No.11869972]

>reading Serre's "Faisceaux Algébriques Cohérents"
Comfy as fuck

[Anonymous No.11869976]

>>11869972
En français?

[Anonymous No.11869983]

>>11869976
Oui.
I don't like translations, I try to avoid them, unless the original text is in some language I have no clue about like japanese or Chinese.

[Anonymous No.11869993]

>>11867252
Lads, I'm going to be blunt, I'm a bit fucking stupid. If I've got a function of 2 variables, and I want to change one of them, let's say from [math]x[/math] to [math]y[/math], so [math]f(x,t)=g(y,t)[/math], but [math]x[/math] has explicit dependence on [math]y[/math] and [math]t[/math], but not the other way around, is the partial derivative with respect to [math]t[/math] the same?

[Anonymous No.11869996]

>>11869993
If A=B then d/dt (A) = d/dt (B)

[Anonymous No.11870000]

>>11869983
Je n'aime pas translations.

[Anonymous No.11870004]

>>11869993
Ok, so [math]\frac{\partial g}{\partial t}=\frac{dg}{dt}[/math]
since [math]y[/math] has no explicit dependence on [math]t[/math] and vice-versa, but since [math]f(x,t)=g(y,t)[/math] you also have [math]\frac{dg}{dt}=\frac{\partial x}{\partial t}\frac{\partial f}{\partial x}+\frac{\partial f}{\partial t}[/math]? Have I misunderstood something here?

[Anonymous No.11870007]

>>11870004
Oops, meant for>>11869996

[Anonymous No.11870009]

>>11870004
You mean the same thing by t on both the RHS and LHS. So you take partial derivative w.r.t. t on both sides and you get the same thing. It's not that hard, dude.

[Anonymous No.11870014]

>>11870009
Why doesn't x being a function of t change this though?

[Anonymous No.11870019]

>>11870014
f(x(y,t), t) = g(y,t)
They're the same function of y and t. Taking partial derivative w.r.t. t gives you the same thing.

[Anonymous No.11870032]

>>11868075
>notes

[Anonymous No.11870038]

>>11869942
Connections aren't really generalizations of derivatives, tho, even with the whole "differentiating a vector along another vector" intuition, they're more along the lines of generalizations of trivializations of vector bundles.

[Anonymous No.11870040]

[math]sum_{x_{k+1}(sum_{u_{k+1}}(p(w_{k+1}|x_k,w_k)=p(w_{k+1}|x_{k+1},u_{k+1})p(x_{k+1},u_{k+1}|x_k,w_k)))=
[/math]

[Anonymous No.11870042]

>>11870004
Remember that f has only an implicit dependence on t through x, not an explicit dependence, so the total derivative of f with respect to t is also the same as the partial derivative with respect to t.

[Anonymous No.11870045]

>>11870004
>>11870042
and with your second formula you are misleading yourself by using f in place of g on the right hand side, so you've tricked yourself into thinking that's why the partial derivative of f also has to transform. Actually you should have (dy/dt)(dg/dy) on the right hand side where you've used f, and then you'd see that the only term that isn't zero is f's partial derivative wrt. t.

[Anonymous No.11870072]

Fields -> vector spaces
Rings -> modules
Groups -> group actions
Am I getting it right?

[Anonymous No.11870077]

>>11870072
https://en.wikipedia.org/wiki/G-module

[Anonymous No.11870098]

>>11870072
>group actions
There's no addition on rotated triangles, tho :P

[Anonymous No.11870115]

>>11870098
Yes, and?

[Anonymous No.11870116]

>>11870072
In a sense yes: Cayley’s theorem tells you that any group is a group of permutations of a set (its underlying set), so the natural thing for groups is to study actions on sets.
Likewise, a unital ring is naturally a ring of endomorphisms of some module (its underlying abelian group) so it is natural to study modules over a ring.
So yes it is probably the most analogous thing. Now the closest idea concretely to that of a module/vector space is probably more that of a linear representation

[Anonymous No.11870124]

>>11870116
Name one (1) mathematician who made a bigger contribution to group theory. I'll wait.

[El Arcón No.11870136]

>>11870124
Tooker showed the the reals aren't an additive group. This was a big misconceptions about the structure of groups for a long time. Not sure if bigger.

[Anonymous No.11870154]

Love Möbius transformations, lads.

[Anonymous No.11870155]

>>11870124
Lagrange, Sylow and Schur.

[Anonymous No.11870163]

>>11870124
This >>11867603 anon, who proved that any two abelian groups are isomorphic, since abelian groups form an abelian category.

[Anonymous No.11870171]

>>11870124
These questions are highly subjective and make no sense. You could count eg. Galois, Abel, Lie or Klein but it depends on what you value

[Anonymous No.11870174]

>>11870124

[Anonymous No.11870279]

is there any logic that nothing can be proved in?

[Anonymous No.11870300]

>Professor, what are some applications of this theorem?

[Anonymous No.11870340]

>>11870279
Yes. It is the obscure field of axiomless logic. Also known as anaxiomatic logic.

[Anonymous No.11870365]

I'm reading the 7 color theorem for toroidal graphs, and it starts with 2e>=3f (e = edges, f= faces) and goes on to say because every face has Atleast 3 edges, but a face can be made through 2 parallel edges.

I've triple checked the definition of toroidal graphs and there's nothing inherent to them being simple graphs, so why doesn't the seven color theorem state "simple toroidal graphs"?

[Anonymous No.11870371]

>>11870300
typically building weapons and computer technologies used to guide and better utilize weapons. fucking retarded whore.

[Anonymous No.11870373]

>>11870371
Thanks doc!

[Anonymous No.11870375]

>>11870371
Cope.

[Anonymous No.11870379]

>>11870371

she's in a applied category theory for computer science elective course

[Anonymous No.11870381]

https://en.wikipedia.org/wiki/Missile_guidance

does this help anyone?

[Anonymous No.11870390]

>>11867278
Well you can always generalize more, but I would say that at the most general level reasonable, derivation is the inverse of anything that could be called continuous summation. This wording requires a bit of imagination, but I think that it's the most intuitively simple way to think about the essence of it.

[Anonymous No.11870391]

>>11867475
I do the second one. Anyone who's ever thought about math for themselves does the second one.

[Anonymous No.11870397]

>proves your pet problem by exhaustion

[Anonymous No.11870400]

>>11868392
It's a matrix but matrixier

[Anonymous No.11870401]

>>11870365
>so why doesn't the seven color theorem state "simple toroidal graphs"?
Vertex-colouring theorems are implicitly about simple graphs since adding loops kills the problem and adding multiple edges doesn't change anything.
Maybe it should technically point out that the graph is simple but it doesn't matter if it's not since you can just delete all your repeated edges before you start.

[Anonymous No.11870404]

>>11867309
why is complex dynamics worth studying ? what was the motivation for this field ?

[Anonymous No.11870411]

>will this be in the exam?

[Anonymous No.11870425]

>>11870365
Graph implicitly stands for "the broadest definition of graph that makes this make sense", anon-chan.

[Anonymous No.11870430]

>>11870425
Also, the coloring problem for a torus graph with a non-contractible loop de loop is just the coloring problem for a closed cyilinder, innit?

[Anonymous No.11870437]

>>11870411
don’t do this!

[Anonymous No.11870443]

>>11870390
how is differential or covariant derivative inverse of continuous summation ?

[Anonymous No.11870448]

Are there still any modern mathematicians who also do research into the philosophy of mathematics?

[Anonymous No.11870454]

>>11870411
as a TA, fuck this question very much. "no" means "I don't have to pay attention now" and "yes" means "I'm gonna ponder about how difficult this is and how long it will take me to learn this instead of trying to understand right now"

[Anonymous No.11870475]

>>11870454
Mate, I recognize you from /r/math!

[Anonymous No.11870478]

>>11870390
>This wording requires a bit of imagination, but I think that it's the most intuitively simple way to think about the essence of it.
actual brainlet who shouldn't be in Math

[Anonymous No.11870483]

>>11870475
do you? I don't post there very often and IIRC I've never posted anything regarding TA stuff

[Anonymous No.11870492]

Bros... how do I become an Algebrachad and beat up the analsissies?

[Anonymous No.11870527]

>>11870492
learn both things

[Anonymous No.11870534]

>>11870483
yeah, the formatting is very redditesque

[Anonymous No.11870536]

>>11870454
>as a TA, fuck this question very much
>weird faggy dichotomizing
I see it now you are definitely from reddit, desu

[Anonymous No.11870546]

My postdoc housemate just recommended me that I stop looking at porn to achieve mathematical enlightenment.
Thoughts?

[Anonymous No.11870549]

>>11870546
Name one successful mathematician who was a coomer.

[Anonymous No.11870550]

>>11870411
As I always say, "Assume that everything that I talk about may appear on the exam."
I also tell my students not to panic about the difficulty given how short exams are. There is only so much you can ask for on a 2 hour exam

[Anonymous No.11870551]

>>11870549
charles ehresmann

[Anonymous No.11870554]

>>11870549
How would one know ? Newton probably was a coomer

[Anonymous No.11870559]

>>11870550
what a dishonest cunt you are

[Anonymous No.11870560]

>>11870483
nigga they are making fun of you

[Anonymous No.11870563]

>>11870549
that would be me

[Anonymous No.11870565]

>https://youtu.be/Rb5Zd_cJxB4?list=PL41FDABC6AA085E78&t=2087

mathematicians literally name shit after pokemons and they expect us to take them seriously?

[Anonymous No.11870576]

>>11870565
Wildburger invented Pokémon, dummy.

[Anonymous No.11870577]

>>11870550
I feel like some subjects are hard to properly make a difficult exam out of. For example, I remember my Riemannian geometry exam was piss easy for the simple fact that asking any proper question that involves more than some simple computation would turn impossible real quick (and also the fact that at least 50% of the content in any differential geometry course is definitions). On the other hand, number theory is extremely easy to make difficult exams out of.

[Anonymous No.11870578]

>Remember guys, there is no such thing as a dumb question! :3

[Anonymous No.11870582]

Do you guys have dover books? Would you mind posting a picture of them?

[Anonymous No.11870584]

>>11870565
>mathematicians literally name shit after pokemons
the fuck are you talking about

[Anonymous No.11870586]

watch the video, it's outright disrespectful

[Anonymous No.11870587]

>>11870586
I did, there's no Pokemon names in it, at least not anywhere near where you linked
which is why I asked what the fuck you're talking about

[Anonymous No.11870590]

>>11870587

[Anonymous No.11870591]

Is there a complete classification of singularities of a variety?

[Anonymous No.11870592]

>>11870559
Let me tell you, I try so hard to get these kids to pass. I will send them solutions to any exercise they want, I answer all of their class questions in tutorial, even about the other classes. The one thing I will not do is give them the test in advance. And given how hard I and the other TA try to make it as easy as possible for these spoiled brats to pass, I really resent being called dishonest about this.

[Anonymous No.11870594]

>Let me tell you, I try so hard to get these kids to pass. I will send them solutions to any exercise they want, I answer all of their class questions in tutorial, even about the other classes. The one thing I will not do is give them the test in advance. And given how hard I and the other TA try to make it as easy as possible for these spoiled brats to pass, I really resent being called dishonest about this.

[Anonymous No.11870599]

>>11870492
Algebrachad? What's an algebrachad? Is that some sort of arab dish? Do you want to become an arab and throw sissies off buildings?

[Anonymous No.11870605]

>>11870411
I go with "I don't know, I haven't written the exam yet"
Which is true anyway.
If you aren't handing out exam sheets that are still warm from the printer you're doing it wrong.

[Anonymous No.11870607]

>>11870000
Personne n'aime les traductions
Also checked

[Anonymous No.11870617]

>>11870577
Well it depends what the approach is. If you want to test a large portion of the class material, then yeah, definitely. But if you just want to see if students can do math, you can just ask some very specific questions that can be solved with the class material and some insight.
I once had an operator algebras exam with a Russian professor. Exam was just 3 questions for three hours and it was the hardest, most fun exam I have ever taken.

[Anonymous No.11870646]

>>11870599
As an algebraist myself, I wish someone would throw me off a building.

[Anonymous No.11870650]

>>11867475
because no one does [math] \frac{16660-16397}{16397} [/math], they do [math]\frac{263}{16397}[/math] because that's always how the information is formatted and given prior to the calculation

[Anonymous No.11870663]

>>11870646
Do you want a sissy to do it?

[Anonymous No.11870668]

>>11870663
No.

[Anonymous No.11870684]

>>11870668
I see, I see.
Algebrachads are an extremist muslim faction that wants to throw sissies of buildings for doing anal. Some algebrachads want to be thrown off buildings due to the profound guilt, but not by sissies, since they believe that this means they won't go to muslim heaven.
This is going to make for a superb article in tomorrow's newspaper, thank you very much.

[Anonymous No.11870689]

>>11870527
You can't if you want to get anywhere.

[Anonymous No.11870722]

What's the difference between analysts and algebraists and why are combinatorialists better than both of them?

[Anonymous No.11870741]

>>11870684
You are most welcome.

[Anonymous No.11870748]

>>11870722
>What's the difference between analysts and algebraists
Analysts deal with objects that don't exist, algebraist deal with objects you wish didn't exist.
>why are combinatorialists better than both of them
Because they're practical and elegant.

[Anonymous No.11870823]

>>11870381

there's a book called "chases and escapes" (or something) that goes into the math behind missile guidance

[Anonymous No.11870898]

>>11867309
If I knew complex analysis i would, but I only took a shitty complex analysis course last semester and forgot it all already
I couldn't explain holomorphic functions if my life depended on it.

[Anonymous No.11870911]

>>11870898
>can't explain what differentiability means after a semester
man that really must've been a shitty course

[Anonymous No.11870967]

>>11870911
thats not quite what i mean, I could write out the limit definition, or the power series definition, but I cant see it in my head
I cant explain it like i can explain algebra shitter shit
I get why conjugation isnt a holomorphism, because [math]\displaystyle \lim \frac{\overline{z+h}-\bar{z}}{h} =\bar{h}/h [/math] gets fucked in the argument as you approach 0
but it feels like im just following the symbols, not like im telling the symbols where to go, i cant see it ahead of time

[Anonymous No.11870990]

>>11870549
Euler

[Anonymous No.11871009]

>>11870967
Conjugation isn't a holomorphism because the differential mapping associated with conjugation is conjugation on the tangent plane, and conjugation doesn't commute with [math]J[/math].

[Anonymous No.11871047]

>>11870967
>>11870898
http://www.maths.lth.se/matematiklu/personal/olofsson/CompHT06.pdf

[Anonymous No.11871061]

>>11871047
thanks anon, I have Gamelins book, but never made it far since Id rather do something else, but I think i should just sit down and do this

[Anonymous No.11871089]

Are there sheaves in number theory?

[Anonymous No.11871112]

>>11870594
I'm taking a sadistic pleasure in failing students. In particular, thots.

[Anonymous No.11871122]

>>11871112
Has anyone offered to suck your dick for a better grade yet?

[Anonymous No.11871125]

>>11871112

very sad, women are queens

[Anonymous No.11871128]

>>11871125
does that include transwomen though?

[Anonymous No.11871130]

>>11871125
Cringe.

[Anonymous No.11871132]

>>11870594
Based.

[Anonymous No.11871135]

>>11871128

if they're cute sure

[Anonymous No.11871137]

>>11871125
Based.

[Anonymous No.11871140]

>>11871089
https://en.wikipedia.org/wiki/Arithmetic_geometry

[Anonymous No.11871145]

>>11871089
https://en.wikipedia.org/wiki/Étale_cohomology

[Anonymous No.11871166]

>>11871140
What's a good introductory book to Arithmetic geometry?
>>11871145
What's the link between étale cohomology and arithmetic? Does it have something to do with the Weil conjectures?

[Anonymous No.11871208]

>arithmetic geometry


STOP DOING MATH

[Anonymous No.11871257]

Best books on getting into axiomatic set theory?

[Anonymous No.11871275]

>>11870722
Analysts are responsible for enabling the discovery and description great majority of scientific achievements and natural phenomena that we enjoy the fruits of today such as literally all of classical mechanics, electrodynamics, statistical physics, continuum mechanics, all of the engineering disciplines. Algebraists are homosexual autists that despise physics and reality, and have slowly eroded the beauty and utility of mathematics over the last century.
>>11870592
You speak like a human cockroach, you speak like a man with no honor, a man of meager endowment, unwilling to own up to the necessity to punish and cull stupidity, yet still so slave minded and in need of validation as a good person that you cling to a false image of being a benevolent guardian to your students when you are in all likelihood a do-nothing, academic weevil, a parasite in most respects, and probably a poor mathematician. I hate you.

[Anonymous No.11871278]

>Analysts are responsible for enabling the discovery and description great majority of scientific achievements and natural phenomena that we enjoy the fruits of today such as literally all of classical mechanics, electrodynamics, statistical physics, continuum mechanics, all of the engineering disciplines.

[Anonymous No.11871284]

>>11871275
shame that analysis cope cant solve Fermat

[Anonymous No.11871285]

I'm going to submit a proof that's just a splitscreen of a 3d animation displaying the concept and the output of the computer program and there's nothing you can do about it. This is the future of mathematics, get over it.

[Anonymous No.11871294]

>>11871285
Your proof will be rejected, you will still never become a mathematician nor be said to do mathematics. Cope until the end of time, you chose to play games with your fag machine instead of creating knowledge.
>>11871284
Don’t care, jump off a bridge.

[Anonymous No.11871302]

>>11871275
>classical mechanics
Symplectic and Poisson Geometry.
>electrodynamics
Differential Geometry.
>statistical physics
Probability theory and symplectic geometry.
>continuum mechanics
Alright, I'll concede that continuum mechanics is analysis.

[Anonymous No.11871309]

>>11871302
How do I into Poisson geometry?

[Anonymous No.11871313]

>>11871309
Read the wikipedia page on Poisson cohomology and pretend you understand the subject.

Alternatively, learn symplectic geometry and pick up Vaisman's book or something.

[Anonymous No.11871318]

>>11871309
grab your geometry and go to the blacksmith with a poisson stone

[Anonymous No.11871319]

>>11871309
keep your boat on the great circles and fish for geodaces

[Anonymous No.11871321]

>>11871313
>wikipedia page on Poisson cohomology
There's one?

[Anonymous No.11871323]

>>11871321
There's a wikipedia page for everything.

[Anonymous No.11871327]

>>11871323
uh not for me
and apparently not for poisson cohomology either

[Anonymous No.11871328]

>>11871321
I've literally just found out that there isn't, which is disappointing.
There is an nLab page, but it's kinda shitty.
I suppose you'll have to just read the wikipedia page for Poisson geometry.

[Anonymous No.11871329]

Proof.

Qed.

[Anonymous No.11871332]

>>11871328
>just read the wikipedia page for Poisson geometry
which doesn't talk about cohomology

[Anonymous No.11871333]

>>11871328
As opposed to figuratively?

[Anonymous No.11871336]

>>11871332
Yes.
I'm not editing in a shitty explanation, go fuck yourself and read Vaisman.
>>11871333
Yes.

[Anonymous No.11871339]

>>11870124
frobenius lagrange. also how about the nigga who done invented group theory, Niels Henrik Abel

[Anonymous No.11871341]

>>11871339
>the nigga who done invented group theory
you mean galois, right?

[Anonymous No.11871348]

>>11870300
> Professor, what are your thoughts on quantum mechanics and partial derivatives?
> Professor, two of a kind is two flocks in a bush

[Anonymous No.11871350]

>>11871341
No.

[Anonymous No.11871352]

>>11871348
No

[Anonymous No.11871354]

>>11871352
oops meant for
>>11871341

[Anonymous No.11871356]

>>11871348

>that CS kid who brings his computer to classes at the mathematics department
>nothing related to the class, just has reddit open and some IDE

[Anonymous No.11871360]

>>11871356
I hate those people too , but one of the guys who did this in my differential geometry class was unironically one of the best students among the undergrads. Also he has a girlfriend.

[Anonymous No.11871362]

>>11871360
How does become ironically one of the best students?

[Anonymous No.11871363]

>>11871362
I don't know, how does become? You tell me.

[Anonymous No.11871367]

>>11871362

You can get good at something Ironically. For example if you study a lot of Kant just to make fun of him at /lit/.

[Anonymous No.11871368]

>>11871362
You intellectually crush your classmates but you get the worst grades in the class because of basic arithmetic.

[Anonymous No.11871369]

>>11871363
It's a secret.

[Anonymous No.11871371]

>>11871368
i haven't had a class that required basic arithmetic (unless you count finding JCF, which admittedly I was bad at) since first semester of first year

[Anonymous No.11871373]

>>11871371

I think he meant basic algebra

[Anonymous No.11871380]

>>11871373
N-word

[Anonymous No.11871395]

>>11871356
>That guy who spent the first two weeks of class reading the textbook 12 hours a day so he could ruin all discussions for the rest of the semester

[Anonymous No.11871400]

>>11871395
heard you talking shit

[Anonymous No.11871406]

>>11871395
>not skimming most of the textbook before the semester starts
N G M I
G
M
I

[Anonymous No.11871409]

>>11871395

Had this happen to me, kid brought up a problem from the appendix to the professor. The look on his face.

[Anonymous No.11871415]

>>11871406
>textbook
NGMI

[Anonymous No.11871419]

>>11871409
The first time I had a class with one of these fuckers (one of my algebra sequence) the prof took to making fun of him every day before he started lecturing
I don't think spergmaster actually understood he was being made fun of though.

[Anonymous No.11871433]

>>11871419

That's good, freshmen need to take some humble beatings else they won't make it to academia without commiting suicide.

[Anonymous No.11871478]

>>11871433
How do we fix the suicide rates in higher academia?

[Anonymous No.11871481]

>>11871478
>fix

[Anonymous No.11871485]

>>11871278
Stay mad pussy

[Anonymous No.11871487]

>>11871481
Yes fix, it should be much higher what should we do?

[Anonymous No.11871489]

>>11871487
Increase the number of tranny PhD's, no other steps are required.

[Anonymous No.11871491]

>>11871489
Based and category theory pilled

[Anonymous No.11871510]

>>11871491
Category theory is tranny repellent.

[Anonymous No.11871517]

>>11871510
Category theory is for repellent trannies

[Anonymous No.11871522]

I don't want to repel the cute T-girls tho

[Anonymous No.11871524]

>>11871522
>>11871510
I simply want them to suffer and then to die. Nothing more, nothing less.

[Anonymous No.11871528]

>>11871524

I want to give them (if cute) a prostate orgasm

[Anonymous No.11871533]

>>11871528
Then I want you to suffer and then to die as well. It's a good thing that HIV infection rates are significantly higher among transexuals than even among ordinary homofaggots.

[Anonymous No.11871534]

>>11871522
your actions are not repellant to a null set anon
this is vacuously true

[Anonymous No.11871540]

>>11871524
>>11871533
Cope.

[Anonymous No.11871550]

>>11871528
good take

[Anonymous No.11871552]

>>11871524
>>11871533
Fag

[Anonymous No.11871553]

>>11871533

I choose to die with empty balls

[Anonymous No.11871559]

>>11871540
Pretending to be a woman, engaging in unsafe and physiologically degenerative sexual practices, suffering high rates of drug abuse, mental illness, pedophilia, STI infection, and ultimately suicide sounds like a terrible existence. I wouldn't wish that on my worst enemy and hoping that these people end up in an early grave is much more compassionate than taking advantage of them for sexual gratification as bisexuals and closet cases are wont to do.

[Anonymous No.11871560]

/mg/ - Mathematics General

[Anonymous No.11871562]

>>11871553
Bro she is soo cute, I'd smash 100% no question

[Anonymous No.11871567]

>>11871560
category theory is mathematics anon

[Anonymous No.11871574]

>>11871567
Incorrect.

[Anonymous No.11871575]

How far in to mathematics do you have to go to attain a basic understanding of physics? I'd like to learn more about physics and the world around me but I'm admittedly not very well studied when it comes to math. So I figured building a solid math foundation would probably be essential before I try to delve into physics and I'm just not sure how far I need to go. Any insight on this would be much appreciated.

[Anonymous No.11871579]

>>11871575
Define 'basic understanding'. If you want to get into Lagrangian mechanics, then you need to know up to at least PDEs.

[Anonymous No.11871584]

>>11871579
>Define 'basic understanding'.
I kind of knew this was coming. I'm honestly not sure. I'm not trying to become a physicist or anything, I just want to know more about how things work. I know that's probably not very helpful, but I don't have a certain goal in mind so it's hard to say.

[Anonymous No.11871597]

>>11871584
Calculus through Vector Calc, basic probability theory, diff eq, linear algebra, trigonometry and basic analytic geometry (think highschool and middle school geometry). You can now understand everything through sophomore physics at a state uni in America.

[Anonymous No.11871602]

>>11871597
Thanks anon, that's really helpful.

[Anonymous No.11871604]

>>11871567
Mathematics is the study of ZFC
Category Theorists work in ZFC+TA, its different

[Anonymous No.11871612]

>>11871604
>Mathematics is the study of ZFC
this might be the dumbest post I have ever seen on these threads

[Anonymous No.11871614]

>>11871602
No problem. Don't forget to check the link in the sticky for textbook recommendations, and good luck anon!

[Anonymous No.11871621]

>>11871612
But is he wrong?

[Anonymous No.11871622]

>>11871614
Not him but isn't the sticky kind of ass?
I guess it's a starting point

[Anonymous No.11871624]

>>11871621
yes you are wrong samefag

[Anonymous No.11871629]

>>11871622
>isn't the sticky kind of ass?
Extremely.

[Anonymous No.11871640]

[Anonymous No.11871651]

>Still talking about recommendations

we solved that already https://www.fireden.net/sci/thread/8903319/

[Anonymous No.11871669]

>>11871640
>Why yes, my kids are name [math]\epsilon[/math] and [math]\delta[/math]. What made it so obvious?

[Anonymous No.11871710]

>>11871257
Enderton

[Anonymous No.11871711]

>>11871651
Are you the guy that spammed that list everywhere

[Anonymous No.11871718]

>>11871710
Cheers, lad.

[Anonymous No.11871727]

>>11871624
that wasnt a fucking samefag, but this is
how is it wrong

[Anonymous No.11871731]

>>11871711

yeah I'm misha verbitsky

[Anonymous No.11871737]

>>11871731
You linked a whole thread. I thought you meant the other list being built there.

[Anonymous No.11871740]

David Mumford browses /sci/.
http://www.dam.brown.edu/people/mumford/blog/2020/Ridiculous.html

[Anonymous No.11871741]

>>11871740
Unironically who?

[Anonymous No.11871743]

>>11871740

he got filtered by kurisu

[Anonymous No.11871745]

>>11871741
just one of the most important algebraic geometers. no one for you to worry about

[Anonymous No.11871747]

>>11871727
>how is it wrong
nobody outside of pure set theory is "studying" ZFC
nobody outside of pure set theory even USES ZFC; go ask any prof in your department who does any kind of regular math to name some ZFC axioms and I guarantee nobody will get over half.

[Anonymous No.11871751]

>>11871727
make sure you know what ZFC is before replying to me

[Anonymous No.11871765]

>>11871740
explain

[Anonymous No.11871786]

>>11871751

[Anonymous No.11871801]

>>11871786

what's the symbology behind empty sets looking like a pussy?

[Anonymous No.11871806]

>>11867572

You know Jean, I've been thinking again about the ordering of the major parts of the text, and I really think that integration ought to be treated before topological vector spaces. What do you think?

[Anonymous No.11871826]

>>11871786
ok, now do the continuum hypothesis

[Anonymous No.11871840]

What are some books on mathematics that could advance my understanding of mathematics? or transition to advanced mathematics in general

[Anonymous No.11871845]

>>11871840
What did he mean by this?

[Anonymous No.11871850]

>>11871840

I'm going the dump the infographic if you keep teasing

[Anonymous No.11871853]

>>11871740
yo mums if you're reading this, what are the solutions to the goat problem

[Anonymous No.11871855]

>>11871840
a course in arithmetic, serre

[Anonymous No.11871860]

>>11871840
https://nrich.maths.org/unipure
start here

[Anonymous No.11871861]

>>11871840
fuchs fomenko

[Anonymous No.11871862]

Sometimes I think I don't want to do research, I just want to learn what's already been discovered. I don't like that I have to skip around full understanding. I'll do research if I know everything I want to know and want to know more.

Now how do I explain this to my supervisor?

[Anonymous No.11871864]

>>11871840
Charles C. Pinter - A Book of Abstract Algebra

[Anonymous No.11871866]

>>11871840
https://venhance.github.io/napkin/Napkin.pdf

[Anonymous No.11871881]

>>11867252
bump limit reached. new thread:
>>11871878

[Anonymous No.11872529]

>>11871850
Yes plssss

[Anonymous No.11872539]

>>11871855
>>11871860
>>11871861
>>11871864
>>11871866
Thank you, thank you.