/mg/ - Mathematics General

[Anonymous No.11889375]

John Tate edition <3
previous thread >>11882271

[Anonymous No.11889399]

first for intuitionist foundationalism

[Anonymous No.11889405]

>>11889375
first for #shutdownSTEM

[Anonymous No.11889488]

>Elliptic curves

[Anonymous No.11889491]

4th for functional analysis and combinatorics

[Anonymous No.11889496]

I have learned by heart and by brain to figure out every trigonometric identities and formulas. Ask me questions for training.

[Anonymous No.11889504]

>>11889496
Let [math]S(x)=\sum_{n=1}^{\infty}\frac{\cos nx}{\cosh n\pi}.[/math] Find [math]\frac{1}{\{1+2S(x)\}^2}+\frac{1}{\{1+2S(ix)\}^2}.[/math]

[Anonymous No.11889524]

>>11889504
>didn't learn infinite sums or hyperbolic functions yet
guess i'm gonna go f myself for now

[Anonymous No.11889525]

>>11889488
You're not him...

[Anonymous No.11889526]

>>11889496
Show that for all odd k,
[math]\sum_{n=1}^{\frac{k-1}{2}} \cos(\frac{2 \pi n}{k}) = -1/2 [/math]

[Anonymous No.11889528]

>>11889504
I know this one. It's [math]\frac{8\pi^3}{\Gamma^4(\frac{1}{4})}.[/math]

[Anonymous No.11889547]

>>11889504
what's the closed form for [math] S(x) [/math]?

[Anonymous No.11889577]

>>11889526
can't make this out

[Anonymous No.11889654]

>going back to school so my shitposts can be of higher quality
other than elliptic curves, what should i look for?

[Anonymous No.11889703]

>>11889654
a way to turn back time to when you were 16

[Anonymous No.11889753]

>>11889491
>functional analysis
Is it worth it to get into free probability theory? I find the concept of non-commutative probability pretty neat.

[Anonymous No.11889767]

>>11889488
>filename not gigachad-universe
Ngmi

[Anonymous No.11889852]

>>11889504
no idea
can you post the solution?

[Anonymous No.11889863]

>>11889852
>>11889528 is actually correct

[Anonymous No.11889894]

for infinitely diff. scalar functions on n variables, d you need the nth derivatives to determine critical points? or just 2nd derivatives

[Anonymous No.11889904]

>>11889863
proof?

[Anonymous No.11889914]

>>11889904
Think.

[Anonymous No.11889920]

Stuck on this exercise.
Suppose that H, a subgroup of G, is the only subgroup with cardinality k. Prove that H is necessarily normal.

[Anonymous No.11889923]

>>11889920
Conjugate groups have the same cardinality

[Anonymous No.11889969]

>>11889904
Technically the guy who posted this was being a smartass because this is really more of an identity for elliptic functions.

The idea is [math]\operatorname{nd}^2(u,\frac{1}{\sqrt{2}})+\operatorname{nd}^2(iu,\frac{1}{\sqrt{2}})=2.[/math] This identity is pretty much down to this relation, using the fact that [math]k_1=\frac{1}{\sqrt{2}}[/math] is a singular value of the elliptic modulus, and when you have these singular values which are typically denoted [math]k=k_n[/math] then you can express [math]K(k)[/math] and so on in terms of the gamma function. A fuckload of their special values are tabulated like this.

So from that first identity, what you then do is write down the Fourier series of dn, which is just

[math]\operatorname{dn}(u,k)=\frac{\pi}{2K}\left(1+2\sum_{n=1}^{\infty}\frac{\cos n\pi u/K}{\cosh n\pi K'/K}\right)[/math]

and then lastly you "remember" (or look up on a table which is what I did) that [math]k_1=\frac{1}{\sqrt{2}}[/math] and [math]K(k_1)=\frac{\Gamma^2(\frac{1}{4})}{4\sqrt{\pi}}[/math] and then you can finish up by setting [math]u=\frac{K(k_1)x}{\pi}[/math] and [math]k=k_1[/math] in the first identity for nd I posted.

Sorry if some of this is a bit unclear, I keep getting connection error and it's hard to see my full post as I'm typing it.

[Anonymous No.11889978]

>>11889969
>in the first identity for nd I posted.
meant in the Fourier series, which you then substitute into the identity for nd

[Anonymous No.11890034]

>>11889753
>why yes, I exclusively study mathematical theories initiated by Romanians, such as free probability theory, how could you tell?

[Anonymous No.11890116]

Found a kitten that was dumped alongside the road and I'm going to take him in, lads. What should I name him? I was thinking Abel or Jacobi.

[Anonymous No.11890151]

>>11890116
Kitty

[Anonymous No.11890177]

>>11890116
Dog.

[Anonymous No.11890185]

>>11890151
>>11890177
These aren't math related.

[Anonymous No.11890192]

>>11890185
Better than giving it a nerdy fag name like Cauchy or some shit.
>>11890116
I vote pussy

[Anonymous No.11890194]

Recommend me good math books that aren't too expensive. Hard mode: not pic related.

[Anonymous No.11890196]

>>11890185
>he doesn't know about the great mathematicians Kitty and Dog, who invented CAT(k) theory
NGMI.

[Anonymous No.11890200]

>>11890194
The GOAT.

[Anonymous No.11890203]

>>11890200
Are there any books like that but for analysis or topology? Like good encyclopedia-like textbooks? I know about Spivak's differential geometry, but I can't think of anything else.

[Anonymous No.11890205]

>>11889375
What are some good problem solving workbooks for math before calculus?

I have AoPS Vol 1 & Vol 2 by Rusczyk already

[Anonymous No.11890213]

>>11890200
I'm talking about actual math books, not textbook. I'm not an undergrad, I've taken abstract algebra a few years ago.

[Anonymous No.11890228]

>>11890116
Doesn't matter, just don't pick a name you would be embarrassed to write in the dedication page of the book you'll write.

[Anonymous No.11890270]

>>11890203
dummit & foote is not really encyclopedia like. analysis now by pedersen is not quite encyclopedic but i think it is what you're looking foar. also stein and shakarchi covers a lot of analysis but it is 4 volumes (like spivaks diff geo)

[Anonymous No.11890296]

>>11890203
simon's 5 volumes on analysis

[Anonymous No.11890301]

>>11890296
>>11890203
A Comprehensive Course in Analysis by Barry Simon

[Anonymous No.11890309]

>>11890203
Dieudonne’s series

[Anonymous No.11890313]

>>11890203
Stitz and Zeager for Precalculus

[Anonymous No.11890315]

>>11889504
Whats a cosign, and the weird E

[Anonymous No.11890339]

[math]Let \ R=Z/12Z \ and \ consider \ the \ subring \ S=\{0,4,8\}. \\1_R = 1 \neq 1_S = 4[/math]

[Anonymous No.11890342]

>>11890339
Yes

[Anonymous No.11890350]

Is escher's analysis I good? I want to revise my analysis, and no, I do not want to read rudin.

[Anonymous No.11890354]

>>11890339
not a subring

[Anonymous No.11890398]

>>11890354
Depends on what's a ring to you, if you aren't a dumbass then yes.

[Anonymous No.11890416]

>>11890116
call him tits
after jacques tits

[Anonymous No.11890418]

>>11890416
https://en.wikipedia.org/wiki/Tits_group

[Anonymous No.11890431]

>>11890116
doroboneko

[Anonymous No.11890440]

>>11890116
It would be best if you show the photo of your
kitten. I would be able to give him something good.

For now, I would say he should be...
Carathéodory

[Anonymous No.11890444]

>>11890116
Catalan

[Anonymous No.11890459]

Nigger hunter
Nigger slayer
Niggerbane
Niggerenslaver
Niggerslaughterer
Niggerhater
Emperor over Niggers
Nigger displacer
Nigger disenfranchiser
Nigger disrespector
Nigger conqueror
Niggers can't do math (NCDM)
There are no great nigger mathematicians (TANGNM)
ThankGodWe'reNotNiggers (TGWNN)
AllNiggersMustDie (ANMD)

[Anonymous No.11890461]

>>11890116
Egory.

[Anonymous No.11890465]

>>11890459
all good names for a pet, especially a cat (aryan)

[Anonymous No.11890466]

Love Euclidean domains, lads.

[Anonymous No.11890468]

>>11890116
Serge Lang

[Anonymous No.11890477]

>>11890116
Topos

[Anonymous No.11890485]

>>11890116
I forgot:

Fagslayer
Fagslaughterer
Fagdragger
Fagexteriminator
Faggotsarepedophiles
Faggotsareevil
Faggotsshoulddie
AIDSisnotReal
sterilizeallfaggots
euthanizeallfaggots
Faggotskinner
FaggotsareresponsibleforAIDS
Faggotsarementallyill
41%
pushtranniesinfrontoftrucks
runovergayswithtrucks
therearenogreatgayscientistsormathematicians
ifyou'regayyouareevilandnothuman

[Anonymous No.11890489]

>>11890485
These are fair

[Anonymous No.11890490]

>>11890485
Wow, I like those names :)

[Anonymous No.11890503]

>mathematicians can't be cha-
https://www.youtube.com/watch?v=dOAWuwbbfwY

[Anonymous No.11890509]

Engineerlet here, I want to fully transition to Control theory, but damn, i'm way behind some of the math, what the hell must I study to fully grasp this proof?

[Anonymous No.11890511]

>>11890503
Who has ever said that? Mathematicians and philosophers, by definition, are the only people who can be chads.

[Anonymous No.11890516]

>>11890509
>control theory
not science or math >>>/g/ >>>/r/eddit >>>/out/

[Anonymous No.11890519]

>>11890516
Control theory is reddit repellent.

[Anonymous No.11890524]

>>11890516
The control theory subreddit is meh, I've found better advice here, but if you don't know shit, you don't need to answer anything, cuck.

[Anonymous No.11890533]

>>11890509
Analysis and differential equations.

[Anonymous No.11890534]

>>11890519
>>11890524
>he can't do math
Sad!

[Anonymous No.11890535]

>>11890509
literally be even remotely competent or literate
alternatively, learn some children's analysis

[Anonymous No.11890542]

>>11890533
Any book on analysis recommendation ?


>>11890535
Thanks you fucking faggot

[Anonymous No.11890543]

>>11890535
>learn some children's analysis
You overestimate *ngineers.

[Anonymous No.11890549]

>>11890542
What is your math background?

[Anonymous No.11890550]

>>11890116
Commodore Hot Dickings

[Anonymous No.11890554]

>>11890549
I know basic calculus, linear algebra and differential equations(though from a modelling of physical systems standpoint).

[Anonymous No.11890560]

>>11890554
>from a modeling of physical systems standpoint
so you don't know anything about differential equations then. have you considered if you're retarded?

[Anonymous No.11890562]

>>11890554
https://www.amazon.com/dp/1493927116

[Anonymous No.11890567]

>>11890560
Lay off dude, you literally haven't given any advice and that's because you don't know shit, spotted the 1st year undergrad trying to feel cool.


>>11890562
Thanks

[Anonymous No.11890577]

I named my cat category theory.

[Anonymous No.11890581]

>>11890567
>you haven't given any advice
Yes. This isn't an advice general, you're off-topic posting and shitting up the thread.

[Anonymous No.11890583]

>>11890560
>TAing for an intro to ODEs class
>Entire class is just 'how to solve [x] diff eq'
Why is this allowed?

[Anonymous No.11890586]

>>11890581
Got what I was looking for anyway so suck my dick and see ya later.

[Anonymous No.11890588]

>>11890583
>why is this allowed
Engineers and (dumb) physicists

[Anonymous No.11890590]

>>11890567
>>11890586
Just a heads up, while that book is both easy to read and fairly rigorous, it's still just an intro to analysis and won't give you the same breadth and depth as something like Rudin; but for someone with little formal mathematical background, it's a great text and should be interesting if you've done the standard calculus sequence because it'll actually go into the formalization of a lot of things that are taken for granted in those classes.

[Anonymous No.11890593]

>>11890586
Congratulations, man. Bet you're not gonna understand a single fucking thing in that book.
FUCK OFF!!!

[Anonymous No.11890598]

>>11890590
can you stop helping the literal self-described redditor? okay thanks.

[Anonymous No.11890601]

>>11890598
There's nothing wrong with helping someone who wants to learn more math.

[Anonymous No.11890603]

>>11890590
Thanks senpai, you've been of great help.


>>11890593
>>11890598
>ss-ss-stop shitting my circle jerk we want to discuss quirky p-p-pet names

[Anonymous No.11890609]

>>11890583
isn't it fucking annoying? qualitative theory of ODE is so beautiful and elegant, especially that of planar nonlinear ODE

[Anonymous No.11890616]

>>11890601
yes, there is, because you introduce the possibility that he will come back and continue bothering us
let him go to fucking /sqt/
>>11890603
>that post
>that picture
you do not belong in this general

[Anonymous No.11890617]

>>11890598
Tip: just give him bad advice. Tell him to read Simon's four volumes back to back or something.

[Anonymous No.11890621]

>>11890609
It is and it's the same with linear algebra. The introductory courses don't actually teach the subject and instead just teach algorithms. It sucks that these courses are pretty much tailor made for engineering majors.

[Anonymous No.11890627]

>>11890617
yes, i do that in many places on /sci/ if people don't ask their dumb questions in the fucking stupid questions thread, it's there for a reason
why do you think i have this picture saved

[Anonymous No.11890637]

>>11890627
>Galois theory, Lie groups, Dedekind cuts
>High school
Never fails to make me laugh.

[Anonymous No.11890640]

>>11890637
You could teach high schoolers about Dedekind cuts, tho.

[Anonymous No.11890645]

>>11890640
Not rigorously.

[Anonymous No.11890651]

>>11890645
>dude it's a subset of the rationals such that, if it contains a number, it also contains every number to its left in the number line
I dunno bro, sounds pretty doable if you aren't teaching underfed african child soldiers.

[Anonymous No.11890654]

>>11890651
you could just say blacks

[Anonymous No.11890665]

>>11890654
Nigerians are the most successful ethnic group in America.

[Anonymous No.11890682]

>>11890665
Are we forgetting a certain 2% of the population?

[Anonymous No.11890692]

[Anonymous No.11890695]

[Anonymous No.11890700]

>>11890692
Kek

[Anonymous No.11890707]

Am I a brainlet if I'm good at problem solving but have trouble with proofs?

[Anonymous No.11890710]

>>11890707
Give an example of a proof that's giving you trouble.

[Anonymous No.11890712]

>>11890710
I just in general have a lot of trouble with proofs. I can understand them but there isn't that moment of eureka that allows me to feel the proof if that makes any sense. I have trouble separating complete proofs from incomplete ones.

[Anonymous No.11890718]

>>11890712
Just read more proofs bro. You'll become better at them!

[Anonymous No.11890721]

>>11890712
First thing you should always do is write down definitions. Especially for easier proofs, something will usually pop out and then it's a matter of rearranging terms with justification.

[Anonymous No.11890725]

>>11890718
>>11890721
It's not even that I can't solve the problems in my classes, I can get through them. I just don't see the beauty. I see beauty in mathematics but proofs just seem dull to me.

[Anonymous No.11890728]

What are some good texts/resources for differential equations from an analysis point of view?

[Anonymous No.11890731]

>>11890725
Read a proof. Wait a while. Try to write down the proof from memory. See how it compares with the proof in the book. Repeat.

[Anonymous No.11890732]

>>11890725
I take it you haven't gotten to Galois theory or complex analysis yet?

[Anonymous No.11890734]

>>11890731
I guess I should probably try going back and giving it another shot

>>11890732
I've done a little bit of complex analysis. I enjoyed it but the proof portions were rough

[Anonymous No.11890754]

>>11890418
yeah that guy
he also had a hand in the tits-ping-pong lemma

[Anonymous No.11890758]

>>11890192
Naming a cat Cauchy would be bad, yes.
However, naming a cat after the american pronounciation of Cauchy, "Coochie", is the definitive math cat name. First, it pays homage to a great mathematician. Second, it kind of sounds like a dog name. Third, coochie is slang for pussy, which fits in with the cat theme. Fourth and final, it makes the french seethe.
I see no reason not to do it.

[Anonymous No.11890761]

>>11890758
Without Cauchy, there's no complex analysis.

[Anonymous No.11890763]

>>11890718
how do you like my swimming

[Anonymous No.11890804]

>>11890763

[Anonymous No.11890817]

>>11890725
You aren't understanding them then, the idea codified behind the proof. Look for other books until something clicks I guess, or rest for a while and go back to it.

[Anonymous No.11890839]

Is information theory math?

[Anonymous No.11890851]

>>11889969
There's something magical about knowing your way around the transcendental functions like that

[Anonymous No.11890853]

>>11890444
Underrated and checked

[Anonymous No.11890858]

>>11890817
I get them mechanically, but not in an elegant way

[Anonymous No.11890862]

>>11890725
>. I see beauty in mathematics but proofs just seem dull to me.
Mathematics IS proofs -- you're just sexually attracted to calculators.

[Anonymous No.11890865]

>>11890862
I rarely use actual numbers, I just like unfolding statements like oragami

[Anonymous No.11890880]

[Anonymous No.11890881]

>>11890758
>sounding like a retard to own the french

[Anonymous No.11890885]

>>11890865
>I just like unfolding statements like oragami
That is just being a fancy calculator.

[Anonymous No.11890886]

>>11890862

[Anonymous No.11890887]

>>11890881
That's the whole English language.

[Anonymous No.11890894]

>>11890886
[eqn]\mathbb{CRINGE}[/eqn]

[Anonymous No.11890896]

>>11890886

[Anonymous No.11890897]

>>11890885
Maybe you're right, but I love doing it. I love problem solving

[Anonymous No.11890903]

>>11890886
Based.

[Anonymous No.11890906]

>>11890897
>I love problem solving
No Problem which can be trivially solved by a computer is interesting.

Proofs are problem solving by the way, mathematicians are interested in problem solving, the problems are questions about mathematical objects, the answers are proof.

E.g. how many prime numbers are there? That is a problem. The answer is the proof that there are indeed an infinite amount of prime numbers.

[Anonymous No.11890909]

>>11890906
Again, maybe you're right, but what's so bad about me enjoying it?

[Anonymous No.11890913]

>>11890903
>>11890886
Well, proofs *are* important. A mathematics without proofs is basically impossible to think about, but at the same time I also think that his main point is correct.
Proofs are not the end all be all to understand concepts, often geometric intuition is generated from imagination, rather than just reading proofs.

Just imagine a differential geometry text where the usual terminology is replaced with arbitrary terms and without images. It would be the most idiotic and dull theory in existence, full of seemingly arbitrary definitions and considerations!

[Anonymous No.11890914]

>>11890906
>No Problem which can be trivially solved by a computer is interesting.
[math]\int _{-\infty} ^{+\infty}exp(-x^2)dx=\sqrt\pi [/math] is an interesting problem with a clever solution using polar coordinates.

[Anonymous No.11890915]

>>11890909
I truly do not care whether you enjoy puzzle solving, but you will not see any mathematical beauty without looking at proofs.

[Anonymous No.11890922]

>>11890914
And it can not be trivially solved on a computer.
I doubt that any CAS is advanced enough to solves this without having the identity being part of an identities database, in which the computer solves nothing and just repeats facts.

[Anonymous No.11890929]

Friendly remember avoid begin undergrad category theorist

[Anonymous No.11890932]

>>11890929
I have a lot of trouble believing any of these narcissistic types can actually produce anything. They seem so preoccupied with themselves that I doubt that they have any time to spend actually being productive.

[Anonymous No.11890934]

If [math]\mathbb{Z}_m \times \mathbb{Z}_n[/math] is cyclic, does it always follow that [math]\mathbb{Z}_m \times \mathbb{Z}_n \cong \mathbb{Z}_{mn}[/math]?

[Anonymous No.11890935]

>>11890929
>transitioning makes you smarter
That's it, cisbros. We've officially lost. I kneel to my transexual overlords.

[Anonymous No.11890941]

>>11890934
The first part implies that m and n are coprime, so yes.

[Anonymous No.11890942]

>>11890934
> doesn’t even know the fundamental theorem of finite abelian groups

[Anonymous No.11890943]

>>11890886
>Understanding isn't something separate from the proof. Rather, the individual analyzes the phenomenom, elaborates possible explanations for its truthfulness or falsity, and these suggestions crystallize as a proof, the perfect explanation that asserts itself as truly explaining by its result, its capacity to prove. An explanation that can't prove is hot air.

[Anonymous No.11890945]

>>11890934
if a group is cyclic and has mn elements, then it's Z_mn

[Anonymous No.11890949]

>>11890935
>overlords
Overladies.

[Anonymous No.11890951]

>>11890942
I guess I do now.

[Anonymous No.11890953]

>>11890116
Epsilon minus one

[Anonymous No.11890957]

>>11890942
>appealing the fundamental theorem of finite abelian groups to justify that a cyclic group with mn elements is a cyclic group with mn elements

[Anonymous No.11890960]

>>11890929
>Didn't even take calculus 1 until I was 21

[Anonymous No.11890967]

>>11890929
Why is doing Algebra still legal?

When will society be able to admit the harm it does to it's practitioners?

[Anonymous No.11890973]

>>11890941
>>11890942
You're overthinking it!
>>11890945
Best answer.

[Anonymous No.11890975]

>>11890967
>Algebra was a mistak-

[Anonymous No.11890976]

>>11890975
e

[Anonymous No.11890998]

The only good proofs are primarily picture-based with anecdotes.

[Anonymous No.11891006]

>>11890929
I don't see how what they are saying has anything to do with being trans, why do they emphasize that in the sentence?

[Anonymous No.11891011]

>>11890886
Traditional japanese mathematics is/was trash and never reached a serious level! Hardy said something about how the Greeks were the first people whose mathematicians rose above the level of "clever schoolboys." Japanese people didn't advance past the level of clever schoolboy until the 20th century ! Ching Chong!

[Anonymous No.11891013]

>>11891006
Being a sexual degenerate is the essence of their being

[Anonymous No.11891019]

>>11891011
>What is Itô calculus

[Anonymous No.11891024]

>>11891019
>until the 20th century
>posts work of a guy who wasn't even born until the 20th century
what's the relevance here?

[Anonymous No.11891025]

>>11890943
who

[Anonymous No.11891026]

>>11891019
>Ito calculus
Read my post again weaboo!

[Anonymous No.11891028]

>>11891024
>>11891026
https://en.wikipedia.org/wiki/Seki_Takakazu

[Anonymous No.11891032]

>>11891028
would have been less embarrassing if you had just started with Seki Kowa

[Anonymous No.11891033]

>>11891011
>Hardy said something about how the Greeks were the first people whose mathematicians rose above the level of "clever schoolboys."
Hardy was a retard and got BTFO by Chad Control theorists, but he is correct here. If you ever read Euclids elements you will see how much it has inspired the last two thousand years of mathematics.

[Anonymous No.11891034]

>>11891028
Where's the innovation?
>>11891033
Just looked it up and apparently Hardy attributed that notion to Littlewood (although he agrees with it). It's kinda rich to call Hardy a retard though!

[Anonymous No.11891039]

>>11891034
Takakazu discovered the importance of the determinant independently and before Leibniz.

[Anonymous No.11891042]

>>11891034
>It's kinda rich to call Hardy a retard though!
OH NO NO YOU CAN NOT USE MATHEMATICS TO SOLVE REAL WORLD PROBLEMS! HOW DARE THOSE FILTHY PEOPLE DEFILE MY PURE WAIFU MATHEMATICS!

[Anonymous No.11891043]

>>11891042
Yes, and?

[Anonymous No.11891046]

>>11891039
Are you a hardcore weeb or an actual Japanese ultra-nationalist?

[Anonymous No.11891048]

>>11891042
The goal of maths is maths itself.

[Anonymous No.11891050]

>>11891046
>Are you a hardcore weeb

[Anonymous No.11891052]

>>11891043
That is a retarded take on mathematics.
Thankfully he got totally BTFO.

>>11891048
Mathematics has no goal. It just is.

[Anonymous No.11891056]

>>11891039
Nope! He treated the determinant like a gooky anime spell; the determinant was not used for serious mathematics until the 19th century!
>>11891042
Hardy never said this! Read "A Mathematician's Apology"!
>>11891050
I like anime too but you can't let that love delude you into thinking that Jap guy deserves to shit on the mathematics heritage!

[Anonymous No.11891057]

>>11891025
No one in particular.

[Anonymous No.11891058]

>>11891046
are you that polish or whatever anime tranny or some other cringelord?

[Anonymous No.11891061]

Sure is math in here

[Anonymous No.11891062]

>>11891056
>Hardy never said this!
Indeed, this was just me being hyperbolic.

>Read "A Mathematician's Apology"!
No thanks. I am not a cuck who feels the need to apologize.

>>11891058
No, neither am I polish, nor am I deeply into anime nor am I questioning my gender identity.

[Anonymous No.11891065]

>>11891061
Always has been

[Anonymous No.11891067]

>>11891056
>but you can't let that love delude you into thinking that Jap guy deserves to shit on the mathematics heritage!
Yes he can. I am sure that it is the same guy who unironically believes that Japanese are flawless human beings with super human moral who literally can do not wrong.

We had that discussion a few months back...

[Anonymous No.11891068]

>>11891062
ok i would have wanted ask how his/her phd is going

[Anonymous No.11891070]

>>11891056
not every single sentence has to end with an exclamation mark, you know

[Anonymous No.11891072]

>>11891070
Not him! But it is better than no punctuation at all!

[Anonymous No.11891075]

>>11891062
Your loss pal, it's a great essay. Also that's not what he means by apology!
>>11891067
I didn't know this. Origato!
>>11891070
Sorry, I'm just excited for my date next week!
>>11891072
Origato!

[Anonymous No.11891076]

>>11891056
>He treated the determinant like a gooky anime spell
And that is somehow wrong?

[Anonymous No.11891077]

>>11891056
>gooky anime spell

[Anonymous No.11891079]

>>11889405
STEM has been shut down long enough.

[Anonymous No.11891087]

>>11891056
>>11891075
jesus christ
please kill yourself

[Anonymous No.11891088]

>>11891075
>Your loss pal, it's a great essay. Also that's not what he means by apology!
Hmm. I might tomorrow!

[Anonymous No.11891095]

Ok my niggers I need to broaden my horizon in terms of actual research. I thought about stochastic PDEs, any expert here who can give me a qrd on the current state of research?

[Anonymous No.11891099]

>>11891095
>n*ggers
Why the racism?

[Anonymous No.11891102]

>>11891095
Why not Lie theory and its applications to PDEs?

[Anonymous No.11891103]

>>11891052
>It just is.
Why would then one pursue mathematics if it already exists? Every action has an end and thus every action has a goal which is that end, for if it had no end, then it has no reason to be pursued.

[Anonymous No.11891104]

>>11891099
>racism
Why the anti-white propaganda?

[Anonymous No.11891107]

>>11891103
>Why would then one pursue mathematics if it already exists?
Mathematics is not created by mathematics, but by mathematicians.
Mathematicians pursue mathematics for a huge variety of reasons, some of them intrinsic to mathematics itself, but others external.

[Anonymous No.11891109]

>>11891107
no

[Anonymous No.11891116]

>>11891102
I worked through Olvers book some time ago. Variational calculus and in particular Euler-Lagrange equations are really nice and I'm trying to understand h-principle stuff for that as well. Which is really difficult stuff. It is however a tad too close to what I have been working on in the past, so I thought about some related topic (PDEs) but with probability/measure theory because I never really worked with that.

[Anonymous No.11891144]

>>11890116
Yes, definitely Carathéodory.

[Anonymous No.11891160]

Is Munkres still the the de facto topology book or do you guys recommend something else?

[Anonymous No.11891161]

good night /mg/

[Anonymous No.11891168]

>>11891161
Night, lad.

[Anonymous No.11891179]

>>11891160
It's still the standard choice for general-purpose intro to topology. Honestly it's basically still the _only_ choice for that, IMO; there are lots of options for higher-level books that focus on algebraic topology, or for little baby topology courses that barely make it to the fundamental group, but for the course structure of "basics of general topology followed by basics of algebraic topology" there are very few viable alternatives to Munkres even today.

[Anonymous No.11891193]

>>11891179
>there are very few viable alternatives to Munkres even today.
How'd he do it?

[Anonymous No.11891213]

>In dimensions 1, 2, 3, any pair of homeomorphic smooth manifolds are diffeomorphic. In dimension 4 or greater, examples of homeomorphic but not diffeomorphic pairs have been found. The first such example was constructed by John Milnor in dimension 7.
ok seriously FUCK GEOMETRY, going beyond 3 dimensions was a mistake

[Anonymous No.11891217]

>>11891213
I find it more surprising that dimensions 2 and 3 are still so restrictive desu.

[Anonymous No.11891220]

>>11891213
https://en.wikipedia.org/wiki/Seven-dimensional_cross_product

[Anonymous No.11891228]

>>11890851
>theres something magical about having memorized some relations and being able to search a table
Okay.

[Anonymous No.11891243]

>>11891213
I never understood the perception that topology is somehow supposed to be the "intuitive" part of math. Topology has more bizarre bullshit per capita than any other part of mathematics.

[Anonymous No.11891244]

>>11890509
dude this shit should be easy as fuck even for a fucking engineer

[Anonymous No.11891253]

>>11891213
>FUCK GEOMETRY
t. little babby who can only hande easy and well behaved objects.

[Anonymous No.11891259]

Is a proof an array of numbers?

[Anonymous No.11891263]

>>11891259
a proof is an array of letters, and letters are numbers hence the answer to your question is yes.

[Anonymous No.11891266]

>>11891259
viewed as the binary of a TeX file, yes

[Anonymous No.11891284]

>>11891160
>>11891179
https://pi.math.cornell.edu/~hatcher/Other/topologybooks.pdf
This may be of interest (although I don't like Hatcher's AT at all)

[Anonymous No.11891366]

>>11890116
cauchy
>>11890192
fuck you

[Anonymous No.11891406]

>>11890758
>Be me
>Study at a french university
>In baby analysis class introducing Cauchy sequences
>Accidentally say Couch-y during the lab
>Only my friend hears
>Never live it down
>friend is close with prof, he changes his mind on a recommendation
>The disability center calls me
>mfw

[Anonymous No.11891414]

>>11891406
It's Kō-shē.

[Anonymous No.11891419]

>>11891406
Please tell me you made this up, this shit genuinely gets me concerned.

[Anonymous No.11891439]

>>11891406
I thought Europeans all learned analysis in 7th grade
has /sci/ been lying to me again?

[Anonymous No.11891490]

>>11891439
Why would anyone do that, go and lie on the internet?

[Anonymous No.11891599]

What are the properties of ]0,1[?

[Anonymous No.11891600]

>>11891179
If you speak German, a great alternative would be "Mengentheoretische Topologie" by Querenburg.

[Anonymous No.11891602]

>>11891439
100% true except for France, Grothendieks ghost of algebraic insanity still haunts them so analysis and geometric intuition is forbidden by law.

[Anonymous No.11891603]

>>11891600
Je ne parle pas l'allemand.

[Anonymous No.11891611]

>>11891599
Using ][ for open intervals is the single worst atrocity Bourbaki ever committed against mathematics

[Anonymous No.11891618]

>>11891611
What's the second worst?

[Anonymous No.11891628]

>>11891618
The books.

[Anonymous No.11891632]

Is there some guide for the absolute bare minimum of mathematical logic/set theory someone who studies geometry/analysis/topology/combinatorics should know?

[Anonymous No.11891636]

>>11891048

So it's just mathsturbation

[Anonymous No.11891647]

>>11891632
How familiar are you with working within the framework of ZFC?

[Anonymous No.11891654]

>>11891632
Yes
here it is

[Anonymous No.11891658]

>>11891628
Id say that
The second worst thing theyve done is the first book
The third worst is the the second, etc

>>11891632
>who studies geometry/analysis/topology/combinatorics
you mean someone who studies math but avoids the simplifications allowed by using algebra?

[Anonymous No.11891662]

>>11891647
I can usually tell whether or not something needs choice or not by looking, and I consider myself to be a reasonable hand at abusing Zorn's lemma and choice. Don't think I've ever used well ordering on a proof tho.
That's pretty much it, I couldn't actually list you the axioms off the top of my head.
>>11891654
Kek.

[Anonymous No.11891665]

>>11891632
Set theory up to AOC at most

[Anonymous No.11891732]

Can someone explain hyperbolic geometry?
I did a module in it this year and from what I've read online, we were taught it directly as the hyperboloid model in Minkowski space
Is this the proper way of learning it? Whenever I was looking for resources for assignments, I couldn't see many connections between hyperbolic geometry and the terms we were using (like lorentzian dot/cross product)

[Anonymous No.11891748]

>>11891732
If you want a proper and most general answer, try studying Sharpe's "Differential Geometry". iirc the preface should give you a good idea.

[Anonymous No.11891753]

>>11891732
>Is this the proper way of learning it?
It's irrelevant because all the models are isometric (obviously, otherwise they wouldn't be models).
You usually learn stuff in the Poincaré upper half plane or the Klein disk model tho.

[Anonymous No.11891796]

Name a more important figure in the development of topology, I'll wait.

[Anonymous No.11891801]

>>11891796
Pereleman for acutally proving his shit

[Anonymous No.11891804]

>>11891796
Whoever created the donut

[Anonymous No.11891814]

>>11890881
The french sound retarded to anger me 24/7, can't I do the same on occasion?

[Anonymous No.11891850]

>>11889504
What course is this for? Calc II? I may be able to help if you provide further detail.

[Anonymous No.11891896]

>>11891814
sorry to break this to you anon but you might have the 'tiseauxms

[Anonymous No.11891930]

>>11891228
Yeah, the special functions have incredible properties and I do think it's a shame how many mathematicians nowadays have no idea what to do with them.
I do personally think there was quite a bit of beauty in seeing that series posted earlier evaluated like that, but I suppose some prefer category theory too so there's no accounting for taste.

[Anonymous No.11891935]

https://drive.google.com/file/d/1-9fqbg_MJBCdjvvPY5HzXkWfmSQJzHMm/view?usp=sharing

solving for pokemon red

[Anonymous No.11891936]

>>11891263
>>11891266

[Anonymous No.11891955]

>>11891796
Hausdorff and Kolmogorov.

[Anonymous No.11891960]

>>11891662
>I couldn't actually list you the axioms off the top of my head.
Don't worry, pretty much no working mathematician needs to.

[Anonymous No.11892045]

You are given a $30-60-90$ triangle $ABC$. Point $C$ is joined to $M$, which is $AB$ midpoint ($C$ is right angle). Can you find sin $A$ and cos $B$ without drawing additional lines?You are given a $30-60-90$ triangle $ABC$. Point $C$ is joined to $M$, which is $AB$ midpoint ($C$ is right angle). Can you find sin $A$ and cos $B$ without drawing additional lines?

[Anonymous No.11892052]

>>11892045
>$

[Anonymous No.11892064]

>>11891603
You guys need to take care of the immigrant problem. Theyre ruining your country.

[Anonymous No.11892066]

>>11892045
Cringe and texletpilled.

[Anonymous No.11892126]

>>11892064
How would you know?

[Anonymous No.11892139]

>>11892126
Went to France last year.

[Anonymous No.11892147]

okay anons. I'm going to uni and apparently on compsci there will be a lot of heavy math for first two years. how od I become math genius so I can flex my brain muscles in front of retards? (how do I stop being a retard?)

[Anonymous No.11892167]

do I just go to khan acedemy and learn math?

[Anonymous No.11892206]

>>11892167
If you haven't mastered all the topics there already, sure.

[Anonymous No.11892235]

>>11891109
Lol

[Anonymous No.11892238]

>>11892064
Literally the same in Germany...

[Anonymous No.11892294]

>>11891602
There's a joke that goes like: a French 2th grader is asked what is 1+2. His answer: 2+1 because addition is commutative.

[Anonymous No.11892296]

guys... the ghosts of past courses are assaulting me...
before i'm gone... i want to tell you... learn everything properly and don't stop studying unless you understand the topic completely...

[Anonymous No.11892462]

>>11891801
lmao
>>11891955
good choices but nah

[Anonymous No.11892499]

>>11891732
What exactly do you want explained?

[Anonymous No.11892675]

>>11891801
You realize the Poincare conjecture is just one of the dozens and dozens of things Poincare came up with, right?

[Anonymous No.11892690]

>>11892147
Hmmm... First you go to r/mathematics, then you never come back here again and leave us the fuck alone.

[Anonymous No.11892699]

>>11892294
What's e + pi?

[Anonymous No.11892709]

>>11892675
Name a dozen.
Also, you can't use the half plane and disk model, since they've already been mentioned in the thread.
You also can't use Poincaré recurrence, because it's a meme.
IIRC Poincaré proved the conjecture for n=2 (maybe it was someone else, but I do recall the result being old), and if that's the case, you can't name that either.

[Anonymous No.11892728]

>>11891850
the solution was already posted >>11889528
>>11889969 and it's definitely not a calc II problem lmao

[Anonymous No.11892736]

>>11892709
Poincaré–Bendixson theorem
Poincaré–Birkhoff theorem
Poincaré–Birkhoff–Witt theorem
Poincaré complex
Poincaré duality
Poincaré–Einstein synchronization
Poincaré group
Poincaré homology sphere
Poincaré–Hopf theorem
Poincaré inequality
Poincaré–Lelong equation
Poincaré lemma
Poincaré–Lindstedt method
Poincaré map
Poincaré plot

[Anonymous No.11892747]

>>11892736
>he actually named a dozen things
I'm impressed but not surprised.

[Anonymous No.11892770]

What the fuck does this cartoon mean, /mg/?
More importantly, what does it say about us?

[Anonymous No.11892772]

>>11892709
I'll be honest, I (the guy you responded to) couldn't have done it, but this guy >>11892736 really came through in the clutch.

[Anonymous No.11892775]

>>11892770
what could possibly make you care about this

[Anonymous No.11892783]

>>11892770
I remember when /lit/ was wondering why known leftist Gayatri Spivak was there until they realized it was the calculus book

[Anonymous No.11892786]

>>11892775
Simple curiosity.
>>11892783
lol

[Anonymous No.11892788]

>>11892783
>he thinks it's the calculus book

[Anonymous No.11892793]

>>11892788
It's the Diff Geo book isn't it?

[Anonymous No.11892799]

Daily reminder to stop using proofs by contradiction.

[Anonymous No.11892803]

>>11892799
Why should I?

[Anonymous No.11892807]

>>11892788
>>11892793
It is the calc book, I don't have the image showing it but brain couch guy recommended it at one point along with all the other books there

[Anonymous No.11893002]

>>11892799
Proofs by contradiction are fine as long as you aren't one of those subhumans who phrases all their contrapositives as contradictions.

[Anonymous No.11893004]

What would be the best place to start learning math again? The place I am coming from would be viewed as a non-nigger coming from a inner city school but just slightly less niggered cause it's in the south.

[Anonymous No.11893023]

>>11892799
>"Suppose X doesn't exist"
>constructs X
>"We have reached a contradiction, therefore our original assumption of non-existence was false and X with the desired properties indeed does exist."

[Anonymous No.11893025]

>>11893004
Homological algebra, you little butt boy.

[Anonymous No.11893030]

>>11893004

[Anonymous No.11893038]

>>11893023

[Anonymous No.11893040]

>>11893023
Some of the smartest people I know do this.

[Anonymous No.11893046]

>>11889375
Fucking hell, just sit the whole day, then the next, and next month and a whole year, maybe in 10 years time brain will come up with something. It doesn't matter. What life, while other people have to go to work.

[Anonymous No.11893050]

Does anyone else feel like real math is not that fun?

The only classes I have actual fun doing (as in the math is intrinsically fun) are things like Knot Theory and Graph Theory and Group Theory.

But all the math that I need for my future is like Functional Analysis, Operator Theory, PDEs, ...etc. Honestly I find it all very boring. In some sense I guess, I prefer to work with this stuff than doing some spreadsheet in excel for business, but it's still quite dull.
The only interesting aspect of my research is the applications. I get to actually contribute something and help people in other fields.

Does anyone else feel like this?

[Anonymous No.11893054]

>>11893023
top kek
didn't expect to laugh out loud in fucking /mg/

[Anonymous No.11893065]

>>11893050
Where did you get this dumbass idea that the only "real" mathematics is analysis?

[Anonymous No.11893069]

>>11893023
Sometimes you actually use the hypothesis of non-existence in the construction tho.

[Anonymous No.11893078]

>>11893065
That is not what I wanted to say.
More like, analysis (and stochastic) are the biggest research areas and the ones who are most involved in cool shit.

Fields like Group Theory and do have applications too but usually there is not much opportunity there and applications are often far fetched too.

[Anonymous No.11893083]

>>11893023
I do this and I always feel like an idiot when I realise what I have just done.

[Anonymous No.11893088]

>>11893023
Hey fuck you too buddy, I don't know the future nor plan things ahead.

[Anonymous No.11893089]

>>11893004
Dumb racist.

[Anonymous No.11893092]

>>11893050
>>11893078
for me, analysis is the fun kind of math and algebra / combinatorics are the slog

[Anonymous No.11893095]

>>11893078
>but usually there is not much opportunity there and applications
Cryptography has a lot of opportunity, though.

[Anonymous No.11893097]

>>11893069
I would enjoy seeing an actual example of somebody explicitly constructing an object using the property of not existing.

[Anonymous No.11893102]

>>11893023
>suppose [math]|x - x_0| < \epsilon[/math]
>half an hour of inequalities
>then [math]|f(x)-f(x_0)| < disgusting ~ constant \times \epsilon[/math]
>"Bro I'm not redoing the whole proof with [math]\epsilon / disgusting ~ constant[/math] to get an isolated delta at the end, go fuck yourself."

[Anonymous No.11893103]

>>11893092
>algebra / combinatorics are the slog
You mean measure theory.

[Anonymous No.11893109]

>>11893103
No, combinatorics sound about right.

[Anonymous No.11893111]

>>11893103
Is measure theory the most universally disliked course/topic in mathematics? Even gay foundations nonsense has its fans but I've literally never met somebody who actually liked measure theory.

[Anonymous No.11893113]

>>11893109
Sounds like you need to get into Ramsey theory.

[Anonymous No.11893114]

>>11893103
I don't mean measure theory. I like measure theory, it's fun. Especially measure theoretic dynamics.

[Anonymous No.11893118]

>>11893113
That one's cool, the cool member of the family, let's not associate with with combinatorics.

[Anonymous No.11893122]

>>11893097
I'm thinking you might be able to rephrase the Weierstrass minima and maxima proof so that it does that.
That is, if there's no minima, you can find a sequence of [math]x_n[/math] such that [math]f(x_{n+1}) < f(x_n)[/math], and then one of those sequences needs to converge to an infima (by sequential compactness and continuity).

[Anonymous No.11893125]

>>11893111
What the fuck? Are you hanging around the undergrads and the autistic algebraic geometry grad students?
Measure theory is beautiful because it is perfectly intuitive on the surface, but has so much depth and pathology underneath. It's one of the easiest ways to grasp the consequences of Choice. It's got such wonderfully tenuous connections with topology, so many things are so close yet so far in ways which greatly enrich mathematical study (see topological groups with haar measure, for example). It's a wonderful wonderful toolkit for fascinating functional analysis, dynamics, and geometry. Don't even get me started on Ergodic theory, that stuff is truly exquisite.

[Anonymous No.11893128]

>>11893122
Clever.

[Anonymous No.11893132]

>>11893125
>it's beautiful because it's pathological
autism

[Anonymous No.11893134]

>>11893069
give example pls, genuine interest

[Anonymous No.11893136]

>my favorite type of mathematics is when you compute disgusting integrals using stupid tricks which cannot be generalized and don't understand any form of structure behind what you're doing

[Anonymous No.11893144]

>>11893136
Name three (3) people who have said this.

[Anonymous No.11893145]

>>11893136
>i am unable to come up with this, so i'll call it "stupid trick"
cracks me up everytime, thank you for the good laugh sir

[Anonymous No.11893149]

>>11893144
Every engineer/physics major ever
>>11893145
Computing stuff isn't math.

[Anonymous No.11893154]

>>11893149
>Computing stuff isn't math.
This but unironically.

[Anonymous No.11893155]

>>11893136
Based.

[Anonymous No.11893158]

>Computing stuff isn't math.

[Anonymous No.11893162]

>>11893092
can you explain your mindset?
what is fun about analysis?

[Anonymous No.11893167]

>Computing stuff isn't math.

[Anonymous No.11893168]

>>11893136
this but unironically

[Anonymous No.11893176]

>>11893168
this but ironically

[Anonymous No.11893177]

bros...

[Anonymous No.11893181]

nu
>>11893127

[Anonymous No.11893187]

Looks like I made a few ANALysis fags seethe with my pertinent comment again...

[Anonymous No.11893190]

>>11893187
based

[Anonymous No.11893191]

>>11893187
anal cysts on suicide watch

[Anonymous No.11893222]

>>11892499
>>11891753
What is the "true" way of showing it, like spherical geometry is exactly the sphere in R^3
Where does the name hyperbolic come from anyway? The hyperboloid model?
I'm vaguely aware of how the whole plane can't be embedded in R^3, but is it ever useful to restrict yourself to some finite subset of the plane that we can embed?

>>11891748
I'll check it out. I've seen people mentioning "Riemannian" geometries, should I look there next? Would it be accessible to an undergrad?

[Anonymous No.11893285]

>>11893222
>What is the "true" way of showing it, like spherical geometry is exactly the sphere in R^3
That's really not how it works.
>I've seen people mentioning "Riemannian" geometries, should I look there next? Would it be accessible to an undergrad?
You need to understand topology and differential geometry for Riemannian.

[Anonymous No.11893300]

>>11893128
>>11893122
It's not clever. The function f(x)=x^2 has a minimum and you can still find a sequence x_n such that f(x_n+1)< f(x_n). Saying the phrase "sequential compactness and continuity" doesn't magically make it a proof.

[Anonymous No.11893306]

>>11893285
What do you mean by topology?
I did a module on normed spaces, metric spaces, and topological spaces

[Anonymous No.11893372]

>>11893222
you need to study differential geometry, Lie groups and homogenous spaces in particular. there's a long way ahead of you

[Anonymous No.11893404]

>>11892139
touristy areas are always worse

[Anonymous No.11893577]

>>11889375
Unrelated serious questions:
I'm doing control and identification on real world sensor data - I take long sequences of data, tensor product the vector to itself to get a matrix, and then I try to take the inverse of that matrix.

because its real world data, sometimes the determinant is big, sometimes its small and sometimes its very small - enough to fuck up any attempt at an inverse matrix. yet there's nothing inherently singular about the process generating the matrix.

Is there some technique to get some approx equivalent version of an inverse from an almost singular matrix? Something involving approximation/ linear nonlinear programming?

[Anonymous No.11894198]

>>11893023
I see no issue with this and will gladly continue to do it

[Anonymous No.11894399]

>>11893577
The entire field of regularization basically exists to solve this kind of problem.
Do this: https://en.wikipedia.org/wiki/Tikhonov_regularization

[Anonymous No.11894824]

>>11894399
>https://en.wikipedia.org/wiki/Tikhonov_regularization
Thanks!