/mg/ = /math/ general

[Anonymous No.9026306]

infantile (cartoon) jokes edition

did you read any interesting problems, theorems, proofs, textbooks, or papers recently?
what is the most erotic math you have ever encountered?
what are you studying this summer?

[Anonymous No.9026508]

Since none of the previous problems got solved I'm going to repost them:
1. >>9023709 (simple but tedious; linear algebra)
2. >>9023767 (simple but requires an advanced background; category theory)
3. >>9023781 (simple but there's a catch; arithmetic)

And adding two more to the list since the other anon who used to post problems seems to be MIA:
4. Let [math] 3 \leq p < n [/math] be natural numbers.
What is the maximum area of a [math]p[/math]-gon inscribed in a regular [math]n[/math]-gon (of a given area)? (harder than it reads, but tedious after you figure out the key aspects; analytic geometry)
5. Let [math] \mathcal{M} = \left\{ M \in {\mathbb{R}}^{n \times m} \mid MM^T = I_m \right\} [/math]. Prove that [math] \mathcal{M} [/math] is a manifold. What is its dimension? (simple but tedious; differential geometry)

Pick your poison! (Feel free to ask if you need any hints or clarifications on how to swallow it.)

[Anonymous No.9026584]

How is that transition going /mg/?

[Anonymous No.9026586]

>>9026508
>[math]\mathbb{R}[/math]
No such thing.

[Anonymous No.9026616]

>>9026508
is the max area p-gon an (n-1)-gon where you connect two adjacent vertices of the regular n-gon?

[Anonymous No.9026639]

>>9026306
I want to read math research articles, but I don't know where I should start. So far, I have read papers on niche statistical methods in GIS and Wildberger's "A Rational Approach to Trigonometry." Would any of you be able to recommend a good starting point? A reputable journal or an accessible research topic would be all I need. I am 75% done with a BS in math, if that helps.

[Anonymous No.9026644]

>>9026306
So the pure braid group representation [math]\theta: P_n\rightarrow A_n[/math] given by [eqn]\theta(\gamma) = 1 + \sum_{m=0}^{\infty}\int_\gamma \omega^m[/eqn] can be used to create a symplectic form [math]\Omega = \nabla\hat{\theta}[/math] where [math]\hat{\theta}: Q_n \rightarrow A_n[/math] is the generalization to paths on the configuration space [math]\mathcal{Q}_n(\mathbb{C})[/math], which gives a representation of the full braid group [math]Q_n = P_n/S_n[/math]. If the connection [math]\omega[/math] is flat, then [eqn] \Omega = \nabla\hat{\theta}(\gamma) = \sum_m d\int_\gamma \omega^m = \sum_m \int_{t_1<\dots<t_m}dt_1d\dots dt_m d\nabla(\gamma^*(\omega))^m = \sum_m \int_{t_1<\dots<t_m}dt_1\dots dt_m\sum_{i=1}^{m}\gamma^*\omega(t_1)\dots [\nabla,\gamma^*]\omega(t_i)\dots \gamma^*\omega(t_m) \\
\quad = \sum_m \sum_{i\leq m} \int_\gamma \left(\nabla - \gamma^*\nabla(\gamma^{-1})^*\right)|_{\text{i-th power}}\omega^m = 0,[/eqn]
where the simply conencted-ness of the universal cover [math]\mathcal{R}_n[/math] of the configuration space, which is just n copies of the halfplane [math]H_+[/math] glued together along their boundaries, is used. This would imply that [math]\hat{\theta} = \nabla \phi[/math] by Poincare lemma.
Now if the connection isn't flat such that [math]\nabla \omega = \alpha[/math], then
[eqn]\Omega = \sum_m \sum_{i\leq m} \int_\gamma \omega \dots \alpha \dots \omega,[/eqn]
where [math]\alpha[/math] appears at the i-th position.
Not sure what this entails but it's interesting.

[Anonymous No.9026673]

>>9026644
I have no idea what any of this means.

[Anonymous No.9026686]

>>9026644
There are a few typos there; in the middle of the first equation it should be:
[eqn]\sum_m \nabla \int_\gamma \omega^m = \sum_m \int_{t_1<\dots<t_m}dt_1\dots dt_m \nabla (\gamma^*(\omega))^m.[/eqn]
>>9026673
Until I can find a physical interpretation for what that means (my intuition tells me that it's related to non-Abelian statistics a la AB effect) I don't understand it either.

[Anonymous No.9026691]

>>9026686
What do all these characters and equations represent? What is their function? What are they supposed to be?

[Anonymous No.9026698]

>>9026616
The problem is about the maximum possible area of a [math]p[/math]-gon for a given [math] p [/math], fixed.
But to answer you question, if [math] p = n-1 [/math], yes, that is the inscribed [math]p[/math]-gon with maximal area (and the one with the greatest area for all values of [math]p[/math] but that's trivial). Also, [math]what[/math] is that area (as a function of the area of the [math]n[/math]-gon)?
Prove it and generalise it for other values of [math]p[/math]. You're going in the right direction.

[Anonymous No.9026705]

>>9026584
90% of the content in this infographic is pseudoscience.

[Anonymous No.9026712]

>>9026691
[math]A_n[/math] is a formal series Lie algebra generated by indeterminants [math]X^{ij}[/math] modulo some relations, and [math]P_n[/math] is the pure braid group, i.e. the group of actions that braids n particles together such that the initial and final configurations the same. [math]\theta[/math] uses the KZ monodromy [math]\omega[/math] (which gives rise to a conformal field theory) to define a representation of [math]P_n[/math] with values in [math]A_n[/math], and this is useful for finding holonomies of the field theory with connection [math]\nabla = d + \omega[/math] (just take the exp).
Holonomies are important because it tells us the particle statistics of the theory, namely how our wavefunction transforms [math]\psi \rightarrow e^{-i\int_\gamma A} \psi[/math] under [math]P_n[/math], and this is directly linked to the Aharonov-Bohm effect. It is also important in constructing a gauge theory equivalent to the CFT due to the equivalence shown here https://arxiv.org/abs/1504.02401..
The symplectic form obtained from the holonomy [math]\exp\left(-i\int_\gamma \theta\right) = \exp\left(-i\int_B \Omega\right)[/math] where [math]\partial B = \gamma[/math] can also tell us quantization conditions that govern the CFT via the first integrality condition.
The rest are just calculations based on these.

[Anonymous No.9026720]

>>9026712
So this is the mathematics behind how particles interact with each other? Are these equations even set in stone? If so how do we know that they are?

[Anonymous No.9026722]

>>9026644
fuck, I hope I will get good at differential geometry one day. what is the non-meme book where I can learn this stuff?

[Anonymous No.9026734]

>>9026698
is it A*(1 - 4 (1 - p/n) sin^2(180/n))?, where A is the are of the regular n-gon?

[Anonymous No.9026739]

>>9026720
The mathematics itself is set in stone, as shown by Artin who characterized the pure braid group [math]B_n = \pi_1(\mathcal{Q}_n(\mathbb{R}^2))[/math] and other mathematicians that followed who generalized it to higher dimensions and other manifolds. The connection of this concept to particle statistics in physics arises from the observation of the quantum Hall effect and the Laughlin variational wavefunction that describes it, which is a wavefunction that transforms exactly like how I described above under [math]P_n[/math]. (((Jacak))) has a good article on this https://arxiv.org/abs/cond-mat/0308530 if you'd want to check it out.
If you're more interested about the more preliminary stuff regarding CFTs and geometric quantization I recommend the books by Kohno and Woodhouse, respectively. The results established there are my starting points; all I'm doing here is taking concepts from one place and apply it to another to see if there's anything new popping up in the context of physics.

[Anonymous No.9026753]

>>9026705
Then as a well versed scientist, how would you advise someone young to become very cute and feminine?

[Anonymous No.9026762]

>>9026739
Is there any new studies or equations being found that apply to physics????
How do we know if the content being found inside mathematics is applicable or if it even works???

[Anonymous No.9026765]

>>9026762
>How do we know if the content being found inside mathematics is applicable or if it even works???
How do we know if it does or doesn't if we don't try?!?!?!?!?!

[Anonymous No.9026770]

>>9026765
If it doesn't apply, then what's the point of creating the mathematics in the first place?

[Anonymous No.9026772]

>>9026770
I don't know ask the mathematicians rofl

[Anonymous No.9026782]

>>9026508
On problem (5), it should be [math] M^TM = I_m [/math]. Also, [math] m \leq n [/math].
>>9026734
Nope.

[Anonymous No.9026883]

>>9026639
You start in an area that interests you. There is no guideline to reading original papers. You're on your own.

https://zbmath.org/

[Anonymous No.9026924]

>>9026722
Lee's Manifolds.

[Anonymous No.9026934]

>>9026924
I would avoid Lee's. If you are looking to get good, try Tu's book for a good introduction (if needed), otherwise if you are already acquainted, try Spivak's volumes to improve.

[Anonymous No.9027028]

I'm having a fleeting moment of appreciation of the notation in linear algebra.

Let [math]\alpha = (e_1,\dots,e_n)[/math] be an ordered basis (organized in a formal row vector) of some vector space [math]V[/math]. Denote [math](u)_{\alpha}[/math] the column vector of coordinates of [math]u \in V[/math] with respect to [math]\alpha[/math]. Let [math]\beta[/math] be another basis and denote [math](id)_{\beta \alpha}[/math] the transition matrix from [math]\alpha[/math] to [math]\beta[/math]. Considering FORMAL matrix multiplication, all of the following identities and manipulations are valid (notice how the greek letters connect)

[math]u = \alpha \,(u)_{\alpha}[/math]

[math](u)_{\beta} = (id)_{\beta \alpha} \, (u)_{\alpha}[/math]

[math]\beta \, (id)_{\beta \alpha} = \alpha[/math]

[math]u = \alpha \, (u)_{\alpha} = \beta \, (id)_{\beta \alpha} \, (u)_{\alpha} = \beta \, (u)_{\beta} = u[/math]

Furthemore, denote [math]\alpha^* = (f^1,\dots,f^n)^T[/math] the ordered dual basis of [math]\alpha[/math], but organized into a column vector, let's also agree that for a form [math]\omega[/math] we will write [math](\omega)_{\alpha^*}[/math] for the ROW (!!) vector of coordinates with respect to [math]\alpha^*[/math]. Once again considering formal matrix multiplication, we have

[math]\omega(u) = (\omega)_{\alpha^*} \, (u)_{\alpha}[/math]

[math]\alpha^* \, \alpha = E[/math], here [math]f^i . e^j[/math] means evaluation

And of course the "dual" properties showing that [math]^*[/math] is just transposition really

[math]\omega = (\omega)_{\alpha^*} \, \alpha^* [/math]

[math](\omega)_{\beta^*} (id)_{\beta \alpha} = (\omega)_{\alpha^*}[/math]

[math]\beta^* = (id)_{\beta \alpha} \, \alpha^* [/math]

For a linear map [math](\varphi)_{\beta \alpha}[/math] it's similar.

[Anonymous No.9027072]

>>9027028
>notice how the greek letters connect
Like how the physicists did back in 1920?
Coordinates in the dual basis can be written as contravariant indices so that [math](u^*)^\beta u_\alpha = \delta_\alpha^\beta[/math]. The bra-ket notation is also another example of good notation: the kets [math] |\psi\rangle \in \mathcal{H}[/math] are elements of a Hilbert space and bras [math]\langle \phi | \in \mathcal{H}^*[/math] is an element in the dual, so that the pairing ca be written as [math]\langle\phi |\psi \rangle = \phi(\psi) \in \mathbb{C}[/math].

[Anonymous No.9027382]

Imagine being a fan of anime and a fan of math, but instead of watching anime or studying math, you spend your whole day talking about those two things on an anonymous Bangladeshi child porn sharing site. And you repeat that every, single, God, damn, day. Isn't that just a waste of time?

[Anonymous No.9027547]

>two qualifying exams in 30 days
>depression and incompetence reaching maximum
I should have went into the Biomath program instead
No qualifying exams and the research interests are closer

[Anonymous No.9027558]

>>9026739
You're obviously out of almost everyone else's league, so why the fuck are you here and not on /r/math or stackexchange/stackoverflow?

[Anonymous No.9027564]

How many of you actually are Math PhDs?
Reading this thread I get the feeling it's full of undergrads and CS undergrads with a minor in Math. Not to mention the casuals who "self study".

[Anonymous No.9027569]

>>9027564
I'm gonna be a Math PhD one day
I'll make you proud

[Anonymous No.9027578]

Neurotypicals cannot be mathematicians because they lack the creativity to visualize the Math inside their brains. All they do is memorize formulas and condition themselves to solve problems.

[Anonymous No.9027587]

Is there any simple way to prove that the diophantine equation [math] x^4 + 4y^4 = z^2 [/math] has no all-positive solutions?

[Anonymous No.9027609]

>>9027578
H-how do I know if I'm neurotypical?

[Anonymous No.9027612]

>>9027564
about to start my PhD. I've got a fresh hot-off-the-presses Bachelor's in math. Got accepted to the same medium-good uni I did my undergrad at. I am satisfied with this.

[Anonymous No.9027617]

>>9027609
I'm not the anon you responded too, but you will know if you can answer this question:

>What exactly is a vector?

[Anonymous No.9027634]

>>9027609
Consider all of these questions:
-back in school days, did other students and teachers consider you as annoying?
-do you feel itching a lot?
-are you somehow sensitive to sounds?
-does hugging, cuddling, touching, etc, disturb you?
-do you spend plenty of time (at least one hour every day or so) fantasizing/daydreaming?
-do you carry any "strange" childhood habits (severely chewing pencils, spinning coins, etc)?
-do you feel as if things should make mathematical sense?
-do you often repeat many things over out of pure habit?
-do you find it difficult to concentrate?
-do you enjoy solving difficult puzzles?
-do you often spend a lot of time staring at things (buildings, the moon etc)?
-do you find it difficult to relate to normal people?
-do you have trouble when trying to socialize?

[Anonymous No.9027639]

>>9027617
>What EXACTLY is a vector?
I really fucking hate these kinds of questions with a passion, because if I say something stupid like "an element of a vector space" or whatever, I'm sure to get it really fucking wrong, and I've probably already proven that I'm neurotypical or something, so that's just another data point to back the at this point undeniable conclusion that I'm fucking worthless.

I didn't want to have a good night anyway.

[Anonymous No.9027644]

>>9027558
Because I love you guys.

[Anonymous No.9027647]

>>9027634
Not the anon you responded to, but this is /spectral analysis general/ now.

>-back in school days, did other students and teachers consider you as annoying?
Possibly.
>-do you feel itching a lot?
I used to.
>-are you somehow sensitive to sounds?
No.
>-does hugging, cuddling, touching, etc, disturb you?
No.
>-do you spend plenty of time (at least one hour every day or so) fantasizing/daydreaming?
I used to.
>-do you carry any "strange" childhood habits (severely chewing pencils, spinning coins, etc)?
No.
>-do you feel as if things should make mathematical sense?
Yes.
>-do you often repeat many things over out of pure habit?
Maybe? Not sure what you mean exaclty.
>-do you find it difficult to concentrate?
No.
>-do you enjoy solving difficult puzzles?
Yes.
>-do you often spend a lot of time staring at things (buildings, the moon etc)?
I used to.
>-do you find it difficult to relate to normal people?
Somewhat.
>-do you have trouble when trying to socialize?
Yes.

>>9027617
Element of a vector space.

[Anonymous No.9027649]

>>9027634
>-back in school days, did other students and teachers consider you as annoying?
No.
>-do you feel itching a lot?
I don't know what constitutes "a lot", but from what I've seen from other people, not especially, no.
>-are you somehow sensitive to sounds?
Yes
>-does hugging, cuddling, touching, etc, disturb you?
Yes.
>-do you spend plenty of time (at least one hour every day or so) fantasizing/daydreaming?
Definite yes.
>-do you carry any "strange" childhood habits (severely chewing pencils, spinning coins, etc)?
Yes.
>-do you feel as if things should make mathematical sense?
Yes.
>-do you often repeat many things over out of pure habit?
Yes.
>-do you find it difficult to concentrate?
Yes.
>-do you enjoy solving difficult puzzles?
No, because I know I won't be able to solve them, so I usually don't try in the first place, and when I do, I fail.
>-do you often spend a lot of time staring at things (buildings, the moon etc)?
Yes.
>-do you find it difficult to relate to normal people?
I'm not sure.
>-do you have trouble when trying to socialize?
Yes, but I always pull through, and people always think I'm friendly and nice (which disturbs me).

So what's the verdict doctor?

[Anonymous No.9027673]

>>9027634
>-back in school days, did other students and teachers consider you as annoying?
Yes
>-do you feel itching a lot?
No
>-are you somehow sensitive to sounds?
Extremely
>-does hugging, cuddling, touching, etc, disturb you?
Only if someone else initiates it
>-do you spend plenty of time (at least one hour every day or so) fantasizing/daydreaming?
Yes, though it usually involves math/physics
>-do you carry any "strange" childhood habits (severely chewing pencils, spinning coins, etc)?
Yes, I used to take the green twist ties from the supermarket and I'd make soldiers, vehicles, dragons, boats, I never had a reason, I just did. I also used to do this thing where if there were tiles I could only step from one to another by going three units up and one to the left or the right, basically to how a knight in chess moves, always just seemed fun. I also used to divide up any shapes by their axis of symmetry.
>-do you feel as if things should make mathematical sense?
Yes
>-do you often repeat many things over out of pure habit?
Yes
>-do you find it difficult to concentrate?
No
>-do you enjoy solving difficult puzzles?
Yes
>-do you often spend a lot of time staring at things (buildings, the moon etc)?
Yes
>-do you find it difficult to relate to normal people?
Sometimes, for the most part I can guess why someone does something, but I never really "get" it, some behavior/social convention that's supposed to be normal just seems a bit weird/useless.
>-do you have trouble when trying to socialize?
Yes

[Anonymous No.9027676]

>>9027647
>>9027649
>>9027673
Neurotypicals, all of you.

[Anonymous No.9027683]

>>9027676
Cool, guess I'm not the autismo I thought I was, this is great news, time to sell out and become a chad

[Anonymous No.9027693]

>>9027683
The easiest way to tell if someone is autistic is by asking the person directly, if you have ever thought to yourself "I have autism" you most certainly don't. Autists are too oblivious to care about such matters, those who make claims like I have autism are usually just attention whores.

[Anonymous No.9027695]

can anyone gave me a problem for a math brainlet like myself

[Anonymous No.9027699]

>>9027695

What is 2+2?

[Anonymous No.9027701]

>>9027699
((2)+(2))

[Anonymous No.9027708]

>>9027699
fish XD

[Anonymous No.9027733]

>>9027676
What criteria did you use?

[Anonymous No.9027742]

>>9027733
You're not autistic, just an attention whore.

[Anonymous No.9027758]

>>9027742
I never said I was autistic, I've never been diagnosed and autodiagnosis is retarded as fuck.

[Anonymous No.9027762]

>>9027695
Honestly, I hate this kind of "so far above that tedious shit" attitude in math. I had one fellow math friend in my grad program who wasn't like that but have lost contact, feels bad.

I don't know where you're at so it's hard to guess what problem might fit you. Probably you're in the wrong place though, more due to the attitudes than the content though.

[Anonymous No.9027773]

What is this type of problem called?
I'm studying for the accuplacer for College. I have always done poorly in math and basically needed to learn arithmetic and Algebra again through self study but I can't study this because I have no idea what the fuck I'm trying to do.
I know this is very basic to all of you so I figured I would ask

[Anonymous No.9027784]

>>9027762
>Honestly, I hate this kind of "so far above that tedious shit" attitude in math.
What are you talking about exactly, anon?

[Anonymous No.9027787]

>>9027773
It's basic arithmetic, here's a hint, distribute the sqrt(50) to each of the terms and try working it out form there.

[Anonymous No.9027847]

>>9027644
How long did it take you to get to your level of knowledge? How many hours a week do you study, and since what age do you do that? Did you get a Math Ba or was it self taught? I'm sorry for being overly curious, but I guess it would help having someone as a compass.

[Anonymous No.9027850]

>>9027695
You have one meter of rope. Someone asks you to form the rope into a right isosceles triangle. What's the area of the triangle in square meters?

For the record, if you can't answer this question you are a turbo-brainlet who even brainlets look down upon.

[Anonymous No.9027854]

>>9027847
Why even bother? They were probably acoustic about maths and physics their whole life, were born a genius of some kind and now are just reaping the benefits of superior genes.

[Anonymous No.9027864]

>>9027854
1- I didn't ask you.
2- If a Finnish 2hu poster can without trying then so should I.
3- Even if not, you clearly don't understand what a compass is.

[Anonymous No.9027871]

>>9027847
>How long did it take you to get to your level of knowledge?
24 years since I'm almost 24 now.
>How many hours a week do you study, and since what age do you do that?
I don't have a set schedule. Since I don't have data on my phone whenever I commute I bring a couple of texts/articles with me to read on the train. That'd probably amount to 4 hours per day back and forth. I've been doing this since sophomore year when I was 18.
>Did you get a Math Ba or was it self taught?
My bachelors was in mathematical physics. Most of the topics here are self-taught but it does help me understand theories in physics better, and vice versa.
Also I'm not Finnish.

[Anonymous No.9027879]

>>9027847
You forgot the single most important and universally relevant question for this type of inquiry

>>9027871
What is your family's academic background and area of profession?

[Anonymous No.9027882]

>>9027879
inb4 phDs, professors, did math with me as a child

[Anonymous No.9027888]

>>9027871
>commute
>4 hours per day
What third world country are you from?

[Anonymous No.9027890]

>>9027864
I can sense you got really flustered. How so, anon?

[Anonymous No.9027891]

>>9027879
Dad was an insurance broker and mom was a trader for an international corporation.
>>9027888
I live two towns away from where I work/studied.

[Anonymous No.9027900]

>>9027639
>>9027647
Element of a vector space is the correct response. The mark of a true mathematician, congrats.

[Anonymous No.9027912]

>>9027891
I asked what country you live, not the distance between your place of residence and place where you studied/worked measured in human settlements.

[Anonymous No.9027923]

>>9027871
>4 hour daily commute
Damn, sounds rough, though I guess if you can get quality reading time in then it's not so bad. Did ya already finish your PhD or are you still a student?

[Anonymous No.9027938]

>>9027923
I've just finished up a MSc in physics. I'm heading elsewhere for a PhD (also in physics) soon.
Doesn't mean I'll stop self-studying math though.

[Anonymous No.9027940]

>>9027938
What country are you from?

[Anonymous No.9027947]

>>9027938
Was your master's thesis also on cft or maybe some other topic (I know in the US you do a thesis for your masters, don't know about elsewhere). What math? Non-commutative geometry, knot theory, algebraic geometry, K-theory...

[Anonymous No.9027956]

>>9027947
I did do a thesis, it was in Canada. It was about graphene; it's a very archetypal "physics" thesis. Don't dox me btw.
>What math?
Mostly what you see here. CFT, TQFT, geometric quantization, knot theory, etc.

[Anonymous No.9027960]

>>9027956
Can you please tell me what country you are from?

[Anonymous No.9027962]

>>9027960
>>9027940
I was born in Taiwan.

[Anonymous No.9027965]

>>9027962
Your racial group is Asian?

[Anonymous No.9027966]

>>9027956
Wait, Canada? Huh, that's kind of funny, of the three guys I work for one was a prof at waterloo and the other got his master's there. I actually wanted to do a masters (or PhD) at perimeter (if I went to waterloo it'd likely be in pure math with an eye towards theoretical physics, I know of few guys in the pure math department that do that sort of thing) though from what I've heard it's difficult as all hell to get in

[Anonymous No.9027969]

Some time ago there was someone who declared themselves to be latino, and now there is a self declared Asian. I used to think the worst that could happen to this thread were Americans.

[Anonymous No.9027970]

>>9027966
>though from what I've heard it's difficult as all hell to get in
That's correct, and it's extremely competitive. Your CV and recs have to be stellar in order to get into Perimeter, since they'd only take in students that they're willing to give substantial fundings for. I've tried when I was looking for masters but to no avail.

[Anonymous No.9027975]

>>9027970
Worst comes to worst I apply and get reject but thanks to the fact that they've uploaded the video lectures for their courses it makes a great supplement to learn a lot of these topics independently so it won't be all bad. Would be nice if they uploaded problem sets, though I guess at that point asking for more would just be greedy.

[Anonymous No.9027986]

>>9027975
Yeah that can't be helped. Good luck anon.

[Anonymous No.9027987]

>unable to find a professor with a research position
>scared of failing my qualifiers
>considering dropping out
>repeat this sequence of thoughts over and over for the last 3 months
>receive an email a few hours ago from a professor with a possible research project in something I'm not experienced in

Is it a sign?

[Anonymous No.9027991]

>>9027987
How far out of depth is it? Is it a tangentially related field?

[Anonymous No.9027995]

>>9027991
I haven't got the details yet, but it's a project in PDEs requiring experience in numerical linear algebra and finite differences. The later two I'm well versed, but I won't even take the first course in graduate PDEs until this coming semester.

[Anonymous No.9027997]

>>9026883
Thanks man, that's all I needed.

[Anonymous No.9027999]

>>9027995
I can suggest a few grad level PDE books you can check out during the summer. If you already have a decent amount of knowledge it couldn't hurt to contact the prof and see if you can handle it.

[Anonymous No.9028002]

>>9026306
>what are you studying this summer?
The amount of alcohol and opium/opioids that can be combined without croaking.

[Anonymous No.9028050]

>>9026508
2. is easy, assuming we know the following things:
>module categories satisfy two topos axioms but not necessarily the subobject classifier thingy (lawvere-tierney)
>in a topos an arrow whose codomain is an initial object is an isomorphism
>trivial modules are both initial and terminal
>there are non-trivial modules over unitary rings
It follows that there can be no subobject classifiers for these module categories, in particular the category of abelian groups.

[Anonymous No.9028199]

>>9027969
If you're so concerned with where everyone is from why don't you start off by telling us where [math] you [/math] are from, ass-hat.
>>9027956
>Don't dox me btw.
Too late for that. Gorilla has been so talkative that I already know who both of you are.

[Anonymous No.9028214]

>>9027558
The fact that his posts often go un-replied is his fault actually, since most of what he's posting, when it is correct, are elementary constructions ("it follows from the definitions" stuff), and of the rest quite a few are inane symbol salads.

[Anonymous No.9028247]

>>9026306
I'm just here to post this (real, a professor at my school put this on their social media) image because it's relevant to the thread theme.

[Anonymous No.9028253]

>>9027987
I mean if the prof emailed you that's probably a good thing? Don't let the impostor syndrome get to you and keep at it.

[Anonymous No.9028327]

Help I can't see the mistake, I suspect is something related to the fact that you may get [math\frac{h}{h}= \frac{0}{0}[/math] but I'm not quite sure

[Anonymous No.9028338]

>>9028327
This captures the essence of the proof, but there is a technical problem. You know as h -> 0 that g(x+h) - g(x) -> 0 as well, so you'd like to say that f'(g(x)) is equal to lim_{h -> 0} (f(g(x+h))-f(g(x)))/(g(x+h)-g(x)). But this isn't actually the definition of the derivative, and you would need to show formally that you get the same limit. Doing this properly really requires messing around with epsilons and using the definition of the derivative.

[Anonymous No.9028341]

>>9028327
let g(x) be a constant function.

[Anonymous No.9028354]

>>9027564
>Not to mention the casuals who "self study".
Just like Software Engineers program for fun so should Mathematicans self-study for fun. Don't you think it's academics who self-study rather than "casuals"?

[Anonymous No.9028374]

>>9028050
Anon please...
>module categories satisfy two topos axioms but not necessarily the subobject classifier thingy
This is "proof" by assertion/begging the question. What you have to prove is exactly that they don't satisfy it.
>in a topos an arrow whose codomain is an initial object is an isomorphism
This is trivially false. Were it true, every set would have cardinality [math] 0 [/math]. ([math] \textbf{Set} [/math] is a topos.)
>trivial modules are both initial and terminal
True and potentially pertinent to the proof, depending on how you'd choose to approach it.
>there are non-trivial modules over unitary rings
True but not actually relevant.

This anon >>9025804 was going in a good direction. (I hadn't noticed his post yesterday. And by the way, I posted a link with it that you might want to read. Section 5 is particularly useful.)

[Anonymous No.9028400]

>>9027634
Damn, all of them

[Anonymous No.9028402]

>>9027693
To be fair i never told anyone and denied my diagnosis for a while

[Anonymous No.9028532]

>>9027634
>back in school days, did other students and teachers consider you as annoying?
No
>do you feel itching a lot?
No
>are you somehow sensitive to sounds?
Quite
>does hugging, cuddling, touching, etc, disturb you?
No
>do you spend plenty of time (at least one hour every day or so) fantasizing/daydreaming?
Meh
>do you carry any "strange" childhood habits (severely chewing pencils, spinning coins, etc)?
Penspinning
>do you feel as if things should make mathematical sense?
Not necessarily
>do you often repeat many things over out of pure habit?
Yes
>do you find it difficult to concentrate?
It depends
>do you enjoy solving difficult puzzles?
Meh, I like thinking about them, but I usually don't solve them
>do you often spend a lot of time staring at things (buildings, the moon etc)?
Yes
>do you find it difficult to relate to normal people?
It depends, not necessarily
>do you have trouble when trying to socialize?
Yes

[Anonymous No.9028567]

>>9027999
Yea I'll contact him. There's only a month left of summer and at the end I have qualifiers, so I don't think there's a whole lot of priming I can do until after that.

[Anonymous No.9028574]

If God isn't real then what created this Universe?

[Anonymous No.9028585]

>>9028574
I did, and then I entered it myself as an incompetent mathematician so I could understand suffering

[Anonymous No.9028588]

>>9028585
We're almost the same, the only difference is that I'm actually competent.

[Anonymous No.9028616]

>>9028374
Ok, let's reformulate it so that even you can understand what is going on. Since those categories satisfy 2/3 topos axioms, suppose they satisfy the third one too. Then use the fact that zero objects are terminal to get an arrow from each object to the trivial module, and then the fact that such modules are also initial, giving us isomorphisms between all modules and the trivial one. Since this is false, these categories can't satisfy the classifier axiom.

Did you just realize you claimed there are functions [math]\emptyset\neq S\to\emptyset[/math]? https://ncatlab.org/nlab/show/strict+initial+object

[Anonymous No.9028637]

>>9028616
Damn, I haven't been so thoroughly BTFO in years.
Thank you for the lesson.

[Anonymous No.9028657]

>>9027587
Use Fermat descent on solutions with gcd(x,y,z)=1 by considering 4y^4=(z-x^2)(z+x^2) or x^4=z^2-4y^4

[Anonymous No.9028664]

>>9027695
A stick is divided by red marks into 7 equal segments and by green marks into 13 equal segments. Then the stick is cut into 20 equal pieces. Prove that any piece (except the two end pieces) contains exactly one mark, which may be red or green.

[Anonymous No.9028774]

>>9027587
Use an inconsistent system or add it as an axiom. That's the only way to prove what you're trying to prove.

[Anonymous No.9028854]

>>9028354
Academics self-study, while casuals "self-study". Big difference there.

[Anonymous No.9028865]

>>9028637
Genuine question: how did it feel? I'd like to know how /mg/ handles failure, and knowing how it felt might help me.

[Anonymous No.9028867]

>>9028637
>>9028865
Also, are you the Yukari poster?

[Anonymous No.9028871]

>>9028865
Lying is very un-ladylike.

[Anonymous No.9028882]

>>9027564
What is that white stuff on her face?

[Anonymous No.9028886]

>>9028657
I am sorry, could you elaborate? It looks like you just changed the order of the equation, and I already tried descent on the equation and I could not make it work.

Could you elaborate on what you achieve by rewriting the equation like that?

[Anonymous No.9028896]

>>9028871
I'm not lying. I handle failure horrendously and I want it to stop.

[Anonymous No.9028901]

>>9028886
Using elementary number theory techniques, you can discern properties of the differences of squares. Give me a minute and I'll attempt it.

[Anonymous No.9028906]

>>9028865
I'm not good at describing these things. Have you ever forgotten your backpack at school? I have, once, in 3rd grade. One of my classmates ran after me to bring it to me. Reading anon's post felt like that memory.
I've always been extra mindful of where my stuff is after that happened.
>>9028867
Nope. My favourite Touhou character is Patchouli.

[Anonymous No.9028931]

>>9028906
Sorry for reminding of such things. I've been taught by strict men and harsh women. It has affected the way I correct mistakes, but I believe it is a good thing to get a few things wrong and fixed every now and then. Being too sure is not necessarily a good thing.

[Anonymous No.9028945]

>>9028906
>I'm not good at describing these things. Have you ever forgotten your backpack at school? I have, once, in 3rd grade. One of my classmates ran after me to bring it to me. Reading anon's post felt like that memory.
>I've always been extra mindful of where my stuff is after that happened.
That's a very nice way to put it anon, thanks for the answer, it was adorable in the best sense of the word.

>>9028931
Are you pretending to be me? Cause I don't like it.

[Anonymous No.9028962]

>>9028567
Personally my favorite pde books are Arnold's Evan's, Jost's, and Brezis', all are very readable and thorough only requiring some measure theory and, depending on the text, functional analysis.

[Anonymous No.9029000]

>>9028886
I haven't finished, but the rest is easier and similar. So I ended up with if [math](x,y,z)[/math] is a solution, then you end up with an equation of a similar form. If you keep doing what I did, you will eventually find that there is a solution to the initial equation which is strictly smaller than the original solution.

Then apply descent: assume there is a solution with [math]xyz[/math] minimal. Then we can find another solution to the equation that is strictly smaller. Contradiction

[Anonymous No.9029017]

>>9028945
I wish I was someone else, but I'm just this fucker here >>9028616

[Anonymous No.9029025]

>>9029000
You have nice handwriting, anon, I really like it.
>>9029017
>I wish I was someone else
Why though?

[Anonymous No.9029078]

>>9029025
Idk, I'm a retard posting infantile cartoons on a Polynesian tattoo site.

[Anonymous No.9029084]

Is the failed actuarial (lmao) grad student that thinks he is advancing his field still here? i wanna btfo him some more

[Anonymous No.9029085]

Do any of you memorize any proofs?
If so, which ones?

[Anonymous No.9029090]

>>9029085
>Memorize at all
You dont belong here

[Anonymous No.9029092]

ITT: People who will not make it through grad school

[Anonymous No.9029095]

>>9029000
I think you ran into the same problem I originally did. After applying all the identities in preparation for descent, as you did, I ended up with a different equation. The same happened to you, you ended up with a different form.

How do you conclude? How do you take it back to the original form? That is the problem I had.

[Anonymous No.9029096]

>>9029090
Alright Mr. Pretentious Cunt who can re-invent the entirety of mathematics rigorously.

[Anonymous No.9029099]

>>9029096
Cant you? I thought that was the minimum requirement to get into grad school as well as posting in this thread

[Anonymous No.9029102]

>>9029095
sorry i dont think our issues are the same. you might br suffering from brainlet disease

[Anonymous No.9029107]

>>9029099
>putting grad school students and 4chan shitposters on the same level
This must be a unique form of autism.

[Anonymous No.9029109]

>>9029107
Are not we all in grad school? WTF

[Anonymous No.9029112]

>>9029109
Seek help my dude.
But to answer your question, I'd imagine some are amateur and some are undergrad/grad.

[Anonymous No.9029115]

>>9029102
Okay, let me explain. You started with the equation [math] x^4 + 4y^4 = z^2 [/math] but then ended with the equation [math] a^4 + x^2 = b^4 [/math]. It is not the same form. My question is simply, how do you conclude from that? You say if I keep doing what you did I can go back to the original form of the equation, but I am not seeing how. Please elaborate.

[Anonymous No.9029118]

>>9029115
I am not that guy, still working on it

[Anonymous No.9029121]

>>9029118
I did not post this. Someone is impersonating me. I am gonna get a tripcode. This is getting ridicolous

[Anonymous No.9029124]

>>9029118
>/pol/ gets poster ids but we don't

What a shame. But I kinda suspected it wasn't you as smart people usually aren't rude. At least no in the /mg/. But I posted just in case.

[Anonymous No.9029141]

>>9029112
Everyone in math is a pretentious cunt. I dont know what love you live in

[Anonymous No.9029148]

How does it feel to put a lot of time and effort and get so little in return?
>inb4 this is easy
lmao you wouldnt be posting here if you it was that easy fag

[Anonymous No.9029157]

>>9029148
But what if we get pleasure from this?

[Anonymous No.9029161]

>>9029157
Then you're a lucky anon.

[Anonymous No.9029165]

>>9029157
how can you have pleasure of doing maths knowing that people with lesser dedication and IQ make more than you ll ever make? I mean at this point only Math Hobbyisy deserve respect because they do math without being obliged or forced. Anyone doing math for a living that isnt backed financially by their parents plus uni is plain retarded in the US

[Anonymous No.9029166]

>>9029148
What are you talking about?

[Anonymous No.9029169]

I just realized my undergrad differential equations class won't include Laplace Transforms. Is this normal?

[Anonymous No.9029175]

>>9029166
I am dissapointed. Dissapointed that i see my peers and other fucking idiots who will never appreciate the beauty of math making more money and living more comfortably. I dont get it. Pursuing grad school for math in the US is not love for math, it s fucking madness. Unless you are a genius, have your parents backing, there is no fucking point. i already have very little and cannot aford to do math grad school despitr loving .i love it, when i am studying math is the only time i feel whole, a human being. But now i have to leave my dreams behind and hopefully can do it as a hobby. Thats why i fuckimg hate grad math students, they are either well off with their parents backing or they are too stupid to realize that they wont make it financially. I understand why there are so many foreigners grad students, because math in their countries pays shit but it also pays shit but it s better to be paid shit here rather than in their shithole countries. At last i see

[Anonymous No.9029176]

>>9029169
From what I understand, they're mostly taught in Physics and Engineering courses and not so much in Mathematics ones because they only offer an advantage in practice when dealing with discontinuous functions, or at least that's the case up to the level I was taught, I don't know if there's more to them, but that's the explanation our proffessor gave us (we did have a lecture and exercises on it, though).

[Anonymous No.9029177]

>>9029165
I'm too autistic to care about money, I have no desire to buy stuff, no desire to travel, no desire to party, no desire to go to a restaurant, etc. I don't think I'm gonna get a place as a PhD student, and certainly not as a researcher, but I don't care. I'm just studying it because it's nice.

[Anonymous No.9029182]

>>9029175
Did you not apply for any grants, scholarships, or fellowships? NSF graduate alone has over a 10% acceptance rate, tons of people can get in grad school without their parents backing, plus if you work as a TA or get paid by your PI there usually shouldn't be much of an issue. You do also know a lot of people in the private sector pay quite a bit for a math researcher.

[Anonymous No.9029202]

>>9029148
I just want to learn math. That's my only goal in studying math. It's rewarding in a way similar to many hobbies, I think. People who like playing music or drawing probably feel the same way. Any improvement or new thing they figure out makes any difficulty worth it. I don't play instruments or draw so I have no idea how true this is.

>>9029175
>>9029165
Math isn't beautiful by nature. It's not for everyone. Most people can't even handle basic algebra, and they never will either. They avoid math as much as possible. They do terribly because they just don't want to get good at math.

Successful math students are the opposite. You have to prefer studying math to other things in your life. That's a big reason why you don't see much people talking or caring about money. Most of us really wouldn't do much with the money like>>9029177

Math grad schools don't cost money for many. In fact, here in the US at least, schools pay you to be a PhD student. Though you are expected to have responsibilities besides studying and researching.

Other people seeming more happy is always a poor metric. No one actually gives off a public impression of being unhappy. Don't compare yourself to others and focus on improving yourself. I'm not saying that you can definitely succeed at your goals in math, but it is possible, and your chances are very connected with your efforts.

>>9029169
>>9029176
Don't worry. Physics and Engineering students are taught them because they think the inverse table method is why they are useful. It's not. Look at the final chapter of Marsden's complex analysis to see how Laplace transforms are actually useful. You can compute the inverse by doing a complex integral.

[Anonymous No.9029254]

>>9029124
I keep going in circles. Looked on the internet and found no mention of it anywhere. A good approach that has failed me is using the theorem for pythagorean triples, but as i said i keep generating more and more cases (I basically found that if such a solution exists, then there exists some number [math]m[/math] where [math]2^km[/math] is a sum of two squares for all [math]k\in\mathbb{N}[/math])

[Anonymous No.9029284]

>>9029254
Yeah same. Applying the solutions for the normal pythagorean equations you can prove that the existence of solutions for this equation implies the existence of solutions for some other equations but I can't find a direct way.

I think this should be easy. If you put the equation into wolfram alpha and ask for integer solutions, it generates all of them in like 10 seconds and they all have 0 in them. But wolfram alpha does not count as proof. This is making me crazy.

[Anonymous No.9029295]

>>9029284
fug mayne, if only I knew a bit more algebraic number theory...

[Anonymous No.9029333]

>>9029085
You know, I feel strongly that one shouldn't learn even poetry by rote. The difference between a reciter who has learned the poem by rote and one who has learned the poem by heart is stark, but it's even more pronounced when clear understanding of the poem is on display.
By the way /math/ematicians, how do you like poetry? I like to read poetry as a means to cool off after mathematics, like a walk after a run. I started doing it in high-school, with one of Lucian Blaga's poems (it was mandatory reading for a literature class but I ended up being captivated by it because it espoused a view that was completely alien to my nature).

>>9029175
Orthodox monks confine themselves in monasteries, monasteries that are sometimes built inside caves, with the hope that one day, in the midst of darkness, they may witness the Light of Tabor.
The difference between us is that we do not seek light, but music. We retreat inside our cavernous minds with the hope that one day we might hear God humming in the distance. And if that day comes, we write the song down in the marrow of our bones, and every time we share that song with others we share a little piece of ourselves, which has become a little piece of God.

Mathematics is our hesychasm.

[Anonymous No.9029358]

>Wasting your time posting number theory and algebra problems
lmao nigger this is a math general, either post some topology or go jerk off to your comp sci degree

[Anonymous No.9029359]

>>9029175
Stop complaining, turn off your computer, get off your chair, and go to a library. There, now you can learn Math by yourself. What is so hard about it? You frankly sound like a loser, one of these people who always talk but don't take any proactive stance. You'll never be successful with that mindset.

[Anonymous No.9029364]

>>9029358
Now now, what if I have a Comp Sci degree, but with a minor in Math?

[Anonymous No.9029369]

>>9029333
Don't get me wrong, I try to understand every proof I meet, it is just that sometimes, some details get lost when you're thinking of the big picture, and I find myself having to revise the proof of a theorem just to clarify any little doubts I had.

[Anonymous No.9029372]

>>9029364
>minor
Maybe >>>/sci/sqt/ is more up your speed

[Anonymous No.9029374]

>>9028327
If [math]\lim_x a(x) = a[/math] and [math]\lim_x b(x) = b[/math] then [math]ab = \lim_x\lim_y a(x)b(y)[/math], not [math]\lim_x a(x)b(x)[/math].

[Anonymous No.9029380]

>>9029372
Remind me what Ivy League you went too?
CS in a top school gets more and better Math than Math in a pleb school.

[Anonymous No.9029387]

>>9029380
Keep telling yourself that. CS undergrads are the definition of brainlet.

[Anonymous No.9029395]

>>9029380
I mean, if that makes you feel better about yourself, then who am I to ruin it for you? Congrats, you won the maths, you're the best.

[Anonymous No.9029413]

>>9029387
>CS undergrads are the definition of brainlet.
Then why are admissions to CS courses much lower than to Math and Physics, and why do CS undergrads make much more than Math and Physics undergrads? Also, why are there more cute programmers than cute mathematicians? Are you so insecure that you must somehow tell yourself studying Math was the right thing to do, despite all facts pointing otherwise? Are all mathematicians like this, or is this just a rare incident of a regret you cannot accept?

[Anonymous No.9029416]

>>9028199
>Gorilla has been so talkative that I already know who both of you are.
Truly a suboptimal situation. Well, I'm leaving town in a month so I guess I don't need to worry too much.

[Anonymous No.9029426]

>>9029413
>why are there more cute programmers than cute mathematicians?
>using homosexual tendencies as an argument for intelligence

[Anonymous No.9029428]

>>9029369
That's to be expected. Even among the most able, there are few people with large enough working memories to devour a proof in one bite.

[Anonymous No.9029444]

>>9029426
Not him but.
http://www.thephora.net/forum/archive/index.php/t-56300.html
https://calgaryqueerhistory.ca/2013/07/18/gay-men-are-smarter-than-straight-men-so-says-history/
It's the same thing with virgins

[Anonymous No.9030265]

>>9026306
What is the best book for learning probability?

[Anonymous No.9030290]

reminder that posting anime makes the math thread awful and decreases the audience

[Anonymous No.9030302]

>>9030290
Yeah honestly I tried to participate in an earlier thread thinking that it would be a nice place to hang out with mathfags, but I checked out when I realized it was just a bunch of homosexuals masquerading as mathematicians.

[Anonymous No.9030311]

>>9027558
he does not know that much, on the sci/reddit discord he talks a lot of air but never is able to follow ph.d. students

[Anonymous No.9030405]

Alright, you guys seem okay so I figure I'll get an answer out of ya, what the fuck are the mods of this board doing? The number off topic threads/replies is staggering, people post fucking porn here and no one does anything about, good threads start and then some asshole comes in and derails it with "fuck chinks" and it just keeps escalating cause no one stops it, there was multiple threads about jews with no connections to science, a fucking thread highschoolers talked about SAT scores, constant talk about university ranking, and the fucking iq threads (it's not even about the topic, it's just the fact that's always there, it's the samee thread every time and it just keeps getting started). Aren't mods supposed to stop this shit? I genuinely think /sci/ would be more active board if someone would properly do there job with this board.

[Anonymous No.9030410]

>>9030402
I'm impatient, is this correct?

[Anonymous No.9030433]

>>9030311
>on the sci/reddit discord
What's that?

[Anonymous No.9030436]

>>9030405
Fuck off commie.

[Anonymous No.9030645]

>>9030265
Depending on the didactic style you prefer: Ronald Meester's A Natural Introduction to Probability Theory (for the bottom-up approach -- argues [math]to[/math] abstractions), or Geoffrey Grimmett's and Dominic Welsh' Probability: an introduction (top-down approach -- argues [math]from[/math] abstraction). Both have many neat exercises and encourage self-study.
After you've finished either of these you can move on to Olav Kallenberg's Foundations of Modern Probability for an advanced overview of the topic.

(I'm assuming you're an undergrad reading pure maths or thereabouts. If that assumption doesn't hold, I'm afraid I can't provide any assistance. I don't know what sort of books the stats and other sciences folks prefer.)

[Anonymous No.9030877]

>>9030645
What's her ethnicity?

[Anonymous No.9030995]

>>9026508
4. rough solution: Notice that all vertices of the maximum area p-gon must lie on the border of n-gon: take some vertice A of the p-gon and its neighbours B, C. Look at the triangle ABC, and imagine that BC is the base; then the area depends only on the height from vertex A. If A was strictly inside the n-gon, you could change A to another point A' which has bigger height, therefore contradicting the maximality of p-gon.
Using the same argument, we can see that there is a p-gon with maximum area and vertices which are among vertices of the n-gon.
Finally, again let B, A, C be consecutive vertices of the p-gon. Suppose there are [math]k[/math] edges of the n-gon between B and A, and [math]l[/math] edges between A and C. Using same argument, we see that if [math]k+l[/math] is even, then [math]k=l[/math], if [math]k+l[/math] is odd then [math]k-l = \pm 1 [/math]. I won't type everything out but the answer is clear: for any n, p, you will get a maximum area p-gon if you make the distances between consecutive vertices each equal to [math] \lfloor \frac{n}{p} \rfloor [/math] or [math] \lceil \frac{n}{p} \rceil [/math], in the right amount so that they sum up to n.
For example if you want a maximal 3-gon inscribed into 10-gon you make the distances 4, 3, 3
If you want an exact formula: let O be the center of n-gon, let x be the distance from O to any vertex. Then compute areas of both n-gon and p-gon as sums of triangles made up from two consecutive vertices and O. x cancels out when you get the proportion and we're done

[Anonymous No.9031027]

>>9030645
Not him, but thanks. I've been avoiding Probability since I took an intro class but I'm coming to the end of my undergrad and feel I should know more.

[Anonymous No.9031114]

>>9030433
erdos discord

don't bother with it tho, it's like 2 messages about math max

[Anonymous No.9031129]

>>9030995
Good sketch. I counted the vertex distances differently, by excluding the vertexes of the [math]p[/math]-gon from the [math]n[/math]-gon, but the result is the same.
The formula for the area is

[math] A_{p\text{-gon}} = A_{n\text{-gon}} \cfrac{(p-r)\text{sin}\frac{2q\pi}{n}+r\ \text{sin}\frac{2(q+1)\pi}{n}}{n\ \text{sin}\frac{2\pi}{n}} [/math], where [math] n = pq+r [/math] (by euclidean division).

>>9031027
Cool. I've been brushing up on probability theory these last couple of months or so too, since I haven't really read or done much of it since I was an undergrad.

>>9030877
She's from Amestris, which is a fictional fusion of England and Prussia, so let's say she's Danish.

[Anonymous No.9031133]

>>9030290
You need the axiom of choice to prove that.

[Anonymous No.9031136]

>>9029364
That would mean you are a lesser being.

[Anonymous No.9031672]

I'm not sure if this is the right place for this, but I didn't want to make my own thread.

Does anyone have some textbook recommendations for self study?
Specifically I am interested in chaos and nonlinear dynamics. I had the opportunity to take a class on these topics this fall, but due to scheduling conflicts with mandatory courses I could not sign up for it. This is a topic I know only about in a general sense, but next to nothing about the mathematics behind it. For background, I am an undergraduate going into my junior year. I'm double majoring in physics and mathematics. As far as my background for mathematics, I've taken Calculus 1, 2, and 3, ODE, and Discrete Mathematics. I'll be taking Linear Algebra this upcoming semester (so most of the basic mathematics, but none focusing on proofs). I qualified to take this course at my school, but haven't found many books on this topic intended for undergraduates and a cursory examination of online lectures hasn't revealed much.

I'd really appreciate any recommendations. I may get the opportunity to be involved with some research in nonlinear dynamics with applications in physics or mathematical physics next summer so in preparation for that potentiality I'd really like to learn some things about it. I apologize again if this was the wrong place to ask for recommendations.

[Anonymous No.9031691]

>>9031672
Some people won't agree with me, but here it goes. I recommend you to study real analysis already if you want to learn things seriously. After that, a serious study of ODEs can take place. You can use the nice book https://www.math.upatras.gr/~bountis/files/def-eq.pdf which also happens to include an introduction to dynamics, which is what you want.

Of course you can go the other way around: grab the book, skim it, and learn whatever you need for rigor in the way.

[Anonymous No.9031697]

>>9031672
Here https://www.math.upatras.gr/~bountis/files/def-eq.pdf
That's my go-to book for ODEs and it happens to include an introduction to dynamical systems which is what you want

You probably need real analysis to fully follow it. You can learn that from Tao's Analysis I & II, or look up results on the way.

[Anonymous No.9031701]

>>9031691
>>9031697
whoops page crashed while I was posting and I thought it hadn't posted oh well

[Anonymous No.9031733]

>>9031672
I really enjoyed Strogatz. Its written for physics undergrads. First half is chockfull of examples, second half has nice math structures.

Chaos started as an applied field, so its nice to start from there.

[Anonymous No.9031811]

>>9031672
>I may get the opportunity to be involved with some research in nonlinear dynamics
>I'll be taking Linear Algebra this upcoming semester (so most of the basic mathematics, but none focusing on proofs)
>but none focusing on proofs
there's a long way ahead of you kid. in order to rigorously study dynamical systems (I mean if you wanna really understand what's going on), you have to master real analysis (obviously), but you also need a strong foundation in topology, functional analysis, linear algebra (nonlinear doesn't mean you don't need to know the linear case; quite the opposite) and more. In my opinion if you've never taken a math course with proofs, I suggest you first learn the basics.

[Anonymous No.9031842]

>>9031733
Strogatz isn't optimal, since it doesn't nearly prove enough of what it should. It's a great intro text tho.

[Anonymous No.9031861]

>>9031811
I understand you need to learn those things in order to master the subject, but I'm not trying to master it. I was looking for a good introductory text that I might, as you said, learn the basics of the subject.

As I mentioned, I study physics as well as mathematics, but I focus on applied mathematics as that is where my interests lie. Certainly in the next year I will take classes both in Real Analysis and Abstract Algebra and I may even take some Topology if I have the option, but my emphasis is on applied mathematics and physics. Again, as I mentioned, I am an undergraduate. At this point in time I am not trying to "rigorously study" dynamical systems, I want to get a good introduction to the field because it seems like something I MIGHT want to study rigorously at some point. Since I was unable to get enrolled in my uni's introductory course I thought I would try some self study and the rest is history.

>>9031701
I appreciate the recommendation, I've red the introduction and some of the early chapters, it seems like a good book, thank you anon.

>>9031733
Yes, I also just came across Strogatz from MIT's open courseware on their undergraduate course in nonlinear dynamics in the interim since I posted and it seems like what I am looking for. I will probably pick up a copy. The description and syllabus seems very similar to the course my school, and I assume most colleges, offer for undergraduates. Was hoping they might have lectures posted for this class, but it appears they only have syllabus and problem sets. Unfortunate!

Thank you again everyone for the recommendations and advice.

[Anonymous No.9031919]

>>9031733
>Its written for physics undergrads
So in other words it's garbage?

[Anonymous No.9032377]

>>9031129
Winry is cute, C U T E

[Anonymous No.9032439]

The Seeley coefficients are coefficients of expansion of the heat kernel [math]K(x,y) = \langle x | e^{-H_I t}|y\rangle = \sum_n a_n(x,y)t^n[/math] in powers of [math]t[/math], which allows us to calculate the propagators perturbatively. The propagator act as a "connector" between solutions of the equations of motion, i.e. stationary points of the action [math]S = \int L[/math] via [math]\psi(y) = \int dx K(x,y)\psi(y)[/math]. Seeley coefficients are usually computed with zeta-regularized functional determinants, and only very special interaction Hamiltonians [math]H_I[/math] will permit analytic expressions for them.
By enforcing conformal symmetry and mapping [math]x \mapsto z,~y \mapsto 1-z[/math], the KZ equation can be cast into an ODE [math]G'(z) = \left(\frac{X}{z} - \frac{Y}{1-z}\right)G(x)[/math] where [math]X,Y \in A_n[/math]. The asymptotics [math]G_1(z),G_2(1-z)[/math] around [math]z = 0,1[/math], respectively, can be related by the Drinfel'd associator [math]\Phi(X,Y)[/math] via [math]G_2(z) = \Phi(X,Y)G_2(1-z)[/math], which acts like a propagator in the sense above. However analytic expressions can be obtained for the Drinfel'd associator with multiple zeta functions [math]\zeta_{k_1\dots k_n}(z) = \sum_{m_1,\dots,m_n}\frac{z^{m_n}}{m_1^{k_1}\dots m_n^{k_n}}[/math] to all orders regardless of interaction, as long as they follow conformal invariance. It turns out that with the right structure, analytic quantities like the Seeley coefficients can be evaluated algebraically.
Some interesting papers:
https://arxiv.org/abs/0802.4300
https://arxiv.org/abs/1404.2047
https://arxiv.org/abs/1706.01845

[Anonymous No.9032510]

>>9032439
Huh, this is actually pretty interesting, it's at least somewhat relevant to the kind of research I do.

[Anonymous No.9032558]

>>9027649
>>9027647
>>9027673
>>9028532
hey you fucking idiots

neurotypical means youre fucking normal
also, you cant tell if someone doesnt have a neurological disorder by weather or not they experience those things

[Anonymous No.9032822]

How did we let weebs take over this general. I bet if I went on any of your universities' websites and looked at the math undergrad picture gallery I'd be able to pick out each and every one of you fucking weebs based on your horribly pathetic feature. I guess if you can't beat them, leave, bye 4chan

[Anonymous No.9032824]

>>9032822
>bye 4chan
bye (see you tomorrow)

[Anonymous No.9032826]

>>9032822
>I bet if I went on any of your universities' websites and looked at the math undergrad picture gallery
There are universities that bother to make galleries of their undergrads?

[Anonymous No.9032859]

>>9032826
I know of a few https://www.math.hmc.edu/people/students/

[Anonymous No.9032917]

>>9032439
Ha! And you said number theory is "useless".

[Anonymous No.9032944]

>>9032439
And of course I made typos
[math]G_1(z) = \Phi(X,Y)G_2(1-z)[/math],
[math]\zeta_{k_1\dots k_n}(z) = \sum_{m_1<\dots <m_n}\frac{z^{m_n}}{m_1^{k_1}\dots m_n^{k_n}}[/math].
>>9032510
What kind of research is that anon? Please don't say number theory.

[Anonymous No.9032950]

>>9032917
>Ha! And you said number theory is "useless".
where's the number theory in that post?

[Anonymous No.9032992]

Tfw don't get this fucking book god dammit

[Anonymous No.9033016]

who [math] \ ^{g^{r^{i}}} _{m_{e_{s}}} [/math] here?

[Anonymous No.9033020]

>>9033016
pig

[Anonymous No.9033021]

>>9033016
disgusting

[Anonymous No.9033033]

>>9033020
>>9033021
DAMN she's ugly.

[Anonymous No.9033054]

>>9033016
>>9033020
>>9033021
Wymyn truly age like milk.
Can't compare to my eternal algebraic qt3.14s.

[Anonymous No.9033356]

Best book for learning group theory?

[Anonymous No.9033387]

How do you factor numbers in various rings?
Let's say I want to factor 35 in [math]\mathbb{Z}[ e ^{ \frac{i \pi}{4}} ][/math].
Since [math]\mathbb{Z}[ e ^{ \frac{i \pi}{4}}] \supset \mathbb{Z}[i] \supset \mathbb{Z}[/math], I could first factor in [math]\mathbb{Z}[/math] and then in [math]\mathbb{Z[i]}[/math]:
[math]35 = 7 \cdot 5 = 7 = 7 \cdot (1 + 2i)(1-2i)[/math]. But what now?

[Anonymous No.9033529]

>>9033356
Absolute basics? If you know nothing about them already this one is pretty good

[Anonymous No.9033558]

>>9033387
You factor the elements as you would factor polynomials in [math]\mathbb{Z}[x][/math]. An element in [math] \mathbb{Z}[\mathcal{e}^{\frac{i\pi}{4}}][/math] is a polynomial in [math]\mathcal{e}^{\frac{i\pi}{4}}[/math].

[Anonymous No.9033569]

>>9033356
Artin - Algebra

[Anonymous No.9033598]

>>9033387
>How do you factor numbers in various rings?
You find a and b that multiplied give you x.

[Anonymous No.9033846]

>>9029000
>manicured writing
>coloured highlights
I thought we were all girls (male). What's a girl (female) doing here?

[Anonymous No.9033904]

>>9029000
>Let (x,y,z) be a solution. If d=gcd(x,y,z), then (x/d,y/d,z/d) is a solution.

(x/d)^4+4(y/d)^4
=(1/d)^4 (x^4+4y^4)
=(1/d)^4 z^2
=(z/d^2)^2
!= (z/d)^2

[Anonymous No.9033937]

how often do you think about suicide /mg/?

[Anonymous No.9033945]

>>9033937
Atleast 3 days a week. Math used to be a way to suppress that, but it doesn't seem to help anymore. How about you?

[Anonymous No.9033963]

>>9033937
>>9033945
pretty regularly for me too. math grad, i can keep away the thoughts so long as I am currently reading a math book or doing problems. once i put it down the thoughts come back.

been doing some programming in C recently to try and have another interest which should distract me from kms. first i did all of elementary linear algebra, then programming high efficiency ODE solvers using the linear algebra and memory management stuff i made. gonna do sound wave sorting/clustering system next. maybe then i won't want to die?

[Anonymous No.9034027]

>>9032944
Nah, my research concerns harmonic analysis and nonlinear pde's, though we usually do things with applications to physics in mind. Essentially it turns out that propagators give some incredible insight into what's going with more generic pde's in physics than what we have seen explored in the literature. Unfortunately it's nowhere near completion, though we have a lot of nice, albeit scattered results, we still need to get the general framework pinned down.

[Anonymous No.9034046]

>>9033963
If there's calculators that can do almost any math problem in existence... what's the point of learning math beyond algebra?!1

[Anonymous No.9034057]

>>9033937
Nah, not anymore. I might be unhappy with my life, but I have been too lucky to just throw everything away. I want to see where it goes.

[Anonymous No.9034091]

>>9033945
Daily. I am at the point where I am desperately trying to come up with reasons for staying alive and the only thing I can think of is that my family would be devastated if I killed myself.

I dropped out of grad school (math, withdrew my file just 2 weeks ago) and told no one about it. My faculty's dean tried to talk me out of it and I was choking on tears during the entire discussion. It took me 5 years to finish my undergrad already. I made some really dumb decisions during my junior year which started an avalanche of other poor decisions that I have never managed to dig myself out of.

I am 27 now and I have nothing to hold on to. Just the fact that if I take my life, I would ruin the lives of the only people that ever cared about it. I wish I had never been born in the first place.

[Anonymous No.9034095]

>>9034091
The universe either operates by determinism or determinism dictated by random chance, or by some divine operator. If it's the later, he has a purpose for you and you must listen to it. If it's the first, then your future is already set in stone, if it's the middle, then you're just a collection of atoms and chemical reactions interacting randomly. I like to think it's the later. It gives me a sense of direction, even if I can't prove it.

[Anonymous No.9034099]

>>9033904
z/d^2 then, typo, you know what i meant

[Anonymous No.9034111]

>>9034099
I see what this math is, but what is the application anyways?

[Anonymous No.9034115]

>>9034111
who cares? solve it for the sake of solving it, not because you want to get cucked by real life

there are applications to number theory like cryptography (although thats more analytical), and codes (more alg geometry) anyways

[Anonymous No.9034119]

>>9034115
Okay then... I'll just plug in the variables and throw it in a calculator..... wow such science. Could write a program to do the whole damn class I bet.

[Anonymous No.9034122]

>>9034115
I don't understand why I need to know anything beyond algebra, basic mathematics, and basic data anylitics.

[Anonymous No.9034127]

>>9034095
>determinism dictated by random chance
No. It's definitely deterministic. I'm currently working on a proof.

[Anonymous No.9034128]

>>9034119
if only algebraic number theory were that easy...

Challenge question: find all solutions over the integers to [math]x^2+54=y^3[/math]

>>9034122
that's why youll always be a brainlet

[Anonymous No.9034131]

>>9034128
for what purpose

[Anonymous No.9034134]

>>9034131
fun

[Anonymous No.9034135]

>>9034091
>I dropped out of grad school (math, withdrew my file just 2 weeks ago) and told no one about it. My faculty's dean tried to talk me out of it and I was choking on tears during the entire discussion
> Just the fact that if I take my life, I would ruin the lives of the only people that ever cared about it.
are you me?

[Anonymous No.9034138]

>>9034134

[Anonymous No.9034142]

>>9034091
>I made some really dumb decisions during my junior year which started an avalanche of other poor decisions
Elaborate?

[Anonymous No.9034149]

>>9034128
>if only algebraic number theory were that easy
It's actually pretty easy once you realize that it's decidable.

[Anonymous No.9034151]

>>9034027
That's interesting. In physics the propagator is synonymous with Green function (or a generalization thereof), which allows us to calculate correlations without explicitly solving the equations of motion. If I remember correctly nonlinear PDEs can be solved with the theory of distributions so I think you'll make some progress if you can generalize the concept of a Green function to a distribution.
Here's an article https://arxiv.org/abs/hep-th/0506146 about defining QFTs on manifolds with a boundary using Green functions (distributions) that connect solutions in the interior to the boundary of a manifold. Maybe this would help you with characterizing solutions of nonlinear PDEs that reduce to a linear one on the boundary?? I don't know.

[Anonymous No.9034190]

>>9033963
That sounds like a nice hobby, but not necessarily like a salvation.

>>9034091
>my family would be devastated if I killed myself
This and a few other people too is basically why I go on, too. If it makes you feel any better, I don't have any degree after 4 years either, and I'm gonna be 25 this year. t >>9033945

[Anonymous No.9034199]

>>9034190
I have your tears in a bottle, I wish you many good animes and fun vidiya

[Anonymous No.9034224]

>>9034119
I had a similar attitude to number theory. You're forgetting that arithmetic is undecidable. And whatever can be proven isn't amenable to algorithms in a straightforward manner (or really at all, with out current knowledge).

Have you actually ever tried seriously engaging the topic before?
I wonder if it's also a matter of the culture in the domain. For example, my number theory professor was a huge fan of the IMO. Olympiads are a pretty big thing here in general, one of the cultural leftovers of communism, which is perhaps part of the reason why this country has been punching way above its weight in the IMO, even after the playing field got wider. Anyway: He used to submit problems yearly (I think he still does). An utter dude-bro olympiad nerd this guy. So the entirety of our applications and homework consisted of international math olympiad problems. That class was brutal. I hated every single lecture and seminar.

[Anonymous No.9034228]

>>9034199
Cheers, m808.

[Anonymous No.9034230]

>25 and still in my undergrad

just reminder that some of you have it worse

[Anonymous No.9034244]

>>9034228
What is she smoking?

[Anonymous No.9034245]

>>9034046
so true. should neck myself now.

>>9034190
I'm hoping that if i have hobbies then I'll think life is interesting enough that i would rather stay with my hobbies than end it all. medium success so far.

[Anonymous No.9034261]

>>9034230
why are you 25 and still an undergrad ?

[Anonymous No.9034267]

>>9034244
Oregano.

>>9034245
Not impossible (in the non-classical sense).

[Anonymous No.9034277]

https://www.youtube.com/watch?v=3-f7zsW7EV4

>Didn't add up
>Forgot to carry a zero

[Anonymous No.9034286]

>>9034151
You got the basic gist of it anon (our hope is to also generate new techniques in numerically analyzing and solving these pde's as well, since, as you know, after you have the propagator you have a powerful tool at your disposal, one not already found in the theory of distributions), though since we're trying to do this rigorously (prof wants to send it to a pretty heavy mathematical physics journal) so properly developing the functional calculus necessary to justify the technique and establishing that the appropriate properties of the propagator follow through makes the analysis tricky. The saving grace though is that there has been a lot of great development in the analysis of nonlinear pde's thanks to gauge theory (and the whole of mathematical physics more generally). The link you posted is pretty interesting, (I actually found a question on physics stack that had linked similar papers https://physics.stackexchange.com/questions/5773/quantum-mechanics-on-a-manifold you might be interested in them), I hadn't really considered thinking about in terms of an ads/cft type relation, though that might work, thanks anon.

[Anonymous No.9034356]

>>9034286
>properly developing the functional calculus necessary to justify the technique and establishing that the appropriate properties of the propagator follow through makes the analysis tricky.
That's definitely the case. When you're dealing with quantized fields (i.e. operator-valued distributions) directly in the action instead of quantized measures in the partition function you cannot use classical means to evaluate the variation [math]\delta S[/math], since any Taylor expansion you might do will not in general give you the cancellations you want due to non-commutativity.
This is one of the reasons why many had abandoned the QFT approach a la Wightman or Schwinger and instead focused on the stat mech or Feynman path integral approach in order to do calculations.

[Anonymous No.9034376]

>>9034267
She is a bad girl, isn't she

[Anonymous No.9034378]

>>9034356
Yeah, that's accurate for the most part, though as long as certain results follow through I imagine there shouldn't be too many issues as you can go from one formalism to the other (calculating propagators via path integrals)

[Anonymous No.9034382]

>>9034376
Just a little silly, but who isn't?

[Anonymous No.9034392]

>>9034111
It's a little ironic to ask that. Look up RSA encryption. It relies on number theory(group theory). Keys for encryption can be made public by a Receiver, a Sender uses the key to make an encrypted message public, and only the Receiver can actually read the message. The internet relies on this.
>>9034131
>>9034122
You guys probably won't ever need advanced math. People in hedge funds will though
https://en.wikipedia.org/wiki/Neil_Chriss
https://en.wikipedia.org/wiki/James_Harris_Simons

[Anonymous No.9034411]

>>9034378
What's important in QM is calculating correlations.and Feynman path integrals allow you to calculate them perturbatively while the ab initio QFT makes you take into account all quantum effects before you can proceed. It's true that these formalisms are equivalent but one is much more useful than the other.

[Anonymous No.9034431]

What is a good textbook for a first course in graduate level complex analysis?

[Anonymous No.9034437]

>>9034411
Yeah, there are so few exact solutions that most things come down to being able to sufficiently approximate the solutions (the path integral and propagator making this task much more tractable, at least that's what I gather. Though I'm aware of aspects of gauge theory insofar as it is useful in pde's and have the functional analytic background, I'm still learning qft and very much a beginner at it.), being able to reproduce this in more generic nonlinear pdes is one of the goals of the project.

[Anonymous No.9034465]

I'm studying surface integers

Is it possible that spherical coordinates are the parametric form of sphere?

[Anonymous No.9034472]

>>9034437
The classical theory might be much easier to manage since you won't need to mess with operator algebras. Even if you do find what you're looking for, an application of it to QFT will still be a while off. I'm thinking that it's likely we'll need a new quantization scheme (e.g. taken from concepts in geometric quantization) instead of trying to patch up second quantized theories like what Wightman was doing if any new PDE/analysis techniques are developed.
Good luck to you tho anon what you're doing seems to be very interesting and useful even if QFT can't use it for a while.

[Anonymous No.9034483]

>>9034472
True, commuting variable make things much easier, at that point the difficulty comes in the right quantization procedure (as you said), I actually looked Woodhouse to try and see if it could be applied to what we are doing. There's also apparently some interesting results coming out of Kontsevich's scheme which may come in handy down the line. Thanks anon, I'll also keep that interesting comment about connections between interior to boundary solutions in mind.

[Anonymous No.9034598]

>>9034431
Barry Simon has a 5 volume set on analysis, part 2 a/b covers complex analysis very well, possibly the best I've seen.

[Anonymous No.9034603]

>>9034598
>the Barry shills are back in full force

[Anonymous No.9034612]

>>9034603
I'm not the guy who always posts the Barry simon image and links it to the ams website, that's another guy, I just like the book, it's a hell of a lot better than needham, though ahlfors or Rudin are also great, Simon is fantastic, have actually read of these books?

[Anonymous No.9034634]

>>9034612
>Simon is fantastic, have actually read of these books?
No.

[Anonymous No.9034675]

>>9034634
Then just download on lib gen like everyone else and take a look

[Anonymous No.9034896]

Here is a sequence.
1 3 5 9 12 21
What is the next number?
Tomorrow I will post the answer.

[Anonymous No.9035093]

>>9034896
I would love to have my feminine penis inside Akizuki's pussy, but the best shipfu is Warspite.

[Anonymous No.9035124]

>>9034483
Sounds like you have a good direction. If anything comes of my idea don't forget to credit Yukari Yakumo haha.

[Anonymous No.9035198]

>>9034134
I'm some random who's bad at math, but what I noticed is that clearly y >= 4. From that, I stumbled upon the solutions (17, 7) and (-17, 7) (obviously -x is a solution as well). Also, I proved that x must be odd. The reasoning goes as follows: it's impossible for a perfect cube to be congruent to 2 mod 4, and 54=2 mod 4. Therefore, x^2 can't be equal to 0 mod 4, or x^2=1 mod 4 which implies x is odd.

[Anonymous No.9035206]

>>9035198
Oh, this also means that y=3 mod 4.

[Anonymous No.9035212]

>>9035206
Continuing, x^2=1 mod 3, which implies that y=1 mod 3.

[Anonymous No.9035381]

>>9026770
Disregarding the obvious infinite regress:

Mathematics explores what possibilities exist for consistent patterns. Physics attempts to map a subset of those patterns onto nature with the maximal predictive power.

Yes, this assumes a lot.

[Anonymous No.9035392]

>>9035198
hint: those are the only two solutions

Im not too sure if you can show that through elementary methods.

[Anonymous No.9035412]

>>9035392
>show that through elementary methods.
Fuck that meme. Be a pragmatist and use all the tools at your disposal.

[Anonymous No.9035427]

>>9035412
https://math.stackexchange.com/questions/2228704/find-all-solutions-to-x254-y3-over-the-integers
my solution

[Anonymous No.9035659]

>>9035124
>(((Yukari Yakumo)))

[Anonymous No.9035675]

This is the first axiomatic field proof in
Apostol's Calculus, and it uses a property that
is (I think) the converse of the theorem proved, and is never mentioned before, nor after. It's not a field axiom, so what is it?

[Anonymous No.9035676]

>>9035412
>Fuck that meme
>>>/b/

[Anonymous No.9035717]

>>9035675
Maybe a better way of phrasing it would be "sum is well defined"? If a = b, then a+c = b+c, otherwise the addition operation wouldn't make sense.

In a field, + is a binary operation, which is just a function, so you're definitely allowed to make substitutions of this form.

[Anonymous No.9036071]

>>9026508
>3.
how do you define elliptic curves and what's the catch?

[Anonymous No.9036090]

>>9034896
i am math illiterate but i would say

1 3 5 9 12 21 25 35 50 55 61 79 89 107 115

[Anonymous No.9036101]

>>9035124
>Write paper
>"The author would like to thank Mongolian tapestry user Yukari Yakumo for helpful discussions"

[Anonymous No.9036110]

>>9034896
>>9036090
1, 3, 5, 9, 12, 21, 23, 25, 29, 31, 33, 35, 39, 41, 43, 45, 49, 51, 53, 55, 59, 61, 63, 65, 69

Numbers ending with "e"

[Anonymous No.9036115]

>>9036110
are you >>9034896 ?

[Anonymous No.9036118]

>>9036115
Nah, just a guy using oeis.org

[Anonymous No.9036123]

>>9035675
The addition is just a map [math]+ \colon \mathbb{R} \times \mathbb{R} \to \mathbb{R}[/math], only instead of [math]+(x,y)[/math] you write [math]x+y[/math]. Images in any map are uniquely determined by definition, all the more so in the [math]+[/math] operation.

[Anonymous No.9036129]

>>9036118
ok.

this is what i came up to

f(x) = x * (x / 2 + 1) - something involving log2(x)?

1*1-0 = 1

2*2-1 = 3
3*2-1 = 5

4*3-3 = 9
5*3-3 = 12
6*4-3 = 21
7*4-3 = 25

8*5-5 = 35
9*5-5 = 50
10*6-5 = 55
11*6-5 = 61
12*7-5 = 79
13*7-5 = 86
14*8-5 = 107
15*8-5 = 115

[Anonymous No.9036152]

>>9035675
>Where does this come from?
To give a more 'proximate' answer - it 'comes' from the first paragraph in 'I 3.2' in the book

[Anonymous No.9036190]

>>9036123
>[math]\mathbb{R}[/math]
No such thing, anon.

[Anonymous No.9036235]

>>9030290
It's really just two anons posting anime as avatars

[Anonymous No.9036238]

>>9036190
elaborate

[Anonymous No.9036240]

>>9030405
Yup. Mods are a fucking joke

[Anonymous No.9036242]

>>9036240
>Yup. Mods are a fucking joke
Mods don't work unless you report posts.

[Anonymous No.9036252]

>>9036242
This meme again *yawn*

Are you the same halfwit from the meta thread? Die in a lake

[Anonymous No.9036256]

>>9036252
>This meme again
>>>/b/

[Anonymous No.9036259]

>>9036238
What is there to elaborate on?

[Anonymous No.9036262]

there are clearly more than 2 people posting anime.
and stop samefagging

[Anonymous No.9036264]

>>9036262
Indeed, but I wouldn't consider avatarfags to be "people".

[Anonymous No.9036270]

>>9036252
>Are you the same halfwit from the meta thread?
I've been posting in the meta thread, which halfwit do you mean?

You don't think mods just sit around browsing /sci/ looking for posts to delete do you?

[Anonymous No.9036276]

>>9036259
I've yet to hear a convincing argument why to reject real numbers

[Anonymous No.9036279]

>>9036264
let me guess: your ban expired so you returned to shitposting in /mg/
kys

[Anonymous No.9036289]

>>9036240
Mods have given up on this thread. /sci/ has minimal moderation as it is and they can't spend every minute of their time playing whack-a-mole with ban evading avatarfags

[Anonymous No.9036294]

>>9036289
Avatar bans only last a day or two

[Anonymous No.9036295]

>>9036294
Ban evasion bans last 30 days

[Anonymous No.9036301]

>>9035717
Thanks, it's nice to know that there's a proper name for this concept in general. Is well-definition
of sums (and products) a consequence of the field
axioms in Apostol, or is it necessary to state that
sum and product are binary operations?

[Anonymous No.9036305]

>>9036295
>Ban evasion bans last 30 days
Then they're probably waiting out their avatar bans (like I did), not getting banned for evasion

[Anonymous No.9036311]

>>9036276
It's a joke based on this guy called Wildberger (who actually has a pretty decent video series on the history of math) who is an ultrafinitist who not only says that infinity doesn't exist but that only algebraic numbers and certain transcendentals should be considered real and the the real line doesn't actually exist.

[Anonymous No.9036314]

>>9036311
>who not only says that infinity doesn't exist
he doesn't even believe in [math] \mathbb{N} [/math]?

[Anonymous No.9036324]

>>9036314
>he doesn't even believe in N?
He doesn't believe in a lot of things anon.
https://www.youtube.com/watch?v=WabHm1QWVCA
https://www.youtube.com/watch?v=REeaT2mWj6Y

[Anonymous No.9036332]

>>9036314
He believes [math]\exists \max \mathbb{N}=[/math](№ subatomic particles in the universe).
We will never need a bigger [math]\mathbb N[/math]

[Anonymous No.9036337]

Oh, the spammer is back. Is whining about anime in /mg/ your hobby or something? You didn't answer last time I asked so I have to ask again: did you get cucked by a weaboo with a phd in math? Is that why you can't stand anime and math?
>>9036071
A nonsingular projective curve of genus 1 with a rational point. (There actually isn't any catch.)

[Anonymous No.9036339]

>>9036262
Not samefag. Probably more but I do know animeposters in /mg/ spam more than anywhere else

[Anonymous No.9036346]

>>9036339
I was talking about the 1 or 2 guys who do nothing but complain about anime itt
post math anytime fags

[Anonymous No.9036424]

>>9036337
>Is that why you can't stand anime
I actually love anime. I just hate avatarfags (subhumans).

[Anonymous No.9036434]

>>9036311
>It's a joke
But it isn't.

[Anonymous No.9036451]

>>9036276
Looks like your brain has already been tampered with.

[Anonymous No.9036475]

>>9036311
>who actually has a pretty decent video series on the history of math
What about his videos on algebraic topology?