/sci/ - Science & Math

Is there any good mathematics behind stock market analysis?

Most of these wall street people who claim to be professional analysts don’t actually have the maths education to interpret the mathematics seen in statistical mechanics, stochastic processes, and dynamical systems, which undoubtedly should be able to explain market movement better than drawing lines on a candlestick chart.

But I do damnit and I want to use my meme education to make money. I just can’t help but think there must be some deeper mathematics which can analyze these processes in a far more coherent manner than the wishful-thinking, hand-wavey arguments seen in most so-called “technical analysis.” I just haven’t been able to find proper resources to learn myself, because most of the material on technical analysis is written by people who don’t understand mathematics, for people who don’t understand mathematics.

>>10167530
Most of these wall street people who claim to be professional analysts don’t actually have the maths education to interpret the mathematics seen in statistical mechanics, stochastic processes, and dynamical systems,
They do. Stochastic processes is easy stuff, you can teach it to children.

>>10167530
>I just can’t help but think there must be some deeper mathematics which can analyze these processes in a far more coherent manner
I don't know why you would think this.
The stock market is not a natural phenomenon. Even in its modern computer-driven state it's still fundamentally determined by human behaviour, and humans very rarely make mathematical sense.

>>10167530
hmmm

>>10167585
Human behavior in terms of retail investors making market decisions can still be categorized and produce trends. The majority of market volume is not retail investors, and by mandated liquidity of markets via market makers, as well as ever increasing algorithm driven high-frequency traders, the end result is that decisions are not as human as they might seem from the outside looking in. But regardless, a random process in which each state is equally probably should provide some means of meta-analysis.

why is she so perfect?

Are analytic sets used for anything or are they just measure theoretic wankery?

>>10168685
help me frens

>>10167486
what job did you get with a BS in math?

>>10168778
part time at any fast-food restaurant

>>10168778
>bs in maths and browsing /mg/
What would be the point? If I were studying maths at uni I'd discuss maths with my uni friends, not random high schoolers on a mongolian checkers forum.

https://www.youtube.com/watch?v=nMT44uK5ke0
is he /our guy/ ?

About to start a Masters where I'll focus on diff geometry and its applications to physics.

How good are my prospects after this? Is there funding in this shit? Career opportunities?

Is [math]||f||_{p}[/math] being well defined sufficient enough information to claim [math]f\in L^{p}[/math] ?

>>10168855
>categories

>>10168855
Kudos to him, but it seems to me that he is just parroting definitions, some of which he doesn't understand.

>>10168855
I'm puzzled by the comments on the videos. Who the fuck decides to learn Category theory from some prepubescent kid on Youtube?

>>10169083
Try reading the definition.

>>10169299
It is, since for the p-norm to be defined, [math]|f|^{p}[/math] has to be integrable.

What's the intuition behind the norm of [math]L^{\infty}[a,b][/math] as defined: [math]||f||_{\infty} = \text{ess}\sup{|f|} [/math] ?

>>10169385
For simple functions it's literally just the limit as p approaches infinity. Then you generalize.

>>10169410
Do you mean simple functions in the strict sense or are you talking loosely ?

>>10169424
I mean simple functions in the sense of "finite linear combination of indicator functions"

>>10167486
>True or false? A local artinian ring has finitely many prime ideals

I think this is true, but my proof never uses the local assumption. Tell me if this makes sense.

Let [math]\{P_\lambda\}_{\lambda \in \Lambda}[/math] be the prime ideals in [math]R[/math], and suppose we have a well-ordering for [math]\Lambda[/math]. Then we have a descending chain [math]\sum_\lambda P_\lambda = I_0 \supset I_1 \supset ... [/math] of ideals formed by removing the ideals [math]P_\lambda[/math] from the sum one by one. By the artinian assumption, this must terminate in finitely many steps. So if [math]P_0,...,P_n[/math] were the first to be removed, then the remaining sum must be 0, because the chain [math]I_0 \supset I_1 \supset ... [/math] will eventually reach 0 after removing all the [math]P_\lambda[/math]. So [math]P_0,...,P_n[/math] were the only (nonzero) prime ideals after all.

>>10169385
Essentially, its just the largest value of the function while ignoring any "single" points that might be larger. (By "single" I points from a set of measure zero.)

>>10169610
You don't need localness. All Artinian rings have this property.
Although it's not clear to me that there's any part of your argument that refers to the fact that the ideals are prime, and you do need this assumption.

I think it's cleaner to do the contrapositive of this personally, but with your additional assumption the statement is completely trivial if you know enough theory to claim that prime ideals are maximal in an artinian ring.

>>10169646
>prime ideals are maximal in an artinian ring
What theory do I need for this? Is there a quick proof?

>>10169661
>Is there a quick proof?
It's not very long. You can prove in a paragraph that Artinian integral domains are fields.

Then modding out by a prime gives you an artinian ID, so you get a field which means the prime ideal was maximal.

>>10169663
Neat, thanks anon

I don't want to do a PhD

>>10170459
pussy ass nigga

>>10167486
>first semester real analysis
>first eight weeks covered the usual shit in a logical order: naturals, integers, reals, topology of the reals, and convergence
>second eight weeks has been helter-skelter shit: continuity, derivatives, power series, fundamental theorem of calculus (after skipping riemann integrals entirely), and now change of variables in multiple integrals
>no shit, the prof had us taking jacobian determinants and computing double integrals in lecture today--not sure if we're even going to cover riemann integrals at this point
I seriously hope this shit hole doesn't lose its accreditation, but I would not be surprised if it did. The curriculum is a shit show, and the prof (whose credentials are a MA in Education) is teaching the same course graduate students. The only proper PhD in math in the department is stuck teaching college algebra and calculus. It's hot bullshit.

>>10170584
>""""""""analysis""""""""""""'
>skipping Riemann integration
you sure you signed up for the right course?

>>10170584
Just learn it yourself its relatively simple. Did you at least go over darboux integration and establish an equivalence?

>>10170660
>tfw just now realizing that we were taught Darboux integration instead of Riemann integration in my analysis i class
I mean the equivalence doesn't seem too complicated from the wikipedia skimming I just did but still

>>10170746
>doesn't seem too complicated
>literally half a line showing that a Riemann sum is smaller than an upper sum and larger than a lower sum

>>10170595
Yes, unfortunately.
>>10170660
The only integration we've covered so far was in the fundamental theorem of calculus and our most recent lecture on multiple integrals. I plan to learn it myself before the final and revisit it in my gap year before grad school.

>>10170749
I've never seen the actual Riemann sum definition before jeez anon. I agree it's intuitively obvious but I don't do much analysis and am cautious about these things

>If [math]R[/math] is a finite ring, some powers of each element is an idempotent.
why?

>>10168821
>uni friends
Mathematically speaking, is it even possible to make friends in uni?

>>10171161
Tautologically true.

>>10171170
How?

>>10171175
Trivially.

>>10171177
I don't follow.

>>10171161
Say the ring has n elements. Now take any element of your ring (let's call the element A) and make a list of that element to each power from 1 to n+1 with n+1 included (i.e. A, A^2,....A^(n+1)). Each of those is an element of your ring, but by the pigeonhole principle two of those elements are the same, let's say A^k and A^(k+h) with 1=<k<k+h=<n+1. Now,
[math](A^{kh})^2=A^{kh}A^{kh}=A^{k(h-1)}A^kA^hA^{h(k-1)}=A^{k(h-1)}A^{k+h}A^{h(k-1)}=A^{k(h-1)}A^{k}A^{h(k-1)}=A^{kh}A^{h(k-1)}[/math]
repeat this procedure until you're left with [math](A^{kh})^2=A^{kh}[/math]

>>10170660
Why do we still use these weak ass integral definitions when measure theory exists?

>>10171211
measure is harder to define and difficult to motivate until you see the limitations of the RI

>>10171202
B&R.

>>10167530
extensive research and assessment of the planned future actions of a company will yield you far better results than numerical analysis. practice with small sums of money to build experience and learn how to recognize trends. specialize in one industry (preferably one on an uptrend) and learn its inner workings as well as possible, then invest in the company you are most confident in. good luck

>>10171216
>measure is harder to define
Is it? I feel like you could teach enough to define the Lebesgue integral in a first year course assuming your students aren't mentally challenged
>and difficult to motivate
I disagree, it's pretty intuitive as long as you don't get into the harder stuff

>>10171164
I have friends at uni, but I'm studying money and people in maths are probably somewhat more autistic.
But I could make friends with bricks so the point stands.

>>10167530
no. the efficient market hypothesis is correct enough that any meme analysis technique is worthless

>>10171211
What undergrads think Lebesgue integration is
>ayoo lemme just use the lebesgue equivalent of the fundamental theorems and measure literally anything
what Lebesgue integration actually is
>do I have a Riemann-integrable function that's equal a.e. to that? No? Hmmm, seems like I'll have to use some other tricks to turn this into a Riemann integration problem

>>10171260
Even if what you were saying was true, it doesn't adress my point.

>[math]L^{1}[a,b]\subsetneq L^{2}[a,b][/math]
Would not [math]f(x)=\frac{1}{\sqrt{x}}[/math] prove this instantly?

>>10171274
Yeah.

>>10171282
Is there a stronger counter-example though? Something which is in [math]L^{1}[/math] on an arbitrary interval but not in [math]L^{2}[/math]?

>>10171211
you still have to prove that the integral can be computed using antiderivative

>>10171260
Agree. If you are encountering integration for the first time, the case you are most interested in is that of continuous functions. In that case Riemann/Darboux is sufficient to have differentiation theorem (fundamental theorem) and fubini, which is what you need in other contexts (basic geometry and such).
It is true that measure theory and Lebesgue (and such) integration are interesting, but it is much work which you won't even need.

>>10171211
Riemann-Stieltjes is the real redpill.

>>10171306
>but it is much work which you won't even need.
Dominated/monotone convergence theorem.

>>10171309
That's still a special case of generic integration with an arbitrary measure.

>>10171310
Uhm, you want to ensure Lebesgue integrability? What I am claiming is that for continuous (or smooth) functions the basic theory is well seen with Riemann integrals. I am not saying that Lebesgue is not useful, even in that context it has many applications. And I like it very much (for someone who is not 'interested' in analysis). But I fail to see how one first year undergraduate is expected to study Lebesgue integration. In particular
>Why do we still use these weak ass integral definitions when measure theory exists?
is a bad comment for 10170584. We use them when it is sufficient, that's all.

>>10171320
What I'm saying is that Lebesgue measure is a lot stronger for slightly less work.

Is it true that if I have an open subset [math]A\subset\mathbb{R}^{2}[/math] and I take a point in it [math]x[/math] and I take [math]r=d(z,Fr(A))[/math] then the ball of this radius and center [math]z[/math] is the largest ball contained in the set with that center?

>>10171240
Maybe it is possible, then.

Does anyone have a proof of [math]\displaystyle \lim_{p\to \infty} ||f||_{p} = ||f||_{\infty}[/math] or at least a sketch? My professor mentioned it but skipped out on the details due to time and it's not shown in the textbook.

>>10171462
google is your friend

>>10171462
Here is a stupid way of thinking about it, consider some simple function, let's say is takes value 10 on the interval [a,b]. This function is quite nice, it's bounded, and is in every L^p space over the real line. Let's consider the limit you're looking at, this integral is easy to compute, it is (10)*(b-a)^(1/p), and as p goes to infinity this is just 10, which is what you want from you L^infinity norm. This sketch is basically what you do, decompose your function into simple functions, which they themselves are finite linear combinations of scaled indicator functions as above and run the same process with them. Because you have a linear combination of simple functions it requires one of two more steps, but not much else. Then you merely note that these simple functions are dense in your L^p spaces and since you can run this procedure with them you can run the procedure with linear combinations you have the desired limit. That's really it.

>>10171472
Trying to mimic another proof which used a squeezing arguement. Got as far as saying [math]\displaystyle ||f||_{p} = ||f||_{\infty}\left[ \int_{a}^{b}\left(\frac{|f|}{ ||f||_{\infty}}\right)^{p}\right]^{\frac{1}{p}}[/math] but I need to get rid of that messy integral with some inequality. I know that [math]|f|\leq ||f||_{\infty} \implies \frac{|f|}{||f||_{\infty}}\leq 1[/math]. Just not sure what to write here: [math]||f||_{p} \leq ||f||_{\infty} ?^{\frac{1}{p}}[/math] . Perhaps: [math]||f||_{p} \leq ||f||_{\infty} ||f||_{1}^{\frac{1}{p}}[/math] ?

>>10171531
well no, you get the inequality:
[math]||f||_p \le ||f||_{\infty}(b-a)^{1/p}[/math]
Now of course, if you want to use a squeeze argument, you have to get a lower bound. How do you suggest we do that ?

Let $n=p$ be prime. Suppose $[a], [b] \in \bZ_p$ with $[a] \neq [0]$.
Show that there is a unique $[q] \in \bZ_p$ such that $[b] = [a][q]$.
Can you make sense of ``$\frac{[b]}{[a]}$'' in $\bZ_p$?
(Hint: Show that ``multiplication by $[a]$'' in $\bZ_p$ is an injective function,
and hence bijective.)

anyone? pls. pretty confused.

>>10171895
[math] [/math] instead of $$
e.g. [math] n = p [/math] instead of $n=p$

>>10171899
Sorry I mean: [math] [ /math] (without the space between [ and / )

Let [math]p[/math] be prime. Suppose [math][a], [b] \in Z_p[/math] with [math[a] \neq [0][/math].
Show that there is a unique [math][q] \in Z_p[/math] such that [math][b] = [a][q][/math].

(Hint: Show that ``multiplication by [math][a][/math]'' in [math]Z_p[/math] is an injective function,
and hence bijective.)

>>10171909
>Let p be prime. Suppose [a],[b]∈Zp with [math][a] \neq [0][/math].
>Show that there is a unique [q]∈Zp such that [b]=[a][q].
>(Hint: Show that ``multiplication by [a]'' in Zp is an injective function,
>and hence bijective.)

>>10171911
I got to the point where I have x(pn+a)=y(pn+y) and therefore x=y to show that it is an injective function, but my problem is I dont feel my reasoning is sufficient. More specifically what if p was a composite integer, how would that change the steps i took. I represented [a] with pn+a, [x] with pn+x, and [y] with pn+y

>>10171913
sorry i have y(pn+a) on the right side and because multiplication is well defined i just multiplied it out.

>>10171289
If x is in [-1, 1], f(x)=x^(-1/2)
Otherwise, f(x)=0.

>>10171846
some proofs bound it below by [math]||f||_{\infty}[/math] but I have no fucking clue why.

>>10172147
that is to say, [math]||f||_{\infty} \leq ||f||_{p} \leq ||f||_{\infty}||1||_{1}^{\frac{1}{p}}[/math], but I have yet to see a justification for this step.

>>10171911
Hint: this is actually a property of units, hence since Zp is a field, for every Nonzero element:
>an element a of a commutative ring R is a unit if and only if multiplication by u is bijective.
In fact, you only have to prove injective or surjective in a finite ring since bijective is automatic from that

I’m considering majoring in maths while in the army reserves. Will it be too hard?

>>10172276
Why would it be?

>>10172279
I get the impression that a lot of you guys are students that don’t work on the side

>>10172283
I worked 6 hours a day while doing my master's degree. I graduated with the best possible grades.

>>10172276
>Will it be too hard?
Only if you slack.

>>10171462
>but that's wrong
Denoting Lebesgue measure by [math]\lamba[/math], we can construct new measures by [math]a \lambda=\mu[/math], where a is any postive.
[math]||f||_{\infty}[/math] is invariant under any [math]/mu[/math], while any other [math]||f||_p[/math] clearly isn't.

Ever since I heard people can learn math in their sleep I've began thinking more about it in my sleep without lucid dreaming. Anyone else share this?

>>10172391
I've had some insights during sleep, but only after hours of studying non-stop. I don't believe you can do that without being heavily exposed to the material.
But I have to say that most of the time it's just hallucinations. One time I dreamt of solving the riemann hypothesis, but it was only a hallucination, of course. It's pretty cool.

>>10172391
>>10172391
I've had some Eureka moments in my sleep, sadly most of them I forget after I wake up. In one of them, I truly understood projective space which is killing me not to know.

hmmmmmm

HMMMMMMMMMMMMM

>>10172511
I beg your pardon

>>10172526
LAX YOU SHILL I KNOW IT'S YOU
BUT THE BOOK IS GOOD SO I'LL FORGIVE YOU

>>10172338
There is no contradiction. The scaling factor that appears in front of [math]||f||_p[/math] converges to 1 when p goes to infinity.

>>10172147
Well I don't know about that, it looks suspicious (on [0,1], it would imply that all positive functions are a.e. equal to their sup). However, we have the next best thing.
Recall that, for each [math]\varepsilon > 0[/math], we have [math]\lambda(\{x \in [a,b], |f(x)| \ge ||f||_{\infty} -\varepsilon\}) > 0[/math], where [math]\lambda[/math] is the Lebesgue measure.
I am not sure what your definition of [math]||\cdot||_{\infty} [/math] is. Either this is by definition or, if you are working with continuous functions and defining it as the supremum, this should be an easy exercise.
Then, for each [math]\varepsilon > 0[/math], set [math]A_{\varepsilon} = \{x \in [a,b], |f(x)|\ge ||f||_{\infty} - \varepsilon\}[/math]. We have:
[eqn]||f||_p^p \ge \int_{A_{\varepsilon}} |f|^p d\lambda \ge \int_{A_{\varepsilon}} (||f||_{\infty} - \varepsilon)^p d\lambda = \lambda(A_{\varepsilon})(||f||_{\infty} - \varepsilon)^p.[/eqn]
Then, we have: [math]\lambda(A_{\varepsilon})^{1/p}(||f||_{\infty}-\varepsilon) \le ||f||_p [/math]
Letting [math]p[/math] go to infinity and recalling that [math]\lambda(A_{\varepsilon}) > 0[/math], we get [math]||f||_{\infty} - \varepsilon \le \liminf\limits_{p \to \infty} ||f||_p.[/math]
This being the case for each [math]\varepsilon > 0[/math], we get [math]||f||_{\infty} \le \liminf\limits_{p \to \infty} ||f||_p.[/math]
The other inequality [math]||f||_p \le ||f||_{\infty}(b-a)^{1/p}[/math] yields [math]\limsup ||f||_p \le ||f||_{\infty}[/math], which completes the proof.

abolish ZF (and C)

>>10172636
>not even trying

>>10172636
>rejecting the fact that every surjective function has a right inverse
weak

>>10172654
proof?

>>10172271
Im not in abstract algebra yet. This is my introduction to proofs class

>>10172271
Yea i know that [math] Z_p[/math] is finite, i am having trouble proving surjectivity or injectivity

>>10172799
(1) Suppose f(x)=ax is bijective. Then it is surjective, so f(y)=1 for some y in R, but then ay=1=ya.
(2) Suppose a is a unit and define f: R -> R by f(x) = ax. If x is in ker f and b is the inverse of a, then you have 0 = bf(x) = bax = x, so ker f = 0 and f is injective.

>>10170746
riemann implying darboux is easy to prove, but darboux implying riemann is much more difficult.

>>10172951
>implying
Darboux implies Riemann because to any partition, the lower sum is lower or equal to a Riemann sum, which is lower or equal to the upper sum. If the partition can be refined until the upper and lower sums are arbitrarily close, the Riemann sum is boxed in. Done.
If the lower sum has no supremum, then Riemann sums can be made arbitrarily small. If upper sums have no infimum, Riemann sums can be made arbitrarily big. Done.

>>10172981
obviously, it's much easier to prove something once you've already taken that class and have all the foresights... I don't think you can come up with
>refined until the upper and lower sums are arbitrarily close, the Riemann sum is boxed in
if you had just started an analysis class, and only have Riemann and Darboux integrability definitions to work with.

>>10172930
I have not taken abstract algebra yet. I am proving it using properties of equivalence classes and injective/ surjective functions

>>10173055
I literally never had an analysis class, and the other proof was made on the spot.
We all start stupid tho, you'll get there someday.

I like analysis and PDE but I feel bad because I think it's a brainlet field. Help.

>>10173069
Don't let others judge you. Analysis is fun and full of cool people. Pursue your passion anon.

>>10173069
How is analysis a brainlet field?
>inb4 real analysis
Maybe, but functional analysis, Fourier analysis and analysis on manifolds are fairly hard.

>>10173082
>analysis on manifolds
You mean differential geometry?

>>10173092
Yeah, but then it doesn't have analysis on the name.

I think I wouldn't find analysis such a brainlet field if there wasn't so much personality cult around it.

>>10172654
Abolishing AC isn't the same as postulating it's negation. It's just assuming a much weaker form of it like countable or dependent choice. That's perfectly valid because if you cannot write a set explicitly you shouldn't be able to choose elements without defining properly such function.

>>10173064
you didn't come up with using refinement, dipshit, you already knew what a refinement is because it's literally the first idea given in any textbook on analysis. if you already defined what a refinement is, and the necessary lemmas to make that proof, then it's obviously easy.

>>10173126
>the only way to learn analysis is taking an analysis course
Imagine actually believing this.

>>10173131
didn't say that at all.
i don't care where you get your material, if you've been already given enough intuition on the subject, then saying something that's on the first chapter's easy is literal autism.

>>10173058
I have not taken "concrete give a fuck" yet. I am proving it like that.

>>10173156
>the proof is literally trivial if you know what a partition is and can actually read the definition
>I said it wasn't but fuck you for saying otherwise and actually knowing stuff you bastard

>>10172798
>>10172799
Then why the FUCK are you here, dipshit? This is MY board, MY thread, MY fucking conversation. I gave you a hint, dickwad, and what PATHETIC excuse you give me. I didn't ask you what you know or don't know because I DON'T FUCKING CARE. Next time considering injecting a COCK up your ass and surject CUM all over your face.

how would you go about proving that the only entire function that satisfies [math]f(z)=c(f\circ f)(z)+z(1-c)[/math] must be a translation [math]z+k[/math]

>>10173484
Did you try differentiating both sides?

>>10173540
Yes, but I'm trying to avoid using that. It's pretty easy doing that, but maybe there's some wizardly way to do it.

>>10173545
iirc the only linear holomorphic functions on the complex plane were translations and scalar multiplications. Did you try using that?

>>10173565
Nevermind, forgot translations weren't linear.

>really like math
>also like money
>hate finance
What do? Quantitative analysis is boring as shit, but I don’t want to be a poorfag after grad school. Where are the well-paid but interesting mathematician jobs?

test

>>10173611
You can use 4channel.org/banned for that.

>>10173225
Ok cocksucker weebfuck. Let me stab you in the mouth when i see you

>>10173425
My professor requires that i prove this stuff using the material he taught us. Also is it recommended that I study ahead for future classes that I have not yet taken, over break i will try to learn complex analysis because my teacher sux balls. Is this a good habit?

>>10173666
An angry amerimutt sent me an anonymous threat. I'm so scared now.

>>10173672
I was joking dipshit

>>10173669
>is learning stuff on your own a good habit
Not if it's curriculum material, no. If you're studying maths, learn physics or economics on the side.

>>10173675
No shit. american_intelligence.txt

>>10173672
Report her for a violation of US law, she will be banned.

>>10173680

>>10173425
based and merciless

How do you get better at problem solving?

>>10173768
solve problems

>>10173768
be my gf

>>10173792
I'm a guy though??

>>10173813

>>10173813
literally telling you to be his guy friend

>>10173828
But don't you just say buddy or friends? Why specifically gf? What is your solution?

>>10173850
why do i have to purpose a solution
not my problem

>>10173768
Unironically masturbating to ebony midget porn enhances iq. All the professors in my math department do it

>>10173082
>fairly hard
Messy maybe, but you can get quite strong results by proving things with families of seminorms. It's stupidly powerful

Why do engineers love cock?

>>10167530
>Most of these wall street people who claim to be professional analysts don’t actually have the maths education to interpret the mathematics seen in statistical mechanics, stochastic processes, and dynamical systems, which undoubtedly should be able to explain market movement better than drawing lines on a candlestick chart.

That is to maintain the pyramid scheme up. There is needed a huge amuont of succers to be benefitted from, so that the illusion of opportunity to gain from the stock market is not lost. If only 5% of the pyramid drops out in a year burning their bank accounts so that the higher ups can "rob" them there is no panic or loss of belief in the system. Then you can induce an economic "crisis" every now and then to keep idiots who seem to have figured it out at bay.

So no there is no mathematical shit that can give you an advantage. Read the papers and deduse things to come your self.
Keep in mind, "If it looks too good to be true, it usually is".

>>10173082

> >>10173069
> How is analysis a brainlet field?
> >inb4 real analysis
> Maybe, but functional analysis, Fourier analysis and analysis on manifolds are fairly hard.

Functional, and fourier analysis is hard if u'r iq is low, say <140. WHO standard, not american standard, in wich case it would propably be 160 or 180 IDK.

Seems there is a huge difference in scoring, though it should be gaussian graph over world population.

I tend to get 20 - 50 points boost to my score in american tests compared to the ones done on my own language, regardles the language barrier and incoprehencible instructions in some parts in the americanesian tests.

>>10173092 >>10173897

Also warpfield analysis is pretty dificult.

>>10173969
Idiot

Why do I enjoy real math when I'm severely depressed and contemplating suicide, and applied "math" when I'm otherwise content to stay alive?

>>10174163
Only brainlets are content with living, and they are the ones who enjoy applied """math""". True intellectuals appreciate pure math but are usually on the verge of suicide. That's just how things work.

>>10174170
nice projection here anon

Will Spivak's Calculus on Manifolds help me actually understand something about tensor calculus, or does it cover a separate topic?

>>10174221
its a good transition from advanced calculus to real differential geometry. if that's what you're looking for go ahead.

>>10173594
If it’s interesting, it’s usually not well-paid.

What's the name of the function defined as
[math]\lceil x \rfloor ^ y = |x| ^y \normaltext{sign}(x)[/math]
where x and y are real numbers?

>>10174683
It's called the x^y function, because if you'd remember you don't define powers of real numbers by interpolation, but by the exponential function.

>>10174686
wtf you're talking about. this isn't x^y

>>10174683
>>10174686
Also this comes up all the time in sliding mode control. But I hate this notation because[math] \lceil x \rfloor ^ y \neq (\lceil x \rfloor ) ^ y [/math]

Consider it as
def f(x,y)
if x!=0:
return np.abs(x)**y*x/np.abs(x)
return 0

>>10173969
>iq posting
>warpfield analysis
You sound like a turbo brainlet.

>>10173897
>fun anal isn't hard it's just messy
You're showing too much of your power level, it's impolite.

I'm currently doing a BS in math at pretty good university. I've noticed that when it comes to people doing their masters, or PhD students, they all seem like cool people, there's one autist or two, but everyone is overall pretty nice.

However, in my class we have one or two assholes. Real smug, superiority complex type people. They're smart, smarter than me, and probably among the smartest in the class. Where do these people go? Have I've just been lucky in not encountering these kind of people higher up, or do they actually disappear?

>>10175197
They get too busy IQ posting on /sci/ that they fail all classes and drop out.

>>10175197
I noticed that to. Those people go to better schools. Eventually do they meet their match and then they smarten up and stop being assholes.

>>10175204
They get so*

>you'll never be a mathematician in the early 20th or late 19th century when there was a world of possibilities and fields were just starting to be explored in depth
>your contributions will instead be limited to proving small results on hyper-specific classes of objects no one cares about
it's not fair

>>10175205
So I guess they just do their masters and PhD somewhere else? I mean, I don't go to the best uni, and I don't want to reveal too much since they're the kind of people that would browse these threads, but it's a top 100 uni, and we've had a couple of fields medalists come out of it. Most people, including these guys, are international students, meaning they specifically chose to come to this school rather than another. I should also point out that the actual smartest guy in class is super nice.

>>10175217
Yeah. I did undergrad in a top 50 uni and there were a couple of people like that there. They all went to top 10 unis for postgrad.

>>10175218
>tfw doing undergrad at poorly ranked uni
why do I even bother thinking about postgrad?

>>10175218
It honestly makes me upset knowing that these people will succeed. Hearing them outright insult my classmates makes my blood boil, and I've had to tell them off multiple times. It gets even worse since we have some other people on the autism/asperger spectrum who can't handle their rudeness at all, meaning they almost break down.

>>10173594
quant finance is actually a pretty interesting subject if you're into analysis/stochastic PDE/ Machine Learning

>>10173594
Try being an applied mathematician or computer scientist at Google, Facebook, Uber, or that type of companies more generally. It is doable if you are *very* (and I stress) good with algorithms, combinatorics, computer vision, statistics, that sort of things. Also, be a good programmer.

For the love of god

i have an exam in an hour and aside from otherwise being prepared, i forgot how to solve for V using these two equations, could someone quickly show me how?

math brainlet here

>>10175280
you fucked up

>>10175281
yes i did.

>>10175280
what is f?

>>10175338
darcy friction factor, it's unknown, solutions to these types of problems on line just say to solve these two equations to find V

I think "bidule" is a great word. Even before I read the parenthetical definition, this is pretty much what I assumed it meant.

I invented a word like that: "multiplex." I use it to refer to an array of unspecified dimension and transformation properties.

>>10175344
obviously I didn't invent this word, but I meant I rely often on a deliberately non-specific math word.

>>10175280
oh nvm, i guess the sensible thing to do would be to isolate V from (1), then just plug in that value in (4) to find the f value then plug that back into (1) for the V value eh

thanks sci

>>10175280
> [math] \epsilon [/math]
>D
>f
>V
>four variables
>three equations
Nigga I don't know what you expect me to do but I can't.

>>10175341
So is just dividing by the parenthetical stuff on the right side of the second equation then taking the square root not enough?

>>10175344
>Jon no longer namefagging
Officially no longer /the board faggot/, but /the board madman/

>>10175230
What kind of country is this? Cause it sounds really unprofessional. I mean, I met arrogant people but they still keep it low key.

>>10175512
Like I said, I don't want to reveal too much. He's an international student, as well, so he's not from here. He gets told off by teacher's assistants and PhD students as well, whenever they're around, and they see him doing this shit, so it's not like it's accepted behavior.

I'm trying to think of the most economic description of the function that maps sequences of zeroes and ones onto natural numbers. Suggestions?

>>10175647
describe the map more

>>10175569
Sounds like a one off asshole. Really weird. I am going to assume you are in the UK. Because this shit would not fly elsewhere. It can only be a really complacent culture. I am also an international student. I studied in non-English countries, though, and if I acted up, I'd immediately be blacklisted by the whole department, professors and students alike.

>>10175661
Literally the function that takes binary and maps it to natural numbers.
On one hand, "all sequences of zeroes and ones" is much cleaner, but using "all infinite sequences of zeroes and ones such that, for each [math]a_n[/math] there is N such that n>N implies [math]a_n=0[/math]" enables me to use bijection to just say that if a has 1 instead of 0 for some i, and b has no n>i such that b has 1 and a has 0, then f(a)>f(0) and this actually completes the whole thing, but it's disgusting to look at.

>>10175667
>>10175569
>>10175512
>>10175230
>>10175218
>>10175217
>>10175205
>>10175197
Since when are math majors such a bunch of namby pambys. Accept the fact that you wont be able to compete with them because of whatever reason you give and move on. Stop comparing yourself to other people.

>>10175858
>frogposter
>retarded opinion
like clockwork

>>10175240
Yeah that’s the problem, I’m not much into programming, I prefer fields like analysis, geometry or topology.
>>10175234
Most quants seem to describe the work as soul-crushing, hence why they often quit early.

>>10175902
you never attacked my argument. If you are going to get flustered at someone being a condescending prick to you, then perhaps you are more interested in the ego that comes with studying math than studying math itself

>>10175671
Just look up the conversion formula for binary to decimal.

>>10175985
Hm, I can't say I've heard that. A lot of people say it's a great balance between intellectual sttimulation and pay. However, I think those are the good quant jobs. Some quant jobs are literally algo babysitting, and I'll agree that that is not fun at all.

>>10175985
But a lot of the research that one of my analysis professors did on variational analysis of PDEs has many applications in derivatives pricing. Probelm is is that ever since 2008, the derivatives industry is not as lively as it used to be because of regulations and whatnot, which is a shame because it's the closest to pure analysis you might get to in the industry.

>>10176091
Unfortunately there seems to be no way to separate the good “quantitative researcher” job offers from the bad ones, and that’s assuming good jobs are even available, since high level quant positions are usually filled with talent already.
You might be right though, the people I talked to who quit mathematical finance were somewhat involved the software development aspect even if they weren’t devs themselves. They usually complained about the models being boring shit and having to deal with C++.
>>10176094
I don’t know anything about finance and markets, but PDEs are neat so I’ll look into that. I’m trying to find resources on any applications of general topology to finance, as well.

>thought I failed my oral quals
>turned out I didn't

>>10176135
For topology you could do topological data analysis. I have a professor at my school who does all kinds of applied topology. He even worked with topological robots.

http://www.kurims.kyoto-u.ac.jp/~motizuki/news-english.html
>2018-11-26
>(Past and Current Research) Updated the webpage containing a report and related documents on discussions conducted at RIMS in March 2018 concerning IUTeich.

http://www.kurims.kyoto-u.ac.jp/~motizuki/[Rpt2018]%20Revisions.txt
>(2018-11-26)
>Added (RLFU) and modified (VUC1) accordingly

http://www.kurims.kyoto-u.ac.jp/~motizuki/Rpt2018.pdf

>>10176057
The formula is trivial, I'm trying to find a prettybsolution.

>>10176201
Good job.
>>10176364
I promise to read him later, but not now.

1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...

To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit. For example:

1 is read off as "one 1" or 11.
11 is read off as "two 1s" or 21.
21 is read off as "one 2, then one 1" or 1211.
1211 is read off as "one 1, one 2, then two 1s" or 111221.
111221 is read off as "three 1s, two 2s, then one 1" or 312211.

What a fucking autistic sequence

>>10175344
"bidule" is just a french word meaning "some undefined thing", could be translated to "thingy" or "stuff"

>>10175280
>fluid mechanics
Just like plug in the numbers 4head

>>10170584
wtf I studied most of this in Calculus I & II in an engineering school
"Proofs" were given but most people slept through them

>>10175066
such is expected from Reimu but not Yukari.

Imagine a world where mathematicians and physicists switch places

What is the most obscure area of mathematics that you're familiar with?

Algebra feels insanely forbidden.

>>10177476
The homotopic Morita theory of differential graded categories.

Whats the most satisfying maths you've taken?

>>10177613
Morita theory is "very abstract linear algebra"

>>10177772
Euclidean Geometry is the absolute best fucking field in the entirety of maths, but it's basically entirely solved.
Second place is probably measure theory.

>>10177793
>satisfying
>basically entirely solved
by definition duh x)

>>10177787
And?

>>10177476
Bruhat-Tits theory

>>10177772
I always get perverse pleasure from long strings of inequalities in analysis, but it's not exactly satisfying.

>>10171911
I really hate when people write Z_n for Z/nZ. Z_p is reserved for p-adic numbers.

>>10178008
getting triggered about ambiguous notations that are literally never unclear from context is a great indicator of autism

>>10177801
Not only that but it's solved by very simple polynomial factorization algos via Groebner bases. Literally the most boring piece of math of all time

>>10177326
>imagine this world
What did he mean by this?

>>10177326
"Is the Riemann conjecture true?"
"Oh, definitely. We'd have found a counterexample by now if it wasn't."

so you want to get a PhD in mathematics

Evens: I study applied, modeling and simulations
Odds: I study mathematical physics

can anyone help me with this?

>>10179723
yeah

>>10179727
nice

>>10179723
>can anyone help me with this?
What have you tried?

>>10179723
D I V I S I O N
W I T H
R E M A I N D E R

anything missing from this?

>>10180449
Basically, until the sophomore year it's stuff every grad student eventually learns, but from then on it's random stuff. Learning all the random stuff is just about undoable nowadays.

Guys, apparently there is some book that explains basic linear algebra in an intuitive visual manner. It's what 3blue1brown based his videos on. Does anyone remember the name of it? I had is saved but lost it.

>>10180724
Probably Linear Algebra done right.
But in all seriousness learn Linear Algebra properly or Abstract will fuck you up the ass.

>>10180731
I've already graduated, lol. Never had a problem with Linear Algebra but I thought I should get around to learning about this new way of visualizing it.

>>10180449
This is absurd and pointless.

Guide to understanding modular forms from a representation theory perspective?

>>10180804
>This is absurd and pointless.
What do you mean?

>>10180818
Unachievable for a start, but also involves learning a ton of stuff which will never be relevant to whatever you specialise in.

Let U_i be an open cover of a topological space X, and let g and f be two continuous functions X->Y. Suppose the restriction to each U_i of f and g make the same function. I have to show that f=g globally.

Is it fair to conclude this with the argument?:
>f and g must be the same because they are completely determined by their values, which must coincide everywhere on X since the U_i are a cover

>>10180830
yeah. God I used to hate questions like that as an undergrad. Asked to prove something that's right there and obvious.

>>10180830
Gluing lemma.
>is it fair
Not sufficient

>>10180836
I wasn't asked to prove this, but I read that for schemes that argument is invalid in general, and since I'm working towards scheme theory, perhaps there's an obvious flaw to the argument here

>>10180837
I'm not gluing anything, that's the next step tho

>>10180830
Suppose that, for some point x, f(x)=/=g(x). There's an U_j that contains x. The restriction of f and g to U_j are equal in x. Thus, f=g.
It's either literally just that or I'm retarded.

>>10180855
>I'm not gluing anything
Yes you are. You're gluing the 0 function on each patch

>>10180874
There are no "0s" in general topological spaces

>>10180869
It's just that

>>10180882
But there is in abelian sheaves

>>10180869
>proof by contradiction
yikes

>>10180896
We name A the set on which f(x)=g(x). Thus, A contains every U_i. Since the union of every U_i contains X, A contains X.

>>10180818
If you need to be explained why this is ridiculous, then you need to get a math degree already and realize that math is more than titles of sections from a book.
Also, not everyone wants to be an arithmetic or complex algebraic geometer or topologist.
This board is obsessed with algebraic geometry to an unhealthy degree. It is ridiculous and detracts from the fact that there is a whole world of mathematics out there.

This is a general test of the level of /mg/. Don't post the answer, just comment if you don't get it.
If a set has an open cover such that no element of the set is in two elements of the cover, every set in the open cover is also closed.

>>10180989
Obvious, that means that each set is a maximal connected component which is equivalent to being closed and open

>>10181003
>using anything other than the literal definition of a topology
Failure. Complete and total failure. 0/10.

>>10181022
Nigga, just spell it out

You are saying that you have a cover of X which is completely disjoint. Choose any element U of the cover, and consider the union V of the rest of the elements. V is open as an arbitrary union of open sets, and V disjointunion U is X, so X\V = U is closed.
QED retard, next time you want your homework done just post it as such you fucking brainlet

>>10181053
>specifically asks people not to answer
>"if you want people to do your homework just ask it"
>calls people brainlets

>>10181059
Next time ask something that goes a bit further than applying the definition, brainlet. Even the anime poster that keeps posting TQFT parlance who has only ever read definitions would be able to answer that garbage of a question

>>10181068
That was the point.

I wanna test the level of /mg/, don't reply if you got the answer, reply if you couldn't get it.

Show that every connected regular Hausdorff space with at least two points is uncountable

I wanna test the level of /mg/, don't reply if you got the answer, reply if you couldn't get it.

Let [math] n [/math] be an odd integer [math] >2 [/math] and let [math] f(x)\in \mathbb{Q}[x] [/math] be an irreducible polynomial of degree [math] n [/math] such that the Galois group [math] Gal(f/\mathbb{Q}) [/math] is isomorphic to the dihedral group [math] D_n [/math] of order [math] 2n [/math]. Let [math] \alpha [/math] be a real root of [math] f(x) [/math]. Prove [math] \alpha [/math] can be expressed by real radicals if and only if every prime divisor of [math] n [/math] is a Fermat prime.

>>10167486
this may seem like a networks question, but it's just math. I tried to calculate the efficiency of a network with two groups in two ways. The first fails, the second works. Uses the regenerative method.

eta: efficiency
p1: probability of a success from group 1
p2: " " group 2

First way: E is number of failures
eta = 1 / (E + 1)
E = 0 wp p1, 0 wp p2, 1 + E wp 1 - (p1 + p2)


Second way: E is the number of slots taken to transmit
eta = 1 / E
E = 1 wp p1, 1 wp p2, 1 + E wp 1 - (p1 + p2)

Why does the second way create an incorrect result? This is for CSMA/CD if that matters

>>10181127
Can't because my Galois theory is absolute trash.

>>10180940
cope

>>10181879
Typical. I know that this is classic bait: either you study AG and you are trying to detract people from following, either you don't and you are coping.
It is still a point I wanted to make. There is nothing wrong with AG (I am getting a PhD in the area at the moment), but I feel like a lot of people are tricked into getting into it because of bald math guy, samurai math guy, memey category buzzwords and diagrams, and somehow believe that math is a pyramid with probability and PDE at the bottom and arithmetic geometry at the top, which anyone who knows anything about research math knows is ridiculous (first of all because nobody is going to be impressed by the field in which you work and second of all because these areas intersect in many cases).

>>10177476
Ask me anything in the Tits Group

>>10182885
I agree with what you said. I also work in AG and nobody cares if you do AG or any other field. But it's funny how younglings picture the pyramid.

>>10182885
Anyone who actually thinks PDE is an easy subject can do us all a solid and solve Navier-Stokes.

>>10182885
>math is a pyramid with probability and PDE at the bottom and arithmetic geometry at the top
It's literally true though. Pure math is real math, applied trash is physics at best.

>>10183364
pde is real math, """"algebra"""" is masturbating over stupid worthless definitions and structures. kind of like being a child playing with building blocks.
analysis is the only real type of math, and pde and harmonic analysis form the two pillars of the domain

>>10183364
Imagine still thinking like this
AG is unique in the sense that it combines a lot of disciplines that were otherwise relatively separated
The more research in mathematics will progress, the more we will see these interconnections
Remember that a lot of useful mathematical objects were constructed by physfags and refined by mathematicians, and that physfags are becoming more and more concerned with abstract mathematical objects and the mathematical reasoning behind

What do you think of this? Calculus book written in 1910 called Calculus Made Easy

>>10183437
>Now any fool can see that
Based

>>10183437
Telling people that things are really easy is good pedagogy, but you should be careful so that the stupid students don't feel that they are really stupid for struggling with the simple thing.
The whole text really makes me think of 1910.

>>10183364
Pure math is pure math, applied math is applied math. There is pure algebraic geometry, just as there is pure probability theory and pure PDE and there is applied algebraic geometry (used eg. in statistics, computer vision, cryptography), applied probability theory, and applied PDE (eg. numerical approximation schemes etc.), and obviously all of these interact.
You really have to the underest of grads to not realize that.

Ehrenfeucht-Fraisse Games:

Suppose that player Duplicator has a winning strategy for the game:

E((A, R), (B, S), 2)

(a) Suppose that R is transitive, prove S is transitive.

(b) Give an example to show that E cannot be dense.

I'm a complete hack. I'm "good at math" in the sense that I'm good at logical thinking and am moderately intelligent, but I have no passion for it beyond the passion I have for any intellectual pursuit. I certainly haven't dedicated myself to it. I've memed my way through REU and now I'm memeing my way through an honors thesis. I hate living this lie. It wouldn't be so bad if I was passionate about _anything_, but I honestly don't seem to be. I managed to trick myself into thinking math was my thing for a few years but I can't pretend anymore.

>>10183915
stop being a faggot

>>10183915
>I'm a complete hack. I'm "good at math" in the sense that I'm good at logical thinking and am moderately intelligent, but I have no passion for it beyond the passion I have for any intellectual pursuit. I certainly haven't dedicated myself to it. I've memed my way through REU and now I'm memeing my way through an honors thesis. I hate living this lie. It wouldn't be so bad if I was passionate about _anything_, but I honestly don't seem to be. I managed to trick myself into thinking math was my thing for a few years but I can't pretend anymore.
drop out

>>10183915
>I certainly haven't dedicated myself to it
>REU
>honors thesis

How come he never published?

>>10183978
I'm about to graduate, it would be pointless not to finish

>>10184034
I fell into those largely by luck and coasted through them with the bare minimum I needed to get by. I succeeded only because I'm clever enough to fake competence.

>>10184171
if you seriously think you are smart enough as a 3rd year undergrad to fool a mathematics professor for an entire thesis, then you suffer from some kind of pathological narcissism
if you don't, then you're being a drama queen for attention

either way, stop being a faggot

>>10184219
How do I know wether or not I am cut out for grad school. I am extremely interested in mathematics and I am willing to sacrifice anything to study it, I just have this nagging feeling that I am to stupid. Perhaps it is imposter syndrome and I know I am acting like a little attention seeking faggot, I would just like to here the opinion of other grad students who overcame their doubt. Is it a gradual process or are there indications? Why do I feel so stupid?

>>10184109

>>10184395
Bluepilled.

>>10184395
WTF is going on? He seems to be a brilliant guy with extremely insightful answers. I never looked up what he published to avoid butthurt, so I am really suprised now.

Perhaps, academia is really fucked? Can you be somehow a freelancer researcher?

I wanted to move out from this German shithole to some Portugal or whatnot. But I can't see how to get moneys without affiliation.

>>10183915
>babby's first mental breakdown
You're just hit a snag with you thesis and come crying about it on /sci/.
Best to just get over it and keep going, you'll probably be satisfied when you finish it.

>>10183436
>Remember that a lot of useful mathematical objects were constructed by physfags and refined by mathematicians, and that physfags are becoming more and more concerned with abstract mathematical objects and the mathematical reasoning behind
Wew, back up a bit there. It's more like mathematicians got inspired by physicists, who didn't really construct anything mathematically interesting.
There's a long way between writing down improperly defined integrals and talking about cobordisms or cohomology theories.

>>10184395
This is why I am not sure about mathematics. At least in physics you know the problem you are working on is important. In math, not so much. That doesn't really sit well with me.

Why is Algebraic Geometry so popular these days, whereas Differential Geometry is much less so? I am applying to grad programs and pretty much every single school proudly says they do ALGANT (Algebraic Geometry and Number Theory) but very few do differential geometry, I think many more do diff geo in the context of mathematical physics. Is diff geometry basically solved?

>>10184375
It's okay, it happens to anyone working in a creative and competitive field. No matter where you are in your career, you will always be surrounded by or competing with people who are doing things you don't understand, or people who are impossibly smart, or people who have an impossibly wide-ranging understanding of math, and it is hard to deal with it.
Certainly all the professors I have asked have this nagging feeling, and they are the ones who made it through. They just learned to tune it out.
But of course, you do not *have to* go through this. Just know that if you pursue math, you will feel dumb a lot of the time, either because you don't know what to look for, or because you tried something that does not work, or because you realized something you were working on for a week was a one-liner, or because some guy is doing alien-tier work in your field and you don't know what to make of it.

Which subjects in math have the least amount of calculations? Having to solve integrals and ending up with monstrous expressions makes me want to kill myself, I like expressing clean, theoretical relationships between objects. Number and variable crunching doesn't interest me

>>10185187
Literally any subject whose name doesn't have "analysis" or differential geometry.
Group theory has some autistic enumeration stuff too, but it's not as bad.
If you really like simple stuff, I'd recommend Category Theory.

>>10185189
Yeah, I prefer "complexity in simplicity", as pompous as that sounds. Never liked analysis, especially diffeqs.
Category theory is really neat, I'll look into it more deeply.

>>10185007
DG is basically solving PDEs on manifolds now, so mostly belongs to the analysis department

>>10185187
>Having to solve integrals and ending up with monstrous expressions makes me want to kill myself,

pretty sure most math is taught in this way to make you think of it as a collection of useless algorithms and rote pattern recognition, rather than a useful abstraction of real-world phenominon.

>>10185265
cont.

and someone here linked me to a guy who said as much. does anyone know who i'm talking about? didn't bookmark his page, but i might want to get in touch with him at some point.

>>10185265
What I meant is that using three pages and half an hour to integrate some ugly expression isn't really my idea of fun, whereas I enjoyed things such as my set theory course, complexity theory, or even some topology stuff. But as you put it, "rote pattern recognition", i.e. applying methods to convoluted but ultimately simple problems is not interesting.
>a useful abstraction
I'm aware of the usefulness of analysis. Even then, applied math isn't just about analysis, right?

>>10185270
>complexity theory
What the fuck is complexity theory?

>>10185271
The only interesting part of CS.

>>10185270

analysis is a good topic though. i've only ever had to grind through complicated integrals in calc 1 and calc 2. beyond that it gets much nicer, but unfortunately that's where most people's formal education ends, if they even get that far.

>>10185274
>i've only ever had to grind through complicated integrals in calc 1 and calc 2
Diffeqs can often get pretty nasty from what I've seen.

>>10185276

never took diffeqs.

>>10185274
>multivariable calculus is nicer than calc 1 and 2
>>10185273
CS has good parts?

>>10185282
Yeah, computational complexity theory. Some anon had posted papers that dealt with the application of CCT to cosmology, it was pretty cool but I lost the link.

>>10184849
>Perhaps, academia is really fucked?
took you THIS long?

>>10185276
diffeqs can get ugly in the computation but the theory alone gets my dick hard

>>10185418
>but the theory alone gets my dick hard
What about it is so satisfying?

Suppose we have a sum S of n-th roots of unity and suppose the norm of S is 1. Is S itself a root of unity?

>>10185422
something about eigenvalues and eigenvectors defining linear systems of equations just does it for me
i'd fuck a damped harmonic oscillator

>>10185195
>Yeah, I prefer "complexity in simplicity", as pompous as that sounds.

low barrier to entry and you haven't been conditioned to avoid the subject matter. everyone likes a good puzzle.

>>10185435
I don't think set theory has a low barrier to entry.
>you haven't been conditioned to avoid the subject matter
Once you get to university math, you're not taught to hate calculus anymore.

>>10185441

most books that derive the subject from first principles and don't take things too quickly are easy to get into. anyone can pick up intro to mathematical logic or intro to analysis, or any other junior to first-year-grad level book and go through it. these books have a much different way of presenting material due to their emphasis on logical consistency and inference rather than algorithmic plug-and-chug exercises.

>>10185187
Guess what, variable crunching is what real math is about deep down.
You will not escape from calculation, it is the mathematical equivalent of experimentation in physics.
Mathematicians do not spend their days in deep thought and suddenly come up with "clean, theoretical relationships between objects". They work with many examples then observe how they relate to one another, try to infer relations and then try to prove these conjectures.
All of that involves lots of calculations. Not necessarily computing integrals, but maybe computing reducing long algebraic expressions, multiplying matrices, drawing huge diagrams and checking commutation, computing intersections of ideals of polynomials, numerical simulations etc.

[math] x^x = 3. \implies x = e^{W(\ln(3))}.[/math]
[math] x^{x^x} = 3. \implies x = \text{New troll}. [/math]

>>10185008
Thanks, are there any indications that im not cut out for a math phd? Im in an introduction to proofs class and i have an A with the curve but I am unsatisfied with my performance. Also this is my first upper level maths class