/mg/ - Math General - Separable spaces edition.

[Anonymous No.14616492]

Previously >>14591893.

Talk math.

[Anonymous No.14616498]

First for kähler manifolds

[Anonymous No.14616549]

>>14616498
Uhm sweaty, Kahler was a nazi, ok???
Those gross ideas were debunked

[Anonymous No.14616591]

>>14616492
Algebra and CS aren’t math.

[Anonymous No.14616602]

>>14616591
Is there something that precipitates this comment?

[Anonymous No.14617233]

This one has me stumped…

[Anonymous No.14617339]

I might be retarded here, but bear with me.

I am studying the asymptotics of a function. I know that
[math]\limsup_{n\to\infty} \frac{\log f(n)}{n}[/math]
is finite and positive, and I know that it has some nice properties I want to use.
But then I encounter the expression
[math]\limsup_{n\to\infty} \frac{\log \left( f(n) - 1 \right)}{n}.[/math]
Is it just the same thing? Do I need to assume anything about f for it to work out? I can't for the life of me prove that the two expressions are the same, I must be missing something.

[Anonymous No.14617365]

>>14617233
Strategy? Don't they mean probability of being freed or something?

[Anonymous No.14617392]

>>14617339
When you say lim sup ln(f(n))/n is positive, do you mean > 0 or >= 0?

If it's the former, then it's easy:
lim sup log(f(n))/n > 0 => log(f(n))->∞ => f(n)->∞ => (f(n)-1)/f(n)->1

Therefore there exists N such that 0.9f(n)<f(n)-1<f(n) for any n>N and you can use the squeeze theorem noting that log(0.9f(n))=log(0.9)+log(f(n)).

If lim sup log(f(n))/n = 0, I don't think it's true. Funky things could happen if f(n)->1.

[Anonymous No.14617697]

>>14616602
Skeleton jelly 5000™

[Anonymous No.14617839]

I gotta be honest, I'm pretty bad at math.

[Anonymous No.14617976]

>>14617839
You'll fit right in. How are your arrow-drawing skills?

[Anonymous No.14617990]

Anyone here that knows about algebraic toplogy?

We know that the Serre spectral sequence is natural with respect to the fibration. My question is whether it's also natural with respect to the coefficient group. So, basically if I have a group homomorphism [math]G \to H [/math], do I get some naturality diagrams? Do you know any reference for this?

[Anonymous No.14618159]

have any recommended books on formal language theory?

[Anonymous No.14618201]

>>14617233
only thing i see is checking the opposite 50 of the person before you
survivor's bias means the previous person found their number, so repeating their area means you only have 49 potential boxes with your number
this can then be staggered up somehow across multiple consecutive prisoners

[Anonymous No.14618205]

underrated topics missed in undergrad that should be studied? looking to expand my Undergrad Experience™

[Anonymous No.14618246]

>>14618205
What topics have you encountered so far?

[Anonymous No.14618248]

>>14617339
[math]f(n) = 1 \,\forall n[/math]

[Anonymous No.14618262]

>>14618246
multivariable calculus and basic analysis, linear algebra, some abstract algebra, probability & statistics, topology, geometry

[Anonymous No.14618291]

Hi geniuses.
I have this practical problem, which I can solve in some way, but my geometry skills aren't very high up, so you might think of something better.
I want to make an empty cone, so ideally, I'd like to print out the flattened surface of it onto paper and just cut it and glue the sides together.
OK, that would be trivial, just a part of a circle. The catch is that I want the base of the cone to be an ellipse. I'm trying to write something like a python script that receives the cone's height and the lengths of the two ellips's perpendicular "eigenvectors".
Without your help, I'll just bruteforce it and move by small lenghts and always draw a point at the relevant point (cause computing euclidean distance is easy), but any ideas on how to make the script less dumb are appreciated.

[Anonymous No.14618371]

>>14618262
Galois theory, functional analysis, differential geometry

[Anonymous No.14618382]

>>14616602
Ywnbadbhag

[Anonymous No.14618462]

>>14618382
You will never be a damn beautiful high-functioning autistic girl?
Really hard really long acronym you've got there.

[Anonymous No.14618499]

>>14618291
Clarification: I need to "plot" a flattened elliptic cone.

[Anonymous No.14618531]

>>14617233
The answer is pretty cool to understand at least intuitively.

Consider you are a prisoner that goes to open boxes, doesn't matter the order in which you go. Forget about the 50 boxes limit, consider you could open all boxes.
Step 1 is open the box with your number.
Step k+1 given that you did step k is that you go and open the box with the number you got in the box of step k.

This creates a loop that repeats when a box tells you to go to your number, aka the box you started with. Best case scenario, you get your number at the first try. Worst case scenario, you go through all 100 numbers. Consider the random variables [math]X_n[/math] being the number you get from the [math]n[/math]-th box. Then consider the random variable [math]Y[/math], being the step in which you get your own number ([math]X_1 = X_Y[/math]).
Now, you can only open 50 boxes, so what is [math]P(Y\leq 50)[/math]?

Then you have to prove that if you don't follow the algorithm in at least one step, the probability of finding your number will decrease ([math]P(Y\leq 50)[/math])

I say this is a bit intuitive because if you imagine all loops, you would be inclined to think the median would be a loop of length 50. And a different process would imply more "randomness", less chance of getting your number than this orderly process. But I didn't say it's easy. I haven't calculated anything nor did I solve this.

[Anonymous No.14618624]

>>14618531
yea this is the answer, there can only be one loop >= 50 possible

[Anonymous No.14618731]

>tfw I finally understood Zariski topology

[Anonymous No.14619066]

>>14616776
What is the physical interpretation of an array?

[Anonymous No.14619077]

>>14616492
What are separable spaces used for?

[Anonymous No.14619088]

>>14618731
brain should be bigger in prefrontal cortex

[Anonymous No.14619165]

>>14619077
Broadly speaking, analysis. Without approximation no analysis. Without ways to approximate no approximations. Without separability no ways to approximate.

[Anonymous No.14619172]

>>14618731
ok, gimme an explicity example of a set thats open in the standard topology in [math]\mathbb{R}^2[/math] but not open in the Zariski topology

[Anonymous No.14619463]

>>14619077
the spaces that come up in quantum mechanics are always separable.

[Anonymous No.14619471]

>>14619463
How is it applied in quantum mechanics?

[Anonymous No.14619491]

is inductive reasoning part of analysis?
sorry for the novice question; I've heard learning inductive reasoning would improve my programming skills

[Anonymous No.14619548]

Youngfag here.
>Took the placement for first-year college math
>Haven’t taken math for a year as my high school did not permit me after I had met the grad requirements
>none of the problems are too hard, sneak in the use of a graphing calculator for a few of the function ones because my visualization skills are shit
>couple questions about the natural logarithm whose terminology I understand but not really the mathematics
>Whatever, I’m decently confident in my answers for the Alg 2 and geometry questions
>feel pretty good about it at the end
>test came in
>placed in math 98
How should I kill myself, bros?

[Anonymous No.14619550]

>>14619548
Meant to say “results came in”.

[Anonymous No.14619595]

Are there any good math blogs?

[Anonymous No.14619659]

>>14619595
Every math blog is shitty by a virtue of being a blog.

[Anonymous No.14619684]

>>14619172
The open unit ball.

[Anonymous No.14619701]

Who the top living mathematicians?

[Anonymous No.14619737]

>>14619701
I am.

[Anonymous No.14619745]

>>14619701
Mochizuki is probably the no. 1 working mathematician.

[Anonymous No.14619765]

>>14619745
Based and redpilled

[Anonymous No.14619774]

>>14619745
>>14619765
Bluepilled

[Anonymous No.14619775]

>>14602946
Afaik x^x has an antiderivative, its just that cannot be written down as an finite compositions of elementary functions.
Try looking up pdfs of Risch algo and Liouville theorem, i know its easy to get lost in the myriad of details.

[Anonymous No.14619780]

>>14619774
Cmon you can't not read this https://www.kurims.kyoto-u.ac.jp/%7Emotizuki/Essential%20Logical%20Structure%20of%20Inter-universal%20Teichmuller%20Theory.pdf and say it isn't one of the most redpilled math papers written in the XXI century

[Anonymous No.14619785]

>>14619780
I stand corrected. Biased Wikipedia fails again

[Anonymous No.14620154]

How much about field extensions and Galois theory do I need to learn before I can into QFTs

[Anonymous No.14620183]

>>14617976
(:

[Anonymous No.14620229]

[Anonymous No.14620826]

Is this correct?
Given the set of integers, let [math]\{S_i\}[/math] be the set of all subsets of Z with cardinality i.
Then this set is countable because there is a bijection mapping to [math]Z^i[/math]
If I take the union of [math]\{S_i\}[/math] over all possible i, then this union set is still countable, right?

[Anonymous No.14620828]

The wikipedia articles on Hahn-Banach and Banach-Alaoglu theorem are more informative than my shitty functional analysis lecture. Are university lectures useless in general or is my university just particularly midwitted?

[Anonymous No.14620866]

>>14618262
Differential equations. That seems to be the big thing you're missing. Numerical methods too, the basic stuff is pretty easy, but it's SUPER useful just to know.

[Anonymous No.14620877]

>>14619077
Classification problems, machine learning. You can look up support vector machines if you want some basic applications.

[Anonymous No.14620925]

>>14620826
A countable union of countable sets is countable.

[Anonymous No.14621040]

>>14620925
Thanks.
I know it's true somehow but I just can't wrap my head around it because it sounds really big.
But it's still just |Z|.

[Anonymous No.14621078]

>>14615660
>>14615812
>>14616776
>refuses to elaborate
>leaves

[Anonymous No.14621153]

>>14621040
Intuitively, most subsets of the integers are like the even numbers: infinite sets with an infinite complement. There are only countably many subsets which are finite or have a finite complement.

[Anonymous No.14621287]

Is Finsler geometry a niche subject or is it applied in other fields of math/physics?

[Anonymous No.14621635]

>>14620229
>"I claim X."
>Belabored proof anyone could have come up with once they knew it was X.
>No explanation of X was arrived at in the first place.
Why are mathematicians like this?

[Anonymous No.14621651]

>>14617339
log(f(n)-1) > log(f(n)/2) = log(f(n)) -1 (assuming base 2)
log(f(n))/n > log(f(n)-1)/2 > log(f(n))-1 / n
lim n->inf log(f(n))/n = lim n->inf log(f(n))-1 / n
By the squeeze theorem, lim log(f(n))/n = lim log(f(n)-1)/n

[Anonymous No.14621666]

>>14621635
Get gud

[Anonymous No.14621736]

Why do I need calc 3 to do an intro to probability/statistics course?

[Anonymous No.14621754]

>>14621736
If cal3 is a prereq, you're probably going to be learning about univariate/multivariate continuous distributions, but honestly the most you'll really need from cal3 is just knowledge of double integration.

[Anonymous No.14621762]

>Wanting do research
>Academia positions generally have shit pays and a lot of non-related work (grant writing, teaching class, etc.)
>Industry doesn't actually do research in math, at most it's Machine Learning shit
What should I do?

[Anonymous No.14621795]

got a novel idea on a thing, wish me luck

[Anonymous No.14621797]

>>14621795
Good luck anon.

[Anonymous No.14621866]

>>14621762
win the lotto

[Anonymous No.14621908]

Are there any /mg/ infographs?

[Anonymous No.14621949]

>>14619745
>>14619765
>>14619774
Um except he's continuing the work of a literal nazi

[Anonymous No.14622365]

>>14621762
The pay is not shit, but when you'd get tenure you'll probably be 45.
There are positions without pedagogic responsibilities, but you need to be really good.
So, it's probably better do machine learning shit.

[Anonymous No.14623104]

>>14621762
Look at DoD positions.

[Anonymous No.14623345]

I'm working as an excel menial worker and learning programming but I figured I should learn math to have something challenging in my life. I've only ever done high school math, what kind of goal should I be setting for myself? Learn calculus by the end of the year? Spend x hours learning every week? Please help me out.

[Anonymous No.14623390]

>>14621908
>Are there any /mg/ infographs?

[Anonymous No.14623404]

>>14623390
lol. Anything that isn't so basic?

[Anonymous No.14623753]

Is the following always true?
Let [math]f,g,h[/math] be continuous functions in [a,b].
Then [\math] \int_{a}^{b} |f - g| \,dx \le \int_{a}^{b} |f - h| + \int_{a}^{b} |h - g| [/math]

[Anonymous No.14623756]

Is the following always true?
Let f,g,h be continuous functions in [a,b].
Then [math] \int_{a}^{b} |f - g| \,dx \le \int_{a}^{b} |f - h|\,dx + \int_{a}^{b} |h - g|\,dx [/math]

[Anonymous No.14623785]

>>14623756
Yeah L1 metric on definite integrals is metric.

[Anonymous No.14623802]

>>14616492
How to git gud at Math??

[Anonymous No.14623826]

>>14623802
Hard work every day, what else?

[Anonymous No.14623828]

>>14616492
>Talk math.
Fuck off zoomer. Suck my dick.

[Anonymous No.14623831]

>>14623826
elaborate, what makes people good at math? Studying everyday, learning the concepts, like, whats a good study plan?

[Anonymous No.14623838]

>>14623831
Working through the books until you're familiar enough to explore the subject. For example, once you're familiar enough with abstract algebra, you can investigate questions like "what's the structure of a ring with size n^3"

[Anonymous No.14624095]

>>14616492
>Kelley General Topology
do you recommend this booK?

[Anonymous No.14624143]

>>14623345
You should learn math that makes your excel work even better and makes you more deeply interested in your work.

No joke, there are likely high level things you can do even with your basic data. It also helps when you can practice what you're learning as you learn it. I recommend learning statistics and picking up calculus as you go.

[Anonymous No.14624145]

>>14623802
Learning physics or some other application that utilizes a lot of math. No joke. It will make you better and gives you intuitions which is how you get good.

[Anonymous No.14624155]

>>14620229
>since the number 661 is prime
Literally irrelevant.
661 and 662 are coprime since they're consecutive integers. You can raise either to any non-negative power and they'd still be coprime.

[Anonymous No.14624161]

>>14623828
Not cool

[Anonymous No.14624180]

>>14620229
Generating function of C(n,k) for a fixed k is x^k/(1-x)^(k+1)
Substitute x = 1/662, k = 662

[Anonymous No.14624187]

For what [math]x[/math] does
[math]f(x)=\Sigma_{k=1}^{\infty}\frac{(-1)^k}{k}h(kx)[/math]
where
[math]h(x) = \min\{x-frac(x),ceil(x)-x\}[/math]
converge/diverge?

[Anonymous No.14624190]

>>14624180
Proof: use C(n,k) = C(n-1, k) + C(n-1, k-1), split the sum, reindex, factor out x's, solve, induct, use geometric series formula.

[Anonymous No.14624196]

>>14624187
(I meant floor(x) instead of frac(x), oops)

[Anonymous No.14624202]

>>14621949
What could have been...

[Anonymous No.14624223]

>>14621797
not enough luck
what do the primes 23, 53, 79, and 2083 have in common that all numbers in that range don't?

[Anonymous No.14624225]

>>14624187
>>14624196
So h is just the minimum distance to the nearest integer, i.e. by how much you round.
Seems like a really fucky function.
If you pick an integer, then the output is zero, but if you pick half an odd, then it diverges.
If I'm going by intuition, I'd say that it converges for the irrationals.

[Anonymous No.14624231]

>>14624187
>>14624196
>>14624225
Graphing it, it does seem like the ONLY place at which it diverges is the half-odds.

[Anonymous No.14624236]

>>14624231
How do you even graph something accurately when you are dealing with irrationals?

[Anonymous No.14624255]

>>14624236
Graph the partial sums.
They're continuous.

[Anonymous No.14624272]

>>14624223
and another prime set in some range:
7, 29, 101, 773, 1063, 1069, 2153
thought p +/- 1 might be smooth somehow but there's no apparent pattern

[Anonymous No.14624296]

>>14624223
What's special about them is that they are the numbers you wrote.

[Anonymous No.14624301]

I am incapable of thinking about logarithms intuitively

[Anonymous No.14624350]

>>14624296
yes, but as you can probably guess, i haven't optimized computation of these values yet and want to know if there's anything not in the direction of my work that i may have missed

[Anonymous No.14624375]

>>14624301
log(x)_b = y
means that y is the exponent to which b must be raised to equal x

[Anonymous No.14624390]

I saw this numberphile video about antiprime numbers and I got interdasted in it and made a thing showing their family tree. Here you go.

Btw I'm mentally retarded and illiterate

[Anonymous No.14624391]

>>14624301
Okay, think of a ruler. It normally has your counting
numbers in it and the fractional lengths in between
(regardless of unit). Logarithms are the powers
of a certain base that counts normally. That is,
the markings read 3^1, 3^2, 3^3, etc. for a base
of 3.

Thus, if I say [math]\log_3(9)[/math], then I know
it is the marking 2 on a ruler because 3^2=9.
Does this help?

[Anonymous No.14624404]

>>14624143
That's what I've been thinking as well, but the tasks I've been doing so far have like 0 mathematical complexity (e.g. calculating what percentage of the yearly revenue came from each month).

Maybe once I start learning I'll start noticing the use cases though.

[Anonymous No.14624438]

>>14624391
the ruler analogy does help make the arithmetic of logarithms more intuitive; thank you

[Anonymous No.14624445]

>>14624438
>>14624391
Of course!

Further, you can make quick calculations of
logarithms without a calculator and the rules
of logarithms by this ruler analogy.

[Anonymous No.14624477]

>>14624391
>>14624438
My nigger how in the world did that help you when you had trouble understanding logarithms before? He merely restated the definition of a logarithm with reference to a measuring device. Are you one of those faggots that has a blank space mindspace? I hate you. Every time someone asks for the 'intuition' behind a mathematical statement/structure whatever I get an aneurism. Especially since you braindead faggots always seem satisfied with restatements of the concept using everyday objects.

>what is the intuition behind addition
>well if you have one apple and put another apple next to it and you count them you get two apples
I HATE YOU MOTHERFUCKER, I HATE YOU!
YOU UNDERSTOOD NOTHING. IF YOU CAN'T ABSTRACT DON'T DO MATH. DIE.

[Anonymous No.14624581]

any fun math book to reaad?

[Anonymous No.14624582]

>>14624581
Geometry and the Imagination by Hilbert and Cohn-Vossen

[Anonymous No.14624590]

https://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/
sirs is this good?

[Anonymous No.14624716]

I can learn Single Variable Calculus in a week right?

[Anonymous No.14624767]

>>14624716
Sacrifice your schedule and all you hold dear,
run through calculus videos or call an expert,
don't go anywhere but for some food and to sleep,
and maybe, just maybe, you might get there.

[Anonymous No.14625603]

>>14624767
Written almost like a poem.

[Anonymous No.14625699]

What are open questions in math?

[Anonymous No.14625722]

>>14625699
gf for anon equation

[Anonymous No.14625909]

the proofs were easy enough with cross multiplication, but is it worth remembering these by themselves? will there be a moment where I'll simplify using this?

or (x^3+1)/(x+1)=x^2-x+1

[Anonymous No.14625938]

>>14625909
These are more useful to think of as factorizations than as divisions. It happens occasionally where you will have x^3-y^3 and want to write it as (x-y)(x^2+xy+y^2)

but these aren't hard to remember anyway, they all follow the same pattern. [math]x^n-y^n = (x-y)(x^{n-1}+x^{n-2}y+\dots+xy^{n-2}+y^{n-1}[/math]

[Anonymous No.14625943]

>>14625909
Put y=1. This is just the formula for geometric progression.
Conversely, taking the formula for geometric progression and formizing you get the formula with y.
Formizing = taking polynomial P(x) and multiplying each term by a power of y to make the sum of powers of y and x is equal.
You could also do this for any formulas involving polynomials in x. For example,
x^2 + 1 = (x-i)(x+i)
becomes
x^2 + y^2 = (x-iy)(x+iy)
and vice versa.

[Anonymous No.14626064]

>>14625909
it's true for any x^n - y^n so it's worth remembering

[Anonymous No.14626316]

>>14624350
got the lead out
p-1: 7, 29, 101, 773, 1063, 1069, 2153, 4363, 5471, 12101, 22147, 24007, 49057
p: 113, 1129, 16421, 19991, 21859, 32647, 38839
p+1: 23, 53, 79, 2083, 10457, 19309, 25243, 26489, 27109, 29077, 30449, 30469, 30703, 31859, 35837, 38851, 41893, 45677, 47657, 47797
guess i get to name these

[Anonymous No.14626531]

>>14618159
Yes I do

[Anonymous No.14626532]

>>14618262
Algorithms and Data Structures

[Anonymous No.14626573]

Not math but i'll ask anyway, How do you suppress the urge to kill and mutilate the filth in your department? such thoughts plague me for a while and I find it harder and harder to contain them.

[Anonymous No.14626606]

As i go deeper in math I'm starting to believe in God. There's no way a normal human can develop the level of abstraction needed to prove some of the theorems in higher math.

[Anonymous No.14626621]

Drop ink on the finest snow-white paper and it will inevitably absorb into black. Its purity demands it. Tainted men have immunities. Black does not absorb black.

[Anonymous No.14626750]

what's the final redpil?

[Anonymous No.14626756]

>>14626750
4chan is a complete waste of time. I'm never coming back here after this thread, this will be my goodbye to this entire site. It's been a rollercoast of emotions those generals, but the reality is that there's nothing of worth here. If I used the time spent here reading more math books, I would have much more knowledge than now. Oh well, no point in regretting the past, I'll just move on and try to make things right from now on. I recommend you to do the same, 4chan might look magical at first, it might seen like a mountain of hidden knowledge, but all knowledge derived from here is either superficial or linked from somewhere else and this place corrupts you little by little until you just keep coming back not because of the knowledge you thought was hidden here, but because you just can't stop anymore, the instant gratification you gain from posting shallow comments is already too ingrained in your brain and you spend your days wasting your time here when you could be doing better things. One might argue that all life is a waste of time or that this place is just another way to spend your free time, but this is nothing but delusion, free time spent making unneducated comments for unneducated people is not a good way to spend your free time and if you really think that posting on 4chan is a waste of time in the same way that reading a literature book is a waste of time then you're already too far deep into nihilism and I have nothing to tell you anymore. There are simply no benefits in posting here, you're just intoxicating yourself and perhaps you're not even aware of that, perhaps you are aware of that but you think you just can't leave anymore, whatever the case may be, know that there's only one option to make your life better: Leave. You know yourself better than anyone, if you're addicted then find a solution and leave as fast as you can, if you think spending time here is fine then meditate on what I said for a few days.

[Anonymous No.14626761]

>4chan is a complete waste of time. I'm never coming back here after this thread, this will be my goodbye to this entire site. It's been a rollercoast of emotions those generals, but the reality is that there's nothing of worth here. If I used the time spent here reading more math books, I would have much more knowledge than now. Oh well, no point in regretting the past, I'll just move on and try to make things right from now on. I recommend you to do the same, 4chan might look magical at first, it might seen like a mountain of hidden knowledge, but all knowledge derived from here is either superficial or linked from somewhere else and this place corrupts you little by little until you just keep coming back not because of the knowledge you thought was hidden here, but because you just can't stop anymore, the instant gratification you gain from posting shallow comments is already too ingrained in your brain and you spend your days wasting your time here when you could be doing better things. One might argue that all life is a waste of time or that this place is just another way to spend your free time, but this is nothing but delusion, free time spent making unneducated comments for unneducated people is not a good way to spend your free time and if you really think that posting on 4chan is a waste of time in the same way that reading a literature book is a waste of time then you're already too far deep into nihilism and I have nothing to tell you anymore. There are simply no benefits in posting here, you're just intoxicating yourself and perhaps you're not even aware of that, perhaps you are aware of that but you think you just can't leave anymore, whatever the case may be, know that there's only one option to make your life better: Leave. You know yourself better than anyone, if you're addicted then find a solution and leave as fast as you can, if you think spending time here is fine then meditate on what I said for a few days.

[Anonymous No.14626791]

>>14626750
someone in government did what you want to study 40 years ago and they conspired to teach you incorrectly from before you were born

[Anonymous No.14626816]

>>14626756
/sci/ is shithole

the only good thread is /med/

[Anonymous No.14626904]

>>14626756
cu tomorrow

[Anonymous No.14626982]

>>14616492
I have a good question for anyone here, as I am
having trouble putting the math together for this...

>How can I prove a person is faster that a regularly scheduled bus/train in any path?

[Anonymous No.14627134]

18 y/o hs student future mech engineer here. I've easily taught myself stuff like systems of equations, matrices and later algebra stuff. I've yet to self study calculus (I am self learning trig rn, hopefully could finish it very quickly to jump into calc).

I saw this post and made me wonder, is higher applied math like calculus, differential equations demanding of creativity? because I can't fathom how the first post came up with that answer. I've only done calculations in math with the process of practicing the calculation process and getting used to it. Do higher level applied math stuff present more novel problems that are not solvable by orthodox/textbook methods, that fully require one's craftiness and creativity?

I hope my post was not too long. I will appreciate every helpful replies.

[Anonymous No.14627252]

>>14627134
You require absolutely 0 creativity for any subject at university, perhaps with the exception of fine arts. When you do a homework or exam problem set, you are solving things specifically tailored around the course, methods they have taught you, and most importantly, things that have a well-defined beginning and end. You are neither answering open problems, creating conjectures, nor developing new theory.

>Does math research require creativity?
Absolutely yes
>How did the anon come with that?
He guessed the form (which looks absolutely incorrect, there's no reason why this sequence would be exponential) and adjusted the values using a computer.

>6 letter captchas
Is that new?

[Anonymous No.14627269]

I took arts in college. Now I'm interested in math and programming. How do I start reading? Any text books or links to courses where I can cover all the topics? I don't want to hop sites for every concept.

[Anonymous No.14627298]

>>14627269
CS50 for programming. Includes everything, including problem sets and something that checks your solutions
https://cs50.harvard.edu/x/2022/

I don't know your math background and it's concerning that you think there is something like "all the topics", but if you're also interested in computer science I'd recommend Rosen's Discrete mathematics since it has very little background needed and pairs well with computer programming (even some exercises are designed for it).
https://libgen.li/edition.php?id=138095394

[Anonymous No.14627328]

>>14627298
I'm just interested in math and want to learn everything that there is to it

[Anonymous No.14627338]

>>14627298
>https://libgen.li/edition.php?id=138095394
I learnt all of it in highschool

[Anonymous No.14627344]

>>14627328
>>14627338
Then you are ready for Stanley's Enumerative Combinatorics

[Anonymous No.14627347]

>>14627338
nvm. the book goes into more detail and covers more. thanks anon. I'll start with this

[Anonymous No.14627376]

>>14617233
check veritasium's newest video

[Anonymous No.14627520]

>>14617233
kill the ones that failed
easy

[Anonymous No.14628619]

how do i find the square root of a really big number
or any number for that matter
how do you find the square root of two to be 1.414....

[Anonymous No.14628634]

>>14628619
https://en.wikipedia.org/wiki/Methods_of_computing_square_roots

[Anonymous No.14628668]

>>14628634
wikipedia man
thanks
i don't know if it will be good for the number i am trying
but it will be good for the square root of two

[Anonymous No.14628709]

>>14626756
Based

[Anonymous No.14628756]

>>14627134
Other anon says there's no creativity in higher-level undergraduate math, but I'd disagree. Yes, not *as much*, but just because your experience is curated doesn't mean there's no value in it for *you*. In the same way that a project in English requires editorial choice while still satisfying requirements, or a computer program has specifications but (outside of the baby CS courses) no or few implementation requirements, many upper-level math problems require significant enough logical leaps, and provide enough alternative routes of proof, that'd I'd consider there to be creative elements in them. And there's certainly creativity required in discovering the solutions for yourself, at least in a competently-taught class that doesn't spoon-feed you. (There's also imo a surprising amount of crossover with English/writing in forming proofs -- math is about communication, and framing/ordering/phrasing for maximum comprehensibility is an acquired skill.)

Oh wait you said applied. I mean... Meh? Not an expert, but in my experience there's definitely a lot of experimentation involved in any decent problem, so there's definitely that sort of scientific-method approach to things.

To be clear, though, calculus doesn't count as higher level math. Upper level abstract algebra or real analysis will require more. There's some limited degree of intuition involved, and I've seen (say) some integrals or whatever that required really interesting approaches to solve (sidenote: look into complex analysis if you end up liking this sort of thing), but you mostly won't see those in your calc classes.

[Anonymous No.14629112]

Mathlet here, just started going over power series and radius of convergence.
So, are black holes defined as power series where its size is determined by its radius of convergence with the inclusion of possible values for x in the complex plane?
I'm low IQ and need some sort of physical application to truly get things. Thinking about the design of cement mixers and power plant smoke stacks is how I got through volumes of revolution.

[Anonymous No.14629278]

>>14628634
The fixed decimal approach is interesting and I'll have to go through that in more detail and see if it can generalize to cubic roots and such

[Anonymous No.14629320]

so there are some results whose proof requires the Axiom of Choice, but which in turn themselves imply the AC, e.g. all vector spaces having a basis and arbitrary products of compact spaces being compact. what are some other results of this kind that are equivalent to the AC? i want to hear ones outside of set theory/logic (i.e. not ones like Zorn's lemma or the well-ordering theorem), but ones that have to do with "regular" mathematics, e.g. does the existence of a maximal ideal in a ring imply the AC?

[Anonymous No.14629330]

>>14629112
>So, are black holes defined as power series where its size is determined by its radius of convergence with the inclusion of possible values for x in the complex plane?
no

[Anonymous No.14629489]

>>14616492
Hello

I was looking to apply for a CS masters. Though looking at course syllabus (georgia tech), I'm super surprised with how much I already have pretty deep knowledge in. There's actually little value in learning through an institution, because they don't have much to teach me.

I learned everything I know on the job (I'm one of FANG swes) and off the net

So instead, I'm building a DAG that represents all my knowledge, and what knowledge I want to obtain in the future. I'm then building a plan, and I'm going to execute.

[Anonymous No.14629519]

>>14629489
>CS masters. Though looking at course syllabus (georgia tech)
GT online CS masters is the definition of a diploma mill. Thousands of retards on reddit flooding to it with their undergraduate degrees in marketing, trying to "pivot" to a new career they know nothing of besides high salaries. It serves nothing besides purchasing the title for your resume, which will promptly find itself in the trash.
Look at programs from actual respectable institutions. If it must be online, look at university of Washington or JHU.

[Anonymous No.14629530]

>>14629519
>diploma mill
Fucking exactly. Especially masters. I pretty unimpressed with the courses. It seems to me that masters are only signals for people to get dead end jobs. Luckily I've established myself quite well.

Masters in general are kinda.. bullshit. Just more courses? I can learn all this stuff on my own. I just want to have the door open to do research when I eventually retire. I need to fraternize with my local university academics.

I'll just learn it off wikipedia and books, and build really undeniable shit. I really don't need a degree, like at all. I just need a guided from first principles learning experience. MIT open courseware doesn't look so bad desu

Remember when universities were about learning?

[Anonymous No.14629734]

>>14617392
why didnt u just use fucking lhopitals

[Anonymous No.14629741]

>>14629320
>does the existence of a maximal ideal in a ring imply AC
What is it you’re trying to say? Some rings have maximal ideals, some don’t

[Anonymous No.14629792]

>>14629734
When you first encountered Vulpes at nipton how did you handle the situation?

[Anonymous No.14629916]

>>14626982
>>14616492
How can I prove a person is faster that a regularly scheduled bus/train in any path?

[Anonymous No.14629942]

The duality of anon.

[Anonymous No.14630066]

How tf do i start getting math? I can understand it but as soon as i move to the next topic i forget most of it. I hate this

[Anonymous No.14630190]

>>14629741
by Zorn's lemma (which is equivalent to the AC) every ring has a maximal ideal
>Some rings have maximal ideals, some don’t
in case you're thinking of (0) in a field, it's still a maximal ideal

[Anonymous No.14630248]

>>14626982
>>>/x/32287740

[Anonymous No.14630277]

>>14629734
Then you have to assume f is differentiable on (a,∞).

[Anonymous No.14630279]

>>14629320
Existence of maximal ideals is equivalent to AC, yes

Let M be an R-module, S a linearly independent subset. The existence of a maximal linear independent subset containing S is equivalent to AC.

A function is surjective function iff it has a right inverse - is equivalent to AC.

Existence of algebraic closures requires the compactness theorem of first-order logic which is weaker than AC.

There were some equivalents with free abelian groups being projective/injective that I can't remember

[Anonymous No.14630286]

>>14629320
I posted
>>14628634
and this is another such question which is verbatim resolved by the Wikipedia page.
Please guys put SOME effort into your posts

[Anonymous No.14630411]

A UI can be naturally modeled as a state machine that reacts to events (user interaction) and changes state. Can you think of other alternative models to represent a UI?
Yes this is math.

[Anonymous No.14630445]

>>14630277
ok, tell me what happens for the 2nd expression if f < 1

[Anonymous No.14630500]

>>14626791
Lol. Feels like that sometimes

[Anonymous No.14630520]

can't stop getting sidetracked by cool and novel ideas, that ultimately, aren't important to me.

[Anonymous No.14630607]

>tell coworkers about the prison problem with the 100 boxes and 50 tries
>no reactions
lesson learned, no more math autism irl I guess

[Anonymous No.14630720]

>tfw once again I wasn't awarded a fields medal
My outstanding research on triple integrals remains unnoticed.

[Anonymous No.14630732]

>>14630720
>turning 50 in 2 years

Is there anything I can do within 2 years that'll raise my chances of getting one?

[Anonymous No.14630804]

>>14630732
The age limit for Fields medal is 40 years not 50

[Anonymous No.14630938]

>>14630445
If f(x)<1, then log(f(x))<0 and log(f(x)-1) = log(1-f(x))+i*pi.

[Anonymous No.14630944]

Can someone explain to me what groups are useful for ?
I understand the 4 axioms and how to make most proofs, but I have not a single clue as to what you use them for.

[Anonymous No.14631005]

>>14630944
If you can prove a certain mathematical object has an underlying group structure, then you have just unlocked a bunch of properties about that object for free. Groups are studied because it so happens that lots of objects have an underlying group structure

[Anonymous No.14631009]

Anyone here have experience reading "Introduction to the Theory of Computation" by Sipser or "Automata and Computability" by Kozen? I'm going through Sipser right now but ive seen it mentioned that Kozen has a little bit more mathematical rigour, and I wanted to see if anyone can say the same.

[Anonymous No.14631259]

>>14631005
Okay thanks dude.

[Anonymous No.14631496]

>>14630944
What other >guy said, but from experience the only interesting groups that you see in undergrad are found in Galois theory. For the most part, most courses will have abelian groups which are less interesting.

[Anonymous No.14631583]

>>14631009
sips

[Anonymous No.14631777]

>>14630732
Learn to decrease your age by at least ten years.

[Anonymous No.14632038]

>>14631005
Like what?

[Anonymous No.14632057]

>>14630520
Like what?

[Anonymous No.14632170]

>>14630732
reroll and hope for better stats next time

[Anonymous No.14632499]

The more algebraic geometry I learn and see how abstractions like algebraic spaces are actually necessary and not just an academic joke, the more i see AG really is geometry.

If anyone is wanting to get into algebraic geometry, im just a noob but my advice is to not get lost in the (algebraic) sauce. There are ways to draw sheaves and schemes, dont lose sight of the geometric motivations.

[Anonymous No.14632632]

>>14616492
How can I prove a walking person is faster than a regularly scheduled bus/train in any path?

I find that if I have somewhere to be and have to
use Google Maps or my intuition I can get to
my destination faster on foot, or a combination of
walking and trains, than wasting time waiting.
Great thought, but I need to put math to this
reasoning. Any ideas?

[Anonymous No.14632647]

>>14626316
whoops didn't get the lead out, don't trust these numbers
they were meant to be primes where the number of points where b^x mod p = x is exciting
apparently all of two papers have covered this topic in any detail

[Anonymous No.14632687]

>>14632647
haha disregard this, those results are correct after all
looking for patterns in dlog is the path to madness

[Anonymous No.14632690]

>>14632499
Same. I'm still learning the very basics about varieties and so far I like I very much. I hope to get to schemes later.

[Anonymous No.14632928]

Does anyone know what [math]\ll [/math] means when appearing in a sum?
For example, say the sum is [math]\sum_{1\leq k\ll \textrm{log}x}k [/math]
What the fuck is the range I'm summing this shit over?
On a related note, what does it mean when one writes
something like [math]A(x,T)\ll B(T)[/math] uniformly for [math]C(x)\ll T\\ll D(x) [/math]? These bounds with [math]\ll [/math] are confusing me.
Halp

[Anonymous No.14632929]

>>14632928
fuck, I messed up the code
it should read
uniformly for [math]C(x)\ll T \ll D(x)[/math]

[Anonymous No.14633176]

>>14632038
Homotopy, homology, cohomology al describe certain group structures on topological spaces

[Anonymous No.14633398]

>>14633176
>>14631005
spotted the undergrad

[Anonymous No.14633426]

>>14633398
you there post doc
i want you to hold nothing back and be completely blunt where did i fuck up? i want all the brains of /sci/ and /mg/ to give me an accurate interpretation of what should have been said in order to seduce said creature and produce an offspring

[Anonymous No.14633443]

Can someone help me out here? I'm supposed to calculate [math] \pi_n(SO(4)) [/math] for [math] n=1,2,3,4.[/math] I am aware to that we use the fibration [math] SO(3) \to SO(4) \to S^3 [/math] where the last arrow is the map [math] R \to Re_4 [/math], say, [math] e_4 [/math] being the vector [math] (0,0,0,1). [/math] So I did the first two homotopy groups easily using the l.e.s. induced by the fibration. I am aware of the fact that [math] \pi_n(SO(3)) \cong \pi_n(S^2) [/math] for [math] n \geq 2 [/math], since this is an universal cover of [math] \mathbb{R}P^2 \cong SO(3). [/math] I am also given as fact to use that [math] \pi_4(S^3) \cong \mathbb{Z}/2 [/math].

So I have the s.e.s. [math] \pi_4(S^3) \to \pi_3(SO(3)) \to \pi_3(SO(4)) \to \pi_3(S^3) \to \pi_2(SO(4)) [/math] and this reduces to [math] \mathbb{Z}/2 \to \mathbb{Z} \to \pi_3(SO(4)) \to \mathbb{Z} \to \mathbb{Z}/2 [/math]. Can anyone help me from here on? I can't for the life of me figure out the morphisms here. Assume I don't know anything about Bott periodicity (I couldn't even use it here, anyway).

[Anonymous No.14633470]

>>14633443
There's a single morphism from [math]\mathbb{Z}_2[/math] to [math]\mathbb{Z}[/math] and exactly two morphisms from [math]\mathbb{Z}[/math] to [math]\mathbb{Z}_2[/math]

[Anonymous No.14633479]

>>14633470
I know that, the first one is trivial the other one either [math] 1 \mapsto 0 [/math] or [math] 1 \mapsto 1 [/math]. I did that the first time around but it doesn't really say much except that one copy of [math] \mathbb{Z} [/math] embeds into the group, while the other... well either the kernel is all of the integers or the even ones. What then? If you have the time to explain this approach I'd appreciate it.

Anyway, I managed to argue like this: since [math] SO(4) \cong SO(3) \times S^3 [/math], then [math] \pi_n(SO(4)) \cong \pi_n(SO(3)) \oplus \pi_n(S^3). [/math] Using the Hopf fibration [math] S^1 \to S^3 \to S^2 [/math] one can easily calculate the two groups, to obtain [math] \mathbb{Z} \oplus \mathbb{Z} [/math]. Now the 4th groups is the only left, lol.

[Anonymous No.14633503]

>>14633470
>>14633479 (me)
Same anon as before. I believe the argument would go as follows. Let [math] f: \mathbb{Z}/2 \to \mathbb{Z}; g:\mathbb{Z}\to\mathbb{Z}/2. [/math] In either case, [math] \pi_3(SO(4)) \cong \text{im} f \oplus \ker g [/math]. If [math] g [/math] is trivial, we get [math] \mathbb{Z}\oplus\mathbb{Z}. [/math] If it's not, we get [math] \mathbb{Z}\oplus\mathbb{Z}/2\cong \mathbb{Z}\times\{0\} \oplus \mathbb{Z}\times\{1\} \cong \mathbb{Z}\oplus\mathbb{Z}[/math], so the morphism isn't even important.

[Anonymous No.14633580]

>>14633479
>>14633503
Formally, either [math]0 \to \mathbb{Z} \to \pi_3 (SO(4)) \to \mathbb{Z} \ to 0[/math] is exact, and then it splits, or [math]0 \to \mathbb{Z} \to \pi_3 (SO(4)) \to \mathbb{2Z} \ to 0[/math] is exact, and then it splits, by projectiveness.

[Anonymous No.14633610]

>>14633176
What are those used for?

[Anonymous No.14633633]

>>14629519
Masters pretty much should only be online. If you aren't working and getting a masters, why are you even getting a masters to begin with? Going in person is pretty difficult when you actually have a 9-5 too. Pretty much online is the only way to go and most people I know who have a gotten a masters either got it online while working or just did a straight bachelors->masters at the same institution (i.e., just stayed an extra year).

>>14629530
Yeah masters are more courses. What are you expecting from them? They're essentially just fifth year studies and should be included in undergrad but since you waste your first two years you don't get to take them.

I mean, you can honestly say the same thing about undergrad. It's just courses. if you want the door open to research, you gotta get a PhD. There's literally no other option. You will not do research without a PhD in this age.

[Anonymous No.14633640]

Are there any tried and tested routes to self-learn undergrad level math? Being a CS graduate myself I really find myself lacking the skills mathematicians bring to the table, and think more rigorous understanding of some subjects would make a big difference in my research (mainly AI/ML and crypto).

[Anonymous No.14633652]

>>14633640
Well what DO you know? You should start with that. Then just follow the structure of undergrad math with a focus into probability and statistics since that's what's most applicable to your interests.

[Anonymous No.14633683]

>>14633633
>You will not do research without a PhD in this age.
There are some small universties in Eastern and Southwestern Europe where you can do research as a final year masters/first year PhD student, but yeah, it doesn't change that much essentially.

Genrally the more I study the more I feel like there shouldn't be undergrad or master studies at all. Just give prospective PhD students an entry exam checking if they know all the material they should've covered and have a short interview to see what their intrests are. There's probably no bigger waste of time than being forced to study stuff for 5 years when a reasonable curriculum on your own could be reduced to 3 years. Like, why did my institution think that there was a need to split up analysis on IR into two courses: first based on real sequences and their properties and the other about functions from IR to IR and their properties (integration, derivation etc.) Is that really necessary?

[Anonymous No.14633703]

>>14633580
You are my favorite animefaggot on this site anon. Please post more often in these threads :3

[Anonymous No.14633736]

>>14633683
No probably not necessary. But I wouldn't get rid of undergrad or masters. I genuinely see their use. Coming up with a course structure is not easy for most and many textbooks aren't exactly straightforward to read (many, even 'foundational' texts are often just cleaned up lectures and it shows).

This is doubly true when working. Sure I could self study, but it's hard to know where to exactly stop and start. For example, in many courses I'd waste far too much time on introductory chapters when I've gotten enough information to just move on. A lot of the time, that's what's best too, many things make much more sense once you've gone a bit deeper and then look back. It's often hard to recognize when to just stop and move on without a course in my experience.

I firmly disagree with entry exams as well. I think they're completely useless and a waste of my time. If I've already taken courses in the field, why are you wasting my time with a meaningless exam full of meaningless problems that don't even help me learn? I hate exams already in normal courses, don't fucking give me even more wastes of time.

[Anonymous No.14633816]

Deutsche Mathematik

[Anonymous No.14633842]

Why is nobody discussing this year's Fields medalists?

>Hugo Duminil-Copin
>For solving longstanding problems in the probabilistic theory of phase transitions in statistical physics, especially in dimensions three and four.

>June Huh
>For bringing the ideas of Hodge theory to combinatorics, the proof of the Dowling–Wilson conjecture for geometric lattices, the proof of the Heron–Rota–Welsh conjecture for matroids, the development of the theory of Lorentzian polynomials, and the proof of the strong Mason conjecture.

>James Maynard
>For contributions to analytic number theory, which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation.

Your opinion? Did they deserve the prize? Do you understand their works?

[Anonymous No.14633848]

>>14633610
Proving theorems

[Anonymous No.14633853]

>>14630732
>48yo and still stuck on the college kiddie board
Big yikes

[Anonymous No.14633860]

>>14633842
Why did you leave out Maryna?

[Anonymous No.14633872]

>>14633842
I haven't really followed the Fields medalists since 2010.

[Anonymous No.14633879]

>>14633842
>statistical physics
>combinatorics
>analytic number theory
I'm good thanks.

[Anonymous No.14633916]

>>14616492
>>14616492
Mathematically challenged dummy here, I'm trying to write some basic code that automatically adjusts font size according to how long a string is, so that it always fits nicely on the screen. I've figured out that a string with a length of 5 is good at a font size of 170, whereas a string of 20 is good at 130.

Is there a formula I can create just using those four numbers? I've tried googling but didn't really even know how to formulate the question, something to do with proportions and ratios I guess

I guess a more concise way to ask would be something like:
If 5 = 170 & 20 = 130,
What does 50 equal?
(show your working)

[Anonymous No.14633947]

>>14633916
interpolate? try a linear approximation f(x) = ax+b, solve f(5) = 170, f(20) = 130 for a and b
I get f(x) = (-8/5)x + 550/3 and f(50) = 103.3 repeating
you could probably do a rounding down function to the whole result to have even numbers, so f(50) = 103
of course this is assuming linear scaling which mustn't be true

[Anonymous No.14634497]

>>14633916
You have two options. Fit more font sizes and build a model, or actually solve the problem.

You have to figure out the size of the box and how much area a single font size takes up for a single letter/character. From there it's pretty simple to figure out the largest font size to properly fit the box.

[Anonymous No.14634513]

Has anyone here worked through picrel? I've already taken a course in abstract algebra, so I'm looking for a good book to build on that.

[Anonymous No.14634607]

>>14634513
If you are aspiring to be an algebraist, then sure that book is a fine intro.

If you just want to learn algebra mainly to learn something that interests you but requires some algebra like geometry, topology, arithmetic, then I would say a whole book on algebra is overkill and you should just pick up what you need while learning what interests you.

[Anonymous No.14634854]

Can anyone help me double check this ?
https://en.wikipedia.org/wiki/Bring_radical#Glasser's_derivation

I think they wrote the solutions to [math]x^5 - x - t = 0[/math] instead of [math]x^5 - x + t = 0[/math].

Substituting N = 5 gives me the 5 roots
[math]\displaystyle
x_k = \begin{cases}
t f_0(t),\; k = 0\\
(-i)^k f_0(t) - \frac{1}{4}tf_1(t) - i^k\frac{5}{32}t^2 f_2(t) - (-1)^k\frac{5}{32}t^3 f_3(t),\; k \in \{1,2,3,4\}
\end{cases}
[/math]

With
[math]
f_0(t) = {}_4F_3\left(\left\{-\frac{1}{20},\frac{3}{20},\frac{7}{20},\frac{11}{20}\right\};\left\{\frac{1}{4},\frac{1}{2},\frac{3}{4}\right\};\frac{5^5t^4}{4^4}
\right)\\
f_1(t) = {}_4F_3\left(\left\{\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5}\right\};\left\{\frac{1}{2},\frac{3}{4},\frac{5}{4}\right\};\frac{5^5t^4}{4^4}\right)\\
f_2(t) = {}_4F_3\left(\left\{\frac{9}{20},\frac{13}{20},\frac{17}{20},\frac{21}{20}\right\};\left\{\frac{3}{4},\frac{5}{4},\frac{3}{2}\right\};\frac{5^5t^4}{4^4}
\right)\\
f_3(t) = {}_4F_3\left(\left\{\frac{7}{10},\frac{9}{10},\frac{11}{10},\frac{13}{10}\right\};\left\{\frac{5}{4},\frac{3}{2},\frac{7}{4}\right\};\frac{5^5t^4}{4^4}
\right)
[/math]

Which seems to check numerically and matches the one in their reference for the first root.
https://arxiv.org/abs/math/9411224

[Anonymous No.14634864]

Can anyone help me double check this ?
https://en.wikipedia.org/wiki/Bring_radical#Glasser's_derivation

I think they wrote the solutions to [math]x^5 - x - t = 0[/math] instead of [math]x^5 - x + t = 0[/math]

Substituting N = 5 gives me the 5 roots
[math]
\displaystyle
x_k = \begin{cases}
t f_1(t),\; k = 0\\ (-i)^k f_0(t) - \frac{1}{4}tf_1(t) - i^k\frac{5}{32}t^2 f_2(t) - (-1)^k\frac{5}{32}t^3 f_3(t),\; k \in \{1,2,3,4\}
\end{cases}
[/math]

With
[math]
f_0(t) = {}_4F_3\left(\left\{-\frac{1}{20},\frac{3}{20},\frac{7}{20},\frac{11}{20}\right\};\left\{\frac{1}{4},\frac{1}{2},\frac{3}{4}\right\};\frac{5^5t^4}{4^4} \right)\\ f_1(t) = {}_4F_3\left(\left\{\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5}\right\};\left\{\frac{1}{2},\frac{3}{4},\frac{5}{4}\right\};\frac{5^5t^4}{4^4}\right)\\ f_2(t) = {}_4F_3\left(\left\{\frac{9}{20},\frac{13}{20},\frac{17}{20},\frac{21}{20}\right\};\left\{\frac{3}{4},\frac{5}{4},\frac{3}{2}\right\};\frac{5^5t^4}{4^4} \right)\\ f_3(t) = {}_4F_3\left(\left\{\frac{7}{10},\frac{9}{10},\frac{11}{10},\frac{13}{10}\right\};\left\{\frac{5}{4},\frac{3}{2},\frac{7}{4}\right\};\frac{5^5t^4}{4^4} \right)
[/math]

Which seems to check numerically and matches the one in their reference for the first root.
https://arxiv.org/abs/math/9411224

[Anonymous No.14635048]

>>14634513
>saunders maclane
run the other way

[Anonymous No.14635200]

>>14630944
So turns out the answer is nothing:
>>14633848

[Anonymous No.14635212]

>>14633842
Fields is dumb because of the age lim

[Anonymous No.14635228]

>The Korean American Field medalist spent six years to finish his undergrad and only started doing math really late
As an Asian who does math I'm fully prepared to hear people berate me with the "you have been doing math since forever where's your medal?"

[Anonymous No.14635296]

Did you guys ever debug that "infinite sum adding up to -1/12" glitch or is math still broken?

[Anonymous No.14635307]

>>14635228
Kill yourself chink faggot

[Anonymous No.14635314]

Can anyone explain curvature tensor to me?

[Anonymous No.14635402]

>>14633633
>>14629519
>>14629489

Finally had some time to go through the math wiki pages. Here's a tree of learning. Most of it will be review. Thoughts?

[Anonymous No.14635471]

>>14635314
what exactly dont you get?

[Anonymous No.14635481]

>>14635402
okay i added some more

where should I start (and why is it bayesian statistics)?

[Anonymous No.14635494]

>>14635471
I can’t understand any part. Or another tensor if that would be easier

[Anonymous No.14635856]

>>14623756
yes. to prove, look at a Riemann sum of an arbitrary partition the domain and then use the triangle inequality.

[Anonymous No.14635866]

>>14624477
the problem which most people have with math is that they don't think to reread the definition of a mathematical concept. they see it once and think they're supposed to know. eventually, you will also come to a concept which you don't understand on the first try. for example, empathy. don't kill yourself once you realize that your abstract reasoning is just as bad as the typical person's.

[Anonymous No.14636292]

>>14633640
Anon, I'm in the same boat. I'm just learning it all from first principles.
>>14635402

[Anonymous No.14636294]

Can you guys help me with this question?
It's asking me to say if it is an equivalence relation
[math]R={(x;y)∈ N2/3|x−y}[/math]
Here's what I got so far:
We know that for a relation to be considered equivalent it has to attend three basic properties - reflexiveness, symmetry and transitivity, I concluded that they're both reflexive and transitive, but I can't see how it is symmetric, since this is the natural set, there's no way that both x-y and y-x pertain to the relation because that y-x implies a negative number and there aren't any in the natural's set, can we conclude that this is a vacuous truth and thus the relation is equivalent? Answer key says it its, but I'm not sure.

[Anonymous No.14636296]

>>14636294
N2, NxN not N2, sorry.

[Anonymous No.14636408]

Doing Basic Mathematics in the office. Feeling based.

was nice because the exercises looked tedious at first glance but nothing is more boring than doing nothing in the office, so I managed to do them all (and they weren't even tedious after all)

[Anonymous No.14636427]

>>14621635
Theorems are usually guessed at, this one probably with a computer.

[Anonymous No.14636440]

>>14636408
You are stealing from your employer, you sell your time, if you are not attentive to your task, even if that is sitting still doing nothing you are an immoral person and deserve to be beaten to death.

[Anonymous No.14636492]

>>14636440
You could make the opposite argument for sitting still instead of learning math in your downtime.

How would acquiring knowledge that would be potentially useful for future tasks be immoral when the alternative is looking out the window or talking to coworkers?

If you were the boss of a company would you choose someone who sat still doing literally nothing but breathing when he has nothing to do over someone who goes out of his way to better himself?

[Anonymous No.14636505]

Help please guys.
I'm trying to figure out the scaling probability of a dice result being below the number of times the dice had been rolled.
Not just how likely for any 1 given roll, but how likely a roll result below the dice rolled number was rolled in total.
My dumb ass has worked out something like,

Roll 1: %0 (Cant roll below a 1)
Roll 2: %16.5
Roll 3: %45 (so not just the chance of rolling below a 3 but the chance of rolling below a 3 if the previous roll didn't roll below a 2)
Roll 4: %75
Roll 5: %94

[Anonymous No.14636518]

>>14636505
What? Can you clean up what you are trying to describe?

Are you saying what's the probability of rolling under X given X dice are rolled?

[Anonymous No.14636598]

>>14636518
Fug, ok ok so.
Not just rolling under X where is is the number of times the dice has been rolled.

But the probability of rolling under the times the dice has been rolled including the previous rolls.

Roll 3 has a %33.3 chance of rolling under. But the chance of having rolled under on roll 3 AND roll 2 is %45 (I think)

[Anonymous No.14636924]

I left /mg/ a few years ago so I could focus on studying for my quals. I failed my first attempt but passed on round 2. Now I'm near the end of my PhD (numerical analysis). People here were actually quite encouraging back then. I'm glad to see the culture of the general hasn't changed very much since 2018.
Just submitted my 4th journal article. All I have to do now is collect my papers into a dissertation and graduate, deadline is Aug of next year. I've accepted a 3 year government research postdoc in numerical analysis which has a part-time commitment while I write my dissertation. Thanks /mg/.

[Anonymous No.14636946]

I have never gotten a degree.
Is there any hope for me to have the ability to publish anything as an outsider.
Or is it over before it even started.

[Anonymous No.14636974]

Announcement to any undergrad taking cal 1 for the first time:

Just take the natural log of the function, use log rules, then compute the derivative, then exponentiate using base e. Congratulations, you have achieved a 4.0 in the class.

[Anonymous No.14637011]

>>14636946
The difficulty in getting things published is not that you necessarily need a specific qualification, but instead that you have to be properly aware of the wider literature on a specific topic within mathematics. Being affiliated with a university or other research organization usually means you can access their online and physical library archives, which typically contain an insane amount of a specific knowledge which may be difficult to figure out how to download otherwise.
For example, maybe you need to read some specific textbook, but it was only published as a hardcopy in the 1970s and you don't have $1000 to throw around on chasing a rabbit hole which may or may not solve you problem. When resources like this are provided by your institution's library, it is much easier to get work done than having to self-fund.
Another reason why institutional affiliation helps in computational resources. A considerable amount of math uses computers in the modern day. Sometimes it is best done using something much more hefty than any common consumer device. Your research institution usually purchases these computing resources for you.
>Is there any hope for me to have the ability to publish anything as an outsider.
>Or is it over before it even started.
How old are you? If you are older than 30 you should probably look at different career options than mathematics. It is really something you have to dive into at 17-20 years old if you want to build anything resembling a career with decent benefits. If you don't care about job security or anything like that, you can just attend community college courses. They are cheap and will put you on the beginning of a path to later math.
All that said, yeah if you want to write original math, then you should go to university. There really isn't another way to study it while being able to feed yourself.

[Anonymous No.14637028]

>>14637011
Thank you for your reply it is good information, I have already had time where I have struggled to get my hands on specific materials only avaible in certain institutions so I can understand why that is a big hurdle.
>How old are you?
I am 22 years old.
I had studied maths for 3 years in university, starting when I was 17 but I dropped out before completing my 4 year course. My attendance was too poor so I just stopped going altogether.
As for career options in maths, I have never thought about that before. Right now I am just a full time NEET for the last 2 years and my time is split between maths and other neeting activities such as 4chan.
I was just wondering if I kept at studying maths could I actually accomplish anything other than just being a shut in.
But if I have to go to university again, that would just rule that out.
Thank you for your post, I will think about this a lot. Maybe I should pursue something else other than maths in the end.

[Anonymous No.14637052]

Been a while since I've done math since I graduated. Any good books in either algebraic or analytic number theory that don't have too many reqs (arithmetic geometry et al.)? Was thinking Apostol for analytic but heard it's a meme book over here

[Anonymous No.14637063]

>>14637028
>But if I have to go to university again, that would just rule that out.
At 22, you are still extremely young. University can certainly be unpleasant but if you live in the united states then it can actually be entirely free if you are a NEET over the age of 24. In the United States, unemployed citizens in some states can get a full ride for the remainder of their college education if they qualify as an independent, defined here:
https://studentaid.gov/apply-for-aid/fafsa/filling-out/dependency
A friend of mine had 2 years left on his degree, dropped out at 21, worked for a couple years in a coffee shop, was unemployed during covid lockdown, finished some of his credits at community college, then came back when he turned 24 and finished his Bachelor's in math this year June. He's starting grad school this fall and I would say this is a real success story.
>As for career options in maths, I have never thought about that before.
Yeah, I know math has a lot of prestige and romance around it but it is actually a career choice. If you like it a lot, it will be very rewarding. It does need a PhD or Masters in the topic to make a full career and you also have to carefully select what topic you want. Not all subfields hire equally. Picking a good subfield is the #1 way to not hate your work.
>I had studied maths for 3 years in university
>maths
I guess you're not from the US? I only have career and finance advice for the USA system, but you should carefully think about it from the perspective of a job. There are bunch of fine-print subsidies for people who go to graduate school in our student loan system, making grad school in math an excellent choice to pay off debt, if you had any, while also building a resume. I'm not sure how your system works, but these are all things to consider.
>Maybe I should pursue something else other than maths in the end.
Maybe so, but only give up on it if you don't like the work. Don't give up due to temporary life circumstances.

[Anonymous No.14637142]

>My shit uni is going to close its math degree because nobody wants to take it in this third world shithole.
Any theorems for this feel?

[Anonymous No.14637152]

>>14637142
No free lunch theorem

[Anonymous No.14637343]

>>14637063
>Don't give up due to temporary life circumstances.
Wise words indeed

[Anonymous No.14637605]

>>14636924
Please don’t work for the government

[Anonymous No.14637640]

>>14637605
But I like to govern anon.

[Anonymous No.14637743]

>>14637640
Then you may need psychiatric treatment

[Anonymous No.14637778]

>>14637605
Many good mathematics careers are in national labs and aerospace organizations. not sure why anyone should be apprehensive about working there.
>>14637640
stop impersonating me.

[Anonymous No.14637799]

>>14636924
>applied math
you made the right choice, unironically

[Anonymous No.14637931]

I downloaded ullrich’s complex analysis from libgen but it has 7 pages missing in a row.
Anyone have a better place to get it

[Anonymous No.14637991]

>>14635494
I guess /sci/ doesn't understand tensors either

[Anonymous No.14638073]

>>14623756
im a couple years out of college, but do we not have equality here? we're literally just adding and subtracting bounded continuous functions and their areas under the graph.

[Anonymous No.14638146]

>>14637931
Amazon?

[Anonymous No.14638255]

>>14637028
Also, you can finish your degree and learn ML/AI. It is an easy job for someone with math background and it's super well paid, although less stimulating than reserach math.

[Anonymous No.14638408]

>>14630732
Falsify your birth certificate and pray no one notices.

[Anonymous No.14638414]

>>14630944
>Can someone explain to me what groups are useful for ?
Well if you get bored it's nice to talk to other people no?

[Anonymous No.14638420]

>>14633860
She's a woman. She should be at home making babies.

[Anonymous No.14638478]

>>14638255
what would one of these ml/ai jobs entail in practice? I was under the impression that these kinda jobs mostly involve plugging your data into some pre-existing python etc. implementation of certain algorithms. does choosing the right algorithm and tweaking parameters really take that much skill?

bear in mind I have no math degree and my knowledge on ML mostly comes from youtube videos

[Anonymous No.14638506]

>>14638420
incelposting is not /sci/ related

[Anonymous No.14638521]

>>14635314
https://m.youtube.com/watch?v=-Il2FrmJtcQ

[Anonymous No.14638786]

>Let f be an smooth function such that for all x there exists n such that the n-th derivative of f equals to 0 at x, then f is a polynomial

How would I go about proving this?

[Anonymous No.14638796]

>>14638786
Integration.
Or uniqueness theorems for ODE solutions. Doesn't really make any difference.

[Anonymous No.14638830]

>>14638786
The union over all [math]n[/math] of the zero sets of [math]D^n f(x)[/math] equal the entire real line. In particular, for at least one [math]n[/math] the zero set has positive measure.
Sort yourself out from there.

[Anonymous No.14638884]

>>14638830
That was my first thought but I've been told the proof is topological

[Anonymous No.14638903]

>>14638884
You can use the Baire category theorem instead of measure theory, it doesn't actually change anything.

[Anonymous No.14639136]

Between algebraic topology and algebraic geometry which field has more of the abstract nonsense

[Anonymous No.14639143]

>>14623390
https://files.catbox.moe/jzuw6b.png The Motherload
https://archive.org/details/khanacademy

[Anonymous No.14639146]

>>14639136
topology for sure if by abstract nonsense you mean categorical thinking.

[Anonymous No.14639155]

>>14638884
>but I've been told the proof
there is no one proof for any result, have more confidence in making your own proof

[Anonymous No.14639162]

What exactly do you guys/mathematicians mean by "trivial"?

[Anonymous No.14639182]

>>14639162
a solution is at least sketched out in some paper somewhere

[Anonymous No.14639184]

>>14639146
well categorical thinking pervades both modern algebraic geometry and algebraic topology doesn't it?

[Anonymous No.14639193]

>>14639182
"Trivial" just sounds like a really misleading word to use for that. It also doesn't sound like the definition in webster's or wiktionary. Also depending on what you count as "sketched out" virtually anything could be considered trivial, then.

[Anonymous No.14639256]

>>14639146
When I say abstract nonsense I mean as in where there is excess focus on generalization and abstraction without the necessary concrete need for it.
For example, Grothendieck's work in AG was abstract (take etale cohomology for example), but it was also necessary to help solve problems like the Weil conjectures
On the other hand, I'm not an expert but things like higher algebra or higher category theory come to mind when I think of things that are abstract for abstract sake, they don't seem to solve any real problems and it's just as much a wankery to show off how smart and general you can be

[Anonymous No.14639344]

How is
P(x_1) ∨ P(x_2) ∨ P(x_3) ∨ P(x_4) ∨ and so on, for X = {x_1, x_2, x_3,...}
even a satisfactory "definition" for ∃x∈X, P(x)
it is not exactly rigorous, same with the definition for ∀

[Anonymous No.14639375]

>>14639344
How is it not rigorous?

[Anonymous No.14639380]

>>14638478

>I was under the impression that these kinda jobs mostly involve plugging your data into some pre-existing python etc. implementation of certain algorithms.

I'd say that it's a good summary of the technical part. You'd probably have to deal with clients too. This is, of course, not as challenging as research, it's just a backup plan. Since you studied 3 years of math, you can finish your degree in 1 year while you learn ML from some book/lectures/etc.

[Anonymous No.14639386]

>>14639375
it uses the "and so on", or "..." or whatever you want to use, when listing the terms.
That is not very rigorous. The terms could be anything, but are just assumed to follow this pattern. It's just an informal definition.

[Anonymous No.14639387]

>want to understand moduli spaces
>still stuck with quasiprojective varieties and basics of schemes
>not yet smart enough to understand stacks
Will I ever stop being a mathlet?

[Anonymous No.14639390]

>>14639162
Of no significance. The trivial group is the group with one element. The trivial ring is the ring where 0 = 1. The trivial topology where the open set list is the empty set and the whole space.

[Anonymous No.14639395]

>>14639386
Do you score low on IQ tests because you can't answer "Find the next term in the sequence 1,2,3,4,..."? After all it could be anything, right?

[Anonymous No.14639411]

>>14638478
while >>14638255 is a solid backup plan, keep in mind that you actually would need to learn some coding if you don't already have some experience. while the math isnt very hard, coding is time consuming and requires knowing how to read the manual.

[Anonymous No.14639420]

>>14639395
What does estimation have to do with rigorous definitions.
Defining a sequence 1,2,3,4..
is not a rigorous definition of a sequence. Even if you try to insult me for not thinking it is.

[Anonymous No.14639424]

>>14638073
no equality. you can make a counterexample using polynomials. left as an exercise.

[Anonymous No.14639455]

>>14639420
You're exactly right but don't expect chink /sci/ undergrads to understand rigor

[Anonymous No.14639461]

>>14639420
>>14639455
Your unrefined notion of rigor is the epitome of undergrad pseudointellectualism.

[Anonymous No.14639524]

>>14638506
>muh muh
Yeah, I hate women. Problem? They ruin everything. Maths would have advanced greatly more if women didn't even know how to read. They're a plague in university and in academia. Woman is the chain keeping man stranded on this planet. We would've colonised Mars by now if it weren't for the nigger of sex.

[Anonymous No.14639627]

Why don't people learn multiplication tables up to 100x100? More work but the payoff would be immeasurable.

Seems stupid to limit it to 12. Always noticed midwit teachers tried to mess up more complex topics by mixing it with arthetmatic shit or at least do it so you run out of time.

[Anonymous No.14639685]

>>14639395
The next term is 7.

[Anonymous No.14639705]

>>14639627
Examples of the benefit?

[Anonymous No.14639721]

>>14639380
>>14639411
I'm a different dude, self learning math. I'm actually further along the "learning how to code" path, so I guess I could pivot to doing something like this in the future.

though many of these jobs ask for math bsc/msc/phds in my area as a req, but by the time I'll get confident enough to apply to something like this I'll also have some work experience too in a data-related job, so I think I'll be able to talk my way in. guess it'll all depend on whether the HR gatekeepers instantly trash my resume or give me a chance

[Anonymous No.14639771]

>>14638478
Yeah that's most of the job, but it's more nuanced than that. Mathematicians are so removed from real data and real world problems that they think just a fitting algorithm is the hard part of data. 95% of the time it's not.

Actually being aware of your data, the limitations of how it was collected, marrying it with other datasets, justifying why a certain approach is appropriate, and then explaining results and what they mean is a lot of work and not trivial. Even 'clean' problems where you know the final model form (from a derivation in physics) can be fucking atrocious to actually implement because of the data.

This is the real reason why data science was created as field. Standard statistics and math programs don't really get to the heart of data before they start implementing things.

[Anonymous No.14639778]

>Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Bayes' theorem states P(A|B)=P(B|A)P(A)/P(B)
A=the player selects the car door
B=the host selects a goat door
P(B|A)=1
P(A)=1/3
P(B)=2/3
1*(1/3)/(2/3)=1/2
P(A|B)=The probability the player selects the car door given the host selects a goat door is 1/2. It is not advantageous to switch, given advantageous is presumably defined as increasing your likelihood to get the car.

Why is this so difficult for people to understand? I'm trying to explain this to someone and they aren't getting it.

[Anonymous No.14639789]

>>14639627
Because primes are mental cancer and calculators exist. And beyond that you only actually need up to 9 and carries.

[Anonymous No.14639821]

>>14639778
You already fucked up the problem. Even in the problem statement it's fucked up.

You didn't include the update of information. The probability that the host selects a goat door isn't 2/3. The host ALWAYS picks a goat door. So P(B) =1 (same as P(B|A))

This means the probability of you picking the right door given the host opens up a goat door is 1/3. This means that the remaining door has a 2/3 probability of being the right door.

You can also confirm this by counting out all outcomes

The outcomes go
CGG -> CG
GCG -> GC
GGC -> GC

In two of these cases the other door has the car.

[Anonymous No.14639881]

>>14637778
I thought of non-defense for some reason. Defense is still questionable

[Anonymous No.14639914]

>>14639821
>The host ALWAYS picks a goat door.
No? The problem doesn't say that. The problem says the host picks a goat door, not that the host ALWAYS picks a goat door.

Why not infer that the host ALWAYS picks door number 3 instead if you're going to make a random inference not in the problem? The door selection is arbitrary unless stated otherwise and it isn't stated as being otherwise.

>You can also confirm this by counting out all outcomes

Yes, you can.

Player picks 1, 2 is the unselected door to be switched to, Host picks 3.

C,G,G=switching loses
G,C,G=switching wins
G,G,C=case made impossible by the door opening revealing a goat

In one of these two cases the other door has the car. It's a 50/50 after you gain the information from the door opening.

Why would you infer the host has to open a goat door when the problem doesn't say that? Fuck's sake, this is /sci/. I would hope you motherfuckers would be able to manage basic shit like not adding random unstated conditions to problems. I came here for help dumbing this down, not to argue with another motherfucker that doesn't get it.

Without anything specifying the host behavior, the remaining two doors have equal odds of containing the car.

[Anonymous No.14639970]

>>14639914
The host literally always opens a goat door. Again, the problem statement is written to be intentionally confusing. In every possible iteration, the host ALWAYS opens a goat door after you do your first selection.

If the door you pick is a car, he will open either door 2 or 3 and reveal a goat

If the door you pick is a goat, he will pick the only remaining door with a goat.

That is the Monty Hall problem. It comes from the fact that you have a 2/3 chance of picking a goat at the very beginning and thus a 2/3 chance of switching to the car since he eliminates a goat door.

You don't understand the problem. Read the fucking Wikipedia page. It's not complex, just worded intentionally confusingly like many 'pseudo paradoxes'

[Anonymous No.14639980]

>>14639970
And thus a 2/3 chance of winning if you switch*

Read your own problem statement again, eliminating the commas it reads:
>Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door and the host, who knows what's behind the doors, opens another door which has a goat. He then says to you, "Do you want to pick the remaining door?" Is it to your advantage to switch your choice?

[Anonymous No.14639982]

>>14639970
>The host literally always opens a goat door.
The problem doesn't say that. Certainly, if the host DID always open the goat door, the answer would be 1/3, but that's not the problem as constructed.

What is your hangup?

>In every possible iteration, the host ALWAYS opens a goat door after you do your first selection.
Except this iteration, clearly, as that's not the case.

>That is the Monty Hall problem.
Well, no, in the Monty Hall problem, the host is specified as always opening the goat door to get to the counterintuitive 1/3rd result.

The person I'm talking with-much like you apparently-thinks this is the Monty Hall problem, but it isn't. There's no mention of host behavior beyond a goat door being opened by the host. You have to do that to establish the Monty Hall problem.

>Read the fucking Wikipedia page.
I'm reading the fucking problem. You should try it.

>the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat.
Find me the fucking always.

My condolences on your inability to fucking read.

[Anonymous No.14639994]

>>14639982
Is English your second language or something? The way the problem statement is worded, that is an EXAMPLE of an occurrence.

This is literally the Monty Hall problem, and a very poorly worded version of it. I don't know who the fuck assigned you this, but whoever wrote that version of the problem should be roasted.

[Anonymous No.14640040]

>>14639994
>The way the problem statement is worded, that is an EXAMPLE of an occurrence.
Yes. And nothing about the example suggests the goat selection was mandatory.

>This is literally the Monty Hall problem
In the Monty Hall problem it is explained that the host, in an attempt to help the contestant, opens a goat door. Thus P(B)=1. There will always be a goat door to be chosen by the host and the host will always choose it/one of them.

This ultimately makes P(A|B)=1/3.

In this version, the goat door selection is left arbitrary. The host opens a door with no explanation as to why. You can't infer a bias toward goat doors from the host.

>I don't know who the fuck assigned you this, but whoever wrote that version of the problem should be roasted.
It's the famous version of an "attempt" to write the Monty Hall Problem from Parade verbatim. It is, however, obviously NOT the Monty Hall problem as written though, so I don't understand why you're attempting to make it so.

If I wanted to write and explain the Monty Hall problem, I'd write the fucking Monty Hall problem. It's not difficult.

>Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, and the host, who knows what's behind the doors, opens another door, in order to reveal a goat. He then says to you, "Do you want to switch to the remaining door?" Are you more likely to reveal the car by switching your choice?

See? Different problem. Not hard to write.

[Anonymous No.14640053]

Yeah, English is your second language. It's the Monty Hall problem, and if you can't see that, it's your problem not mine. You should email your professor for clarification before you submit your homework though

[Anonymous No.14640078]

>>14640053
>It's the Monty Hall problem
1. In the Monty Hall problem, the host must always select a goat. This is Monty Fall mathematically. Goat selection by the host isn't defined as anything but arbitrary.

2. Learn to read or show me where it says a goat is always selected. For someone trying to paint others as ESL, you sure do like imagining readings.

3. I didn't get this from a college professor.

Hey, let me restructure the problem so it no longer sounds similar to Monty Hall, but otherwise has the same math. A bag contains 2 red marbles and a green marble. You are to predict when the green marble will be drawn. You predict the first marble will be green. The marbles are drawn. The third marble is revealed to be red.

Is your choice of marble more likely to be green if you switch to the second marble? Answer? No, fucking obviously not. It's a 50/50 between the two remaining marbles.

[Anonymous No.14640293]

>>14640078
nta but the revealed marble is not arbitrary because it must be red, so it is not 50/50 and is the monty hall problem after all

[Anonymous No.14640298]

>>14640293
>nta but the revealed marble is not arbitrary because it must be red
That's like saying a coin flip coming up heads wasn't arbitrary because it was heads.

You understand what arbitrary means.

[Anonymous No.14640300]

>>14640293
>nta but the revealed marble is not arbitrary because it must be red
That's like saying a coin flip coming up heads wasn't arbitrary because it was heads.

You don't understand what arbitrary means.

[Anonymous No.14640408]

What is the ebonics of math

[Anonymous No.14640427]

>>14640408
Combinatorics

[Anonymous No.14640542]

>>14640427
You're close but it's actually probability theory.
>An event with a 100% probability of happening will "almost surely" happen.
>An event with a 0% probability of happening will "almost never" happen.
It uses words to murder numbers and numbers to murder words.

[Anonymous No.14640699]

I'm talking a grad course in graph theory next semester-- any recommendations to prepare for it? Texts/websites/etc.

[Anonymous No.14640743]

>>14640408
anything with cryptography-breaking applications, factoring/discrete log have yet to have their difficulty proven and all the best algorithms are in L-complexity

[Anonymous No.14640772]

actually to expand on >>14640743 and help >>14640699 at the same time
graph theory isn't the ebonics of math, but it's certainly the black history of it
a relatively isolated subject that started taking off in the last century, where the methods of its people appear esoteric and confounding to the traditional european ways
when mathematicians are at their wit's end with a problem, they often ask a graph theorist how "you people" might approach it

[Anonymous No.14640852]

>>14639771
True. In my job we don't do a lot of fancy stuff (math wise), but there's constantly a problem solving aspect to it whenever the data is suspicious or when you have to combine datasets that don't have a clear mapping between them. And yeah, there's always the fact that you have to explain it all to non-technical people usually.

Guess I can see now how picking a model is just a small part of the overall process.

[Anonymous No.14640972]

>>14640300
retard-kun we make the choice to switch AFTER it came up red, simply the fact that it is red means there is a restriction making it not-arbitrary. go write a computer simulation if you're too stupid to see it otherwise

[Anonymous No.14640985]

>>14640408
What does this question even mean

[Anonymous No.14641955]

>>14639705
Japanese and Chinese are incredibly hard to learn, with language learning going into highschool, but on average they can read about 30% faster than we can read Roman characters, simply because each character contains more information, and this information is already internalised within the reader.

In the same way, learning a larger multiplcation table gives us more modules of information that are already internalised, and therefore it would be easier to parse through numbers that come in day to day life. It may seem dumb but people have really bad number literacy and stop seeing large data values as anything but arbitrary or "bottom line".

Just to put an example, I worked as a junior consultant for some tech retail company that outsourced their call centre that was bleeding money, and apparently only I noticed at a quick glance that it was probably because the successful sales were barely break-even at even perfect efficiency. Note that this meant multiplying a couple low (but not <10) numbers together. The manager just saw the sum value at the end of the Excel sheet and blamed other factors. Yes it was a shithole company.

[Anonymous No.14642054]

>>14640772
Graph theory is the slums of topology.