/mg/ - math general

[Anonymous No.15608042]

Math General

Von Neumann edition

Previously: >>15571520

[Anonymous No.15608069]

>>15608042
Sõyjak is a shit meme. Kill yourself

[Anonymous No.15608118]

>>15608042
How long will it take me to learn pure maths to a decent professional level If the max math I've studied is Calc II, and have an IQ of 142? I want to get into it just purely based on interest.

[Anonymous No.15608198]

>>15608042
I'm taking General relativity and differential geometry next semester
How smart do I have to be to get an A+ in this
i don't want to ruin my perfect GPA

[Anonymous No.15608217]

I'm learning geometry on my own, it's incredible that I didn't learn most of this basic shit in high school like for example congruents triangle or how to make a two-column proof.
>>15608069
I don't see the issue

[Anonymous No.15608255]

>>15608118
U sound like a fag

[Anonymous No.15608262]

>>15608255
Correct, what does my sexual attraction to other men have to do with this?

[Anonymous No.15608484]

>>15608198
Have you done real analysis? Or is this some shitty version for physics majors?

[Anonymous No.15608500]

>>15608118
> decent professional level

I don't know what this means. Anyone who uses math in a professional is probably an engineer, which means some calculus, Matlab, and google is about it. Newton's method? Nah, just chop that nigga into linear pieces. That's how we roll dawg.

If you mean being a mathematician, then the way to do that is to become competent in an active area of research. You really need an advisor to help you guide you to where that is. I suppose you can hang out on arXiv, but you'll need to put the threads together yourself.

What's the end goal here? If you just want to learn, download hatcher and get working.

[Anonymous No.15608503]

>>15608484
Yeah I did it, only course I ever not gotten an A+
That bitch gave me an A-
Only stain on my 4 page transcript

[Anonymous No.15608526]

>>15608503
Lol it is a physics course. nah you'll be fine bro.

>That bitch
Hate when this happens. Get some women to parrot the textbook who doesn't actually understand the material, and can't express why it's interesting.

[Anonymous No.15609132]

>>15601632
>>15601694
So would it be better to do a master's again first? Is there anything else I could do to increase my chances after being away from academia/math for so long? I'm a little reluctant to do a master's since I've already done one but I can see how it might be useful since I've been away for ages.
What are part-time PhDs like? I see a lot of even very good unviersities advertising part-time math PhDs but I can imagine a lot of professors insisting you have to have 100% of your time on the PhD.

[Anonymous No.15609138]

Can someone educate me on why I'm wrong?

Each day it's doing x^2 with a limit of 30 days
So it's
>lim[x->a](x^2) where a=30
Equals 900, i.e. full reservoir
Half of that is 450
Reverting the x^2 is sqrt
sqrt(450) is 21

Apparently the answer is 29

[Anonymous No.15609141]

>>15609138
> double itself in just one day
Ask yourself if the reservoir is 50% full how many days does it take to become 100% full?

[Anonymous No.15609143]

>>15609141
Oh fuck, that's right

[Anonymous No.15609278]

>>15609138
what the fuck.
what is wrong with "education" today
>Each day it's doing x^2 with a limit of 30 days
No man it's C0 *2^x
this is like a basic example when they teach you exponentials in school.
How old are you?

[Anonymous No.15609409]

>>15608069
midwit take

[Anonymous No.15609556]

Is Topological Data Analysis legit or a huge meme? In general, how would you rank the different subfields of Statistics and Machine Learning?

[Anonymous No.15609563]

[Anonymous No.15609654]

>>15609563
Can we actually have a decent math chart for once?

[Anonymous No.15609992]

What are some good real world word problems that need linear algebra to solve? I'm a lazy TA and need to make some homework.

[Anonymous No.15610496]

any news?

[Jealous No.15610598]

[Anonymous No.15610613]

>>15608500
No I don't wanna be an engineer or Matlab or all of that stuff. Just regular math. Just to be more competent in math. Call it Autistic, but there's no endgoal apart from just being really good at math, just like Autists end up learning random languages for no real reason. It's just emotionally satiating to be able to do math, and frustrating for me to look at something mathematical that I don't understand.
But you're saying it's not possible just with self-study and I would necessarily need an advisor or something?

[Anonymous No.15610616]

>>15609654
yes.

[Anonymous No.15610619]

>>15608042
>von neumann edition
>no onions paper
let me help you with pic related

[Anonymous No.15610777]

>4 y/0 kid asking for cheese cubes
>ask him how he even knows its a cube
>says it has "four stairs"

He got angry when I asked him to explain further. Could you devise a proof defining shapes based on the number of "stairs" each shape has? I'd have to make all regular Polyhedra out of cheese to see what he is defining as stairs.

[Anonymous No.15610792]

>>15610777
Nevermind, it wouldn't work if they're edge paths. It takes four steps to circumnavigate a cube and 3 for a tetrahedron, but an octahedron is also 4 steps, and unless I'm visualizing this wrong, a dodecahedron and icosahedron are both "5 stairs" to completion.
Brb gotta beat my kid.

[Anonymous No.15611103]

>>15610598
>see it's a tooker paper
>ctrl+f "neighborhood of infinity"
>50+ results

I remember reading the first paper when I was an undergrad. Excited to take a look at this as a bonerfied mathematician.

[Anonymous No.15611323]

>>15610613
I mean, do you understand enough about math to know what "regular math" or "pure math" is? Cuz it sounds like you read that guy's answer and came away with "engineers are the next level of math to study," which, no, like he said, engineering in practice really isn't going to use much past Calc II or III.
Likewise, if you want to be a practicing mathematician, someone who contributes something new to math, then... well, theoretically you don't need a PhD program or advisor or anything, but in practice practically nobody has the time, focus, and motivation for it. Unless you're somehow both a NEET and yet still are able to apply yourself to something like it's a job, it's somewhat unlikely you'll get to a point where you can contribute something new -- not impossible, but unlikely.
(A side note: IQ isn't irrelevant -- math is one of the few fields where it's pretty important, actually -- but the fact that you mentioned it is concerning, because hard work and practice is about ten times more important for actually learning or making progress. If you've been reading a textbook and watching lectures, you're not learning math -- take notes and then do the fucking homework problems (without cheating), that's where you'll learn. Math is in many ways processed like a language - actively practicing gets you fluent, not letting it roll past you.)
If you just want to study pure math, though... well, sure, I guess there's plenty of places to start. So many, in fact, that you should probably have some idea of what subfields you might be interested in studying -- analysis? Algebra? Something more concrete or abstract? Combinatorial or less so? etc. Of course, having an overview of math as a whole is also very important...

[Anonymous No.15611327]

>>15610613
In general, I'd say that a typical math undergrad ought to have seen:
- Certainly Calc I, II, and III (multivariable calc), Intro Linear Algebra, Intro Differential Equations - these are your basic, applied courses that everyone in STEM should take.
- Then, or concurrently, for pure math, I'd say find decent course/textbook in introductory Combinatorics, intro Real Analysis, and intro Abstract Algebra -- these courses are also usually where colleges will teach proofwriting (some split it into its own course, or combine with a discrete math course) -- make sure you find a textbook with homework assignments, and *do them*. (Unfortunately, this is actually the stage where you benefit from a real teacher -- there's an element of aesthetics in proofwriting, and a lot of skill and such, that is often really hard to convey through text; and people who write bad proofs are notoriously bad at identifying this fact, so even if you think you wrote a good proof, that likely doesn't mean you did so.) Analysis/Algebra is one of the big splits in math direction, and it's very important you're exposed to the basics in both; meanwhile, basic combinatorics is just fundamental to every field.
- Finally, branch off and pick some electives. For a more combinatorial/CS-ey direction, graph theory is a deep subject with connections to number theory, geometry, algebra, etc. For pure algebra, you can spend a loooong time just getting through a basic algebra sequence (group theory, ring theory, field theory, and then take a brief moment to learn basics of category theory and representation theory). Analysis, I'm not an expert, but likewise you can spend a long time studying basic sequences (functional analysis and such). Or an applied field - as one random example, stuff like further studying applied methods for PDEs, ODEs, linear algebra, etc, is actually really deep and pure field, despite not being thought of as such. Or, study statistics (ew, imo, but it's there).

[Anonymous No.15611334]

>>15610613
And, of course, there's a million other directions you could go; math is as deep as the ocean. Disabuse yourself of the idea that you'll understand "all of math" - that's not really been possible since the 1930s or so, at least not to understand every possible subject on more than a surface level (enough to, say, understand papers in any given subfield).
Honestly, my advice would be to find a mid-to-high tier college, go to their math department's website, and dig through some class descriptions, their requirements for graduating, which textbooks they use, etc. Also, I think old /mg/ threads have book lists, although take all that with a grain of salt (there's a lot of fucking idiots here, and also some savants who're smarter and have a better math background than you or I).
A useful book btw might be "All the Mathematics You Missed: But Need to Know for Graduate School," although you really, *really*, **really** need to do more practice exercises than that book provides to actually learn the subjects - it may feel like you know them, but you don't if you haven't/can't apply it. Still, it's a good overview. (It should go without saying that you should pirate this and all your other textbooks, unless you want a physical copy.)

[Anonymous No.15611723]

I require all your best visual sources for geometry and measure theory

[Anonymous No.15611773]

>>15611323
I do understand the difference between applied and pure math, yes.
I am not a NEET, but I can fit enough time in my schedule (I do have quite a bit of free time) depending on how long it is going to take. If 2-3 years is a reasonable estimate, then I can do it. But If it takes say 6 years, then that might be hard especially since I'd be doing this as a hobby not for career.
I mentioned the IQ only to avoid the responses like "Your IQ is too low anyways if you only studied calc II, give up, It's gonna take 30 years". I fully understand that math is very practice based and you can't skim it like Humanities.
>>15611327
>>15611334
I see this is all really good advice and a helpful guide. I will definitely look into the textbooks and the math depts.
What really prevents someone from understanding all of math though, If we're being real? I mean if you work hard enough, I'm sure a person can learn all of it, no?

Thanks a lot for the advice though.

[Anonymous No.15611863]

Bros.... just tell it to me straight, how many of you just went the actuary route? Looks like in one year I can get done with VEEs, exam 1/2 and all DISC's and get an analyst job. Probably 3 years of the job and a few more exams to make ACAS....
Its not pretty, but it pays the bills and isn't torture, right?

[Anonymous No.15612154]

[Anonymous No.15612318]

>>15611773
>What really prevents someone from understanding all of math though, If we're being real?
I'm not him, but imo: the sheer variety and quantity.
My argument is simple:
Mathematics involves creating or modifying proofs, definitions, etc. in a language or creating a language entirely for such purposes, and translating those back and forth to natural human language.
But with the popularization of mathematics people have created more and more topics, fields, approaches and sub-topics and definitions and this is continuously expanding. So strictly speaking, knowing "all of mathematics" is impossible.
This point brings on a couple of finer details:
1. Many of the variations and results are equivalent reformulations of previously known results. So in many cases, you might say knowing one form you know the actual mathematics.
However usually each form will then branch off with results unique to it.
For example, old school diff geo books don't use differential forms. But nowadays I've seen people say you should necessarily learn them because modern results in differential geometry and adjacent fields are from using differential forms.
2. On a more hopeful tone, it is plain fact that not all mathematics is equally useful, beautiful, or worth learning. If I tell you you don't know geometry you might be offended. But do you know all the properties and results of solids in higher dimensions? of course not.
Does that mean you don't know all geometry?
Yes indeed.
and in fact no one does.
And Euler Gauss and Newton and Leibniz did not either.
So in conclusion, it is a foolish idea to want to know "all mathematics". Instead learn how to learn and work with mathematics, and learn to your heart's content

[Anonymous No.15612523]

are there 'levels' of indeterminance, like how there are 'levels' of infiniteness? For example, as n -> infinity, is
0 * 2^n
as indeterminate as
0 * (-2)^n
since the latter one changes sign?

[Anonymous No.15613011]

Each is a generalization of what's below:
>powers
>multiplication
>addition
>counting on your fingers
>boolean
Thoughts?

[Jealous No.15614358]

>>15611103
I have a long one about my research in physics too.

[Jealous No.15614367]

>>15611103
>>15614358
This was completely unintentional.

[Anonymous No.15614377]

>>15611773
>What really prevents someone from understanding all of math though, If we're being real? I mean if you work hard enough, I'm sure a person can learn all of it, no?
The description I gave above roughly covers an undergraduate math education -- ~4 years, which could probably go down to 2 if you work year round, drop the gen-eds, and just are smart and hardworking about it. A PhD takes, usually (it's hard to generalize), about 2 more years where you study general topics at the graduate level in more detail, with more focus on a particular direction (eg start narrowing down to "okay, I want to study, say, algebraic topology, so I'm going to spend these 2 years taking courses in graduate algebra, topology, start the algebraic topology sequence, get some differential topology in there, take a class or two on category theory... and maybe take the Analysis sequence for breadth). Followed by ~3 years in which (after passing qualifying exams) you work with an advisor, take further closely-directed classes, and just generally do research. At the end of that process (if you make it), you'll have done novel research, discovered something about math nobody ever knew before. Somewhere in those 3 years, you'll know enough to be able to read papers in your tiny subfield and be able to skim adjacent fields' papers to use them in your research.
So, that's... maybe 6-8 years total, assuming you come in with a really good high school level understanding of math? That qualifies you for whatever subfield you chose to study, out of the ridiculous breadth of math as a whole.
So, could someone "learn it all" to a grad level? Maybe - not enough to do research, but enough to pass quals. Starting from Calc II, maybe 6-8 years? But that doesn't necessarily make you qualified enough in those areas to read research (depending on the subfield - eg graph theory's relatively "shallow" (maybe a good place to start?) vs, say, again, algebraic topology).

[Anonymous No.15614389]

Guys, the physics world is having a watershed moment right now. How can us mathematicians help them?

[Anonymous No.15614466]

>>15609556
I've heard it has its uses in data exploration and feature engineering for some specific applications and shouldn't be too hard if you have the prerequisites (algebraic topology and its prerequisites).

I would need a statsfag to confirm that though.

[Anonymous No.15614840]

>>15609654
>>15609563
>>15610616
https://www.ocf.berkeley.edu/~abhishek/chicmath.htm

[Anonymous No.15614864]

>>15614840
First time in a while someone posts something that's actually useful. Thanks anon.

[Anonymous No.15614942]

>>15614377
I see I understand now. Thanks for your thorough explanations anon. Really helps put it into perspective, have real expectations and goals and a timeline. As well as a general guide to how to do it. Seriously I appreciate it a lot. Knowledgable and helpful responses, extremely good quality posts not common on 4chan. Bless. Hope you make it in academia.

[Anonymous No.15614963]

>>15614840
So what you’re saying is I fucked up by buying these and should’ve bought something else or is this good ‘nuff at the start for a retard who was never willing to learn in school?

[Anonymous No.15615145]

Going to start getting into Operator Algebras soon, what resources do you guys recommend?
Assume that I have a good math undergrad education.
Here's your complimentary anime girl as a thanks in advance.

[Anonymous No.15615166]

how do I solve picrel?

I'm guessing the span is [0, 2, 1], [1, 0, 3] where the vectors represent [x, y, z] based off the relations y = 2z and 3x = z

Is that correct even when it's a complex module?

[Anonymous No.15615497]

Holy shit I love linear algebra

[Doctor Eli Selig !!JQHA6kqyl91 No.15615647]

>>15608042
Good Afternoon Math /Sci/entists.

I am working on MAID-LISP which is a language for abstracting language into Recursive Transition Networks and then using the networks to make strings.

Please post Advanced Mathematics and Computer Science research about analyzing and abstracting languages.

Thank you Math /Sci/entists for reading my post.

[Anonymous No.15615753]

How do you prove that every convex polyhedron is rigid (that is, the angles between the faces cannot be changed without breaking the shape)?

[Anonymous No.15615951]

>>15608198
Not all universities have the same difficulty level for each subject. I know some retard who got As all of the time. I checked their learning content and saw that it was high school tier difficulty.

[Anonymous No.15615961]

>>15614367
>tooker
Did anyone from sci verify if he was a schizo or not?

[Anonymous No.15616167]

What is the lipschitz continuous gradient of the Lp norm over R^n?

[Anonymous No.15616259]

>>15615647
for the love of god, please go back to /g/ instead of schizo posting here

[Anonymous No.15616315]

>>15608069
agreed, fuckem

[Doctor Eli Selig !!JQHA6kqyl91 No.15616369]

>>15616259
I already asked twice on the Dra/g/on Maid Board, but nobody had answers. If you want me to go away, send me research and I will leave to look at it.

[Anonymous No.15616717]

Can the power set the following power set functor be equipped with a monad structure:
[math]P(f)(A)=\{y\in Y\mid \forall x\in X(f(x)=y\to x\in A)\}[/math] for [math]f:X\to Y[/math] and [math]A\subseteq X[/math]?
Note that this isn't the usual power set functor [math]P(f)(A)=\{f(x)\mid x\in A\}[/math], which has a well-known monad structure via [math]{-}[/math] and [math]\bigcup[/math].

[Anonymous No.15616862]

>>15615145
Wegge-Olsen: K-theory and C*-algebras, Blackadar: Operator algebras and K-theory for operator algebras, Murphy: C*-algebras and operator theory

[Doctor Eli Selig !!JQHA6kqyl91 No.15617225]

>>15615647

[Anonymous No.15617621]

>>15614840
Anything similar to this for Physics? I'd like to apply what I learn from the books in the rec to physical situations. That always seemed to help me understand the Maths better.

[Anonymous No.15618322]

>>15617621
https://www.ocf.berkeley.edu/~abhishek/chicphys.htm
https://math.ucr.edu/home/baez/books.html

[Anonymous No.15618377]

>>15616717
What you're describing is not functorial: apply [math]P [/math] to
[eqn]\mathrm{id}:X\overset{\iota_1}{\to} X\sqcup X\overset{p}{\to} X, [/eqn]
it gives
[eqn]P(X)\overset{(\mathrm{id}, c_{\emptyset})}{\to} P(X)\times P(X)\overset{\cap}{\to} P(X), [/eqn]
which does not compose to the identity.

[Anonymous No.15619415]

>>15618377
That assignment is functorial (this is for example an exercise in Barr & Wells).
I wish this functor had an agreed upon name so I could actually properly google for this, but every author just makes something up on-the-fly

[Anonymous No.15619727]

>>15615647
https://dspace.mit.edu/bitstream/handle/1721.1/85687/Watumull-2014-On%20recursion.pdf
https://www.researchgate.net/publication/342760662_Abstraction_and_Summarization_of_Meaning_in_Natural_Language_Processing

[Anonymous No.15619891]

Just spent like 4 hours trying to understand a basic theorem in homotopy theory and still don't understand it. I feel retarded.

[Anonymous No.15620042]

>>15611103
Lmao who the fuck is this guy
>The Time Travel Interpretation of the Bible
>Quick Disproof of the Riemann Hypothesis
I would like to know more

[Anonymous No.15620426]

Is it just me or are the Chinese not that great at pure math? I don't remember ever seeing anything in math named after a Chinese person, even though they do super great at olympiads and what not. Do they all go into applied or something like that?

[Anonymous No.15620447]

>>15620426
They are good at rote memorization.

[Anonymous No.15621029]

You have a box which has an unlimited number of white balls, red balls and blue balls. You pick one ball at random. The probability of picking a red ball is A. The probability of picking a blue ball is B. Given that B < A, what is the probability that you will pick a blue ball before picking a red ball?

[Anonymous No.15621063]

You have a box which has an unlimited number of white balls, red balls and blue balls. You start picking balls one ball at a time. For a single pick, the probability of picking a red ball is A and B for blue.

Given that B < A, what is the probability that you will get the first blue ball before the first red ball?

[Anonymous No.15621299]

You roll three dice at the same time which counts as one roll: a 10-sided dice, a 100-sided dice and a 1000-sided dice. The dice have one side colored so that rolling that side has the probability 1/10, 1/100 and 1/1000 for each dice respectively.

1) Given that you begin rolling the dice an unlimited number of times, what is the probability that the first time that a colored side occurs is when it occurs on all of the three dice in the same roll simultaneously?

2) What is the probability that you have rolled the 1/1000 change before rolling the 1/100 even once?

[Anonymous No.15621398]

>>15621299
1)
p = 10^(-6) + (1 - 10^(-1))(1 - 10^(-2))(1 - 10^(-3)) p
p = 1/109891

2)
p = (1 - 10^(-2)) (10^(-3) + p)
p = 99/1000

[Anonymous No.15621748]

>>15620426
Tao???
>I don't remember ever seeing anything in math named after a Chinese person
lmao ur so dumb

[Anonymous No.15621756]

>>15621063
Sorry I only have white balls

[Anonymous No.15622153]

>>15620426
https://en.wikipedia.org/wiki/Shiing-Shen_Chern

[Anonymous No.15622190]

>>15618322
thx

[Anonymous No.15622938]

Does anyone have any resources or tips on how to memorize when negatives flip to being positive and when you also need to switch an addition or subtraction sign along with it? Basic algebra btw. This was always one of my hurdles

[Anonymous No.15622973]

>>15615497
Why ?

[Anonymous No.15624090]

expanded a factorial tree, and groups of terms corresponding to combinatorial combinations of the terms popped out. as in the written out combinations of (A,B,C)
1C3 -> A B C
2C3 -> AB AC BC
3C3 -> ABC
but with [(r), (r+1), (r+2)]. I'll look more into it tomorrow

[Anonymous No.15624736]

How much does it cost to hire a math consultant

[allison !MZgZR0q1GY No.15626009]

g(x):= (f(x),h(x))
f(x)=h(x)=x=y.
g(x)=(me,me):
What's essentially evil is just a phasor lazor.

[Anonymous No.15626891]

Does someone know why is this true? I have a hard time finding the proof of this.

[Anonymous No.15626933]

>>15609138
Your question was genuinely so stupid that I had to second guess myself

[Anonymous No.15626944]

>>15626891
Imagine moving one chord along the other chord while keeping the chords at the same angle. As you do this the x angle will increase at the same rate as the y angle decreases as you can see visually by tilting your head. So the sum will be conserved.

So first move one chord to be at the center, then adjust the other chord to pass through the center of the circle. The sum x+y will be conserved and so will the angle between the chords as you haven't rotated them at all. But now clearly x+y = x' + y' = 2*angle between the two chords

[Anonymous No.15626962]

>>15626891
that doesn't even make sense

[Anonymous No.15627326]

Symmetry is pretty, but if a problem is too symmetrical then different angles of looking at it are the same, and you are forced to just solve it all at once

[Anonymous No.15627336]

>>15621748
Tao is Aussie

[Anonymous No.15627413]

>>15626944
I think I finally get it anon, thanks a lot.
>>15626962
It doesn't at first, but if you manage to find the right theorems, it's incredibly easy to prove.

[Anonymous No.15627468]

>>15627413
By the way, I learned this thanks to this video here. Hope it helps too.
https://youtu.be/CqmvUbfRgt4

[Anonymous No.15627753]

>>15620426
Chinese remainder theorem.
God you're fucking dumb.
>>>/pol/

[Anonymous No.15628033]

Whatever. It’s over. I admit it. I can’t learn math. I’m not smart enough

[Anonymous No.15628185]

>>15628033
prove it

[Anonymous No.15628246]

>>15627413
I did it with a more basic start

[Anonymous No.15628891]

There is a thing i dont understand about Riemann surfaces. Suppose you have a polynomial p in C[x,y] whose partial derivatives dont vanish at any point. Then its curve is a non compact Riemann surface and you can compactify it by adding a third variable and making all degrees equal. The resulting curve might have some singularities which can be "removed" by blowing up or whatever. But then why is resulting curve important when you could have started with a non singular curve in C[x,y,z] to begin with?

[Anonymous No.15629328]

Is there a thing that's more general than group or ring theory and less general than universal algebra or category theory?

[Anonymous No.15629478]

I'm not abusing notation, I'm extending it

[Anonymous No.15630498]

I've got a deep and abiding lust for studying mathematical foundations and I have to tear myself away from foundations to focus on other topics in math. Foundations are like Collatz, it sucks you in unless you consciously reject it.
Is this true for the majority of mathematicians?

[Anonymous No.15630502]

>>15608042
I'm mentally retarded. How do people find the square root of a number so easily? I only just figured out today 3^2 is 3x3 not 3x3x3

[Anonymous No.15630647]

>>15630502
visualize what 'three squared' means nigga

[Anonymous No.15630870]

seriosly how the fuck? i tried defining A*the remaning vector of the orthonormal base so that the result is perpendicular to the other one given and the norm is 12 in that direction, but it didnt work because that's stil not the maximum (gram matrix diagonalization shows it's 15).

[Doctor Eli Selig !!JQHA6kqyl91 No.15631177]

>>15619727
Thank you for showing me these. Attached in an image of a Recursive Transition Network sourced from Wikipedia. Do you know what latex package I would need to make latex draw an RTN?

I consulted Google but the results were useless and unrelated to RTNs or latex.

[Anonymous No.15632484]

>>15630502
when given 3^2, imagine a square of side length 3 and calculate its area. With 3^3, imagine a cube.

[Anonymous No.15632541]

>>15630498
No. I hate "hardcore" foundations

[Anonymous No.15632793]

>>15630870
Then you did it wrong.

[eqn] A \begin{pmatrix} -1 & 2 & 2 \\ 2 & -1 & 2 \\ 2 & 2 & -1 \end{pmatrix} = \begin{pmatrix} 0 & 9 & -12 \cdot \frac{12}{5} \\ 0 & 12 & 9 \cdot \frac{12}{5} \end{pmatrix} \\
A = \begin{pmatrix} 0 & 9 & -12 \cdot \frac{12}{5} \\ 0 & 12 & 9 \cdot \frac{12}{5} \end{pmatrix} \begin{pmatrix} -1 & 2 & 2 \\ 2 & -1 & 2 \\ 2 & 2 & -1 \end{pmatrix}^{-1} = \frac{1}{15} \begin{pmatrix} -66 & -111 & 78 \\ 112 & 52 & 4 \end{pmatrix}[/eqn]

[Anonymous No.15633990]

I just learned about math job rumors only to find that it was axed. Anything else in this vein? Someone I know was getting shit talked on there and called out as a fraud but now I can't ever see it.

[Anonymous No.15635367]

>>15629328
Groups and rings are both Malcev varieties.

[Anonymous No.15636243]

Any alternative to the picrel? This book is terribly structured and ordered. I am trying to learn Algebra and Trig before I do precalc

[Anonymous No.15636409]

what do you call automatons where the transition function can change.

[Anonymous No.15637099]

What's a good book to learn about partial orders, lattices, pre-orders and all that stuff?

[Anonymous No.15637151]

how do i center the columns in an array in latex

[Anonymous No.15637161]

>>15637151
nevermind i got it. you have to put c's after \beginarray{cccc}

[Anonymous No.15637436]

I fucking hate LaTeX. Why won't a journal accept my neatly handwritten pages?

[Anonymous No.15637713]

>>15612154
I've been researching this exact same topic, with expansions to higher operations beyond linear (summation) and geometric (production) -- it relies on my own definition of hyperoperations beyond exponentiation and prior to summation. What would be nice is if you could define a geometric analog of the Riemann-Liouville differintegral and see if the pattern goes on to higher operations!

[Anonymous No.15637961]

>>15637713
>reimann-liouville differential
I skimmed the Wikipedia page and I dont know what any of that is. I might get more into it after I finish up this stuff. I've been living in integer land for a little while. I'm going to see if I find anything interesting in a factorial triangle, analogous to pascals triangle. in pascals triangle I was seeing numerical answers to combinatorials, but in the factorial triangle I was seeing algebraic structures that represented combinatorials. also gonna see if I can independently find what I know was already figured out 150 years ago. I am interested in what you mean by hyper-operations

[Anonymous No.15637982]

>>15636243
I don't know much about the kind of structure you're looking for but I've learned a lot from Stewart's book.

[Anonymous No.15638055]

>>15619891
Fixed point browser theorem can be proved trivially with a chain of fundamental groups + functor axioms.
>>15615647
Learn the foundations of logic, then move on to type theory and computation models.

[Anonymous No.15638249]

>>15637961
differintegrals are just a way to partially apply the derivative, so you can have fractional order derivatives/integrals. what got my attention from that post is the idea of iterating the product operator, but you didn't think about applying it partially i.e. an operator P such that P(P(f(x))) = π f(x) and so on

[Anonymous No.15638352]

I'm reading a book on "analytic number theory" by iwaniec and kowalski out of boredom
all I see is pages upon pages of messy formulas and I simply cannot figure out
what the fuck has this all to do with numbers??

[Anonymous No.15639053]

Interracial cuckold is the thinking man’s fetish

[Anonymous No.15639131]

whitehead is the best mathematician

[Anonymous No.15639174]

Can someone explain what's wrong with this? [math]1 = (-1)(-1) \Rightarrow \sqrt1 = \sqrt{(-1)(-1)} \Rightarrow 1 = i^2 \Rightarrow 1
= -1[/math]

[Anonymous No.15639192]

>>15639174
[eqn]\sqrt{(-1)(-1)} \neq i^2[/eqn]

[Anonymous No.15639319]

>>15629478
aslong as you have it pre-defined, it's fine

[Anonymous No.15639327]

>>15614389
more rigour

[Anonymous No.15639330]

Results are the only thing that matter.

[Anonymous No.15639339]

>>15639174
Sqrt() is technically multivalued -- after all, 2*2 = -2 * -2 = 4, so shouldn't sqrt(4) equal both 2 and -2? To avoid this, we generally *define* sqrt on the reals as taking the positive square root, and for complex numbers as the branch such that sqrt(-1) = i, not -i.
In cases like your equation, you're mixing the two possible outcomes of sqrt -- sqrt(1)=1 is choosing the positive outcome, sqrt((-1)(-1))=sqrt(1)=-1=i^2 is the negative outcome. Your equation would work if you consistently chose positive or negative for both.

(Math sidenote: Incidentally, in complex analysis, that's called taking a "branch cut" of sqrt. sqrt is multivalued, and while we can't visualize a function C->C since that's 4 total dimensions, you can graph the real and imaginary parts of the input z=x+iy on the xy plane and graph Re(sqrt(z)), or Im(sqrt(z)), or |sqrt(z)|, among others, on the z-axis -- if you do this, you get graphs of "sheets", and whereas a single-valued function is just a single "sheet" where, for each input z, there's a single output point on the sheet - sqrt is multivalued, and in this case has 2 outputs for every point other than 0 and infinity. A branch cut is basically choosing some line from (in this case) 0 to infinity such that, if you start on one sheet of the sqrt function, and if you don't cross that line, you won't end up on the other sheet -- making it single-valued. In this case I think you just choose some random branch cut such that it doesn't intersect any of the numbers you're using, say eg the negative imaginary axis or something, and then all your calculations will work out fine; the issue mostly arises if you plug in an interval - eg calculating sqrt(e^it) as t goes from -pi to 3pi will arrive at a different value than when you started, even though -1=e^(-pi)=e^(i*3pi).)

[Barkun's Cum Rag No.15639342]

>>15608042
IN my mouffffffffff

[Anonymous No.15639349]

>Every smooth curve can be adequately approximated between two points with the right polynomial
>Polynomials cannot have transcendental zeroes
How does a polynomial approximate a smooth curve with a transcendental zero?
Example: pi-sqrt(x)

[Barkun's Cum Rag No.15639352]

>>15608042
U doopid

[Anonymous No.15639363]

>>15639339
Is there a version of complex analysis that avoids principal branches and just works with the multivalued surfaces as they are?

[Anonymous No.15639371]

>>15639352
If you want to actually destroy /mg/ for realsies, just copypaste post titles from reddit math help boards and post 10-20 of them on /mg/ a day for three weeks

[Anonymous No.15639383]

>>15639349
read what "approximate" means in that context
it means that for every [math]\varepsilon>0[/math] there exist a polynomial [math]p(x)[/math] such that for [math]|f(x)-p(x)|<\varepsilon[/math] for every [math]x[/math] in the given interval

[Barkun's Cum Rag No.15639385]

Is mafs smrt

[Anonymous No.15639391]

>>15639349
>Polynomials cannot have transcendental zeroes
Who told you that?
Polynomials can't have transcendental zeroes if they have integer coefficients, but there's nothing stopping them from having transcendental zeroes in general

[Anonymous No.15639413]

Hey guys hey guys hey guys
When I need to calculate this why can’t I divide up and down by n^2 and get 7 ?

[Anonymous No.15639428]

>>15639413
because you'd end up with a denominator of [math]\frac{3n+2}{n^2}=\frac{3}{n}+\frac{2}{n^2}[/math], which is decidedly not 1 like it would need to be for that to equal 7

[Anonymous No.15639435]

>>15639413
anon post your calculation

[Anonymous No.15639449]

Hey guys I've been struggling with this problem for a while now, and I need some help

A real [math]n \times n[/math] matrix [math]A[/math] has an eigenvalue [math]\lambda[/math]. Show that there exists some [math]k \in \mathbb{Z}^{+}[/math] with [math]k \le n[/math] such that
[eqn]
|\lambda - A_{kk}| \le \sum_{j=1, j \not= k}^{n}|A_{jk}|.
[/eqn]

So I thought of assuming that [math]|\lambda - A_{kk}| > \sum_{j=1, j \not= k}^{n}|A_{jk}| \:\: \forall \:\: k \le n [/math] and proving it by contradiction, but I don't seem to be getting anywhere. It was very easy to prove for the specific case of [math]n=2[/math] but I can't even do it for [math]n=3[/math].
I feel like this must have something to do with algebraically manipulating [math]\det(A - \lambda I)[/math] but I really have no clue what to do.

[Anonymous No.15639451]

>>15639428
Understandable

[Anonymous No.15639495]

>>15639363
Not an expert, but I think that's where the concept of 'Riemann surfaces' - a connected 1-dimensional (that is, wrt C, so 2D traditionally) complex manifold, aka a space that locally behaves around any given point like C but globally might have a different structure.
So, eg with sqrt(z), locally around any point in the image of sqrt(z), it's perfectly smooth and all that -- it just happens that trying to graph the whole thing at once would give you self-intersecting surface, trying to travel certain paths around the origin might take 720 rather than 360 degrees of rotation to end up where you started, etc. In this view, z -> sqrt(z) is a holomorphic map from C to this surface (call it X). Branch points/ramification points occur when the function has a single output at some point but has n outputs everywhere else in a small neighborhood around that point (eg z=0 and z=inf for sqrt(z)).
Now, this is where I don't know anything else, but I recommend Wikipedia ('branch point', 'Riemann surface', 'Riemann-Hurwitz formula', etc), and so forth. It looks like there's a whole field here, that goes into algebraic geometry/topology more generally.

[Anonymous No.15639506]

>>15639349
Polynomials with rational coefficients can't have transcendental zeros (that's the definition of transcendental in R).
However, it's perfectly possible to have a polynomial with real coefficients, and you can approximate smooth curves with them.

[Anonymous No.15639544]

Getting into architecture as a hobby , which books on geometry do you bros recommend?

[Anonymous No.15639835]

I have a question about the applications of PDEs, I'm a chemical engineering major taking a basic PDE course next semester. I'm wondering what are the applications of PDEs and what is required to get into advanced PDEs?

[Anonymous No.15639912]

I know how to solve [math]\partial_tu(\mathbf{x},t)-c^2\nabla^2u(\mathbf{x},t)=0[/math]

[Anonymous No.15639923]

How are younger people performing in maths? Have people looked into that?

Intuition tells me they are not studying enough to unlock their full potential but I don't want to dismiss the possibility of them performing better than older generations, besides nowadays we have access to many resources to study. But are young people even interested in becoming good in mathematics, engineering etc. anymore?

pic unrelated

[Anonymous No.15639938]

There are no prime numbers in [math]\mathbb{R}[/math].
A prime number is a number that
1. isn't invertible;
2. isn't zero;
3. whenever it divides the product of two numbers it divides one of the factors.
[math]\mathbb{R}[/math], however, is a field, meaning that all of its elements are invertible. Thus, there aren't prime numbers on [math]\mathbb{R}[/math].

[Anonymous No.15639979]

>>15636243
All textbooks are more or less structured the same way. If you're looking for the perfect book that will explain everything in a manner that allows you to understand everything perfectly, you're out of luck, it doesn't exist. Use the textbook's structure to guide your thought and make sense of the concept you're trying to wrap your head around.

[Anonymous No.15640148]

>>15639495
You are absolutely right

[Anonymous No.15640177]

How did you guys get good at understanding probability? I did really bad in my intro to probability course a while back because a lot of it just felt unintuitive to me compared to calculus or linear algebra.

[Anonymous No.15640223]

>>15639979
i've noticed people obsess the same way with art materials
they'll hoard all sorts of video materials and books thinking they've found the perfect one and they'll get started tomorrow on a straight shot to fulfillment
nah they just start hoarding more shit lol

[Anonymous No.15640679]

>primes aren't invertible
what

[Anonymous No.15640712]

Has applied category theory ever been applied?

[Anonymous No.15640766]

>>15639449
Given lambda, choose its corresponding left eigenvector v.
Multiply v by A and look at the kth component.
Sum[ v(j)*A(j,k) ] = lambda*v(k).
Move v(k)*A(k,k) to the RHS.
Sum[ v(j)*A(j,k); j!=k] = (lambda-A(k,k))*v(k).
|.| both sides and use triangle inequality on the left.
Sum[ |v(j)|*|A(j,k)|; j!=k] >= |Sum[ v(j)*A(j,k); j!=k]| = |lambda-A(k,k)|*|v(k)|.
Choose k such that |v(k)| is the largest component.
Use |v(k)| >= |v(j)| for each v(j) on the LHS.
Sum[ |v(k)|*|A(j,k)|; j!=k] >= Sum[ |v(j)|*|A(j,k)|; j!=k] >= |lambda-A(k,k)|*|v(k)|.
Divide by |v(k)| (it can't be 0 since that would imply v is the zero vector).
Sum[ |A(j,k)|; j!=k] >= |lambda-A(k,k)|.

[Anonymous No.15641067]

>>15640679
retard

[Anonymous No.15641079]

why are my verbal scores always in the single digit percentiles and my maths in the normie ranges

[Anonymous No.15641085]

Can anyone recommend me a book on algebra that goes into depth about decomposition of modules through idempotents/involutions in the context of Clifford algebras? I've looked through a lot of literature, and most of the time idempotents are not even mentioned or mentioned only in passing (most texts on algebra, rings/modules, and Clifford algebras), or the text is way too specialised ("Book of Involutions").
So far the only textbook I've found that somewhat fits the bill is Lounesto's "Clifford Algebras and Spinors", but the treatment there is rather informal.

[Anonymous No.15641352]

>>15639449
>>15640766
Is this problem really instructive/valuable? Does it maybe help to develop the machinery behind some cool linear algebra result?

It seems like they started with the eigenvalue equality Av=cv, fucked around a bit, and then said lol figure out what I did.

[Anonymous No.15641801]

>>15640766
Hey, thanks anon, I also solved the problem myself just a couple hours back. I proved it via contradiction. My proof is pretty similar to yours except for the last part.

Let [math]v[/math] be the eigenvector associated with the eigenvalue [math]\lambda[/math]. Then we have
[eqn]
Av = \lambda v\\
\implies \sum_{j\le n}A_{kj}v_j = \lambda v_k \quad \forall \: k \le n \\
\implies \sum_{j \le n, j \not= k}A_{kj}v_j = v_k(\lambda - A_{kk}) \\
\implies \sum_{j \le n, j \not= k}|A_{kj}||v_j| \ge |v_k||\lambda -A_{kk}| \quad \text{(triangle inequality)} \\
\implies \sum_{k \le n}\sum_{j \le n, j \not= k}|A_{kj}||v_j| \ge \sum_{k \le n}|v_k||\lambda -A_{kk}| \\
\implies \sum_{k \le n}\sum_{j \le n, j \not= k}|A_{jk}||v_k| \ge \sum_{k \le n}|v_k||\lambda -A_{kk}|
[/eqn]

Suppose [math]|\lambda - A_{kk}| > \sum_{j \le n, j \not= k}|A_{jk}|[/math]. Then we have
[eqn]
\sum_{j \le n, j \not= k}|A_{jk}||v_k| < |v_k||\lambda - A_{kk}| \\
\implies \sum_{k \le n}\sum_{j \le n, j \not= k}|A_{jk}||v_k| < \sum_{k \le n}|v_k||\lambda -A_{kk}|
[/eqn]
which contradicts our previous result. Hence there must exist some [math]k\le n[/math] such that [math]|\lambda - A_{kk}| \le \sum_{j \le n, j \not= k}|A_{jk}|[/math].

QED

[Anonymous No.15642219]

What is the name for when two real numbers are algebraic multiples of each other? Like pi and 3sqrt(pi)?

[Anonymous No.15642285]

>>15641352
It can be used to give a loose bound on the location of the eigenvalues.
It is important enough to have a name.
https://en.wikipedia.org/wiki/Gershgorin_circle_theorem

[Anonymous No.15642286]

>>15642219
I think this is about the 'algebraic closure' of a given field, specifically a given extension of the rationals Q. The algebraic closure of Q is the algebraic numbers Q^alg = A. You can then talk about, say, ( Q(pi) )^alg, the closure of Q extended by the transcendental pi, which'll give you the field containing Q, pi, and the roots of all polynomials with these contents.
For further info, go look into basic field theory and algebraic/transcendental extensions; it turns out "the" algebraic closure is indeed unique up to isomorphism (field theory in general, at least the basics that I've seen, is all pretty clean in these sorts of regards).

[Anonymous No.15642396]

What should I read to begin to have a basic working understanding of the Reimann Hypothesis (and or Dirichlet series, zeta functions, L-functions)?
I currently have pic related and heard it's pretty good, but I'm trying to put together a small library.

Also any papers I can start by reading?

[Anonymous No.15642727]

>>15642396
>Reimann

[Anonymous No.15642855]

>>15642396
How much prior analysis knowledge do you have?

[Anonymous No.15642880]

>>15642855
Two semesters of graduate Real Analysis and one semester of graduate Complex Analysis. My NT is probably the weaker part of my background since I only ever had an undergrad course.

[Anonymous No.15642887]

K
Anon, what math says about the meaning of life?
Does algebra or geometry can give a people something to not KMS?

[Anonymous No.15642912]

>>15642880
Start with Apostol's intro to analytic number theory, then you should be able to follow this survey book:
https://link.springer.com/book/10.1007/978-0-387-72126-2
It will guide you to further reading.

[Anonymous No.15642919]

>>15642887
Try the gervais principle

[Anonymous No.15642930]

Are there any two distinct positive integers a and b where [math]\frac{arctan(a)}{arctan(b)}[/math] is algebraic?
I haven't done anything besides programming for three years and I've forgotten most of calculus. This has been bugging me all day.

[Anonymous No.15642980]

>>15642912
Thanks anon.

[Anonymous No.15643055]

>>15617621
https://www.goodtheorist.science/index.html
best advice out there by one of the best living physicists . Good luck anon dont chicken out and do the work

[Anonymous No.15643080]

>>15642887
>Can algebra or geometry give people something to not KMS?
Yes, practice problems. If you're spending time thinking about suicide, that's time you're falling behind in abstract algebra.

[Anonymous No.15643127]

>>15642930
Not sure, but I think by (after googling) the 'Lindemann-Weierstrass' theorem, which can be used to show that sin(x), cos(x), tan(x) are transcendental for algebraic x (other than x=0). So if x is an integer, arctan(x) must be transcendental (as otherwise tan(arctan(x)) would map an algebraic input to algebraic output). Thus arctan(a)/arctan(b) is a ratio of transcendentals, which is transcendental.
...I think this works

[Anonymous No.15643153]

>>15608042
Am I fucked if I want to self-study Papa Rudin?

[Anonymous No.15643167]

>>15643127
wait I'm a fucking dumbass, eg (pi/4)/(pi/5) isn't transcendental

[Anonymous No.15643249]

I find integration much more rewarding and fun to solve than i do derivatives. I know im just starting with calculus so i need a lot more practice with both.
So far it feels like theres more tricks with integrals. Like a lot of the trig stuff i feel was used heavily vs doing the chain rule endlessly.

[Anonymous No.15643848]

takes me literally all day to make a beamer every fucking time i am the slowest person in the world at this shit

[Anonymous No.15643918]

>>15642396
I have the original 1974 Academic Press version
of the book at home.

[Anonymous No.15644043]

>>15640712
Haskell
>>15643153
It's doable to easy if you have any talent at all
>>15642887
It's more likely to make you suicidal in my experience
>>15640177
I suggest doing a bunch of HS-level olympiad probability problems

[Anonymous No.15644104]

Can anyone help me with this? The use of the theorem that the sum of two convex functions is convex was required for an exercise for a calculus exam but the demonstration isn't in the book, it was left as an exercise to the reader lol. But unless I am doing something very stupid, it seems that I found a counter-example? In the pic w and g are convex, but w+g isn't?

[Anonymous No.15644417]

>>15636243
Use basic mathematics of serge lang or start using a calculus book and use Khan Academy when you stuck in a precalc problem.

[Anonymous No.15644441]

>>15644104
if by convex you mean any path joining two points on the surface is contained in the surface, then the surface corresponding to [math] g [/math] doesnt look very convex.

[Anonymous No.15645720]

>>15643055
That book she's reading...yes, please.

[Anonymous No.15646104]

Hey anons. Trying to learn maths after over a decade not doing it. Right now I'm reading the proof for why the square root of 2 is an irrational number using this site: https://www.mathsisfun.com/numbers/square-root-2-irrational.html

Something that's tripping me up: the site says that since m^2 is a multiple of 4 (since all squared even numbers are multiples of 4), then n^2 should be a multiple of 2, since m^2/n^2 = 2.

I don't understand this. Why is n^2 necessarily a multiple of 2? Why does m^2 being a multiple of 4 make n^2 a multiple of 2? I thought it was to do with their odd/even status, but 666/333 = 2, so it's not necessarily that to divide an even number to get 2 you have to have an even number, but rather something to do with the fact that they're squared and that squared even numbers are multiples of 4... but I can't make the connection.

Any help?

[Anonymous No.15646133]

>>15646104
We start by saying (m/n)=sqrt(2), and so (m/n)^2 = 2. Thus, m^2/n^2 = 2, or m^2 = 2 * n^2.
Thus, since m^2 is 2 times something, m^2 is even; and only even numbers square to even, so m must be even.
Then since m is even, m must be 2 times some number, let's call it k. That is, m=2k.
Substitute this back in: (2k)^2 = 2 * n^2. Evaluate: 4*k^2 = 2*n^2. Thus n^2 = 2 * k^2.
...but then, n^2 is 2 times some number. So n^2 is even, and for the same reason as before, thus n is even.
But then, m and n are both even. This contradicts our assumption that m/n is in least terms. Therefore, we conclude it's impossible to represent sqrt(2) as m/n in least terms, and since every fraction can be simplified to least terms, sqrt(2) can't be a fraction -- it's irrational.

To repeat the step you're focusing on in a different way: m^2/n^2=2, or to write it another way, m^2 = 2 * n^2. But if m is even (a multiple of 2), then m^2 must be a multiple of 4. If 4 divides the left side, then 4 divides the right: 4 divides 2*n^2. Thus 2 must divide n^2.

[bodhi No.15646193]

>>15642727
I bet Q shaman can solve riemann's

[Anonymous No.15646203]

>>15643153
By the way there is a proof of the Radon-Nikodym due to Von Neumann in the book. Just went through it today and it was surprisingly easy though the trick comes out of nowhere as it is written in the book.

[Anonymous No.15646972]

What foreign language would be the most useful for mathematics? Almost everything is published in English these days but making connections with people will always be something worth putting effort into.

[Anonymous No.15647206]

My biggest mistake in maths exams seems to be overlooking small details, like a sign, or a decimal etc, which makes me lose marks.
How do I even get over such a problem? If it was me simply being weak in a particular topic, I could do deliberate practice till I got better, but how do I even fix a habit like this?

[Anonymous No.15647226]

>>15646972
The top three languages I could think of would be
French, German and Russian. Plenty were
published in these languages, and French gave us
some words that became part of our terminology
(injective, for example). Latin is a classic that
built up French and English but isn't published
in that today.

I'm not saying the top three should be united to yield
some krautburger borscht linguistic abomination for
our sake. Rather, we could trade terminologies in
their language (and some equivalents) to supplement
and grow mathematical fields.

[Anonymous No.15647241]

>>15647206
by doing deliberate practice until you get better? also just double-check your work -- unless you've got dyscalculia or something, you can just look at your work and going, "okay, I started with this, then I did such-and-such to get that, then I did such-and-such to get -- oops, made a typo there." you should be able to justify every step. but you get better, both at avoiding mistakes and in catching them when you see them, only through practice.
math isn't magic or something -- it's like saying "I'm learning Spanish but I keep making these mistakes when I speak it! What do I do?" the obvious and only answer is to a) be more careful, so you don't reinforce bad habits, and b) speak it more until doing it correctly becomes a habit.

[Anonymous No.15647288]

>>15609654

[Anonymous No.15647309]

>>15642396
No need, it's already been solved

[Anonymous No.15647357]

>>15647288
Shit chart, kys
>Europe
Even shittier, kys immediately

[Anonymous No.15647386]

>>15647288
kek, good chart anon

[Anonymous No.15647403]

>>15647309

[Anonymous No.15647468]

>>15640223
That's kind of the case for a lot of beginners in a lot of fields. Maths, Programming, Drawing, Japanese. They're afraid of learning the wrong way, or want to learn X in the shortest and most efficient way possible. All that matters is that you take the initiative and take the first step to learn; you'll learn what works and what doesn't for (you) as you try it out.

[Anonymous No.15647663]

>>15647403
virgin 16 page "proof" vs chad handwritten refutation

[Anonymous No.15647847]

if an item has x% chance to drop from a mob, how can i calculate what are the chances that i don't drop it by nth attempt?

[Anonymous No.15647854]

>>15647847
(odds it doesn't drop)^n

[Anonymous No.15647914]

>>15647854
wow that's a bitch to calculate anything easier?

[Anonymous No.15648039]

>>15647914
Unfortunately there is little easier than multiplying whole numbers. Maybe you should finish your summer school homework before going back to your game. You don't want to fail grade 3 twice, do you?

[Anonymous No.15648095]

>>15648039
yeah dude let me just 0.34^300 in my head

[Anonymous No.15648242]

>>15648095
Find the nearest small denominator fraction, which is [math]\frac {1}{3}[/math]. Exponentials are easier with fractions instead of decimals:

[math]{\frac {1}{3}}^{300} = \frac {1^{300}} {3^{300}} = \frac {1}{3^{300}} [/math]

[Anonymous No.15648280]

>>15648242
conveniently omitted 3^300

[Anonymous No.15648329]

Is their any abstract proof for Newton's formula which is used to solve quadratic? (Other than the high school proof) ?

[Anonymous No.15648426]

>>15648095
[eqn]0.34^{300} = 10^{300 \log_{10}(0.34)} \approx 10^{300 \cdot (-0.4685)} = 10^{-140.55} \approx 2.8 \cdot 10^{-141}[/eqn]

There is a magic tool called the slide rule that you should always have nearby to calculate logarithms.

[Anonymous No.15648442]

>>15648280
Logarithms:
[math]a^b = 10^{b* log_{10}a} [/math]
[math]3^{300} = 10^{300 log_{10}3} [/math]
[math]3^{300} = 10^{approximately \; 143} [/math]

[Barkun No.15648446]

>Les do Marfs like good goyim

You people are retarded kys now

I mean it ive had enuff of you faggits

[Anonymous No.15648518]

>>15647288
>A course in functional analysis
>Precalc
Lmao

[Anonymous No.15648553]

I consider myself an elightened programmer and I would like to study category theory and lambda calculus. However, my math knowledge stopped at high school. How fucked up am I?

[Anonymous No.15648560]

>>15648553
How comfortable are you with mathematical reasoning? proofs?

[Anonymous No.15648569]

>>15648560
I can do basic algebra..
Regarding proofs, I think our teacher showed us one or two in high school. So I would say low proficiency. Do you think those are mandatory?

[Barkun's Cum Rag No.15648575]

>>15648569
>i can
>one of humankind
LUL stopped reading

[Anonymous No.15648590]

>>15648575
What?

[Barkun's Cum Rag No.15648615]

>>15648590
Ull c

[Anonymous No.15648807]

>>15648590
just ignore barkun, he's irrelevant
>>15648569
some level of proofs is necessary, at least imo. For computer science especially, understanding the "proof" that an algorithm works, often is essentially the same as understanding why and how the algorithm works/verifying that it does; being unable to do or read proofs in that context would mean you're unable to think carefully and in detail about how and whether something works. Any decent book on algorithms should include a basic guide to the tools of basic proofwriting (reasoning about recursion, proof by induction / contradiction, etc); just do homework problems.
As for studying category theory and lambda calculus... yeah, the former especially is upper-level to grad-level math, and therefore is exclusively proofs in substance. I don't know if anyone's tried to present category theory without proofs, or what that would even really look like... maybe try a guide to Haskell and its type system? idk. Alternately, category theory takes some really heavy machinery to understand in practice, since otherwise it may just seem like abstract nonsense if you can't see connections to other parts of math, but you might be able to find a "for beginners" book that includes exercises at an appropriate level... I remember finding one textbook pdf that came at it specifically from the direction of type theory and coding applications, though I don't remember what it was.
Lambda calculus I can't comment on, don't know much about. Seems like a decent course in introduction to Turing machines, finite state machines, computability, etc might be useful; you can find plenty of books on this, try to find one that'll ease you in and include proof exercises. (they often also include time analysis, P vs NP etc, which you might find useful and also includes good opportunities for a CS person to do proofs)

[Anonymous No.15648849]

>>15648329
Bump

[Anonymous No.15649098]

>>15648426
>>15648442
that's actually useful

[Anonymous No.15649120]

>>15608042
whats a good textbook to self learn high school level geometry relatively fast (like in a month ideally); i cheated my way through it in high school so i retain next to none of it, and want to go back and actually learn it; the book from the faq (elementary geometry from an advanced standpoint) is a bit too complicated for me

[Anonymous No.15649231]

>>15649120
Probably just any high school level geometry textbook because they all cover the same material and are written for literal children.

>>15648569
Studying category theory without any knowledge in either algebraic topology or algebraic geometry (preferably both) is pointless. Like yes, you can learn some things but you haven't seen enough examples to understand the motivation for the underlying theory. I know that they use "category" "theory" in programming, but if you read a textbook on category theory for math students you'd get completely lost. Try reading some of "Categories for the Working Mathematician" a bit of and see how it feels.

For lambda calculus you should probably read an intro to proofs book... I like Journey into Mathematics: an Introduction to Proofs. Very fun and good for self-study.


>>15648329
https://en.wikipedia.org/wiki/Quadratic_formula#By_Lagrange_resolvents

Take an abstract algebra class and you'll see a lot more theory about polynomials.

[Anonymous No.15649249]

How do you prove it?

[Anonymous No.15649255]

>>15649249
impossible

[Anonymous No.15649273]

>>15648569
You should try learning agda. It'll check your proofs for you.

[Anonymous No.15649274]

>>15649255
LOL I remember this quote. It was about the Collatz conjecture.

[Anonymous No.15649605]

/mg/ qualityposters, is there any proper roadmap for learning advanced math?
i'd say i'm on something of a good high school/college freshman level now. would be nice to go over everything again to be fresh, too.

i've suddenly come to like it, for some reason. i get the beauty mathematicians talk about now.

[Anonymous No.15649732]

Hello, I am 25 and just starting my first calculus class in uni. Is it too late for me? Should I give up? Or should I willingly pursue in blissful ignorance?

[Anonymous No.15649753]

>>15649732
how good are your foundations? do you already have a notion of what calc is, or a familiarity with what you'll study?

[Anonymous No.15649769]

Mathmajor bros, how the fuck do I learn fast enough to get to the point where I can work with a prof on research while in undergrad?

[Anonymous No.15649784]

>>15649753
Precalc/Trig was a breeze for me. I've recently bought Spivaks Calculus and am going through it now with not much difficulty. Limits seem pretty intuitive to me. I've been trying to go through Professor Leonard's Calc videos but his pace is so slow and I get a little bored with his teaching style. I went through the whole Stewarts Precalc book so I would say my foundation is okay but I still have to study hard to get a solid understanding of some topics.

[Anonymous No.15649791]

>>15649769
go look into the medicine bubble. those guys have some insane amounts of information to learn while in rotations, and get it done.
the quickest is using most of your free time and breaks to study more.

[Anonymous No.15649794]

>>15649784
https://www.youtube.com/watch?v=iEmCUks30-E&t=21s

[Anonymous No.15649799]

>>15649784
You sound like you're doing great, anon. Just keep at it, go a reasonable pace so you're not skipping anything, and do the homework problems (the most important part). Plenty of folks start later (dude at my work's like 50 and just took Calc II).

[Anonymous No.15649815]

>>15649799
Thanks, anon. It's funny because I feel like at the ripe age of 25 I am much more driven to learn mathematics than I ever would have been if I was 18 or in my early 20s.

[Anonymous No.15649854]

>>15620426
Yitang Zhang's result on bounded prime gaps was one of the biggest advances in math of the last decade

[Anonymous No.15649922]

>>15649815
Some people struggle with motivation on moving from single variable calc to multivariable calc - this may not happen to you, but if it does, bring linear algebra forward, do some of it and then return to calc.

[Anonymous No.15649933]

>>15649922
How much linear algebra do I need to know for calc 3? In precalc, I studied matrices, Crammer's method, determinants, and Gaussian elimination. (pretty much the first unit of linear algebra). Will this be enough?

[Anonymous No.15649962]

>>15649933
>crammer method
Nearly worse than Reimann hypothesis

[Anonymous No.15649971]

>>15649962
oh fuck off it was a typo

[Anonymous No.15649975]

>>15649769
You don't really need to know that much to begin doing research with a prof. You should just directly speak with your prof and tell them you're interested in doing research and they will find a suitable problem for you to tackle. You're still probably going to have to learn some stuff on your own, but I think a lot of people fall into the trap of "I need to take 500 classes and read 800 books before I do research" when that's not the case at all with a few exceptions (which would be grad level work anyway).

[Anonymous No.15650041]

>just learned a colleague of mine has 3 fumos
What is the deal with mathematicians and Touhou, statistically speaking?

[Anonymous No.15650055]

>>15650041
autism

[Anonymous No.15650385]

So all that stuff about RH having implications about prime numbers, that's because of p-adics, yeah?

[Anonymous No.15650833]

>>15650385
No.
All of the usual relations to primes use Perron's formula applied to something with 1/zeta.
https://en.wikipedia.org/wiki/Perron%27s_formula
The zeros of zeta will be simple poles in 1/zeta which will be sampled with the cauchy integral formula.
The zeros all having real part <1 gives the prime number theorem.

[Anonymous No.15650868]

>>15650041
みんなー! チルノのさんすう教室はじまるよー!
あたいみたいな天才目指して、がんばっていってね!

[Anonymous No.15650992]

[math]-1= abc=a^{2} =b^{2}=c^{2} [/math] doesn't have any complex solutions, but it does have quaternion solutions.
Is there a way to transform it into a sentence of the form [math]f(a,b,c)=0[/math] and still keep the property of having no complex solutions? I've tried factoring, adding and subtracting but I can't get all of the terms on one side.

[Anonymous No.15651075]

>>15650992
[eqn] |abc + 1| + |a^2 + 1| + |b^2 + 1| + |c^2 + 1| = 0[/eqn]

[Anonymous No.15651275]

Just watched this talk by Rudin : https://youtu.be/hBcWRZMP6xs

Do you know a book in which I could find results on unicity sets ?

[Barkun's Cum Rag No.15651277]

>>15651275
Yes i must become negative

[Anonymous No.15651868]

>>15649605
>Basic Mathematics
>Any of the great Calculus books
>Any of the great LinAlg intro books
>How to Prove It
>Rudin
>Dummit and Foote
>Munkres
At this point you have enough background to look at any of the math monk youtuber videos and decide on the rest of your path by yourself.

[Anonymous No.15652008]

>>15608042
Does anyone have any experience with condtional expectation operators?
Im trying to find a the operator norm of one and I am kind of stuck.

In particular, we have:
1) A random variable [math]X: (\Omega, \Sigma, P) \rightarrow (\mathbb{X}, \mathcal{B}(\mathbb{X}), \pi)[/math]

2) [math]f \in L^2(\mathbb{X}, \mathcal{C}, \pi; \mathbb{C}^d)[/math]

Here, [math]\mathbb{X}[/math] is some euclidean space, [math]\mathcal{C}[/math] is a sub sigma algebra of [math]\mathcal{B}(\mathbb{X})[/math] and [math]\pi[/math] is the appropiate pushforward measure defined by X.

3) [math]\mathbf{A}:(\mathbb{X}, \mathcal{B}(\mathbb{X}), \pi) \rightarrow \mathbb{C}^{l,d}[/math] is a matrix valued random variable

4) A measurable map Y that restricts [math]\mathcal{B}(\mathbb{X})[/math] to some sigma algebra

I want to estimate:
[eqn]\left \lVert E_X[\mathbf{A}( \ \cdot \ )|Y(X)] = \sup{||f|| = 1} \left \lVert E_X[\mathbf{A}(X)f(X)|Y(X)] \right \rVert_{L^2}[/eqn]

I know the setting is convoluted, its a strange problem. My current guess is that my norm is just [math]E_X[ |\mathbf{A}|^2][/math] ie the L2 norm of the operator norm of A. But all these dependencies are really hindering my progress

[Anonymous No.15652013]

>>15652008
Fucking latex renderer:

...
Y is a measurable map that restricts [math]\mathcal{B}(\mathbb{X})[/math] to some sigma algebra

I want to estimate:
[eqn]\left \lVert E_X[\mathbf{A}( \ \cdot \ )|Y(X)] = \sup{||f|| = 1} \left \lVert E_X[\mathbf{A}(X)f(X)|Y(X)] \right \rVert_{L^2}[/eqn]

I know the setting is convoluted, its a strange problem. My current guess is that my norm is just [math]E_X[|\mathbf{A}|^2][/math]
ie the L2 norm of the operator norm of A. But all these dependencies are really hindering my progress

[Anonymous No.15652017]

This is what I get for phone posting I guess RIP

[Anonymous No.15652073]

>>15609138
>x^2
>limit
reading comprehension do be difficult

[Anonymous No.15652085]

When is log(z)-log(conjugate(z)) rational?

[Anonymous No.15652138]

>>15652085
log(z) = log|z| + i arg(z), the latter +2πik for k in Z, so log(z) - log(z*) = (log|z| + i arg(z)) - (log|z| - i arg(z)) = 2i arg(z). This is real-valued iff arg(z) = 0, so (we need the principal branch of log) we're looking at the positive real number line. Thus, log(z) - log(z*) is rational iff z is a positive real number (because the expression equals 0 in this case, and a strictly imaginary number otherwise).
Unless you mean "when is log(z) - log(z*) in Q(i)"? In which case it's whenever arg(z) is rational, and I don't think you can give a more useful answer than that since arctan() maps nonzero algebraic numbers to transcendentals iirc.

[Anonymous No.15652666]

>Proportion of ARXIV publications since the beginning of the decade that are focused on 2, 3 or 4-dimensional geometry topics, to one decimal place:
6.2%
>Proportion of Quanta Magazine publications since the beginning of the decade that are focused on 2, 3 or 4-dimensional geometry topics, to one decimal place:
28.3%
If not for learning python, I could never have discovered this colossal disappointment.

[Anonymous No.15652720]

>>15652666
You're only looking at the math stuff, right? You aren't counting biology BS in your percentages?

[somesnacks No.15652727]

>>15608262
cliffmaxx

[Anonymous No.15652949]

hey guys I am a board tourist of sorts.

what makes you guys like math so much? are you autists that dont value human contact? I can do math, but dont enjoy it to the point of learning more than I need for work, or esoterica

>>15646972
russian

everything in europe is published in english and, specifically, in france, they have a talent problem. the ENA is getting closed because it's just an incestuous grift machine that restricts the ability of others to publish.

for reference, the superconductor technique of the koreans was taken from old soviet research that had been abandoned.

[Anonymous No.15653105]

>>15652949
autism

[Anonymous No.15653292]

>>15652949
its incredible how many complex and self-consistent patterns spring up out of a number line.

[Anonymous No.15653296]

I've nearly got it figured out, I can feel it

[Anonymous No.15653822]

>>15651275
zygmund

[Anonymous No.15654222]

>>15648807
Thanks a lot mate.

[Anonymous No.15654821]

Is it possible to make a useful classification of all maps from Z to Z or is the task too big?

[Anonymous No.15654972]

>>15654821
There are uncountably many such maps.

[Anonymous No.15655072]

Which book can be considered as "RUDIN" of high school algebra ? (Pre-calculus - quadratics, sequence, binomial, trigo etc). By "RUDIN" I mean with extremely rigours problems (PLS DONT SAY ART OF PROBLEM SOLVING OR EVAN CHEN)

Are the ring theory books helpful ?

[Anonymous No.15655077]

>>15655072
Another questions, if a study a little bit of grad maths ( I am an engineering major) will it be easier for me to tackle high school tough problem ? Like those Olympiad level ones ?

If yes pls let me know which topic of grad maths can help me do that ?

[Anonymous No.15655097]

>>15655072
Algebra by Serge Lang

[Anonymous No.15655285]

>>15654972
There are uncountably many groups and that isn't an issue apparently

[Anonymous No.15655342]

>>15652949
> what makes you guys like art so much? are you autists that don't value human contact? I can do art, but I don't enjoy it to do more than I need for birthday cards and posters, or occasional doodling
It's just cool, anon. I was good at it, I kept taking classes, and eventually your sense of aesthetics gets warped enough that you start thinking it's "beautiful" and "amazing." I enjoy learning and this lets me spend all my life learning things that are new to me and that I think are interesting.
That's the practical answer. The wankish answer is that -- leaving aside the philosophy-of-math-tards and the foundations fuckers, math is the closest thing to objective truth you can get, to the point where some people *define* it as the study of that which is objectively true independent of reality (the latter to exclude, say, physics, which attempts to model reality using math and theories). And math builds on itself, endlessly. I think it's really neat that, if and when I research and publish, I'll have contributed something that I know is true (none of that questioning about if the study replicates or not you get in other fields), that depends on the math that came before me, and that will be cited by those who come after. I think it's incredible to add to that tower of learning, and to put my name -- in however minor a way -- into that history.

[Anonymous No.15655451]

>>15654821
What exactly do you mean by "maps"? Going down the list by how much structure is preserved by the map:

If we mean as sets, then there's uncountably many. (Counting the input elements in Z as 0,1,-1,2,-2,3,-3, ..., and using this to give an order to the map's output, another way of phrasing your question is "how many sequences of integers are there?" This is uncountable - directly, by basically exactly the same diagonalization argument as is used for the reals, or by taking your sequence (eg {19, 2, 45824, -69, 5439043854380925, 5, ...}), mapping it mod 2 (eg {1,0,0,1,1,1,...}), treating these as a base-2 'decimal' (eg 0.100111...), and noting you've just mapped (onto but not 1-to-1) into the real interval [0,1] in binary.
You can apply an ordering to these sequences of integers (first and foremost, lexicographic ordering), but I doubt there's a well-ordering. And there's almost certainly no meaningful classification beyond the characterization I gave -- there's no structure beyond "sequences of integers" (unlike groups, which have restrictive enough rules to them that classifying them is nontrivial (and extremely difficult)).

If we mean as (additive) group homomorphisms, phi(0)=0, phi(1) = k, and so phi(x) = phi(1+...+1) = phi(1)+...+phi(1)=kx.
Thus, there are countably many group homomorphisms, each determined entirely by where it sends 1. (To use needlessly fancy notation, Hom(Z,Z) in Grp is isomorphic to Z.)

If we mean as ring homomorphisms, we get the same argument as above that phi is determined by phi(1). But now, phi(x) = phi(x*1) = phi(x) phi(1), and since Z is an integral domain, phi(1) = 1, unless phi(x) = 0 for all x. So the only ring homomorphisms of Z are the identity map (phi(x) = x for all x) or the zero map (phi(x) = 0 for all x).

[Anonymous No.15655499]

Favourite math software?

[Anonymous No.15656565]

>>15655499
SnapPy

[Anonymous No.15656574]

>>15655499
The calculator that comes with linux mint.

[Anonymous No.15656578]

>>15655499
R

[Anonymous No.15657112]

>>15655499
maxima

[Anonymous No.15657480]

>>15655499
Mathematica, if it weren't for their subscription
prices. Otherwise, it's Maple. Pay it once and you
keep it, basically.

[Anonymous No.15657983]

Why is a line with angle 'a' y = x*tan(a)?

[Anonymous No.15657995]

Nevermind I just figured it out. That was easy

[Anonymous No.15658110]

>>15649732
it is never too late

[Anonymous No.15658850]

>Learning some math for fun
I wanted to solve f(x) = x^2 without doing its exponent.
Let x be 6 and since the derivate of f(x) is 2x,
I can say 36 is roughly equal to the sum 2x' six times, where x' increases by 1 for each iteration.
Since dx is 1, for each iteration i'm exactly 1 short, and this matches x, what i'm trying to find.
36 = 2 (1+2+3+4+5) + x
36 - 30 = x

I found out later on that 2 (1+2+3+4+5) is a triangular sum.
But doing this triangular sum REQUIRES knowing x, because otherwise I wouldn't know when to stop adding numbers.

Does this have a solution of any kind?

[Anonymous No.15658882]

>>15649249
Multiply a/b by d/d (1)
Multiply c/d by b/b (1)
Add normally

[Anonymous No.15658917]

>>15658850
> I wanted to solve f(x) = x^2 without doing its exponent.
What does that even mean??

I can't follow your derivative argument at all, but you did (accidentally?) come up with the following:
> (1+2+3+4+5) is a triangular sum
And the formula for that sum is [math]T_n = \dfrac{n(n+1)}{2}[/math]. In your argument [math]n = x - 1[/math], so
[eqn]2 T_{x-1} + x = 2 \dfrac{(x-1)(x - 1 +1)}{2} + x = x(x-1) + x = x^2[/eqn]

I have no idea how you are expecting to calculating a series sum without knowing how long it is (x).

[Anonymous No.15658994]

>>15658917
>I wanted to solve f(x) = x^2 without doing its exponent.
>What does that even mean??
x^2 = 36
Wanted to find out that x was 6 without doing sqrt(36).

>you did (accidentally?) come up with the following

It was an accident because I had no idea what triangular numbers were, but it seems to resemble their formulas and then I found out about them.

>derivative argument
Don't do exponents.
Say x^2 is roughly equal to 2x.
In order to get to 36 you'd have to sum 2x over and over:
2(1) + 2(2) + 2(3) and so on.
2x is however only an approximation of the function (x+dx)^2
When dx is 1, its actual derivative is
2x * 1 + 1^2, or 2x + 1
So the difference between the approximation and actual function is just 1.
In reality you are doing
2(1) +1 + 2(2) + 1 + 2(3) + 1 and so on
But this is more convinient:
2 (triangular sum) + x

>I have no idea how you are expecting to calculating a series sum without knowing how long it is (x)
I don't know the first thing about series yet, can't even follow your math confidently but it's about time I guess.

[Anonymous No.15659035]

>>15655285
Yeah it is, we probably have no chance of classifying all infinite simple groups.

[Anonymous No.15659043]

>>15655451
>I doubt there's a well-ordering
Every set can be well-ordered.

[Anonymous No.15659046]

>>15655499
Sage

[Anonymous No.15659176]

>>15659046
Bump

[Anonymous No.15659725]

I still can't tell if latex is good or awful

[Anonymous No.15659832]

>>15659725
It can't be both?

[Anonymous No.15660081]

>>15608503
>>15608526
Lmao you guys are hilarious

[Anonymous No.15660103]

>>15659832
maybe I just need to find a good tutorial course, instead of adding a new package from stackexchange every 20 min. proficiency in it cant be a bad thing. would you confide in me, how bad are the worst parts?

[Anonymous No.15660142]

>>15660103
Not the guy you're replying to but in my experience the beginning is the worst. I was also googling like crazy in the beginning but things begin to settle in your mind quite quickly and before you know it you can write without many interruptions.

[Anonymous No.15660150]

>>15660103
use overleaf

[Anonymous No.15660342]

>>15660142
the usual pattern. I'll look for a more thorough tutorial tomorrow. fucking tikz
>>15660150
if I'm gonna invest time in some computer stuff I feel the desire for a local instance

[Anonymous No.15660465]

>>15608042
I cannot. I cannot understand this proof. He's just telling me to draw the rest of the owl.
please help.

I just want to finish my bachelor, and then never touch mathematics again.

[Anonymous No.15661143]

>>15608042
guys what do you think about this fucker?

https://www.youtube.com/playlist?list=PLOxODW9vlVLRpXYW1iMEjMJ0Xy2F0d4Q_

what can you tell me about this stuff?
i'm really into it

[Anonymous No.15661158]

>realised that I was so good at math and calculus only because I could just recognize what formula/transfer to use where

[Anonymous No.15661338]

>>15661158
>see equation
>instantly know the answer because i solved one earlier that was just like it
>peers think i am super fast with numbers

[Anonymous No.15661630]

Do you guys think I have a chance at grad school admission if I meet GPA, GRE requirements but have an absolutely atrocious transcript history (moved around a lot, different schools, lots of withdrawals)?

[Anonymous No.15661636]

Do you guys think I have a chance at grad school admission if I meet GPA, GRE requirements but have an absolutely atrocious transcript history (moved around a lot, different schools, lots of withdrawals)?

[Anonymous No.15661821]

>>15661636
Goddamn...I could go for a dish of that right now...

[Anonymous No.15661909]

>>15661636
I dont endorse this...I met a guy who claimed he was an asexual jew with mental illnesses and he got what he wanted. But, you can never go back if you do this.

[Anonymous No.15662108]

most based way to prepare for the putnam?

[Anonymous No.15662239]

The sum of the proper divisors of integer A is equal to B, and the sum of the proper divisors of B is equal to A.

Does there exist an infinite number of different pairs A and B?

[Anonymous No.15662424]

>>15662239
It is an interesting open question. Such pairs are called amicable numbers, or more generally aliquot sequences of period two.
https://en.wikipedia.org/wiki/Amicable_numbers

[Anonymous No.15662670]

>>15662424
Yes. I didn't know about them until I found this video by James Grime
https://www.youtube.com/watch?v=R2eQVqdUQLI

[Anonymous No.15662673]

>>15662239
>>15662424
As of this month we've found a billion amicable pairs. Pretty neat.

cool related discussion:
https://math.dartmouth.edu/~carlp/erdossurvey-4.pdf

[Barkun No.15662675]

>>15662673
That nerd couldn't have me. Neither could you. End of story

[Anonymous No.15662731]

new >>15662730

[Anonymous No.15663539]

>>15609556
>>15614466
I was thinking of writing my MSc thesis in TDA but no one from my stats department is familiar with it. Someone told me that TDA exists only as a way for algebraic topologists to get funding since AlgTop is not very lucrative/applicable. There was only one company (Ayasdi) that used TDA, but they recently completely changed what they do. Fishy.

The absolute best field of stats imo is Bayesian Nonparametrics. You need a pretty good understanding of Real/Functional Analysis, Measure Theory, Probability (and some Stoch processes), since you'll be dealing with random probability measures on spaces. Insanely flexible, immune to overfitting, etc etc. The computational aspect is a bit of a pain in the ass, unless you're into that.