/mg/ mathematics general -- think edition

[Anonymous No.9427784]

Because the other thread is retarded.

[Anonymous No.9427790]

>>9427784
Isn’t pi like 22/7? Let’s just define pi to be exactly 22/7 and fix the test of math

[Anonymous No.9427847]

>>9427784
>implying /mg/ isn't inherently retarded

[Anonymous No.9427960]

Mathematical notation is fucking dizzying

[Anonymous No.9427968]

>>9427960
Diagram chasing is the shit though.

[Anonymous No.9428064]

>>9427784

Is set theory like in the pic related actually hard? I've never gone into much detail into it.

[Anonymous No.9428121]

>>9427784
Pls prove

[math]{\pi _n}\left( \mathbb{S} \right) \cong {H^{ - n}}\left( {\operatorname{Spec} \mathbb{Z},{\mathcal{O}_{\operatorname{Spec} \mathbb{Z}}}} \right)[/math]

[Anonymous No.9428124]

>>9428121
>πn(S)≅H−n(SpecZ,OSpecZ)
What have you tried?

[Anonymous No.9428125]

>>9428124
asking /sci/

[Anonymous No.9428138]

>>9427784
How can I create a general rule (possibly using linear algebra) for distributing the polynomial
[math]
(x_{1}+x_{2}+x_{3}+...x_{n})^y
[/math]?

[Anonymous No.9428143]

>>9428138
>How can I create a general rule (possibly using linear algebra) for distributing the polynomial
>(x1+x2+x3+...xn)y?
https://en.wikipedia.org/wiki/Multinomial_theorem

[Anonymous No.9428144]

>>9428121
>>9428125
I'd tell you to fuck off, but that animefag will probably come prove it for you anyway.

[Anonymous No.9428148]

>>9428143
sweet, thanks dude

[Anonymous No.9428153]

Why was Devilman Crybaby so disappointing /mg/ ?

[Anonymous No.9428154]

>>9428064
Judging by your pic, yeah.

[Anonymous No.9428243]

>>9428154
i meant op's pic

[Anonymous No.9428386]

hello
i graduated HS 14 years ago and i've been a neet for 8 years, and i just enrolled in a mechanical engineering course at a community college. i studied math with khan academy for a month before taking my placement test, and i placed into pre-calc.

i had three options for tech courses: chemical, mechanical and electrical. i chose mechanical because i have a bit of experience with CAD, but my advisor said electrical engineers are the most sought after but that electrical is also the most difficult.

i have three weeks to change my major. should i stick with mech or switch to electrical?

[Anonymous No.9428426]

>>9428121
For an aspherical topological space [math]X[/math] with a fundamental group [math]G[/math], [math][\pi_1(X)]_\text{Ab}
= H_1(G,\mathbb{Z})[/math]. Try tensoring this with the sheaf [math]\mathcal{O}_(\text{Spec}\mathbb{Z})[/math].

[Anonymous No.9428434]

>>9428386
if you just tested into algebra you might want to stick with mechanical, although there probably isn't that much difference. It depends on what you want to do. Look into what the average mechanical engineer does. However, mechanical engineering is objectively worse because it's less interesting and it's less theoretical. Thermodynamics is mostly pseudo-science and plug-n-chug. Mechanical engineers are usually people who wanted engineering money but didn't really have any particular interests. I'll allow that transistors and amplifiers are pretty fucking boring, but every other area is cool.

[Anonymous No.9428578]

>>9428243
Then the answer is no. Obviously.

[Anonymous No.9428589]

>>9428479
No.

[Anonymous No.9428591]

>>9428138
Who is this nazi qt?

[Anonymous No.9428847]

>>9428589
Yes.

[Anonymous No.9428850]

>>9428144
>>>/r/eddit/

[Anonymous No.9428858]

>>9428386
>>9428434
>>>/sci/sqt/

[Anonymous No.9429164]

>>9428847
Fuck you. Math is even older than Euclid.

[Anonymous No.9429214]

>>9429164
"Fuck you."
That's just cruel.
How could math exist before Euclid if it didn't exist when he was alive?

[Anonymous No.9429217]

Is it too late for me ? I'm 22 and I've recently taken an interest in mathematics and astronomy, but the most advanced maths I've done is algebra. Should I just bin this as a hobby or would I be able to dive deep into subjects after a year or two of freshing up my math knowledge?

[Anonymous No.9429378]

>>9429217
i''m 32 and i had the math skills of a 5 year old a month ago. i studied with khan academy for a month and i placed into pre-calc. i'm a total retard. if i can do it, you can do it.

[Anonymous No.9429393]

why am i such a brainlet? i get stuck on problems so easily and have no clue how to continue with them.

wtf do i do?

[Anonymous No.9429398]

>>9429393
keep working and after a while the fog will clear

[Anonymous No.9429399]

>>9429393
Keep trying for atleast 30 minutes, if that doesn't work you can either:
A: Go take a walk (downside is that you get nothing done and only do it for this problem, this method is good more for concept understanding or one huge problem you have to solve)
B: Go to the next problem and hope to solve previous one later.

[Anonymous No.9429411]

>>9429214
You're wrong and I hate you. Die in a fire.

[Anonymous No.9429419]

>>9429214
Egyptians were doing Trigonometry and other types of math as long before Euclid as Euclid is from us. Actually, even further.

[Anonymous No.9429420]

>>9429411
Why would you say that? Merely because I'm stating the truth? It's mean and disrespectful to mathematics.

[Anonymous No.9429422]

>>9429419
>Trigonometry
But that's not a type of math.

[Anonymous No.9429429]

>>9429422
Then how come it's a part of math class???

[Anonymous No.9429433]

>>9429429
Something bearing the name "math class" doesn't make it a math class.

[Anonymous No.9429490]

>>9429420
Looks like you're too dumb to take a hint and stop spreading lies about mathematics. Now you die bitch.

[Anonymous No.9429491]

>>9428453
And to continue from this, zhô is saying physicists and engineers etc. APPLY this math, for example analysis, in their work, but it is still math. And so we come to the conclusion that, say, calculus of variations is equal in worth to category theory, as all math is born equal.

[Anonymous No.9429492]

>>9429422
this
fiddling randomly with variables is not math

[Anonymous No.9429505]

>>9429491
>APPLY this math
Using math OUTSIDE of mathematics is not itself a field of mathematics, that's blatantly obvious.
>all math is born "equal"
Not invariant under equivalence.

[Anonymous No.9429506]

>>9429491
> category theory
Not math.

[Anonymous No.9429509]

>>9429506
It's certainly more math than the analysis physishits use.

[Anonymous No.9429519]

>>9429505
>Using math OUTSIDE of mathematics is not itself a field of mathematics, that's blatantly obvious.
Why are you repeating this? It should be obvious already. I'm just clarifying things for our engineer friends.
>Not invariant under equivalence.
[citation needed], please refrain from replying to me ever again.

>>9429506
It is, but not as useful as calc of variations.

[Anonymous No.9429520]

>>9429490
I am merely stating some trivial facts about mathematics. You need to take a step back and calm down if you think I am lying.

[Anonymous No.9429526]

>>9429519
I've never seen a category in real life, hence it isn't math.

[Anonymous No.9429527]

>>9429519
>[citation needed]
The paper I'm currently writing.

[Anonymous No.9429529]

>>9429526
Go to any online store, and you will encounter categories naturally.

>>9429527
Please make sure you share it with me when it's done.

[Anonymous No.9429535]

>>9429529
>online store
What makes you think these are real?

[Anonymous No.9429541]

>>9429535
I have indirect but physical evidence they exist. You can use order theory here. Buy something and receive it. It is then a consequence of the Nye-Dawkins principle that the system in between must be non-vacuous.

[Anonymous No.9429545]

how much math do I need to learn before i can post ahegao anime girls?

[Anonymous No.9429546]

>>9429541
>using induction
The anal beads I ordered last year still hasn't come, hence Amazon doesn't exist.

[Anonymous No.9429548]

>>9429545
None. All you need is a smug sense of superiority.

[Anonymous No.9429550]

>>9429546
>using induction
The anal beads I ordered last year still hasn't come, hence Amazon doesn't exist.

[Anonymous No.9429554]

>>9429545
Just get a good idea of the basics of anything that has something "homo" in it.

>>9429550
Did you order them from China, perhaps? It took 3 weeks to get a few socks from that place.

>>9429548
Or a crushing sense of inferiority you mask as superiority in order to be one of the cool guys.

[Anonymous No.9429561]

>>9429550
Fuck meant to quote >>9429541
>>9429554
>China
Ill-defined. And so are their sex toys.

[Anonymous No.9429568]

>>9429561
The quotation was trivial. Chinese people sell cheap stuff, but I wouldn't embed any of their plastic constructions inside myself. Not even with a good covering.

[Anonymous No.9429574]

>>9429568
The quotation was trivial up to post equivalence.
Also I shall immerse the toys, not embeds them. This should be fine with the proper water-based immersion diffeomorphism.

[Anonymous No.9429587]

>all these filenames
It's all just one guy samefagging isn't it?

[Anonymous No.9429596]

>>9429574
That is a good way to do it. Now, excuse me, as I will go wander in the cold darkness. It was fun.

>>9429587
[math]\neg[/math]yes.

[Anonymous No.9429602]

>>9429596
You're not fooling me samefag.

[Anonymous No.9429614]

>>9429596
Good night, slut.

[Anonymous No.9429881]

>>9429509
>It's certainly more math than the analysis physishits use.
Wrong.

[Anonymous No.9429891]

[math] \mathcal{FAAAAAAAAAAAGGGGGGGSSSSS} [/math]

[Anonymous No.9429903]

>>9429891
>FAAAAAAAAAAAGGGGGGGSSSSS
Why the homophobia?

[Anonymous No.9429912]

>>9429903
[math] \mathbb{B}_e^c \mathcal{a}^u s_e [/math] fuck([math] y\ \ \ \ ,o\ \ \ \ ,u [/math]).

[Anonymous No.9430285]

MODS ARE BULLYING ME AGAIN!!! But anyway, what is a hot (not HoTT) topic in algebraic topology nowadays, and how does one get into it?

[Anonymous No.9430304]

>>9430285
>But anyway, what is a hot (not HoTT) topic in algebraic topology nowadays, and how does one get into it?
http://math.mit.edu/conferences/talbot/2013/19-Lawson-thefuture.pdf

[Anonymous No.9430306]

>>9430285
Loop multiplication: https://web.math.rochester.edu/people/faculty/jnei/loopssam.pdf

[Anonymous No.9430314]

>>9430285
chromatic homotopy

[Anonymous No.9430321]

Given an elementary function [math] f(x) [/math] , can there exist another elementary function [math] g(x) [/math] such that [math] g(x)=f(x) [/math] for some intervall, but not the entire domain ? Pic related.

For argument's sake, let's pretend piecewise functions don't exist.

[Anonymous No.9430325]

>>9430321
Yes x and |x|

[Anonymous No.9430334]

>>9430321
Obviously. One of the most trivial examples is the absolute value function and the identity.

[Anonymous No.9430336]

>>9430304
I'll
>>9430306
check
>>9430314
these.
Thanks.

[Anonymous No.9430337]

>>9430325
>|x|
>elementary

[Anonymous No.9430344]

>>9430337
Yes. If you don't like the answer, maybe you should define your terms. I don't know of anyone who would consider the absolute value function to not be elementary.

[Anonymous No.9430349]

>>9430334
Is there any non-trivial example ?

[Anonymous No.9430354]

>>9430349
Sure. Think about interpolation.

[Anonymous No.9430610]

Admit it /classical/ -- Ives is good. https://www.youtube.com/watch?v=ZlxDCXTqmeQ

[Anonymous No.9430624]

>>9430610
Are you lost?

[Anonymous No.9430629]

>>9430624
Sorry, wrong tab.

[Anonymous No.9430635]

>>9430629
np

[Anonymous No.9430755]

>>9429561
Would be nice if you did not post child porn here thanks

[Anonymous No.9430758]

pls explain HOMOgenous coordinates

[Anonymous No.9430860]

>>9430755
why the pedophobia?

[Anonymous No.9430889]

>>9428426
>>9429164
>>9429411
>>9429420
>>9429490
>>9429491
>>9429506
>>9429519
>>9429520
>>9429526
>>9429529
>>9429535
>>9429541
>>9429550
>>9429554
>>9429561
>>9429574
>>9430285
>>9430306
>>9430336
>>9430624
>>9430635
pls get out

[Anonymous No.9430893]

>>9429491
>zhô

[Anonymous No.9430925]

>>9430889
If we leave the 'm' in /mg/ will really be superfluous. When was the last time a non-animefag posted something math related that wasn't a stupid question or his homework anyway? Thought so.

[Anonymous No.9430934]

>>9430758
they're coordinates that are homogenous

[Anonymous No.9430941]

>>9430925
Not worth it

[Anonymous No.9430943]

>>9430925
This. Unironically.
Animefags are the glue that's keeping it together in these threads while poor engineerfags want help with their calculus homework and think linear algebra is hard.

[Anonymous No.9430963]

>>9430344
But it is a piecewise function

[Anonymous No.9430975]

>>9430925
>>9430943
Maybe other people who do know things just don't want interact with these faggots.

[Anonymous No.9430983]

>>9430975
>Maybe other people who do know things just don't want interact with these faggots.
Why the homophobia?

[Anonymous No.9430992]

>>9430975
I somehow doubt that.

[Anonymous No.9431074]

does anyone here know anything about applications of homotopy theory

[Anonymous No.9431075]

>>9431074
>applications of homotopy theory
To what?

[Anonymous No.9431133]

>>9431074
https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.51.591

[Anonymous No.9431408]

>>9430285
Look, it's not that hard, just talk about math. If you're going off topic too much then you're asking for it and have nobody to blame but yourself.

[Anonymous No.9431422]

How does one define and compute the cohomology of categories?

[Anonymous No.9431426]

>>9431075
To applied sewing.

[Anonymous No.9431427]

>>9431422
>How does one define and compute the cohomology of categories?
http://www-users.math.umn.edu/~webb/Publications/CategoryAlgebras.pdf

[Anonymous No.9431570]

Three upcoming lectures:
http://math.sustc.edu.cn/event/10808.html 2018-01-26
http://math.sustc.edu.cn/event/10809.html 2018-01-26
http://math.sustc.edu.cn/event/10810.html 2018-01-29

Introduction to Inter-universal Teichmuller theory I/II/III

In this series of talks, we will explain the main result and some crucial technical points of the Inter-universal Teichmuller (aka IUT) theory of Shinichi Mochizuki. In the end, we also give a sketched proof of the ABC/Vojta conjecture (for hyperbolic curves), as an application of IUT theory.

In IUT, one starts with a suitable elliptic curve E over a number field F and a prime number l (among other technical data), and studies such a collection of data via certain hyperbolic curves, which are used in the theory of etale theta function. In particular, anabelian geometry (for hyperbolic curves) and etale theta function form the foundation of IUT.

A variety of geometric and arithmetic information about the elliptic curve and theta function is recorded in the so-called Hodge theater. More concretely, a Hodge theater is designed to carry two kinds of symmetries associated to a fixed quotient of l-torsions of the elliptic curve, which are represented by the cusps of certain hyperbolic curves. One of them is called the multiplicative symmetry, which is of arithmetic nature as the corresponding set of cusps is naturally a subquotient of the absolute Galois group of the field of moduli of E. The other is called the additive symmetry, which is of geometric nature since the corresponding set of cusps is naturally a subquotient of the geometric fundamental group of a hyperbolic curve determined by E and l. The multiplicative symmetry will be applied to copies of (Frobenioids associated to) the the field of moduli of E, while the additive symmetry assures that the conjugacies of local Galois groups on various values of theta function (at these cusps) are synchronized. These theta values and the number field will determine the...

[Anonymous No.9431578]

>>9431570
hi hankel

[Anonymous No.9431579]

>>9431578
>hi hankel
I'm not "hankel".

[Anonymous No.9431589]

>>9427784
Where is your pic from, OP?

Or if anybody else could point me to the source I would appreciate it.

[Anonymous No.9431595]

>>9427784
Is it okay if I don't actually understand the "why" part of solving problems early in my math career? I mean things like "completing the square" I know how to calculate it and all but I don't have any real understanding of the underlying principles. I've taken a look at proofs books and most of them assume a certain level of math knowledge that I don't have, for example they assume you've already taken a high school level course on calculus/trig/etc. Is it reasonable for me to just go on following the traditional route of algebra -> geometry -> trig -> "precalc" -> calc -> Actual Math

[Anonymous No.9431596]

>>9431595
Why not do what you enjoy?

[Anonymous No.9431599]

>>9430321
Power series expansions rely on this fact.

[Anonymous No.9431610]

>>9431596
because i'm not smart enough

[Anonymous No.9431613]

>>9430321
not one that is continuous.
>>9431599
explain yourself

[Anonymous No.9431615]

>>9431613
>not one that is continuous.
This isn't true, of course.

[Anonymous No.9431616]

>>9431610
But thats bs, you know it.

[Anonymous No.9431618]

>>9430889
>tfw to intelegent to be liked

>>9430925
>>9430943
Diese, ja!

[Anonymous No.9431624]

>>9431570
This doesn't look any more useful than the previous lectures on IUT "theory". Plus, it's in Chinese.

[Anonymous No.9431630]

>>9431624
>it's in Chinese.
Or is it?

[Anonymous No.9431671]

>>9431595
>following the traditional route of algebra -> geometry -> trig -> "precalc" -> calc -> Actual Math
That's a pretty good way to waste time and a pretty retarded way to learn math.

[Anonymous No.9431689]

>>9431671
>There exist 2 differentiable non-piecewise functions that are identical only up to a certain point
proof needed, then I will eat my words

[Anonymous No.9431693]

>>9431689
>>9431671
sorry, meant to reply to >>9431615

[Anonymous No.9431699]

>>9430943
Or maybe your moeshit circlejerks repel anyone with two brain cells to rub together.

[Anonymous No.9431702]

>>9431689
Not true. Let their difference be h(x), then h is zero except for isolated points. But since h is continuous, the support of h being the inverse image of the punctured real line must be open, contradiction.

[Anonymous No.9431705]

>>9431689
>>9431693
The fact that you're a brainlet who can't even read what the problem is and doesn't know the difference between continuity and differentiability is a good enough reason for you to eat your own words.

Retard.

[Anonymous No.9431708]

>>9431702
> then h is zero except for isolated points
No, h is zero only on a certain interval I. Re-read the question.

[Anonymous No.9431714]

>>9431595
>Is it okay if I don't actually understand the "why" part of solving problems early in my math career

No.

>I mean things like "completing the square" I know how to calculate it and all but I don't have any real understanding of the underlying principles.

For a given number a, b, and c you want to find an x such that a*x^2 + b*x + c = 0.

Aside: Why equal to zero? Well for any other number n, the equation a*x^2 + b*x + c = n is the same as a*x^2 + b*x + (c-n) = 0 so make a new c' and let c' = (c-n). Similarly, if you wanted to find where 2 quadratics are equal, a1*x^2 + b1*x + c1 = a2*x^2 + b2*x + c2, that's the same as finding the root of (a1-a2)*x^2 + (b1-b2)*x + (c1-c2) = 0. In general, finding where something is equal to something else can always be rewritten as the problem of finding where the difference between them is 0. So finding the zeros (also called finding the roots) is a question that will frequently comes up in real life. Here we're studying one of the easiest cases where the function is quadratic.

Back to solving a*x^2 + b*x + c = 0. Normally we would try to isolate x but we have an x and x^2 added and we don't know of a way to merge them into one. So.... lets look at simpler problems.
If it was b*x + c = 0, that's easy Algebra 1 stuff. Rearrange and we have x = -c/b.
If it was a*x^2 + c = 0, that's easy since we have one x. Rearrange like before and we have x^2 = -c/a. Now we know how to take square roots so x=±√(-c/a).
What if it was a*(x+r)^2 + k = 0 for some number r and k? That's looks a lot like the above so if we pretend x+r was z we can just find the zero of a*z^2 + k = 0 which gives z=±√(-k/a). Since z=x+r, we can plug that in and get z=x+r=±√(-k/a). Rearrange and x=-r±√(-k/a).
But what if we factored out (x+r)^2 in the equation above? We then would have a*(x^2+2*r*x+r) + k = 0. Simplifying further and we have a*x^2 + 2*a*r*x + (a*r+k) = 0. Hey, that's the general quadratic equation! We found a way of solving it.

[Anonymous No.9431723]

>>9431714
>We then would have a*(x^2+2*r*x+r^2) + k = 0. Simplifying further and we have a*x^2 + 2*a*r*x + (a*r^2+k) = 0.
>~forgot the ^2 on r~

We solved it by making it into a square. That is, by finding a number r such that 2*a*r = b and finding a number k such that (a*r^2+k)=c so that a*x^2 + b*x + c = a*(x+r)^2 + k. Then we know how we can solve the one on the right.

Rearranging to isolate r and k gives
2*a*r = b
r = b/(2a)

(a*r^2+k)=c
(a*(b/(2a))^2+k)=c
k = c - a*(b/(2a))^2

Then plugging these values of r and k into the solution we got earlier:
x=-r±√(-k/a)
x = -b/(2a) ± √(-[c-a*(b/(2a))^2]/a)
x = -b/(2a) ± √[ (b/(2a))^2 - c/a ]
pulling out 1/(2a) from both gives
x = ( -b ± √[ b^2 - 4*a*c] ) / (2a)

Which is the standard quadratic equation.
QED

[Anonymous No.9431726]

>>9431714
Thank you for the in depth explanation, anon. Do you have any rigorous textbooks you'd recommend for a beginner? The one i've been working through does not explain mathematical principles, it just teaches you how to solve particular types of math problems in a heuristic process. It teaches you just enough to figure out how to get the right answer.
>Step 1: Isolate c
>Step 2: add (b*1/2)^2 to both sides
>Step 3: Solve the equation
etc

[Anonymous No.9431728]

>>9431705
Of course I know the difference. I meant to type "differentiable" here >>9431613 instead of "continuous".
It seems you're the brainlet who doesn't understand the difference between "point" and "interval" and that Abs[x] is essentially a piecewise function

[Anonymous No.9431732]

>>9431728
> I meant to type "differentiable"
> you're the brainlet who doesn't understand the difference between "point" and "interval"

[Anonymous No.9431735]

>>9431708
Was answering >>9431689, not the original question. It's easy to find a smooth function with compact support: https://en.wikipedia.org/wiki/Bump_function

[Anonymous No.9431744]

>>9431728
>difference between "point" and "interval"
There isn't really a difference. An interval is a point of the interval space.

[Anonymous No.9431745]

>>9430889
take your meds Billy

[Anonymous No.9431747]

>>9431726
Lang's Basic Mathematics. Gelfand's 4 small supplement books on Algebra, Functions and Graphs, Coordinates, and Trigonometry are good for conceptual understand as well.
If you're willing to read older books, Euler's Elements of Algebra is the best book you can find.

[Anonymous No.9431804]

>>9431744
>infinite number of points and 1 point
>no difference
a point isn't an interval, mr engineer.

[Anonymous No.9431825]

>>9431804
A point is a trivial interval. An interval is a point of the space of intervals.

[Anonymous No.9431929]

>>9430285
The mods are disgusting. It's ok, this is a safe place for you ok? <3

[Anonymous No.9431941]

https://www.youtube.com/watch?v=AsUls0_IXD4
Do you think trying to teach Africans has made him racist?

[Anonymous No.9431943]

>>9431929
Thanks <3

[Anonymous No.9432255]

>>9431570
>tfw IUT will be used to study solutions of Seiberg-Witten self-dual equations
>tfw IUT will solve Yang-Mills mass gap

[Anonymous No.9432272]

/mg/ : the place where failed mathematicians, underachievers and social rejects with big brains gather.
I wonder what a meet-up would look like.

[Anonymous No.9432280]

walk up in the trap like a boss ouu

[Anonymous No.9432281]

>>9431728
>Abs[x] is essentially a piecewise function
What do you mean? It doesn't need to be defined piecewise

[Anonymous No.9432286]

>>9431747
>Lang's Basic Mathematics.
Lang is a meme.

[Anonymous No.9432310]

>>9432272
>meet-up
gay

[Anonymous No.9432389]

>>9427790
ok how do we find the circumference of a circle if we know its radius

[Anonymous No.9432399]

>>9427968
What's that, anon?

[Anonymous No.9432954]

>>9432399
A proof method. Practice by proving the five lemma using diagram chasing.

[Anonymous No.9433774]

is there anything like 'advanced trigonometry'? I'd really like a book on that, or at least one with difficult problems

[Anonymous No.9433791]

Anyone have the instructor solution to calculus by Spivak?
Thanks.

[Anonymous No.9433904]

To anyone who's studied axiomatic set theory, how much of a background in logic did it require, what did you use?

[Anonymous No.9434116]

>>9433774
topology

[Anonymous No.9434129]

>>9433774
Categorical trigonometry which you start with an annular category (ie. with addition and multiplication) and the so called sine and cosine functors which are defined by the identities [math]S(f+g)=S(f)C(g)+S(g)C(f), C(f+g)=C(f)C(g)-S(f)S(g)[/math].

[Anonymous No.9434139]

>>9433774
https://www.amazon.com/Trigonometry-I-M-Gelfand/dp/0817639144/
https://www.amazon.com/Trigonometric-Delights-Princeton-Science-Library/dp/0691095418/
https://www.amazon.com/103-Trigonometry-Problems-Training-Team/dp/0817643346/
https://www.amazon.com/Plane-Trigonometry-Loneys-Original-Classic/dp/1452898499/
https://www.amazon.com/Advanced-Trigonometry-Dover-Books-Mathematics/dp/0486432297/

[Anonymous No.9434144]

>>9430337
sqrt(x^2)

[Anonymous No.9434147]

>>9431595
https://www.youtube.com/watch?v=lZMA8x7VB18

[Anonymous No.9434150]

>>9433904
Requirements for proper study include an introductory course in logic.

[Anonymous No.9434153]

>>9431579
Yeah, you're /sci/'s retarded tranny

[Anonymous No.9434162]

>>9433904
Depends what level set theory it is.

[Anonymous No.9434201]

>>9434150
Many thanks

[Anonymous No.9434312]

>>9433904
Just use Kunen's book. You need a good amount of logic for most of the deeper stuff (e.g. model theory for forcing).

[Anonymous No.9434320]

>>9431699
So you mean, what's keeping people from having a non-brainlet discussion on topics above easy shit like Linear Algebra and Calculus is due to the fear of a person posting an moe anime pic on an anime board in an anime website? Then that settles it, we didn't need those to begin with. Stay where you belong in Quora or Math.Stackexchange.

[Anonymous No.9434323]

>>9434150
Literally nothing.

[Anonymous No.9434325]

How long will it take someone who has learned up to vector calc and ODEs at the undergrad level to work through this book on classical mechanics

[Anonymous No.9434392]

>>9434325
Go ask some physishit.
You are not mai darling.

>not reading Truesdell's properly rigorous book on classical mechanics
Brainlet.

[Anonymous No.9434402]

>>9434325
>>9434392
>ph*sics
>>>/toy/
>>>/sci/sqt/

[Anonymous No.9434408]

>>9434325
That book seems pretty good. What's the name of it?

[Anonymous No.9434413]

>>9434402
Don't out yourself. Classical mechanics can be fully axiomatised and studied as a proper (pure) mathematics subject.

[Anonymous No.9434416]

>>9434408
>>9434413
see >>9434402

[Anonymous No.9434421]

>>9434416
See
>>9434413

[Anonymous No.9434433]

>>9434416
When you finish your undergrad you might learn that there are more fields within math than just "group theory" (or whatever you learned in your single "introduction to algebra" course).

[Anonymous No.9434450]

>>9430321
I guess you can always do stuff like
>arcsin(sin(f(x))) = f(x)
>sqrt(f(x)^2) = f(x)
>ln(e^f(x)) = f(x)
for some intervals but I don't think that's what you want right?

[Anonymous No.9434453]

>>9434433
see >>9434402

[Anonymous No.9434480]

>>9434153
>Yeah, you're /sci/'s retarded tranny
I'm not "retarded".

[Anonymous No.9434483]

>>9434480
Yeah, you're retarded not "retarded".

[Anonymous No.9434510]

>>9434483
>Yeah, you're retarded not "retarded".
How are you?

[Anonymous No.9434513]

>>9434413
>Classical mechanics can be fully axiomatised and studied as a proper (pure) mathematics subject.
Wouldn't mechanics be better thought of as applied maths?

[Anonymous No.9434518]

>>9434510
Fine, thank you for asking.

[Anonymous No.9434552]

>>9434513
It depends what you mean by mechanics. What physishits and engineers do? Then yes, that's just applying math to a different field. A fully axiomatic framework like Truesdell's? Then no, that's pure mathematics. Once you have rigorous definitions and postulates you're working with something that is from the perspective of practising mathematics no different from a p-adic number field, for example.

[Anonymous No.9434564]

>>9434552
>Once you have rigorous definitions and postulates you're working with something that is from the perspective of practising mathematics no different from a p-adic number field, for example.
What constitutes a "rigorous definition"?

[Anonymous No.9434570]

>>9434564
Feel free to skim through an introductory book on logical and formal systems.

[Anonymous No.9434571]

>>9434570
logic*

[Anonymous No.9434602]

>>9434570
>formal systems.
I don't believe in such concepts.

Is there any other way to make a definition "rigorous"?

[Anonymous No.9434628]

>>9434602
No.

[Anonymous No.9434695]

Why is every permutation a product of transpositions? Please

[Anonymous No.9434711]

>>9434695
>Why is every permutation a product of transpositions?
[math] (i_1 i_2 i_3 i_4 \cdots i_n) = (i_n i_{n-1})(i_n i_{n-2}) \cdots (i_n i_2)(i_n i_1) [/math]

[Anonymous No.9434715]

>>9434695
Have you tried reading a proof of the claim?

[Anonymous No.9434716]

>>9434408
http://www.springer.com/us/book/9780817683511

[Anonymous No.9434786]

reminder that this is what happens when physicists are allowed to do math

https://www.youtube.com/watch?v=w-I6XTVZXww

[Anonymous No.9434801]

>>9434786
physishits*

[Anonymous No.9434874]

What's the most mathematical kind of math?

[Anonymous No.9434893]

>>9434874
representation theory

[Anonymous No.9434906]

Reminder that this is what happens when role-players are allowed to post on /sci/

>>9434786

[Anonymous No.9434910]

>>9434786
But that sum was discovered by mathematicians, not physicists.

[Anonymous No.9434921]

>>9434910
>Ramanujan
>mathematician
What did she mean by this?

[Anonymous No.9434924]

>>9434874
algebraic number theory

[Anonymous No.9434958]

>>9434874
combinatorics

[Anonymous No.9434967]

>>9434320
>fear
>implying

[Anonymous No.9434975]

What exactly is meant by "geometric intuition"?

[Anonymous No.9434982]

>>9434874
complex emergent nonlinear dynamical feedback systems

[Anonymous No.9434984]

>>9434975
>What exactly is meant by "geometric intuition"?
It's a feminine trait.

If you're a "him" you simply lack the capacity to understand it.

[Anonymous No.9434986]

>>9434984
>we wuz fee-mayl n shiet

[Anonymous No.9434992]

>>9434984
Huh? Geometry is a very masculine subject. You must know that men are better in visuospatial reasoning. Also, there's a reason why the Ancient Greeks considered it the foundation of all mathematics.

[Anonymous No.9434994]

>>9434921
I'm not a "she".

[Anonymous No.9435002]

>>9434992
>Geometry is a very masculine subject.
It's a poorly kept secret within the upper strata of mathematical circles that most of the best geometers (including Grothendieck, Hilbert, Gromov, Euclid...) were very in touch with the feminine half of their self, some even dabbling in cross-dressing.

[Anonymous No.9435004]

>>9434994
"she" is the nu gender-neutral pronoun, brainlet
get on with the times grandzha

[Anonymous No.9435006]

>>9435004
suck a nigger, mong.

[Anonymous No.9435010]

>>9435006
>suck a nigger, mong.
Why the racism?

[Anonymous No.9435020]

>>9435010
>not sucking my big BLACK dick
bend ova cragga

[Anonymous No.9435024]

>>9435010
What, are you against blacks? Dirty racist, reported.

[Anonymous No.9435092]

>>9434982
Stop trying to force this meme.

[Anonymous No.9435128]

>>9435092
>t. can't get into the study of complex nonlinear stochastic dynamical feedback systems

[Anonymous No.9435170]

>>9434992
>convex hulls, polytopes, resolutions of unity by piecewise functions etc. are hard and pointy
>diffeomorphisms, asphericity, glueing operations etc. are soft and squishy
>tfw geometry is masculine while topology is feminine
They even have COCKSeter groups in geometry.
> You must know that men are better in visuospatial reasoning.
Biological men*.

[Anonymous No.9435176]

>>9435170
no wonder WILDberger is so masculine

[Anonymous No.9435177]

>>9435170
>resolutions of unity

[Anonymous No.9435184]

>>9435176
>discrete is more masculine than continuous, so by induction finite is more masculine than infinite
>tfw you realize Wildburger is doing the most masculine possible maths

[Anonymous No.9435187]

>>9435177
So you can't refute zhôr points so you make fun of a brainfart? Nice, good job.

[Anonymous No.9435188]

>>9435187
>zhôr

[Anonymous No.9435192]

>>9435187
>brainfart
That's a rather demeaning thing to call yourself.

[Anonymous No.9435199]

>>9435188
Yes, and?

>>9435192
I'm not zhå.

[Anonymous No.9435200]

>>9435199
I love you, friend.

[Anonymous No.9435206]

>>9435200
Will your love help me get a phd?

[Anonymous No.9435210]

>>9435187
Excuse me zhîr my pronouns are symplecto/contacto/quanto.

[Anonymous No.9435215]

How autistic is /mg/ in comparison to the rest of /sci/?

[Anonymous No.9435230]

>>9435187
>zhôr
>>9435199
>zhå
>>9435210
>zhîr

[Anonymous No.9435240]

>>9435210
Please learn how to use pronouns. Your linguistical skills make me assume English is your native language. Otherwise you would know how to use it.

>>9435230
>being 100% cis
Nice gender insecurities, m'lady.

[Anonymous No.9435242]

>>9435240
>m'lady
>misgendering this hard

[Anonymous No.9435252]

>>9435240
Yûrt are simply too simple-minded to comprehend my pronouns.

[Anonymous No.9435270]

>>9434975
bump

[Anonymous No.9435289]

>>9435252
>Yûrt
I'm not a "a circular tent of felt or skins on a collapsible framework, used by nomads in Mongolia, Siberia, and Turkey".

[Anonymous No.9435341]

>>9434975
The ability to imagine the objects you're thinking about in a definite way or construct a visual model of what you are studying, even when the problem at hand is not originally/explicitly geometric in nature.

[Anonymous No.9435469]

https://www.youtube.com/watch?v=UAtiv2Gs8CE

>Webinar in Japanese given during the web-event Math Power 2017 on October 6th. The event had 170.000 viewers.

>We aim to explain the ABC conjecture and space theory Inter-universal Teichmüller theory (IUT), so that junior and senior high school students can appreciate their novelty.

>Fumiharu Kato is Professor of mathematics at the Tokyo Institute of Technology School of mathematics.

[Anonymous No.9435486]

How would a brainlet go at learning Differential Equations? Are there any good books for top brainlets?
>inb4 Khan Academy
No.

[Anonymous No.9435492]

>>9435469
Translate this shit, weebs.

[Anonymous No.9435493]

>>9435469
Anime will save math.

[Anonymous No.9435496]

>>9435486
Depends on what you want to get out of them.

[Anonymous No.9435501]

>be /sci/ mod
>be retarded high school dropout
>see weebs having fun
>start powertripping and deleting/banning everything

[Anonymous No.9435508]

>>9435496
My intent? Learning, really. I have no real use for them.

[Anonymous No.9435509]

>>9435493
pls use webm to save bandwidth, friendo

[Anonymous No.9435517]

>>9435508
There's better things to learn about.

[Anonymous No.9435519]

>>9435517
Like?

[Anonymous No.9435525]

>>9435519
How to make the perfect pasta sauce.

[Anonymous No.9435536]

>>9435492
>1h30m
Too long, and it looks entirely worthless after skimming through it a bit.

[Anonymous No.9435656]

>>9434874
combinatoric

[Anonymous No.9435806]

>>9434874
derived combinatorics

[Anonymous No.9435809]

>>9435806
>derived combinatorics
Is that combinatorics in derived categories?

[Anonymous No.9435819]

>>9435809
yes, applied combinatorics in derived categories to be precise.

[Anonymous No.9435884]

>>9427784
>>9428064
>>9428578
Different anon here. I have no designs in being like a mathematical logic guru or foundations of math wizard but I'd like to take these classes simply because I find this stuff fascinating. My only real guru is to get that math major/ comp sci minor and get my 300k starting. If I only wanna dabble, should I just peruse set theory and beyond on my spare time as opposed to taking these classes? To be frank, will taking these set theory/ math foundations classes enlarge my asshole five sizes? Or will it be an enlightening, enjoyable experience?

[Anonymous No.9435889]

>>9435884
*My only real "goal."

srry stupid f**ng autotype

[Anonymous No.9435892]

>>9435819
That would almost make sense if you changed derived categories to infinity categories.

[Anonymous No.9435895]

What are some mathematical applications of vector spaces for which there exists no basis?

[Anonymous No.9435896]

>>9435892
>infinity categories
No such thing.

[Anonymous No.9435899]

>>9434874
category theory

[Anonymous No.9435902]

>>9435895
>free modules over a field for which there exists no basis
It has the same applications as the empty category.

[Anonymous No.9435904]

>>9435469
So what do the Japanese think about Mochi? Are they as skeptical as Westerners about the proof or do they hail him as a national hero?

[Anonymous No.9435906]

>>9435896
Simplicial set satisfying the horn extension property for inner horns

[Anonymous No.9435911]

>>9435906
>Simplicial set satisfying the horn extension property for inner horns
No such thing.

[Anonymous No.9435915]

>>9435906
>set
this need not be well-defined in the "infinite" case.

[Anonymous No.9435926]

>>9435884
>phoneposter
Entire post disregarded. I was typing a reply too.

[Anonymous No.9435934]

>>9435926
...

[Anonymous No.9435938]

>>9435934
>frogposting
>phoneposting
You might want to fuck off to >>>/r/eddit/

[Anonymous No.9435939]

>>9435938
>You might want to fuck off to >>>/r/eddit/
Do you need to swear? It really invalidates your post.

[Anonymous No.9435940]

>>9435911
literally just defined it

[Anonymous No.9435945]

>>9435940
>literally just defined it
Stringing words together doesn't mean that anything has been well-defined (i.e. "infinite"+"set")

[Anonymous No.9435956]

>>9435945
which word dont you like

[Anonymous No.9435963]

Can anyone tell me just how much mathematics is used within Chemistry IRL? My major requires a Calculus I class, but will we actually use this IRL within labs?
>>9430983
>Why the homophobia?
Because it's an entirely natural an rational feeling.

[Anonymous No.9435973]

>>9435963
ask in >>>/sci/sqt/

[Anonymous No.9435974]

>>9435963
>Because it's an entirely natural an rational feeling.
There's nothing "natural" or "rational" about homophobia.

[Anonymous No.9435979]

>>9435956
>which word dont you like
"simplicial set"

[Anonymous No.9435980]

>>9435974
>There's nothing "natural" or "rational" about homophobia
There absolutely is. The majority of the world feels this way because it's an abomination and a scourge on every society it infests. It's not just me saying this, it's the majority of the world saying it.
>>9435973
>ask in
Thanks

[Anonymous No.9435986]

>>9435980
>The majority of the world feels this way because it's an abomination and a scourge on every society it infests.
https://en.wikipedia.org/wiki/Argumentum_ad_populum

In argumentation theory, an argumentum ad populum (Latin for "argument to the people") is a fallacious argument that concludes that a proposition must be true because many or most people believe it, often concisely encapsulated as: "If many believe so, it is so."

[Anonymous No.9435987]

>>9435979
why not

[Anonymous No.9435990]

>>9435986
>argumentation theory
not science or math

[Anonymous No.9435995]

>>9435980
>The majority of the world feels this way because it's an abomination and a scourge on every society it infests.
That's because the majority of the world are religious retards.

[Anonymous No.9435997]

>>9435974
Homosexuality is unnatural from an evolutionary standpoint.

[Anonymous No.9435998]

>>9435986
>"If many believe so, it is so."
It's harmful effects on society are quire apparent and it could be gone through in this thread, but this is /sci/, not /pol/. Let's keep the politics over there.

[Anonymous No.9436000]

>>9435997
>Homosexuality is unnatural from an evolutionary standpoint.
https://en.wikipedia.org/wiki/Homosexual_behavior_in_animals

[Anonymous No.9436001]

>>9436000
I didn't say it other species weren't afflicted. Just that, considering the whole point of life (ignoring religious nonsense) is to reproduce, clearly homosexuality is a defect from an evolutionary standpoint.

[Anonymous No.9436017]

>>9435980
>>9435998
>>9436000
>taking the bait this hard

[Anonymous No.9436020]

>>9436001
>Just that, considering the whole point of life (ignoring religious nonsense) is to reproduce, clearly homosexuality is a defect from an evolutionary standpoint.
Homosexuals can still reproduce, they're not infertile.

[Anonymous No.9436025]

>>9436020
But they are not attracted to the opposite sex, and thus won't naturally reproduce out of pure instinct.

[Anonymous No.9436026]

>>9436025
>But they are not attracted to the opposite sex, and thus won't naturally reproduce out of pure instinct.
Most humman reproduction is not done out of pure instinct.

[Anonymous No.9436027]

>>9436026
Yet as you pointed out, humans are not the only species afflicted.

[Anonymous No.9436029]

>>9436001
>the whole point of life is to reproduce
Says who? This is nonsense.

[Anonymous No.9436030]

>>9436029
From an evolutionary standpoint, it is.

[Anonymous No.9436032]

>>9436027
>Yet as you pointed out, humans are not the only species afflicted.
And?

[Anonymous No.9436033]

>>9436030
>evolutionary standpoint
This is a meaningless notion.

[Anonymous No.9436034]

>>9436030
>From an evolutionary standpoint, it is.
No, it's not. Evolution has no 'ends' or 'purposes'. You're anthropomorphising. It's like saying fire rises because it 'wants to', or water falls because it is ethical to. You're spouting pure nonsense.

[Anonymous No.9436035]

>>9436032
Reproduction should be the most fundamental drive of all species.

[Anonymous No.9436038]

>>9436035
>Reproduction should be the most fundamental drive of all species.
Why?

[Anonymous No.9436039]

>>9436035
>"should be"
Why? Am I supposed to just take your word for it?

[Anonymous No.9436040]

>>9436038
>>9436039
Otherwise the species will die out. The most fundamental desire of any "successful" species will be that of reproduction.

[Anonymous No.9436041]

>>9436040
>species
That's just a spook.

[Anonymous No.9436044]

>>9436040
>successful
In what sense?

[Anonymous No.9436047]

>>9436044
Survival

[Anonymous No.9436048]

>mathematics general

[Anonymous No.9436057]

>>9436048
Evolution is perfectly mathematical.

[Anonymous No.9436087]

>>9436040
>The most fundamental desire of any "successful" species will be that of reproduction.

"Successful" according to what metric? You're using circular logic.

Personally, I don't value my life by maximizing the number of babies I churn out every year. Neither do most people. Your claim to speak for "the species" is absolutely bizarre and amusing.

[Anonymous No.9436101]

>>9436087
The survival of any species on whole depends on reproduction. Clearly humans are no longer driven solely by instinct, but they are also the dominate species on the planet.

[Anonymous No.9436108]

>>9436101
You're not answering the question.

[Anonymous No.9436123]

>>9436101
1. You've moved the goalposts from "some members of the species (homosexuals) don't biologically reproduce" to "ERMAHGERD THE SPECIES IS GUNNA DIE OUT IF WE DINT MAKE EVERY SINGLE PERSON HAVE 999 BABBYS", which is laughable and empirically false.

2. You're still dodging the fact that a "species", let alone evolution, has no goals or purposes. Like a toddler, you are ascribing volition to a process which literally has none.

[Anonymous No.9436126]

>>9436123
>empirically
This is a meaningless notion.

[Anonymous No.9436127]

>>9436123
Believe what you must faggot.

[Anonymous No.9436135]

>>9436127
>Believe what you must faggot.
Why the homophobia?

[Anonymous No.9436138]

Delete all posts from >>9435963 to>>9436135

[Anonymous No.9436142]

>>9436135
>homophobia
This is a meaningless notion.

[Anonymous No.9436149]

Anyone have insight into a question?

I'm working through Stewart's Calculus as a review and noticed that both population growth and radioactive decay are treated in two separate places in the textbook:

-first, very early in the book, with simple exponential function models. They are used to predict things about the phenomena in question.
-second, much later, with differential equations. It is a more complicated process, but the questions the book answers in examples/ predictions it makes about pop. growth and radioactive decay look to be much the same!

I would assume that's because exponential functions and diffEqs are closely related, but why would one go through the trouble of working with the differential equation model over the simple exponential function model?

thanks in advance

[Anonymous No.9436179]

>>9431613
>>9431728
This seems intuitive, but is there any proof of it ?

[Anonymous No.9436184]

>>9436149
differential equations deal with more complicated things (rates of changes and whatnot)
like you would use a differential equation for population growth per capita but the regular exponential model is good for regular population growth

[Anonymous No.9436192]

Anyone feel like actually talking about math?

[Anonymous No.9436270]

>>9436179
>proof
Why would you need a proof when it's intuitively obvious, beyond obvious even?

[Anonymous No.9436284]

>>9436270
Don't you have a counter example then ?

[Anonymous No.9436295]

>>9436284
What are you trying to say?

[Anonymous No.9436315]

>>9432286
Name one better precalc book.

[Anonymous No.9436364]

>>9436149
>pop. growth and radioactive decay look to be much the same!
yes because they both deal with rates of change. the equations for the growth of bank accounts based on interest are also similar.

diffeq helps you solve problems by changing the equations into other equations essentially.

you're kind of asking why use equations for acceleration when there are already equations for velocity.

[Anonymous No.9436414]

>all these garbage non-math posts
Fuck it. I won't even bother to report them. Trying to keep this general clean has become a sisyphean task. I'm outta here.

[Anonymous No.9436419]

>>9436414
>Trying to keep this general clean has become a sisyphean task.
Stop internet policing, it looks bad on you.

[Anonymous No.9436543]

Try to behave, guys.

[Anonymous No.9436703]

>>9435986
>linking to a fucking wikipedia article about a fallacy
Lad don't do that it makes you seem autistic. Just say in your words whats wrong with argument don't even mention the word fallacy.

[Anonymous No.9436836]

>>9435519
How to develop a mathematical model of the subjective perception of sensory input to the taste-buds and use it to derive an optimal control policy for proportions of ingredients in signature Italian cuisine.

[Anonymous No.9437162]

>>9436295
I guess you're being sarcastic and telling me I'm wrong. So I'd appreciate it if you could find an example that backs up your claim.

[Anonymous No.9437316]

Holy shit, my lecturer pressed everyone into buying his book and he said he is going to follow that book in the entire course. There is like 3 weeks until the exam and I am working through it, but it's full of stupid fucking mistakes. There is already a several page long errata online but I keep coming across more careless mistakes. I'm just so fed up with all this, not to mention I just despise math and this is just adding to my frustration. Sorry this probably doesn't belong in the math general, but I have nobody to vent to.

[Anonymous No.9437592]

Is there a theory for studying periodic behavior in non linear systems of diferential equations?
I am a physics fag yes

[Anonymous No.9437741]

>>9435995
>religious retards
so you lash out at those who want to bring some type of meaning to their lives? Highschooler detected

[Anonymous No.9437745]

>>9436836
what are the mods doing
Did they pick a new round of terrible janitors or something?

[Anonymous No.9437762]

>>9437741
>so you lash out at those who want to bring some type of meaning to their lives?
No, just those who bring want to bring some meaning through fairytales/imaginary men in the sky

[Anonymous No.9437776]

Is there some proper way to place the labels of your arrows in a diagram? Like "if it points down you put the label on the left side" or something? Or is it just that you put them there in a way no one will get confused?

>>9435980
Pic related is the truth.

>>9437762
God is not a "he".

[Anonymous No.9437780]

Let's say you have an infinite supply of A, B, C and D in a bowl. P(A) = P(B) = P(C) = P(D) = 0.25.

I need a function f(n), n >= 4 which calculates the probability that you receive AT LEAST one of each, when you take n items out of the bowl. Can you help me, because I can't solve it myself?

[Anonymous No.9437783]

>>9437780
>Let's say you have an infinite supply
What do you mean?

[Anonymous No.9437818]

>>9437592
see >>9434982

[Anonymous No.9437826]

>>9437783
The probability that you pull, for instance, A is always 0.25 no matter how many you've previously pulled.

[Anonymous No.9437840]

>>9437780
I think you need inclusion/exclusion here.
Let PN(S) be the probability you don't draw any letter in set S.
Then f(n) = 1 - (PN({A}) + PN({B}) + PN({C}) + PN({D})) + (PN({A,B} + PN({A,C}) + PN({A,D}) + PN({B,C}) + PN({B,D}) + PN({C,D})) - (PN({A,B,C}) + PN({A,B,D}) + PN({A,C,D}) + PN({B,C,D}))
Exercise for the reader to compute these individual probabilities.

[Anonymous No.9437845]

>>9437780
You can perhaps try calculating the probability that there is one element you never receive, by first calculating the probability that e.g. you never receive A.

You should be able to partition the set of events {no A or no B or no C or no D} into the disjoint union of {no A}, {some A and no B}, {some A and some B and no C}, {some A and some B and some C and no D}.
The probability that you'll never receive an A is (3/4)^n. Then, given that you receive one A somewhere, the probability that you'll never receive a B is (3/4)^(n-1), and the probability that you'll receive at least one A somewhere is 1 - (3/4)^n. By extension you can calculate the probability of receiving at least one A and one B, and the probability of receiving no C given that you've received one A and one B, and similarly for D. There may be a mistake with this line of reasoning somewhere related to conditional probabilities, I don't know.

[Anonymous No.9438217]

>>9436543
>guys
I'm not "guys".

[Anonymous No.9438246]

>>9438217
no one cares faggot

[Anonymous No.9438338]

>>9438246
>no one cares faggot
Why the homophobia?

[Anonymous No.9438352]

>>9438338
>homophobia
This is a meaningless notion.

[Anonymous No.9438638]

>>9432389
Multiply it by 44 and divide it by 7

[Anonymous No.9438654]

>>9427784
do you guys gain sexual pleasure from solving math problems?

[Anonymous No.9438697]

>>9427790
Archimedes defined pi to be somewhere between 3 + 1/7 and 3 + 10/71

So close, but no cigar.

[Anonymous No.9438706]

>>9438338
Why the faggotry?

[Anonymous No.9438734]

>>9438654
yes

[Anonymous No.9439376]

[Anonymous No.9439387]

Is there some correct way to label your arrows in a diagram or is it sufficient to label them in the least confusing way? I'm supposed to have a guy check my stuff and he's picky on diagrams.

>>9439376
>dividing mathematics into pure and applied
Into the trash he goes.

[Anonymous No.9439390]

>>9439387
>Is there some correct way to label your arrows in a diagram or is it sufficient to label them in the least confusing way?
What kind of diagram?

[Anonymous No.9439395]

>>9439390
For example, a square. Is there some rule like "if the arrow points down you put the label on its left side"? He complained about a diagram I had once when he didn't like the way I had placed the arrow labels. This is why I'm asking because I want to get past his checking.

[Anonymous No.9439396]

>>9439395
>For example, a square.
I personally would put all labels on the outside of the square

[Anonymous No.9439397]

>>9439396
And if it gets tight in some spot, then maybe deviate from this norm, like if that was a pullback and the arrow going into C would squeeze g in a nasty way. Of course, I could make them bigger, but I'd rather not. I'll try this and see what he thinks. Thanks.

[Anonymous No.9439435]

>>9439376
>applied math
It's about as real as the "real numbers".

[Anonymous No.9439442]

>>9437592
Yes it's called symplectic geometry.

[Anonymous No.9440095]

Anyone got a good source for/experience with a modular gcd algorithm for multivariate polynomials?

[Anonymous No.9440107]

>>9439397
>like if that were a pullback
Sounds like you're a moron.

[Anonymous No.9440162]

How would you go about figuring out the set-builder notation for something like {0, 4, 16, 36, 64, 100, ... }?
Is there a way of algebraically solving something like this, or do you just have to guess and test?

[Anonymous No.9440183]

>>9440162
Try OEIS
https://oeis.org/search?q=0%2C+4%2C+16%2C+36%2C+64%2C+100&language=english&go=Search

[math]\left\{ (2n)^2 : n \in \mathbb{N} \right\}[/math]

[Anonymous No.9440244]

>>9440107
Looks like you thought I'd care about your opinion.

[Anonymous No.9440475]

Is there any textbook that can help me understand and solve this more-in-depth kind of inequalities?
>5|x+3| - |x-2| + 2|7x-3| > 10
>|6x2+3x-2| - 3|7x3-x+3 + |x+2| > 6
>(5x^4-2x+3)/(2x^5+1) > -3

most books I've looked for don't go in depth and just look at linear/quadratic or simple absolute value inequalities (e.g. 4|x+3| > 7), and I'm not aiming for Hardy&Wright's yet

[Anonymous No.9440486]

>>9440162
>How would you go about figuring out the set-builder notation for something like {0, 4, 16, 36, 64, 100, ... }?
You can't, there's infinitely many sets satisfying that description.

[Anonymous No.9440546]

>>9440475
Partition the real line into regions where none of the absolute values are zero, and handle the inequalities on each partition.
For example, for the first one, you have three points where an absolute value is zero, namely -3, 3/7 and 2 in order. Between -3 and 3/7 for example for example, |x+3| = x+3, |x-2| = 2-x and |7x-3| = 3-7x, so you get 5(x+3) - (2-x) + 2(3-7x) > 10 => -8x + 19 > 10 => 9 > 8x => x < 8/9. Since we've also assumed -3 <= x <= 3/7, we get -3 <= x < 8/9 as one possible range of solutions. Then you go on to other intervals and find similar bounds within that interval.

[Anonymous No.9440602]

>>9440475
for the second one I meant |6x^2+3x-2| - 3|7x^3-x+3| + |x+2| > 6

>>9440546
thanks, this looks very useful. I think the 'rigorous' way is to use |a| > b <=> a>b or -a>b one thousand times right?

[Anonymous No.9441057]

Where can I find a treatment of calculus of variations that doesn't just feel like one big abuse of notation?

[Anonymous No.9441062]

>>9441057
Evans PDE book

[Anonymous No.9441142]

Fellas just finished my PhD applications, let's hope they're not all rejections.

[Anonymous No.9441154]

https://poll.pollcode.com/44839318

[Anonymous No.9441164]

>>9441154
I sure hope Scholze wins instead of some token black arab tranny.

[Anonymous No.9441181]

>>9428138
If you want a slightly more fun way, Multidimensional Pascal Simplexes will get you there.

[Anonymous No.9441243]

Between Herstein and Jacobson (who I never see mentioned here for some reason) will I get a solid background in finite fields? My coding theory has a brief overview in the math section but I want to make sure I understand it better before getting started, but from the table of contents there's only a dozen pages between them (and obviously a bunch of necessary group and ring theory leading up to it).

[Anonymous No.9441587]

>>9440546
>Partition the real line into regions
Doesn't that require the existence of the real line?

[Anonymous No.9441590]

>>9441587
>Doesn't that require the existence of the real line?
Why would it?

[Anonymous No.9441599]

>>9441590
It requires at least assuming the existence of the real line, but that leads to a contradiction so we can conclude that the real line exists.

[Anonymous No.9441633]

>>9441587
>Partition the rational line into regions
there jewniggerfaggot, it leads to the same results

[Anonymous No.9441658]

Probability Pop quiz:
A miner is stuck in a mine, he has three doors to choose from and he will always choose the doors at random. One door leads out of the mine after a 2 hour walk, the other two will lead back to the original place after 3 and 5 hours respectively.
What is the expected amount of hours that the miner will be stuck for?

[Anonymous No.9441664]

>>9441658
2*1/3 + (2+4)*2/3*1/3 + (2+8)*(2/3)^2*1/3 + ...
= 2/3*(1+2/3+(2/3)^2+...) + (2/3)^2*4*(1+2*(2/3)+3*(2/3)^2+...)
= 2/3*1/(1-2/3) + 16/9*1/(1-2/3)^2
= 2 + 16 = 18

[Anonymous No.9441665]

>>9441664
errata
= 2/3*(1+2/3+(2/3)^2+...) + (2/3)*(1/3)*4*(1+2*(2/3)+3*(2/3)^2+...)
= 2/3*1/(1-2/3) + 8/9*1/(1-2/3)^2
= 2 + 8 = 10

[Anonymous No.9441669]

>>9441664
>>9441665
wrong.

[Anonymous No.9441707]

>>9441665
Correct amount of hours but a very unelegant method

[Anonymous No.9441726]

How do I compress (distort) a cartesian field in any direction?

[Anonymous No.9441739]

Let N be the number of times the miner chooses a door, then N is geometrically distributed with success probability 1/3. Defining T to be the total time taken, the law of total expectation gives E[T] = E[E[T|N]]. Given that the miner doesn't choose the door that leads out, the time until the next choice is either 3 hours or 5 hours with probability 1/3/(1/3+1/3) = 1/2. Hence E[T|N] = (3*1/2+5*1/2)*(N-1) + 2 = 4N-2, and E[T] = 4 E[N] - 2 = 4*(1/3)^-1 - 2 = 4*3 - 2 = 10.

[Anonymous No.9441742]

>>9441739
meant to reply to >>9441707

[Anonymous No.9441756]

>>9441739
Nicer approach with expectations by conditioning but this is the more, in my opinion, easy option on how to solve it
Let Y denote the door, wlog 1 is the door to safety, 2 is the 3 hour door and 3 is the 5 hour door, X time taken then E[X] = E[X|Y=1]P{Y=1} + E[X|Y=2]P{Y=2} + E[X|Y=3]P{Y=3} = 1/3(E[X|Y=1]+E[X|Y=2]+E[X|Y=3]
We know that E[X|Y=1] = 2. E[X|Y=2] = 3 + E[X] and E[X|Y=3] = 5 + E[X], thus E[X] = 1/3(2+3+E[X]+5+E[X]) that gives us E[X] = 10

t. the dude that posted the question

[Anonymous No.9441814]

>>9441726
guy who posted it here, let me rephrase that:
Given a vector coming out of the center of the graph, how do I distort the graph so that it looks like whatever is on the graph is perpendicular to the vector in 3D space

[Anonymous No.9441830]

>>9441814
>a vector coming out of the center of the graph
>distort the graph so that it looks like
Unrigorous garbage.

[Anonymous No.9441866]

How do I motivate myself to study linear algebra why I don't care about it at all

[Anonymous No.9441880]

>>9441866
>needing ""motivation""
Just don't study it.

[Anonymous No.9442035]

>>9441830
you know what the fuck i meant

[Anonymous No.9442040]

>>9442035
No, I don't.

[Anonymous No.9442044]

>>9442035
>fuck
Do you have to swear?

[Anonymous No.9442049]

>>9442044
Do you need to be a subhuman g******?

[Anonymous No.9442076]

>>9442049
>g******
What do you mean?

[Anonymous No.9442095]

>>9442035
I don't. It's not clear whether you want to deform the vector field on a manifold or the manifold itself.

[Anonymous No.9442159]

>>9442095
The manifold, I think. I'm trying to program a GLSL shader which turns an image to "face" the mouse pointer in a pseudo-3D space. I've worked out a formula for a scalar that compresses the graph as if it is turning, but I have no idea how to make the graph "turn" (compress it) in any direction. I can only compress it along the x and y axes.

[Anonymous No.9442198]

>>9442159
As usual nonsensical questions get asked by CSlets.

[Anonymous No.9442201]

is this the most BASED prof?

https://youtu.be/gZNm7L96pfY?t=51m15s

[Anonymous No.9442220]

>>9442159
>manifold
These haven't been shown to exist as of right now, aside from some trivial cases.

[Anonymous No.9442221]

>>9442201
No? He teaches watered down Fourier analysis to engineers. Nothing based about that.

[Anonymous No.9442226]

>>9442221
nothing about that, but this is the first time i see a prof said 'bulllshit' in a lecture.

[Anonymous No.9442228]

>>9442201
>The Fourier Transforms and its Applications
>and its Applications
>BASED

[Anonymous No.9442238]

>>9442201
No, otherwise he wouldn't have said "excuse me".

[Anonymous No.9442252]

>>9442226
You must be 18 or older to browse 4chan.

[Anonymous No.9442259]

>>9442252
but this is blue board :0

[Anonymous No.9442282]

>>9442159
apply rotation matrix on the vector??

[Anonymous No.9442335]

>>9442159
Jesus fucking Christ.

[Anonymous No.9442543]

>>9442335
What?

[Anonymous No.9442840]

>heard Category Theory can be used to formalize all of math, even Set Theory

>find a book on 'Basic Category Theory', it states there are no prerequisites

>read up the mere definition of category

"A category C consists of the following three mathematical entities: (1 )A class ob(C) [...] "

>what the fuck is a "class" and when was it defined

[Anonymous No.9442869]

>>9442840
>>what the fuck is a "class" and when was it defined
https://en.wikipedia.org/wiki/Primitive_notion

[Anonymous No.9442911]

>>9442869
>In a [...] formal system, the role of a primitive notion is analogous to that of axiom.
Where is the axiom for "classes"?

[Anonymous No.9442940]

>>9442911
It depends on whether you accept choice or not, but a class is usually understood as a terminal object in the category of axioms.

[Anonymous No.9442950]

>>9442940
To define a "terminal object" you need to have already defined what is a "category".

So, again, what is a "class"? Can it be defined in a formal system of logic, or maybe in (modern) type theory?

[Anonymous No.9442953]

>>9442950
>To define a "terminal object" you need to have already defined what is a "category".
No, you can either choose between primitive notions or minimal circularity.

[Anonymous No.9442959]

>>9442950
>So, again, what is a "class"?
Anything bigger than a set

[Anonymous No.9442969]

>>9442953
>minimal circularity
Oh, nice. So we are already acepting the definition of category, as it stands in its usual form (there may somewhere be a proper form, though) is circular.

>primitive notion
Where is the axiom for the primitive notion of "class"?

>>9442959

In Category Theory, sets are defined using categories and not the opposite.

[Anonymous No.9442971]

>>9442969
>Where is the axiom for the primitive notion of "class"?
In the category of axioms, where else?

[Anonymous No.9442973]

>>9442971
Could you list them?

[Anonymous No.9442984]

>>9442973
>Could you list them?
No, there are uncountably many (easy to prove à la Cantor's diagonalization method), hence they can't be listed

[Anonymous No.9442986]

>>9442984
Where is the proof there are uncountably many of them?

[Anonymous No.9442990]

>>9442986
We're not going to do your homework for you, please take this to /sqt/.

[Anonymous No.9442994]

>>9442990
>damage control
So can't you show it?

[Anonymous No.9442999]

>>9442994
Who are you quoting?

[Anonymous No.9443001]

>>9442999
(You)

[Anonymous No.9443008]

>>9442986
>Where is the proof there are uncountably many of them?
As I said the proof is done à la Cantor's diagonalization method, it's exactly analogous to the proof for real numbers (or any of the many applications in computer science), just assume you have listed them then form a new axiom by proceeding diagonally through your list.

[Anonymous No.9443018]

>>9443008
Cantor's diagonalization method needs natural numbers to be stated.

In turn, numbers require sets to be defined. And within Category Theory, sets are defined from categories and not the opposite.

Now, what is a "class" as it is invoked in the definition of "category"?

[Anonymous No.9443029]

>>9443018
>Now, what is a "class" as it is invoked in the definition of "category"?
Can you at least read the rest of the thread before posting questions that have already been answered? see >>9442940

[Anonymous No.9443032]

>>9443029
> >>9442940
Can you at least read the rest of the thread before posting questions that have already been answered? see >>9442950

[Anonymous No.9443035]

>>9443018
>Cantor's diagonalization method needs natural numbers to be stated.
What do you mean?

[Anonymous No.9443036]

>>9443035
Can you prove otherwise?

[Anonymous No.9443041]

>>9443036
>Can you prove otherwise?
No, it's impossible to prove a negative.

I'm just not sure what led you to mistakenly believe the natural numbers were necessary.

[Anonymous No.9443045]

>>9443041
>No, it's impossible to prove a negative.

I'm just not sure what led you to mistakenly believe you cannot proceed by contradiction.

[Anonymous No.9443048]

>>9443018
>In turn, numbers require sets to be defined. And within Category Theory, sets are defined from categories and not the opposite.
As I said, you just invoke minimal circularity. This is how Gödel defined categories to avoid the paradoxes associated with the previous definition that used primitive notions instead of minimal circularity.

[Anonymous No.9443050]

>>9443048
How is circularity logically valid?

[Anonymous No.9443051]

>>9443045
>I'm just not sure what led you to mistakenly believe you cannot proceed by contradiction.
Because that's an element of the category of axioms, so it can't be used recursively in the diagonal proof.

[Anonymous No.9443054]

>>9443051
>Because that's an element of the category of axioms, so it can't be used recursively in the diagonal proof.

Since contradiction would require no recursion whatsoever in this case, it can be used.

[Anonymous No.9443055]

>>9443050
>How is circularity logically valid?
Why do you think it wouldn't be?

https://en.wikipedia.org/wiki/Circular_reasoning

>The components of a circular argument are often logically valid because if the premises are true, the conclusion must be true.

[Anonymous No.9443059]

>>9443055
>Circular reasoning (Latin: circulus in probando, "circle in proving";[1] also known as circular logic) is a logical fallacy
As expected.

[Anonymous No.9443063]

>>9443054
>Since contradiction would require no recursion whatsoever in this case
I don't follow, how does the proof proceed without recursion?

[Anonymous No.9443065]

>>9443063
How could it not?

[Anonymous No.9443073]

>>9443059
>As expected.
A fallacy doesn't have to be logically invalid, what's the issue?

[Anonymous No.9443074]

>>9443065
>How could it not?
I'm simply not aware of any way to proceed without recursion, are you?

[Anonymous No.9443076]

>>9443073
A fallacy doesn't have to be logically valid per se, what's the issue?

[Anonymous No.9443080]

>>9443074
Are you really not aware of any? Wow.

[Anonymous No.9443082]

>>9443076
>A fallacy doesn't have to be logically valid per se, what's the issue?
There is no issue (at least in our case regarding minimal circularity of categories and classes).

[Anonymous No.9443085]

>>9443082
How is there no issue in circularity?

[Anonymous No.9443091]

>>9443085
>How is there no issue in circularity?
It's a theorem of mine that the circularity is logically valid.

[Anonymous No.9443094]

>>9443091
Can you prove it?

[Anonymous No.9443096]

>>9443094
>Can you prove it?
Of course, it's a theorem of mine.

[Anonymous No.9443098]

>>9443096
Could you show the proof of it?

[Anonymous No.9443108]

>>9443098
>Could you show the proof of it?
Sure, where can I send the .v file?

[Anonymous No.9443112]

>>9443108
Why don't you upload it for free?

[Anonymous No.9443120]

>>9443112
>Why don't you upload it for free?
I didn't ask you for payment.

[Anonymous No.9443124]

>>9443120
>I didn't ask you for payment.
I didn't ask you to charge me.

[Anonymous No.9443125]

>>9443124
>I didn't ask you to charge me.
I wasn't going to.

[Anonymous No.9443127]

>>9443125
Good to know. Can you send it to e-mail, then?

[Anonymous No.9443131]

>>9443127
>Can you send it to e-mail, then?
Of course, that's why I asked where you wanted me to send it to.

[Anonymous No.9443135]

>>9443131
Here you go: [e-mail]

[Anonymous No.9443157]

>>9443135
>Here you go: [e-mail]
Sent.

[Anonymous No.9443165]

>>9443135
Do you have an e-mail that doesn't have third world storage capacity?

>Message not delivered
>There was a problem delivering your message to [e-mail]. See the >technical details below, or try resending in a few minutes.
>The response was:

>552 Message exceeds allowed size

[Anonymous No.9443171]

>>9443165
Sure, [e-mail]

[Anonymous No.9443177]

>>9443171
>Message too large
>Your message couldn't be delivered to [e-mail] because it exceeds the size limit. Try >reducing the message size and resending.
>The response from the remote server was:

>552 5.3.4 Message size exceeds fixed limit

[Anonymous No.9443181]

>>9443177
Damn! Such bad luck. Can upload it to archive.org instead?

[Anonymous No.9443186]

>>9443181
>Can upload it to archive.org instead?
No, the people who run the Archive have zero respect for copyright, I don't do business with those types.

[Anonymous No.9443188]

>>9443186
What about uploading it to mega{,}nz?

[Anonymous No.9443193]

>>9443188
>What about uploading it to mega{,}nz?
As I said, I don't do business with those who don't respect copyright.

[Anonymous No.9443203]

>>9443193
Hmmm. Could you torrent the file?

[Anonymous No.9443208]

>>9443203
>Could you torrent the file?
I'm not a pirate.

[Anonymous No.9443211]

>>9443208
So?

[Anonymous No.9443215]

>>9443211
>So?
So I do not "torrent".

[Anonymous No.9443219]

>>9443215
How is torrenting files you own 'pirating'?

[Anonymous No.9443224]

>>9443219
>How is torrenting files you own 'pirating'?
Only pirates use torrents, otherwise they would obtain files through legitimate means.

[Anonymous No.9443231]

>>9443224
>Only pirates use torrents, otherwise they would obtain files through legitimate means.
Do you have any proof to back up such statement?

[Anonymous No.9443233]

>>9443231
>Do you have any proof to back up such statement?
Of course, it's a theorem of mine.

[Anonymous No.9443235]

>>9443233
Could you show the proof of it?

[Anonymous No.9443240]

>>9443235
>Could you show the proof of it?
Sure, where can I send the .v file?

[Anonymous No.9443242]

>>9443240
Why don't you upload it for free?

[Anonymous No.9443246]

>>9443242
>Why don't you upload it for free?
My work takes both time and effort, I don't just give things away for free.

[Anonymous No.9443295]

>>9443246
How much would you charge me to obtain it?

[Anonymous No.9443327]

>>9443295
>How much would you charge me to obtain it?
Current pricing is 10 AION.

[Anonymous No.9443329]

>>9443327
Do you accept Bitcoin?

[Anonymous No.9443332]

>>9443329
>Do you accept Bitcoin?
No.

[Anonymous No.9443333]

>>9443332
How come?

[Anonymous No.9443336]

>>9443333
>How come?
Too volatile.

[Anonymous No.9443339]

>>9443336
Understandable, have a good day.

[Anonymous No.9444285]

literal autism ITT

[Anonymous No.9444316]

more proof that subhuman gorillas should be shot on sight.

[Anonymous No.9444352]

>>9444316
>more proof that subhuman gorillas should be shot on sight.
What do you mean?