/sci/ - Science & Math

Unanswered and half answered questions:
>>10841392
>>10841504
>>10841552
>>10841966
>>10842629
>>10843518
>>10844355
>>10847584
>>10848579
>>10849440
>>10849698
>>10849799
>>10851375
>>10853121
>>10853864
>>10854257
>>10856073
>>10856252
>>10857421
>>10859939

>>10849440
Lie algebras, ring theory, functional analysis, anything in differential geometry and C*-Algebras.
>>10851375
Handbook of Categorical Algebra, volume three.
>>10856252
All three.
>>10859939
I've been doing arithmetic for decades and still do stupid shit, so that's probably not the best strategy. Might as well just go forward.

I'm rolling a die with N sides. How do I find the expected number of rolls needed to roll any side an arbitrary number of times? An arbitrary number of sides an arbitrary number of times?
It's not the multinomial distribution, because that would be taking a certain number of rolls, and finding the expected number of times a certain side was the result, which seems related, but not what I'm going for.
I'm sure there's some combinatorial wizardry that can be done, for individual cases, but I'm hoping for a more general and preexisting thing that I can google.

>>10861301
Essentially, the average number of times you need to roll until you get a given side n times?
Since any two throws are independent, that's n times the average number of times you need to roll until you get a given side once.
Trying to calculate that gives an infinite series. I leave the remainder of the problem to another anon.

Can you please explain to me why
> -10* -9 ^ x
is different than
> -10 * (-9) ^ x
? I'm following PEMDAS, so parenthesis and then exponents. But there's no actual calculation in the first parenthesis so isn't -9^x exactly the same as (-9)^x?

>>10861611
Looks like they should be the same.

>>10861632
Well for some reason Khan Academy considers the first one wrong and the second one right

>>10861611
No, -9^2=-81, while (-9)^2=81.
- means "multiply by -1", so it passes after exponents in PEMDAS.

>>10861660
wouldn't a more correct version be
>-(9^x)
then?

>>10861611
no, -9^x is not the same as (-9)^x, since following the PEMDAS convention -9^x is the same as -(9^x)
as >>10861679 pointed out

>>10860247
I'll be a freshman in college this fall, and I'm planning on double majoring in CS and Math. Should I do a BA in Math combined with a BS in CS or a BA in CS? The BS course load is a bit heavier, with a Physics requirement and a capstone requirement. I took IB Physics HL in high school, but I can't get credit for that because it's not calc-based despite it being a high-quality course. I'd like to go to grad school in CS, and I'm wondering if it would be worth it to take a slightly lighter course load that would give me an opportunity to take some more non-technical classes that interest me, as well as letting me focus on getting research experience. I really enjoy Physics too, for what it's worth.

I've spent the majority of my life checked out and on autopilot. The other day I realized that I can't remember much about math and science. Can someone recommend good books for a brainlet to start with?

I juuuuust wanna be smaaaaaaaart /sci/. Is that too much to ask???

>>10861706
Go for the harder course load. If it's too much, there's no reason you can't switch.
Focus on getting internships and forging connections with professors, join clubs, and meet people. That's just as, if not more important than getting good grades.

Why cant i have sex? Me have no gf ;-;

>>10860247
Hi, I'm not sure if this is the right place to ask, but I have a question about hearing. So, my understanding is that normal range of audible sound frequencies for humans is 20hz-20,000hz. Sounds below this frequency range (intrasound) or above this range (ultrasound) are not perceived by the human ear.
My question is whether such an "inaudible sounds" emitted at a sufficient "loudness" level, can drown out regular, audible sounds, in the way that regular loud sounds make us unable to hear quiet sounds at the same time.
For example, if one were to play very loud intrasound in a room with some other regular sounds, would people in the room just hear nothing at all, or would they just hear the regular sounds normally?
Thanks and any help is appreciated.

Why can't I build muscle?

>>10861679
No, because using parenthesis in both cases is unnecessary bloat, and -9^2=-81 is consistent with the remainder of Pemdas.
>>10861714
Lang's basic mathematics.
Spivak's Calculus.
>>10861883
tl; dr can ultrasound block sound.
I'll leave it to the board physicists.

>>10861899
Thanks senpai!

Delete these threads. I never use them. When I want a question answered I make a thread.
And so does everyone else.

>>10861885
Could be that:
1) don't lift heavy enough or that you don't train to failure,
2) you don't consume as many calories as you think you do, or you know how much you consume but they are just not enough,
3) you don't rest enough. You wake up feeling like you need more sleep,
4) you just aren't meant to build muscle, but I don't think that's the case because it's almost always the DYEL's bad habbits that are at fault

Given a list of intervals given as pairs,
Eg.
[(0,1),(0.5,10),(11,20),(31,100),(-7,0.1),(99,300),(0.8,0.9)]
return the list with all overlapping intervals merged.
E.g.
[(-7,10),(11,20),(31,300)]

I can write the isSeperate helper function easily, as well as a mergeTwoPiars. But my loops don't get lots of unnecessary pairs and the size changing range is a pain.

How to do that in C++ or Python?

lads

i think i screwed up. i got admitted to a masters program, and im starting soon. however, i chose one where my advisors research is not completely in-line with my own interests.

what do? does my thesis need to be a direct off-shoot of my advisors or can it be more tangentially related?

[eqn]\lim_{x \rightarrow 0} \frac{x}{tan (x)}[/eqn]
Trying to solve this, but I'm stuck. I tried converting the denominator to the square root of 1 - sec^2 x, and then rationalizing a couple times, but I'm still getting 0/0.

And no, I'm not using L'Hopital's rule, because it's for brainlets.

>>10863098
Too lazy to tex it because it is trivial but x/tan = x cos/sin = (under limit) cos = 1.

i.e. just use that sin/x goes to 1.

>>10863098

Idk how to write math, but:

x/tan(x) = x/(sin(x)/cos(x)) = cos(x) * x/sin(x)

Then the multiplicative rule for limits, and x/sin(x) is known to have the limit 1 as x goes to zero. The limit of cos(x) as x->0 is trivial.

>>10863121
Ah, yes. I tried cos/sin, didn't see the sin(x)/x hiding in there.

Grazzi

how did the universe come from nothing

>>10863371
God created it from nothing

>>10862679
use an interval tree

I know that GCD(a,b) = 1 means a and b are relatively prime and there exist some integers s and t such that 1 = as + bt. Is the converse true? Does the existence of s and t such that as + bt = 1 necessarily imply a and b are relatively prime? My book does not present "GCD as a Linear Combination" to be biconditional.

>>10863691
Ehhhhh, sort of.
You have some exceptions like a=1 and b is anything, which doesn't count as relatively prime.
But because a|b and a|c implies a|(bs+ct) for any integers s and t, it does work most of the time. We leave the proper formalization as an exercise to the reader.

>>10863746
My bad, I goofed.
Anyhow, if a|b and a|c, then a|(bs+ct). But bs+ct=1, and thus a|1 and a=1.

>>10863754
>>10863746
Thanks. Let me make sure I interpreted you correctly: Assume a and b are both greater than 1. Then the existence of integers s and t such that as+bt=1 implies GCD(a,b)=1. Accurate?

>>10863781
No, I goofed in the first post, completely ignore it, works in all scenarios.
It's just ar=b, au=c, then 1=bs+ct=ars+aut=a(rs+ut) which is divisible by a. Since only 1 and -1 divide 1, it follows.

>>10863576
you can already guess the follow-up question

>>10863839
He has always existed
He is immortal, eternal, infinite

>>10863781
as+bt has to be a multiple of GCD(a,b). If a and b have some common factor k, then a=kA and b=kB for some A,B => as+bt=kAs+kBt=k(As+Bt). So as+bt=1 => GCD(a,b)=1.

>/sqt/ at page 9
wtf
bump

emailed professor last week to ask about undergrad research for course credit and got no response, should i just email again or try someone else? i emailed on a saturday last time so may have been a bad time

>submitted article to high tier journal back in February
>editor took until late June to come back to me with (very positive) reviewer comments
>just one minor revision request (changing the wording in one supplementary figure) which I made and sent back to them on the same day
>finally get confirmation of acceptance last week
>my paper will be in the September issue
>check out the August issue this morning
>it has a paper by some other team doing mostly the same thing I did, submitted in June and accepted in July

what the fuck

Do I complain to the editor?

>>10865840
just keep in mind that the people involved with publishing are all failed rejects who couldn't make it in their fields, and now they take out their envy and anger on important people like you

>>10860247
Are white people just more prone to violence and pedophilia?
Young white men shoot up schools while old white men rape children.
Now you may say that other races also have creeps, but statistically these demographics are predominantly white.

>>10865866
Didn't you die several months ago, Brenner?

>>10865840
If the journal says when it was submitted, it doesn't actually matter.
If anything it makes the editor looks silly.

>>10866210
It takes the oomph out of all the novelty though.

My work goes from an algorithm that vastly improves over all existing ones for a certain type of problems and an implementation that offers unprecedented flexibility in exploring that class of problems to an approach which slightly improves on one published the preceding month.

>>10866210
Also it looks like the editor worked at the same institution as the authors of the other paper until last year, so it looks like she held mine back for her friends.

Bloody hell this is only my fifth paper and there were some sort of shenanigans involved with three of them. It's really disheartening and makes me feel peer review is rotten to the core.

>>10865758
pleas ehelp

Do vegans swallow semen?

>>10865758
Email again with a shiney title

in which order should i read gelfands books?

>>10868241
Start with Homological Algebra, Trigonometry, Abstract Harmonic Analysis, and finish off with the Method of Coordinates. The remainder is trash.

I binded my thesis the wrong way. How bad is it?

Any good books about dynamic programming that aren't old as shit(Bellman) ?

How do I find the real root analytically? If I expand it and get a polynomial and equal it to zero I can't really find the working root candidate since I only have 1 and -1 in the leading coefficient and the constant.

>>10868857
https://en.wikipedia.org/wiki/Cubic_function#Algebraic_solution

>>10860247
I don't know if it counts as a stupid question but I don't think it deserves its own thread. What are the best study resources for chemistry?

>>10868863
Completely forgot this existed, thanks.

If force equals mass x acceleration, why do I get hurt when hit by a car that is slowing down?

>>10869215
>>10869215
force = m * a is just a special case of force =dp/dt where p is the momentum, or in other words p=m*v. since mass is constant at low velocities this becomes F=m*a. So it's not the acceleration as such that's connected with the force, but rather momentum. So if you're hit by a car that has some mass and velocity, it will transfer some of that momentum on you and cause a sudden change of your momentum (in other words, it will transfer a force to your body). the fact that the car is slowing down just means that it will have less velocity (or momentum) to transfer to you. It'll hurt less, but it'll still hurt

>>10869424
Thanks

>>10868857
-(1/2)(1-x)^3+1=0
=> -(1/2)(1-x)^3=-1
=> (1-x)^3=2
=> (1-x)=2^(1/3)
=> x=1-2^(1/3)
Using the general solution (Cardano, Lagrange, etc) is unnecessary as the original form is almost solved. The complex roots are equally straightforward; just use the complex cube roots of 2 instead of the real cube root.

>>10866204
I don't even know what you're talking about, some schizo?

>>10869545
Sydney Brenner (the Nobel prize winner) would rant about peer review being a corrupt sham populated by incompetent rejects.

He died earlier this year.

is there a concept for the number of ways you can partition a set, but like if all the set elements were the same? Like there are 2 ways a to partition a set of

2 ({a} ,{a} and {a,a}),

3 ways to partition a set of 3 ({a},{a},{a} and {a,a},{a} and {a,a,a})

5 ways to partition a set of 4 ({a},{a},{a},{a},{a} and {a,a},{a},{a},{a} and {a,a},{a,a},{a} and {a,a,a},{a},{a}, and {a,a,a},{a,a} and {a,a,a,a}

and so on

>>10869951
oops I fucked up my example for 4 elements but the point still stands (see pic on the post)

>>10869951
Stirling numbers always pop up here, and sums with powers of -1

>>10869951
>>10869954
see https://en.wikipedia.org/wiki/Partition_(number_theory)

Hi, writefag here

How large would a radio set have to be to be able to transmit and receive messages with a global range?

Thanks.

>>10869834
Oh, well he sounds like an agreeable guy then.

If I start taking SSRIs, will it ruin my cognition or memory?

>>10860247
Why do atoms move?

>>10870031
it's not the size of the set that matters if you know what i mean hehe. If you don't know what i mean, I mean that it's the size of antenna that matters and I guess it depends on its location. if you want more details look for low frequency broadcasting https://en.wikipedia.org/wiki/Low_frequency

Question for resident chemists.

I have a sealed glass bottle of a 5% sodium hypochlorite solution that I wanna use.
The problem is that it is date expired and there are some crystals formed on the bottom of the bottle.
I shook the bottle but the crystals dont seem to go away.
So how can I make the crystals go away and is usable after expiration date of a sealed bottle?

>>10870488
no goy just take your meds

>>10867493
Probably no but as anything else there are extreme examples of people doing it.

This is an extract from a study, can you explain what the stuff in parentheses means?

"Multivariate conditional logistic regression modelling indicates that consumption of eggs is associated with increased risk for colon cancer (odds ratios by quartile: 1.0, 1.58, 2.02, 4.66)"

With that information is there any way to calculate the increase in risk given the number of consumed egg/week?

>>10870816
Fields

>>10871645
Can you explain that a little more?

Who is in the right here?
>>>/a/191687798

Consider a problem similar to the least squares problem, but the input and output data are complex number, and we take the modulus of the squarred difference (pic related). Would the junction J be convex regarding the real parameter a?
Pls no bully, I'm not a mathfag and don't know anything about complex analysis.

>>10870816
to stay healthy

>>10871792
[math] \mid y_1-af(x_1)\mid^2=\mid y_1\mid^2-a y_1\overline{f(x_1)}-a\overline{y_1} f(x_1)+a^2 \mid f(x_1)\mid^2[/math]
second derivative is [math] 2\mid f(x_1)\mid^2\ge 0[/math]
so J is a sum of convex functions and is thus convex

>>10871792

|z^2| = |z||z| = z*conjugate(z) = real^2+imaginary^2

so i think it's exactly the same as R^2

I'm studying Cullen's matrices and linear transformations in my own time. So far i haven't had a problem but i've hit a snag. Essentially i need to show that finding A^-1 is just solving the system AX=K with n different choices of K. It gives a hint to look at the columns of AA^-1=I. I thought that if I used Colj(AB)=AColj(B) i'd be able to figure something out, but i'm really just not understanding the question. Any pointers?

>>10871906
the first column of a matrix is equal to that matrix multiplied by the first standard basis vector. In particular, the first column of A^-1 is x_1=A^{-1}e_1. Thus x_1 satisfies Ax_1=e_1, and similarly for the remaining columns

>>10871858
Thanks, anon. I was thinking about something like this, but was afraid there could be some detail about complex analysis making it wrong.
>>10871814
Many thanks, anon. Didn't know about this identity. Is there a more general version? Would J still be convex if there was another real parameter, like pic related?

I need a curve with a couple of different extrema for demonstration purposes. Are there any particularly good functions for this or alternatively some kind of software that just allows me to freely draw smooth curves by hand? Wikipedia uses cos(3*pi*x)/x as a demonstration which kind of works but I'd prefer something with at least 3 different extrema relatively close to each other.

>>10871940
i just used the fact that [math] \mid z\mid^2= z\overline{z} [/math] and collected terms, i leave the extension to pic related as an exercise :)

>>10871933
Ok, Cullen doesn't use "standard basis vector". But using his notation, i think what you said could be put as: The first column of A^-1 is Col_1(A^-1)=A^{-1}Col_1(I) where I is the identity matrix. Thus Col_1(A^-1) satisfies AX=Col_1(I), and so on for n columns of A^-1, which gives us our system AX=K with n different choices of K?

>>10871944
The derivative of your function is gonna be zero at you extreme values so just do the integral of(x-a)(x-b)...(x-z)

>>10871972
I don't know why I didn't think of that. Thanks.

Can foreign universities access the national student clearinghouse? Moreover, could I get away with omitting records when applying to universities in Germany/Europe if I can account for the time?

I'm trying to show that a sequence [math]a_n[/math] is monotonely increasing. the sequence is [math]a_1:=1, a_n:=a_n^2+(a_n)/2+1/16[/math]. im pretty sure i have it right (see pic) but i think i've overthought it. in a proof by contradiction, does finding one specific counter example like i've done prove the general idea? obviously it shows that our assumption is not the case, and law of excluded middle blah blah, so it should be the case, but i cant help but feel like theres something wrong

Is epidemiology the scientific field with the most short- and medium-term benefit for humanity?

>>10872274
On phone so too lazy to LaTeX.

a_n^2 +a_n/2 + 1/16 = (a_n + 1/4)^2 > a_n^2 >= a_n since a_1 = 1.

>>10872395
does this not assume that [math]a_n\geq1[/math]? i also thought about using this method, but thought that the contradiction method was more "complete". is my contradiction proof valid, even if its needlessly long?

I have an engineering degree with a math minor. The closest thing I know to "real" math came from a proof-writing course which I did decently in. What else do I need to start on Munkres's topology book? Is a full semester's worth of real analysis absolutely required?

Can someone explain the proof that there are infinite prime numbers?

So I'm trying to learn how AES works, and I figured I'd ask here instead of /g/ since the questions I have are more math related. I understand most of it, but just have a few questions.

1.) When generating the round keys, there's the function [eqn]W_{i} = W_{i - N} \oplus SubWord(RotWord(W_{I - N})) \oplus rcon_{i / N}, i \geq N, i = 0 (mod N)[/eqn]. When RotWord and SubWord are used in here, should they actually affect the global state of the keys, or are they just temporary arguments for the operation?

2.) Is the transformation in MixColumns just a simple matrix-vextor multiplication? It says something about a degree 7 polynomial [math]x^8 + x^4 + x^3 + x + 1[/math] XOR'd with 0x1B if the result overflows. Where exactly does the value of X come from? It also says it's multiplied with a fixed degree 3 polynomial [math]3z^3 + z^2 + z + 2[/math], and I also don't know where the value of Z comes from. I haven't studied number Theory, so a lot of the Galois Field stuff the Wikipedia article talks about goes over my head, and I don't know what all needs to be actually be calculated and what all's already given by the transformation matrix.

>>10872881
What exactly do you not understand?

>>10872881
Take any prime number N. Consider N!+1. For every integer x between 1 and N, N!+1≡1 (mod x), i.e. N!+1 does not have any factors <= N. So either N!+1 is prime, or all of its prime factors are greater than N. IOW, there's always a bigger prime.

>>10872446
Eh, sort of. We are given that a_1 is equal to 1, and therefore a_2 is, and so on. It's induction in disguise.

No, your proof is not correct. You only show that there is one spot where it is increasing. You want to show for a contradiction that there exists SOME n where it decreases. I don't think contradiction will be elegant here. I also believe the way I did it was designed that way on purpose, since it's a perfect square.

>>10860247
By reducing to a generic function to an exponential function, does the Laplace transform unify differentiation/integration with multiplication?

And are there any functions, besides e^x, which can be differentiated three times to equal itself?

>>10872881
you suppose that there is only a finite number of prime numbers. thus you can write them all down on a list, and this list will be finite. you use this list to create a new number and show that this number is also a prime number. therefore it has to be somewhere on the list, since it's a list of ALL prime numbers. but this number is bigger than any of the numbers on the list by construction. this is a contradiction.

>>10872817
>Is a full semester's worth of real analysis absolutely required?
the only thing you need for topology is basic set theory (which is explained in the book anyway) and enough maturity to handle proofs. general topology is a branch of math which really starts from scratch, so theoretically there are no requirements. but without at least some knowledge of real analysis, everything will feel terribly unmotivated, you won't understand why are things defined this way. better question is why do you want to read Munkres? if you want to do meme stuff like klein bottles and cups to donuts, then you absolutely do not need to work through this book.

>>10873298
>And are there any functions, besides e^x, which can be differentiated three times to equal itself?
no, only scalar multiples. take the differential equation y' = y, it's a homogenous linear equation, so the space of solutions is a vector space of dimension one. we know that one such solution is e^x, therefore all other solutions are scalar multiples of e^x.

>>10873321
>>10873298
or did you mean like y''' = y ? you can check for yourself by solving the equation

>>10873321
But with second derivatives, you can also have cosx -> -cosx and sinx -> -sinx, along with e^x. What makes second derivatives special?

>>10873326
say you're looking for functions such that the n-th derivative gives the original function. this is just ODE

y^(n) - y = 0

that's a linear homogenous equation with constant coefficients and so the space of all solutions will be a vector space of dimension n. so for n-th derivative you have n linearly independent functions.

>>10873341
>so for n-th derivative you have n linearly independent functions.
So there are three such linearly independant solutions? I can think of seven solutions, but they come in groups of 3, 3, and 1 (the last being e^x) when restricited to linear independence

how would /sci/ solve the normie problem? im sure you all have great ideas don’t be shy about sharing them :)

>>10873326
> What makes second derivatives special?
Higher derivatives give you a higher-degree characteristic polynomial with more roots. So x''=x has both x=e^t and x=e^-t as solutions (along with any linear combination of those). x=e^t => x'=x => x''=x'=x, ..., while x=e^-t => x'=-x => x''=-x'=x, ...

The solution of any linear ODE is a linear combination of terms of the form t^(n-1)*e^kt, where k is a root of the characteristic polynomial and n is the multiplicity of the root. If the coefficients in the ODE are real, so are those of the characteristic polynomial, meaning that the roots are either real or occur in conjugate pairs. The latter case results in real sin/cos terms via Euler's formula.

>>10873359
>I can think of seven solutions
they are not independent

>>10873396
Simple question: are cosx and sinx independant?

>>10873407
is there a real number k such that cosx = k*sinx ?

>>10873407
cos(x)=(e^ix+e^-ix)/2
sin(x)=(e^ix-e^-ix)/2i
So {sin(x), cos(x), e^ix, e^-ix} has rank 2; given any 2 the other 2 are linearly dependent.

Anyone know what I'm doing wrong here?

>>10872881
[math] \zeta(2)=\pi^2/6=\prod_p (1-1/p^2)^{-1}[/math], if there were finitely many primes, the right-hand side would be a rational number

>>10873584
False (it's 1.5 wavelengths), True, True, True, True.

E is the point where the path lengths are equal (constructive interference). D and F have a difference of 0.5 (destructive interference). C and G have a difference of 1.0 (constructive), B and H 1.5 (destructive), A and I 2.0 (constructive).

>>10873854
Thanks for the help dude. I figured E and the rest were true, but I was guessing at this point.

>>10873826
while technically true...
reducing the statement about primes to having to justify
>this product over a set of rationals, of which we don't yet know the cardinality, is is pi^2
as well as
pi isn't rational
is not exactly a smooth move

>>10873826
while technically true...

...reducing the statement about primes to having to justify
>this product over a set of rationals, of which we don't yet know the cardinality, is pi^2 / 6
as well as
>pi isn't a rational number
is not exactly a smooth move for a proof

>>10872881
Suppose there are a finite number of primes. Ennumerate them. Multiply all of them, and obtain n. n+1 isn't divisible by any of the ennumerated primes, and thus not all primes have been ennumerated, by contradiction.
>>10873310
No, not quite.
>>10873182
It's not wrong but it's shit.
>>10873826
Kino.

>>10873914
nigga you've written exactly the same thing as >>10873310

>>10873995
You actual retard.

>>10874003
cool

>>10873396
Based on >>10873480, they are though. There are two sets of three independant, non-e^x solutions to y'''=y.
What's confusing me is why they don't have names, and why I can't find examples of them anywhere.

>>10874162
give me a set of solutions for y''' = y with more than 3 elements and I'm 100% sure they will NOT be independent over R.

>>10874169
You're right actually. I looked over my solutions again, and two of them intersected when x=0. It seems like the only reason cosx and sinx are independant, is the series for cosx starts with "1+..."

Why are imaginary numbers not considered when testing for linearity?

>>10874196
They are, it just happens that C^infty doesn't imply analytic.

>>10874196
>Why are imaginary numbers not considered when testing for linearity?
I have no idea how ODEs work in the complex field, I was just stating what I knew

If I have a statistical model where the relation is nonlinear, I can still say fuck it and do GLS by taking a function of the dependent or independent variable.
But is there some convenient trick for deforming the error? Something like the dependent variable's logarithm's hope is linear in relation to the dependent one, but the error is just a normal around the unmodified hope, so it skews off if you just take logarithms.

>>10874249
Never mind, I'm an idiot.

Is it appropriate to say i*cosx = sinx?
If so, isn't multiplying sines/cosines by 'i' equivalent to differentiating them?

>>10874431
>Is it appropriate to say i*cosx = sinx?
why in the world would you say that ? put x = 0, do you feel like i*1 = 0 ??

>>10874270
stop calling yourself an idiot for the assurance and amusement of an audience/the public fag you’re insulting your entire family and your very being by doing so

>>10874440
>do you feel like i*1 = 0
That is its real part, yes

>>10874456
do you know what equality means for functions ? it means that they share the same domain and give the same value for each input of the domain. now answer this simple question: do the functions f(x)=i*cos(x) and g(x)=sin(x) give the same value for every input x ? hint: the answer doesn't depend on whether the domain is real or complex

>>10874465
Fair enough. I ultimately meant a 90 degree phase shift, so what about cos(x+pi/2)?
And how would you represent 90 degree phase shifts using i?

>>10874444
>quads of fours
Okay, I'll stop.

>>10874534
> And how would you represent 90 degree phase shifts using i?
If Ω=(1/2)e^ix, then Ω+Ω*=cos(x) while iΩ+(iΩ)*=iΩ+i*Ω*=-sin(x). More generally, if k=e^iφ, kΩ+k*Ω*=cos(x+φ).

This is how signal processing theory is usually formulated, i.e. real sinusoids are generally modelled as the sum of a complex exponential and its conjugate. Addition, scaling, differentiation and integration of such terms results in similar terms. For brevity, the conjugate and the exponential itself are often omitted.

Does quieting masturbation a good idea for longevity?

>>10875306
Yep

What's the potential maximum velocity caused by buoyancy?

When i push down a football/pingpong ball/ similar under water it eventually shoots up far above the surface.

>>10875322
why?

>>10875325
To minimize cell division. Cells can only divide so many times and they die.

>>10875329
That's complete bullshit.

>>10875336
You are.

how can I make a new universe to live in?

>>10875491
You must first invent the apple pie.

>>10875499
this

I guess a degree is the equivalent of reading forty textbooks on one subject because a typical degree has ten courses a year for four years. So all I have to do is read forty textbooks to get a good job.

>>10875324
> What's the potential maximum velocity caused by buoyancy?
That's a rather hard problem. The buoyant force is equal to the weight of displaced fluid minus the weight of the object displacing it, and is (more or less) independent of depth. So you can obtain the potential energy by multiplying the difference in weights by depth (it's a bit more complex at the surface, when the object is only partially submerged; provided that the object is submerged to a depth much greater than the size of the object, you can ignore that).

The awkward part is that you can't just equate that to the kinetic energy of the object. When the object is released, most of the energy is probably going to end up either as currents within the fluid or lost to drag, with only a fraction transferred to the object. So to answer your question you'll need to solve Navier-Stokes. Good luck with that.

>>10875758
No, you're paying for the piece of paper that signals to your future employer that you're a good little worker bee who can sit and follow instructions for four years.

>>10875890
I think textbooks have way more instructions in them.

>>10875892
and who will guarantee that you've actually followed them

>>10875924
That doesn't matter if I actually do it.

>>10875981
>That doesn't matter if I actually do it.
yeah well, not necessarily. either you can actually do it OR you can have a paper that says you did it. both is useful

>>10871968

Ax=k might be better notation if x and k denote individual vectors. by definition of the inverse matrix, AA^-1 = I, so in order to find the inverse of A by solving n equations of the form Ax=k, choose your k's to be the columns of the identity matrix.

>>10876078

assuming A is actually invertible, of course.

How do you find what you really want to study/research in math if everything interests you? Unlike my peers I don't really gravitate towards just algebra or analysis or number theory etc. I like everything...it's like walking into a candy store and not knowing which to choose. How do I pick a topic I'm interested in?

>>10860247
I take lithium for my bipolar disorder. My question is: what does increased gray matter do? Will it make a noticeable difference if I have more? I get vague answers everywhere else.

Is it true that a mathematics degree is better than computer science for someone who wants to research artificial intelligence?

>>10876078
Yeah i thought so too, thanks for the input.

I've built an improvised barbell. Does having the plates (well, jugs of sand in my case) closer towards the middle of the bar rather than at the ends change anything? Obviously the total weight is the same but I'm a physicslet and don't know if the mechanics differ.

>>10876997
It makes the weight lighter by bringing it closer to your center of mass/gravity or something. I think.

I got an assignment which states the following
>enumerate the principal divisions of Zoology
>What the branches of zoology under each divisions are and define them briefly

Cannot find anything talking about principal branches. All I know are the following main branches:
>Taxonomy
>Morphology
>Anatomy
>Histology
>Cytology
>Physiology
>Embryology
>Evolution
>Paleontology
>Ecology
>Genetics
>Ethology"

>>10876521
yes

>>10877740
to put it more through:
>computer science: DURR COMPUTER DO THIS AND THAT, HERE LEARN SOME OOP BULLSHIT AND SOME SYSTEM THEORIES
Alot of AI, or Machine Learning in general, is mathematics, using lot's of vector calculations.
Just learn Python on the sidelines and you're almost fully set for AI

>>10877745
thorough*

>>10877739
vertebrates and invertebrates

Chemistry:

This mostly stems from by crappy Google-fu, i wanted to know what were the rules that determine when solids can dissolve into fluids/fluids can mix with each other.

I have been told something along the lines of "the similar dissolves the similar" (ie: polar liquids dissolve polar solids) back in school but i wager that it isn't all the story and is mostly a rule-of-thumb

Example:
Water is polar, so it dissolves salt that's also polar, it also dissolves sugar. From the rule above would follow that sugar, salt and water are all polar.
Alcohol can dissolve sugar but cannot dissolve salt, so alcohol is "similar" to sugar but not to salt?
Water and alcohol can mix with each other so they are similar with each other?
Water and oil definitely do not mix, since one is polar and the other is as non polar as it can get.

Tl;dr: please point me to a series of formulas that i can use to certainly determine if liquids can mix and solids can dissolve

>>10878055
>but i wager that it isn't all the story and is mostly a rule-of-thumb
You're right, there's a lot more to it. Unfortunately, that's all we currently have.
>please point me to a series of formulas that i can use to certainly
every lab has a miscibility chart, and some references have extensive solubility tables

In pic related, aren't all conditions necessary to be a group assumed for H in the theorem statement? Does this need proven at all aside from trivial proofs for identity and associativity? Feels like I'm missing something here.

>>10878103
So no methods/rules to predict if something will mix/dissolve but rather a "here 50 billions chemicals, test all the combinations" kinda deal?

>>10878116
Pretty much. The process of solvation is still an open problem in computational chem, last I heard.

>>10878108
Yes you only need to verify identity and associativity. Your book is just retarded and presented the one-step subgroup test before the much simpler two-step subgroup test.

>>10878134
Duly noted

>>10878116
Actually, I should clarify; in gen chem, you should have learned how to use Ksp to predict the solubility of salts in water. For other solvents, data is rare and unreliable, but the theory should be the same. For organics, and inorganic salts that aggregate (many of them do), it's all up in the air.

this might have been asked before but i couldn't find it
where can i find the most cited and influential papers on a topic?

A thread was posted about pic related yesterday and it got me into researching contour integrals. From what I understand, the integral in the pic needs more information to be computable? A contour from 0 to -2i would have to be given in order to integrate? Because the answer would change depending on whether a straight line or an arc of a circle or any other curve was chosen

What sort of chemistry is necessary to extract / synthesize nootropics? Should I hire a chemist friend to do this for me, or just try it myself? What if I want to sell this to others?

>>10878485
If a complex integral is written in that form, it invariably refers to the integral along the straight line segment between the limits. A path integral would be written as [math]\int_L[/math] with a definition given elsewhere for the path.

>>10876219
similar boat, bump. I would look at what problems different branches are working on, both in industry and academia. Number theorist, for example, can go work in cryptography at the NSA if academia does not work out. Just my two cents, I’m asking myself the same question.

Call me fucking crazy, but I have never been able to understand the reasoning behind the whole "two objects of different mass if dropped from the same height at the same time will hit the earth at the exact same time."
Sure, Earth will exert different amounts of force depending on the mass of the falling body, and this amount converts to the same acceleration regardless of the other objects mass. That much I don't disagree with.
What gets me all twisted up is the amount of force the falling object exerts on the Earth.
Say you had an elephant and a feather falling towards the Earth on exact opposite sides. Same elevation from the ground, same exact drop time. Shouldn't the force exerted on the earth by the Elephant cause it to move ever so slightly towards the elephant and away from the feather, resulting in the elephant hitting ever so slightly before the feather? Doing the math you can see tens or hundreds of zeros before your one, but there is a clear difference in acceleration.

Someone tell me i'm a moron and explain it, or tell me why literally every physics teacher or know it all proudly parrots the "everything falls at the same speed" myth (if I'm not crazy, that is.)

>>10878293
google scholar is a good place to start always, the search tools are relatively useful for a novice’s purposes I’ve found very weird papers on there that led to other stuff I would never have though to ask about.

>>10879132
well yes, of course you're right. but that's completely worthless on such a large scale. far, far too many other variables which would lead to different rates of falling at orders of magnitude much much higher than that of the pull of the objects on the earth.

>>10879208
So then all those people saying that the brick and the feather hit the ground at the exact same time are just spouting nonsense? It's just that that conflicts with every physics teacher I've ever had, which is the only reason I brought it here.

I'm implementing a lorenz attractor as a background animation for my website.

Now i have 10% knowledge about what I'm doing, the rest is basically intuition + trial and error. I've come pretty far, and gotten some weird results, but I can't crack this:

How do i change the "pivot" of the attractor? As seen in webm related, the function currently strives towards (0,0) = top left. I want this pivot point to be wherever I want, but dunno how to write that.

Code for each particle update:
tmp_a = bg_obj.lorenz_a
tmp_b = bg_obj.lorenz_b;
tmp_c = bg_obj.lorenz_c;
tmp_t = bg_obj.lorenz_t;

dx = tmp_t * (tmp_a * (p.y - p.x));
dy = tmp_t * (p.x * (tmp_b - p.z) - p.y);
dz = tmp_t * (p.x * p.y - tmp_c * p.z);

p.x += dx;
p.y += dy;
p.z += dz;

Where lorenz_abct are preset to: 10, 28, 8/3, 0.0001 respectively (I change t in the webm to show different results, both of which converges towards 0,0 or something).

Sorry for blurry webm, the compression gets sudokud by that many stochastic-like particles.

>>10879222
in an idealized universe in which the earth is fixed and perfectly flat and uniform, air doesn't exist, both objects are point masses, etc etc, they certainly do hit the ground at the same time. perturb that idealized universe even slightly and of course you'll get a different result. it's like how we say a ball moves in a parabola when you throw it. no, it's actually moving on an arc of some sort of strange elliptical thing which probably spirals down quickly into the center of the earth. but in an idealized universe it's a fucking parabola, and in real life it's really fucking close to a parabola.
i don't think your physics teachers expected you to think this is some kind of universal truth. like come on now. of course things can always get in the way.

>>10879137
thanks for the pointer, i'll try it out

>>10879132
>force exerted on the earth [...] cause it to move ever so slightly towards
Seems like you don't understand the first part.

>>10878548
>nootropic
bump

i dont understand the process of simplifying an expression. for example
3xy + 3y^2 - 2xy + y^2
this is simplified to
xy + 4y^2
this is all the book i am reading asks me for but i decided to start experimenting by replacing the literals with numerals and i get two different answers depending on if i work out the simplified version verses the original. say i made x = 5 and y = 8, when i work out the original i get 168 but if i work out the simplified version i get 296 (which is correct, according to wolframalpha). pic related is my work showing the original. what am i doing wrong?

>>10880442
>-80+64
>-144
What the fuck man.

>>10880463
you are supposed to add before you subtract, pemdas. so its 80 + 64, not -80. or at least this is my logic

>>10880504
No, addition and subtraction happen simultaneously, left to right

>>10880517
oh alright, thank you. is this the same for multiplication and division? this book words it strangely i think
>do all multiplication AND THEN all division
i must have read this and assumed it said the same for addition and subtraction

>>10880540
>is it the same for multiplication and division
Sort of. You do multiplication and division from left to right, as in addition, but you read [math]\frac{a}{b}[/math] as [math](a)/(b)[/math], for whatever expressions a and b.

>>10880540
i have another problem but ive already found the solution. i simply want to clarify something to myself. when there is a fraction such as pic related the denominator is supposed to be treated as a single term. i know this is the case because if i try to change the fraction to a division symbol it comes out wrong. for example, (9+3):4-1-3+(6:2), which comes out as 2 but the answer is supposed to be 4. what is the rule behind this? are fractions not just divisions? are the numbers in the denominator always going to be treated as if they were parentheses and if so why the fuck do some problems use parentheses in a denominator?

>>10880575
>\frac{a}{b}
would i run this in latex or something?

>>10880625
Turn your adblock off and reload the page.

>>10880635
theres so much to learn

>>10860247
Brainlet here. I've decided to redo mathematics from pre-algebra. I'm reading Algebra by I.M. Gelfand and A.Shen. Came across this:
>After we get this zero, we keep "4" in mind because 8+8+8+8+8 = 40. To get the next zero in the ''tens place" from this "4" , we need to add at least two 8's since 4 + 8 + 8 = 20.
This
>we keep "4" in mind because 8+8+8+8+8 = 40
doesn't make sense to me. HELP

>>10881021
>Context

What are the fastest-growing vertical asymptotes?

>>10878485
https://en.wikipedia.org/wiki/Cauchy%27s_integral_theorem

>>10881233
[math]\exp \frac{1}{x}[/math]

>>10880017
the various journal sites have decent search tools as well. the cited link under a study you’re interested in on scholar is probably the most useful easily missed tool you can utilize though.

In what order are you supposed to learn math in? Not the books but subjects, assuming im learning from scratch, how am i supposed to re learn geometry, trig, alg 2, calc 1? What subject comes after that? Im always confused by peoples books because theres a lot of subjects ive never heard of before. Thank you for your time in advance.

>>10881351
Faster.

Guys, I'm having a literal brainlet moment here.
Reviewing classical mechanics and came across the ODE for Newtonian gravity:
[eqn]\ddot{r}=\frac{GM}{r^2}[/eqn]
How dafuq does one actually solve this? I can't remember solving this eqn explicitly when I took the class.

>>10863849
why can't the universe be the same

>>10881373
start with basic algebra and master it. be able to do some of the more "complex" basic algebra tricks like completing the square, partial fraction decomposition, etc and learn why they work. after that, move on to trig and learn the identities, and you can derive everything else in trig from those identities. if you don't know why the sine/cosine/tangent functions look the way they do on a graph, then you still need to study more. geometry you can pretty much skip if you want to. calc comes next. always devote time to math whether it's actually practicing problems on paper, reading a textbook, or watching math videos. within a year, you should be caught up to a starting college student if you keep at it at least 30 minutes a day.

>>10881583
this can be done in far less than a year, and he absolutely should not forgo geometry

Why is this true?

>>10881583
>geometry you can pretty much skip if you want to
This is number one bullshit.

>>10882218
2^N = (1 + 1)^N
>apply https://en.wikipedia.org/wiki/Binomial_theorem
= sum for i from 0 to N of binomial coefficient (i, N)
>expand binomial coefficient
= sum for i from 0 to N of N! / (i! (N-i!))
>reexamine your relation

Ok so let's say I have a lock that takes a 3 letter alphabet combo on one sideand a 3 letter digit combo on the other.
[ABC,312] for example. Now if I want to get all the combinations possible I simply do permutation(26,3)*permutation(9,3)

But what if the elements are allowed to repeat, for example want to have a [ABC,312] combo?

>>10882218
The sum is exactly (2^n)-1; for i=0..n the sum is exactly 2^n and C(n,0)=1.

Think about the binomial coefficient in the context of combinations. E.g. if you flip n coins, there are C(n,r) ways of getting r heads. If you sum all of the cases, you must end up with 2^n as that's how many different results you can get and each result falls into exactly one case.

>>10882323
Sorry I meant to type [AAA,111]

>>10882323
26^3 * 9^3

>>10882343
Thanks.

is there some special trick to solving this or am I just brainfarting

>>10882360
nevermind holy shit
I realized just as I posted it that I am brainfarting and that it really is a straightforward mth root

I have another shitty combinatorics question, let's say I have the letters

PRESTOLNICA

I need all the permutations that start and end with either E,O,I and A from that word, for example

E-inbetween-A
E- inbetween-I
.
.
.
etc

I have no idea how to write the constraints.

Please, solve this problem by use of integration by parts and show your work. It supposedly had something to do with squaring but I just can't figure it out. It is not my homework, I am just studying on my own and the process isn't shown in the book. Yes, I am a brainlet, and I'm sorry.

>>10882323
This picture just forced me to masturbate
>>10882328
>>10882355
>>10882364
>>10882385
PLEASE STOP POSTING ROASTIES. THIS IS A KID FRIENDLY BOARD. I DON'T WANT TO HAVE TO JERK OFF AGAIN.

>>10882413
Take x^1/2 to be u(x) and then differentiate that term because doing dif/int on trig functions will net you just spinning in a circle.

>>10882413
Plugging this into wolfram shows that the solution is not in terms of elementary functions, so you just got trolled.

>>10882435
shouldn't he get something like
sqrt(x) * cos(x) - integ. [1/2(x)^-(1/2) * integ [cos(x)dx]dx]

>>10882385
How long can your word be, at maximum?

And I agree with anon, quit the roasties, it makes the meat hard and math harder.

>>10882440
As long as the original word or sequence-of-letters (it's a slavshit word meaning capital city).

>>10882385
>>10882449
Looking at your questions, it seems to me that you didn't understand anything about the simplest principle of combinatorics. Go over your study material again, because the questions you're asking are brainlet-tier level.

To solve this you use a very simple principle. Imagine you want to know "how many 2-Letters words can I form if it starts with A or B, and ends with C, D or R ?"
The answer is 2 * 3. Because for the first letter, you have 2 possibilities (A or B) and for the second letter, you have 3 possibilities.

Sometimes, counting possibilities become harder because you don't want to account for repetition, or do some fancier counting. But that's not the case in you example.

Here it'd be
4*(12^10)*4
Because
>it starts and ends with one of the 4 letters A, E, O, I
>in the middle, you have 10 letters that are one of the 12 unique letters from the word Prestolnica

>>10882454
Ah thanks, I asked it the wrong way but your reasoning pawed way for me to find the answer (also there are 11 unique words).

(Ans is 3*(9!)*4)

Please help a brainlet nigga who's seething.
>Take x^2 + ax + b = 0
I learned that solutions S1 and S2 give:
>S1 + S2 = a
>S1 * S2 = b
Is everything OK? Ok. Now take
>x^2 + 3x + 2
So, given what's said before:
>S1 + S2 = 3
>S1 * S2 = 2
But solutions are -1 and -2 so
>-1 + -2 = -3, not 3
Why?!?

>>10882497
You are missing a negative sign somewhere, goyim.

>>10882501
No
INPUT y = x^2 + 3x + 2
ROOTS x = -2 and x = -1

>>10882497
I'm not sure I follow.
x^2 + 3x + 2 = 0
ok so you can write it the following way
(x+1)*(x+2) = 0
For the thing to go to zero x has to be either -1 or -2.

So it's ok? Really not sure what you are asking. The minus sign on the roots come AFTER the vieta formula decomposition, since you are looking for what to plug in to get 0.

>>10882539
If solution are -1 and -2
how can sum of solution be a of ax, that is 3?

>>10882497
S1+S2=-a, fool.

>>10882555
Thank you, that was my error. Jesus Christ... it took 5 posts for someone to notice.
You're not so smart as you think you are, are you

>>10880504
>>10880540
Sorry you're caught up in this, it's really fucked up how they teach it. I know you've gotten responses but I want to clarify the full proper order of operations:
>parenthesis/brackets
>exponentiation
>multiplication AND division from left to right (which includes negative signs, since this is really (-1)*
>addition AND subtraction from left to right
It might seem arbitrary, but as you use stuff like the distributive rule more it begins to make more sense why we have it that way. Remember that if you're ever unsure of how to write something you can always just use parenthesis to make it clear. And lastly, the whole multiplaction/division at the same time thing is because when you divide something by any number x, you're really just multiplying by the reciprocal 1/x. Similarly, when you subtract any number y, you're really just adding -y. So multiplication and division are really the same operation at their core, and so are addition and subtraction.

>>10881373
Arithmetic/prealgebra, Algebra, Geometry, Trigonometry/Precalculus, Differential Calculus, Integral Calculus, Multivariable Calculus, Linear Algebra (you can swap the last two if you'd like), Differential Equations, Discrete Mathematics, Basic Abstract Algebra (Groups/Rings/Fields), Basic Real Analysis, and then Differential Geometry of Curves and Surfaces, Complex Analysis, and Point Set Topology in any order. Honestly probably Topology first.
After that there are plenty of intermediate topics which you would pick based on your interests. You can also go for Set Theory and Logic, but probably not until after Abstract Algebra / Real Analysis.

>>10882565
Rude.

[math]z^2 -3z + 3 - i = 0[/math]

I've been staring at this for like 2 hours now but I still don't get it.
I tried tackling it from every direction possible. I tried just using the standard quadratic formula, but the expression inside the square root (the [math]b^2 - 4ac[/math] thing) doesn't amount to anything neat I can sqrt away. If I try sqrting it, that would mean converting it into a disgusting plane representation with fractional angles.
I tried breaking [math]z[/math] down into [math]a + ib[/math] but that doesn't lead me anywhere.
I tried looking for some sort of trick that lets me isolate [math]z[/math]. That's how Wolframalpha did it, but even the step-by-step solution just jumps straight to [math](z - (2+i))(z - (1-i)) = 0[/math]
I looked up online but no website I found really show how you deal with a quadratic equation with complex numbers, and both books I have never bother even mentioning such a possibility.
fucking kill me
dropping out was a mistake

>>10882680
z = (a+bi).

Write that in and expand, then compare the imaginary and real parts separately to the right hand side and you will get 2 equations with 2 unknowns.

>>10882680
nvm I finally figured it out
apparently that "disgusting plane representation with fractional angles" solves itself out later

Hint says to divide top and bottom by [math]1/n[/math] to turn into a Riemann sum, but I can't figure out what function it is and the bounds of integration.

Why do normies think studying computer science is impressive and that the students are somehow geniuses while /sci/ just shits on them constantly?

>>10882857
Well, if you multiply top and bottom by 1/n, you get terms like 1/(1+k/n) * 1/n. 1/n is the length of each interval, and the sum has n bits. Then the interval has length 1. In fact, due to shifting, we can pick any length 1 interval we'd like. Say 0 to 1 as our endpoints. Then what is the function? Well, the right handed riemann sum wants us to evaluate f at each point k/n from k = 1 to n. That's good, k/n shows up in our sum! So such an f would be 1/(1 + x). Now we have the integral of 1/(1 + x) from 0 to 1.
Notice that if we instead took our endpoints to be 1 and 2, we would find that we should evaluate our function at 1 + k/n for the right handed riemann sum. Then our function would be 1/x. The integral of 1/x from 1 to 2 is of course the same as the integral of 1/(1 + x) from 0 to 1.

Why is it that only mammals are incapable of being brightly colored? Birds, insects, fish, reptiles, amphibians, mollusks, etc. come in all sorts of colors, such as blue, green, pink, purple, etc. Why isn't that the case for mammals? The closest they can get is blonde or red hair/fur, but they're in dull shades.

>>10883656
metabolically costly, low fitness sexual selection driven plumage/coloring would not work. Also many species of monkeys are brightly colored precisely for those reasons.

>>10883178
Because it actually is impressive compared to even worse majors, which normies are notorious for studying. /sci/ may shit on CS majors, but they shit on Women's Studies majors even harder.

>>10883656
mammals are also almost exclusively terrestrial and so do not benefit from the camouflaging that bright coloration provides for many species of insects and birds or the signaling across dense foliage

Is there a way to bump questions on stackexchange?

Suppose you need to choose 4 people from 2 groups A and B.
There are 18 people in A and 12 in B.

How many possible group combinations are there if you need to pick at least 1 member from each group.

>>10883666
>Women's Studies majors
bruh thats not even worth talk about

>>10878548
I too wish to know this.

>every action has an equal and opposite reaction
>the universe did start
>the universe will end
Is it true?

I'm aware that "particles moving backwards in time" isn't accurate, but what was the basis for the description in the first place? Is there any support in the current model that some particles are negatively affected by time, given the strange and flexible nature of time?

>>10884247
:) nice meem

Consider the matrix norms [math] \lVert A \rVert _1 = \max_{1 \leq j \leq n} \sum_{i=1}^{n} |a_{ij}| \\
\lVert A \rVert _{\infty} = \max_{1 \leq i \leq n} \sum_{j=1}^{n} |a_{ij}|
[/math]

Does [math] \lVert A \rVert _1 \leq 1 [/math] imply that [math] \lVert A \rVert _{\infty} \leq 1 [/math] and vice versa?

>>10884281
What am I even asking, it obviously doesn't hold.
All rows zero, and the non-zero row has every entry <1 but they add up to something greater than 1.

>>10861885
Maybe try something other than spamming how you can't build muscle in every thread.

>>10884136
Bump

>>10884136
Split it up into cases

I feel like I've fucked up somewhere, is the following equation actually correct?
[eqn]\dfrac{\mathrm{d}f}{\mathrm{d}x} \sum_{i=1}^n\sum_{j=1}^m \left(w_{ij}\:x_i \right) = \sum_{i=1}^n \dfrac{\mathrm{d}f_i}{\mathrm{d}x_i} = n\bullet\vec{w_{i}}[/eqn]

>>10884998
There shouldn't be a scalar, should there? Since it's a derivative of a matrix, surely it's just the derivative of each individual item? Then the answer must simply be [math]\left[\mathbf{w}\right][/math], since they're all just first degree equations?

>>10884769
>Mozat

>>10885094
Sure thing, lad.
The system is entirely determined only if we have n-1 variables.
A variable is only "optional" if it shows up in only one equation, i.e. the collumn is optional if it's only nonzero in one row.
By triangularity, the system is entirely determined if and only if you skip a single optional variable.
The number of ways you can pick n-1 rows and form an entirely determined system is given by the number of ways you can pick out an isolated variable, which coincides, by invertibility, with the dimension of 1's eigenspace.

What is the significance of surface area of an object being a derivative of its volume? A circle's area is 2πR, volume πR^2. A sphere's area is 4πR^2 while volume is 4/3πR^3. Is it a coincidence and is there some underlying universal truth in there that I'm too stupid to recognize?

I've been going through Tao's Analysis books, but there isn't a solution manual or anything for his exercises. It feels kind of pointless to go through the book and problems without being able to check my answers or anything. Any opinions?

>>10885140
It's not a coincidence at all! This is very closely related to something called the Generalized Stokes Theorem (In 1d, it's the fundamental theorem of calculus. In 2d, it's Green's Theorem, in 3D it's Stokes or Divergence Theorem).
What it tells you is that the integral of a function over some (sufficiently nice) surface is equal to the integral of the derivative of the function (in some sense) over the domain contained by the surface.
For instance, in 1d. If we define the integral appropriately, one could call the integral of a function f over just the points a and b to be f(b) - f(a). Why? Well, it makes more sense if you learn some differential geometry. But if we do this, then that "integral" is the same as the integral of the derivative of f over the segment between a and b.
In 2d and 3d, things are very similar but you have to be careful with how you define "integral" and "derivative". You learn this stuff in Multivariable Calc.
Now, let's consider a circle or a sphere. What is the function we should use to find the perimeter or the surface area? First of all, our function will send points to other points (instead of to numbers) because of how Stokes works. This sort of function is just called a vector field. You can think of it like there being an arrow at each point in space, telling the point which direction it goes. Well, we could make our function point perpendicularly outside of the surface/curve if we wanted, all our arrows with length 1. If we take the "flux integral" around the curve/surface now, that is, we sum up how much our vector field points outside of the curve/surface, we'll get the perimeter/surface area.
Cont.

>>10884998
I don't understand what you're trying to achieve, try doing it step by step, it's just usual derivative rules.
>>10885140
You can imagine that a circle is a bunch of small circumferences with small width added up, or a sphere is a bunch of surfaces added up the same way, that's how they're related.
But since adding up in the continuum is an integral, doing the derivative you get the converse.
>>10885192
I don't study math but I believe the consensus is being able to self check your proofs since there's no unique way of proving it, but if you use all the assumptions and definitions, the proof will typically be correct, if you can do it, since modern math is designed to be clean (with the exceptions of constructions that you have to do which can be more creative). So just try to do it anyways, from what I read of it the books holds your hand in the beginning and then you have to prove pretty much everything by yourself. If you get really stuck, which is the problem, you can just check other books that have the same material for inspiration so I don't think it's a problem

>>10885208
based, high energy :^)
>>10885221
low energy, cringe :(

>>10885192
>It feels kind of pointless to go through the book and problems without being able to check my answers or anything
Only total babby tier math have text books with solution manuals. Most graduate books have no solutions, because at this level you should be able to check your argumentation for yourself (it's a skill that you absolutely need to have, so you better practice it now). Even more advanced books usually have no exercises whatsoever, eventually you need to be able to come up with your own exercises to test your understanding. Just do the exercises, and if you feel unsure about something specific, post it here or (preferably) on /r/learnmath.

>>10885208
Now imagine water is flowing along the direction of our vector field. Well, if the water is leaving the curve/surface at speed 1 on all sides, where is it coming from? There has to be a source somewhere in the middle. Really, the "derivative" we're looking for inside of the object is called the "divergence". It tells you how much fluid is being created per time.
All stoke's theorem says, in essence, is that the amount of water leaving the surface can't be any more or less than the amount being created inside (well, at least one variant of the theorem says this).
Now what about the volume? Well, we can imagine the water "expanding" our object by volume dv over a time dt as it leaves (like a balloon). If a volume of dv leaves the original boundary during time dt, then we need to create dv water over the same time dt somewhere inside. So the total divergence inside the object is going to just going to be the same as the rate of increase in the volume of the object. But the total divergence is the integral of the divergence over the object! Just like how the total area under the graph is the integral of all the heights of the points on the graph.
This tells us that, as long as we measure the surface area and the volume "correctly" in a sense (i.e. from the perspective of a point totally inside the surface) then the derivative of the volume is the surface area.
Note that if you don't measure correctly, you don't get this property. Think about the surface area and volume of a cube in terms of SIDE LENGTH, and then think about surface area and volume of a cube in terms of DISTANCE FROM THE CENTER TO THE CENTER OF A FACE (i.e. inscribed radius). Which of these gives you the relationship we want?

>>10885208
>>10885292
As a final note, I want to be clear that you don't really need stoke's theorem at all to understand my intuitive, nonrigorous argument. But you certainly do need it to formalize this argument for arbitrary "surfaces" (n-volume of compact n-manifolds vs (n-1)-volume of their boundary). I think the same thing should work there via stokes, but I haven't worked it out myself.

how to increase brainpower naturally and logical skills naturally?

>>10885208
>>10885221
>>10885292
>>10885303
I'm sorry that you feel the need to belittle me for my brainlet math comprehension, but you just wasted a perfectly good explanation on me and I'm sorry for that too.

>>10885311
I don't get what you mean by this post, my posts were an entirely physical and intuitive description of the phenomenon. As long as you've seen integrals and derivatives before, you should be able to see what's up.
If you haven't done any integrals, well, keep your question in the back of your mind for when they're introduced.

>>10885140
do you know Fubini's theorem ?

how does this work? is this right or is this a misprint? two separate quotes in the same chapter

>>10885388
in the second paragraph they're probably talking about the binary product

>>10885388
Negative multiplied by negative is positive, while negative multiplied by positive is negative. If you multiply 2n negative numbers, you can put parenthesis every two numbers, and you'll get a multiplication of n positive numbers. Ex:
-4 x -5 x -10 x - 6 = (-4 x -5) x (-10 x -6)
Negative times negative is positive, and positive times positive is positive. You'll only have negative with negative times positive.

Long story short, I shall re-learn fundamentals in science. Primarily the informatiom that us useful in the day to day life of an ordinary man.
I am purchasing used biology, physics and chemistry books but would like to know if there are any other books you lot would reccomend I read in order to have a well-rounded scientific knowledge.

Is there any good explaination for the placebo effect?
Are plant seeds alive?

For those familiar with regular expressions in the context of Finite Automata, can you clear up a syntax question for me?

Is 0 + 1 = 1 + 0

and

is (01)* = 0*1*

>>10885396
>>10885405
what im confused about is the fact that exponents are just numbers multiplied by themselves however many times which means the numbers have the same sign. so -8^3 should be (-8)(-8)(-8) right? so if you use the "same sign" rule as in that image it would always come out as a positive no matter how many powers. thats why im confused, the two rules seem contradictory to each other so i dont understand what its actually solving and it feels arbitrary as fuck.

>>10885498
Same sign is for multiplication, even uneven is for exponents.

>>10885505
but exponents are just multiplication which is why im confused. for example, -8 x (-8) x (-8) is going to be 512 right? because they are all the same sign. but then say you decide to simplify the expression by making it -8^3, suddenly the answer is completely different, becoming -512

>>10885523
-8 x -8 x -8 = -512, lad.
(-8 x -8) x - 8 = 64 x - 8 = -512

>>10885490
yeah 0 + 1 is the same as 1 + 0, but no (01)* isn't the same as 0*1*, the first is 0 or more 01's repeated (e.g. 010101), the second is 0's followed by 1's (e.g. 0111)

>>10885529
oh thank you i understand now. the rule in the image is referring to pairs. i feel like this confusion could have been curved if the writer went over multiplying more than 2 numbers before jumping into exponents

>>10885498
>in the second paragraph they're probably talking about the binary product
is there something you don't understand ?

>>10885446
>Is there any good explaination for the placebo effect?
Suggestibility and psychosomaticism. People are gullible and mood has an effect on some hormones.
>Are plant seeds alive?
They can die, so yes

>>10885751
>Suggestibility and psychosomaticism. People are gullible and mood has an effect on some hormones.
That explains nothing. How can a dose of nothing increase the rate with which the bacteria are getting killed?

>>10885794
>How can a dose of nothing increase the rate with which the bacteria are getting killed?
Either A) it doesn't, or B) happiness truly is the best medicine. So either, happiness boosts the immune system (which is demonstrably true), or you got cheated/lied to (which can also be true)

>>10885801
That still explains nothing, it just acknowledges the existance without giving any serious explanaition.

>>10885810
Good luck with that. Stress produces cortisol, food imagery produces gastric hormones, fear produces adrenaline etc. etc. Sounds like you want a full course on endocrinology.

>>10885829
That would maybe explain something.

>>10885829
>stress produces cortisol
not always
>food imagery produces gastric hormones
not always
>fear produces adrenaline
incoherent, and inconsistent response. None of these things are linear or standardized across phenos

What's the average life expectancy of a modern human who receives zero medical attention or care from birth?

>>10885872
literally no medical attention? so not even food or drink, shelter, protection from the elements?
zero

>>10883291
Thanks a lot, the whole choosing 1/(1+x) vs. 1/x really cleared things up for me.

>>10860247
Explain nonbinary identity to me like I'm 5. I'm having issues understanding it.
As far as I'm aware, no one 'feels' exclusively male or exclusively female, in that their preferred personal expression that society deems gendered expression is only from masculinity or femininity.
I dress in mostly what my local area deems male clothes since I like it, but I do stereotypically feminine hobbies like sewing and cooking since I enjoy those. I'll wear oxfords with a heel on them if I want a bit more height and to show off my arse since I want to.
To me, stating yourself as nonbinary implies that the norm is to either be 100% masculine or 100% feminine in gendered forms of expression, which I really doubt is true.
Or am I missing something here? Help me understand.

>>10886989
> which I really doubt is true.
I guess they want to say it's true and I kind of agree to an extent. For example, I like to dance and kind of don't tell other people because i don't want to be made fun of.
I also can't make any sort of intimate connection since I was taught to "be a man, never show emotions" and stuff that really damages i think. I don't know, I think it's stupid to label things as "male" or "female".

>>10885892
>mooooom I'm hungry
Don't worry honey, the doctor will be here soon

>>10887002
I guess it's related to how I was brought up, which I agreed with even after adolescent adjustment and such.
I was brought up to not care what people think, in that not to let it stop me doing what I want. I was also never exposed to those ideas like 'men do not show emotions' or the like. That only came from external sources far later than early childhood or the like.
If you go by what local society says (which is also different to the society of my family, I'm the 1st/2nd generation born here and they assimilated more with certain elements of Thai and Chinese culture more than the local Anglo culture, as they often worked in those areas) then my mother is by far the most masculine member of my family, while my father and cousin are the most feminine.
But yeah, while I'm aware of things being labeled as gendered, it is also a foreign concept to me in a way. Basically: All this shit doesn't make sense to me. So trying to understand how nonbinary differs from what I see as 'normal' is full of issues for me.

>>10886989
I'm pretty sure it's one of those things the mentally sane can never really grasp.

How the fuck do you either
>Wake up early
>Win over your brain desire to stay in bed
I am having trouble coming up with reasons other than I can be productive more time, which is not good enough for my brain. My train of thought usually goes
>"Why do I have to wake up?"
>>"To write for 8 hours instead of 6"
Then I don't give a shit and go back to bed

Help me bros

I was thinking of having a cup of coffee over my alarm clock to drink it whenever I am about to put off the alarm but I fear of spilling it over important notes or something like that

>>10887342
Just sleep and wake up at regular times.

>>10887348
>just solve your problem bro

>>10886989
I think it's a bit deeper than expression. Like, I get you. I'm really into gardening and flowers and shit. But I'm also 100% sure that I'm a man who just happens to be into gardening.
A lot of times for people who identify as nonbinary, their whole self-perception, identity (think about what that word actually means beyond use as a buzzword) and form of expression is not aligned closely to either a masculine or a feminine profile. It's less about hobbies/interests and more about a way of life and a mindset.
My personal mindset is "who gives a shit, I'll do what I want with my time and it's not going to make me feel as though I am a woman." There are people who are less rigid than that though, and oftentimes nonbinary is a term which describes this.
I also think it's likely that the introduction of the term nonbinary is not so much to capture a new idea but to change terminology around how we group people, since like you've said almost no one is PERFECTLY masculine or feminine.

>>10887342
>>10887361
I set two alarms, one for my "ehhh dont need to wake up" moment and then the second one is easier to stomach.
However, you should do your best to go to sleep at a time such that you naturally wale up right before your alarm goes off.
>But I don't have time in my day!
Yes, you do. Find it. You will thank yourself because once you start sleeping naturally you'll end up more productive and won't need the extra time.

>>10887373
>you naturally wale up right before your alarm goes off

hate when that happens

>>10863121
BuT Sinx/x GoEs To 1 cAn be ProVed By L’HoSpItAL AnD thAtS fOr bRaiNleTs

>>10887471
You can also use power series for that.

>>10887373
This is all the more relevant for me as the Fall semester looms ever closer.
Goodbye free time.