/sci/ - Science & Math

The tally is weird this time and probably missing some stuff. I don't know why this happens sometimes.

Unanswered questions:

Chemistry:
>>11919496
>>11927420
>>11929378
>>11932317
>>11935927 (Tooker answered this one with a question. It might have been an implied answer, but I wouldn't know.)

Biology questions:
>>11926047
>>11929446

Physics questions:
>>11922072
>>11927217
>>11931435
>>11934745 followed up by >>11934756 and >>11934788

Math questions:
>>11924897
>>11925259 [He probably forgot to attach an image, made another post with the image attached, solved it on his own and then deleted it. That or he forgot to post the image entirely.]
>>11936076
>>11937233

Lunar geology questions:
>>11924184

/diy/ questions:
>>11935084

Stupid questions:
>>11921917
>>11923517
>>11924807
>>11924931 [What? What? What?]

Any symbolic logic books with introduction to semiotics (and its application to logic)?

>>11937617
Why was Einstein so racist?

Why does science need philosophy?
Is there science without philosophy?

>>11937617
Can someone help with this? The problem might seem easy but when I tried to put the answers not a single one worked.

>>11938550
I have no idea what the fuck is x supposed to be.
The main candidates are:
>north or south fence length
>west or east fence length
>total fence perimeter
Where we assume that things are determined such that all the money is spent on the fence.
I'd recommend either emailing whoever gave you the problem or exhausting the possibilities. In particular, I'd exhaust them in the north -> perimeter -> west order.

>>11938573
I check the answers:
1)-4
2)100
3)0
4)625
5)12.5
6)50
Maybe I am too retarded to solve this or maybe they don't give enough information.

>>11938585
[math]\text{Area}=lw[/math]
We have the constraint [math]10l+40w =1000[/math]
So either
[math]\text{Area} = l(1000/40-10l/40)[/math] or
[math]\text{Area} = w(1000/10 - 40w/10)[/math]. Based on the answers, its the second one. But I do agree with the above that the question didn't say what [math]x[/math] is, so the question is unclear.

>>11938573
>I'd recommend either emailing whoever gave you the problem or exhausting the possibilities
The professor doesn't give a crap. He doesn't answer any email and he literally mark me wrong because I wrote (x-4)(x-2) instead of (x-2)(x-4). Also, he put repeated problems in different units. There was an exact copy of a problem in unit 1 in unit 5. With the exact wording and numbers

>>11938595
well it seems that the function should be
-4x2+100 based on the answers 1) 2) and 3)

>>11938604
No, the function is
[math]f(x) = 100x - 4x^2.[/math]

>>11938604
My mistake
[math]4x^2+100x[math]

>>11938604
My mistake
[math]4x^2+100x[/math]

>>11938604
[math]-4x^2+100x[/math]
>>11938609
You are right

>>11938550
Who writes a question like that?
Here's my attempt:

Circumference function
2*$5*a + 2*$20*b = 1000$
a+4b = 100
a=100-4b

Area
a*b=b*(100-4b) = -4b^2+100b

From this, I guess:
1=-4
2=100
3=0

Max -> (derivate) -8b + 100 = 0
b=25/2
-> 6=25/2
-> a+4*(25/2) = 100
-> a=50
-> 5=50
a*b = 625
-> 4=625

circumference:
2a + 2b = 125

What happens, at the atomic level, when You have an unbalanced load in a power system. Take for example a three phase system like in a commercial building. Assume the neutral was disconnected, what happens now whenever you have something within the system causing a spike? What causes the heat buildup?

>>11938550
I checked with my uncle and he solved 4,5,6
To find the length pretty much what he did is following.
[math]2(5x)+2(20y)=1000[/math]
[math]10x+40y=1000[/math]
[math]10x+40(1x/4)=1000[/math]
[math]10x+10x=1000[/math]
[math]x=50[/math]
Since x=50 we can find y
[math]10(50)+40y=1000[/math]
[math]500+40y=1000[/math]
[math]y=12.5[/math]
However he couldn't figure out how to get the equation that is
[math]-4x^2+100x[/math]

>>11938661
see 2 posts above

>>11938154
It doesn’t, why would you assume it does. Certain aspects of it deal with common philosophical questions I.e. empiricism being a part of epistemology, but within the field of science itself empiricism is just axiomatically true. To steal a phrase, philosophy of science is as useful to scientists as ornithology is to birds. The problem of induction has zero ultimate effect on science.

>>11938637
>>11938661
Thanks anons.

>>11938688
It's a horrible question though.
Rewrite a*b in terms of a instead, and you have -1/4 for 1 and 25 for 2.

>>11938726
well at least I don't feel that retarded now considering this question is quite bad.

Protons of kinetic energy 10^12 eV are injected into a uniform magnetic field of strength 10 Tesla. The magnetic field exists only inside a cylindrical region of diameter 50cm and is parallel to the axis of the cylinder. At the point of injection, the proton beam is directed towards the axis of the cylinder and is perpendicular to it. By the time the beam exits the magnetic field, it changes its direction by how many radians?

>>11939380
Forgot to mention that the question says to assume the ultrarelativistic case v = c.

>>11938672
You don't need philosophy to do your work in sciencd, but you need philosophy if you want to give meaning to your work that is not subjective.

The reverse algebra is the one with inverted multiplication, right?
Context: Clifford Algebras.

>>11939429
Think this question might be too ambitious for /sci/.
Not sure how to go about with EM & relativity, I know shit goes a bit crazy.

If this is the addendum:
>>11939429
Then assumption is that relativity clearly doesn't have an effect. With v=c, any particle with mass (like proton) would have infinite kinetic energy.

So going with fully classical assumptions then, using your kinetic energy and field strength, you should be able to get something out.
You'd then have to construct the function of what gets affected and how over time.
Particle will rotate around the axis like pic related, to keep perpendicular to the field. Except, as it starts heading towards the axis, it will just shoot out at some point.
There will be only 2d movement.
Get magnitude of force on particle by magnetic field out, which will always be perpendicular to particle's movement and field's orientation, get your acceleration from there. Use this acceleration to get the radius of the circular path proton makes, and what you can do there is just draw two circles, your 50cm cylindrical region and the new circular path that the particle makes and call it done, or get your angle from there from radiuses of two circles (2 sides same size x2) and one angle at 90deg.
Is that good enough for a start?
Also, what is this entrance exam for?

>>11938154
In order to do science, you need to assume explicitly or implicitly certain philosophical questions, otherwise you would be stuck by extremely hard problems and would never advance and make discoveries.

>>11938154
In order to do science, you need to assume explicitly or implicitly certain philosophical questions, otherwise you would be stuck by extremely hard problems and would never advance and make discoveries and definitions or even you would be unable to state basic axioms.

>>11940045
No that's the inverse algebra

>>11940106
>Use this acceleration to get the radius of the circular path proton makes, and what you can do there is just draw two circles, your 50cm cylindrical region and the new circular path that the particle makes and call it done, or get your angle from there from radiuses of two circles (2 sides same size x2) and one angle at 90deg.
Im not sure what you meant by this. I was thinking more about the angular change in the particles direction with respect to its initial direction as it comes out from the field. Also this question is from a master's entrance exam.

>>11939823
Not really. Several different interpretations of quantum mechanics are ultimately reducible to same mathematical equations. It doesn’t really matter what we philosophically mean for two systems to be entangled if no matter what we decide on, the mathematical representation is a bipartite state who’s partial transposition has a negative eigenvalue. In fact, the interpretations will be scientifically indistinguishable from each other. The usefulness of science still remains unchanged. That is, its ability to make accurate predictions. To make a less esoteric example, take medicine. I’m assuming the meaning of the word “life” is a contentious issue in philosophy because, well, everything is yet biological theories still led to the creation of vaccines and other medicines. There’s certainly philosophical problems with the usage of the world since it’s emergent and not even a relevant concept at the atomic level, yet I’d assume you wouldn’t deny the great progress that’s been made in even the last 150 years. Science doesn’t care and simply goes on regardless of what philosophers quibble about.
>>11940265
Only if you define philosophy in the broadest terms which I’m fairly sure would miss the point of what the original question meant to ask. Does science need to make determinations on truth values based on axiomatic principles from a specific subset of epistemology? Yes. Does it care whatsoever what coherentism has to say about wave-particle duality? Not even a little.

>>11938650
Bump.
Fuck, why does /sci/ hate power systems so much

Testing something, one second.
[math]a\pi[/math]

I want to calculate the angle between two 2 dimensional vectors, right now I do
u = v1 - v0;
angle = acos(u);
if (asin(u) < 0) angle *= -1;

but for some reason this doesn't work. Or I think it doesn't work, my overall solution to a thing I'm working on isn't anyway. Is the calculations themselves correct? Should I look elsewhere to why?

I'm taking a course in classical mechanics next semester. The course uses Goldstein. I haven't had many physics courses other than the intro ones and a stat mech course. I'm a mathfag btw so I've taken lin alg, algebra, complex analysis, analysis 1,2, etc. Would I be ready for this course? Is there anything I can do to prepare for it?

>>11940481
the angle between two vectors is just their dot product divided by the product of their norms then taking the arccos of that scalar.

>>11940495
Oh, yes, you're right I'm sorry I'm using this already. Looking now i see I have more inaccuracies (I'm getting tired..). Real question is:

I'm trying to find the the direction/angle of a vector of which i know it's x and y coordinates. I have 2 points, (px0, py0) and (px1, py1) and I want to know what trajectory the vector u = (p1-p0) has, meaning the trajectory the vector created between p0 and p1.

Right now I normalize u, then I do arccos(u_norm), lastly i do *-1 if arcsin(u_norm) is negative (since the angle then is > PI).

Dropping this here so I remember to put it in the OP later.
https://imgur.com/a/skskV0U

>>11940493
you'll be fine, at least in the math. from what I've heard Goldstein is a terrible book at explaining stuff, though.
maybe skim through topics in the book and if the physics concepts are tripping you up, review from Taylor which is slightly lower level but also much more didactic.

>>11940481
1. Given 2 vectors, the angle between them has no sign.
2. The angle can be found via acos(v1·v2)/(||v1||.||v2||) where · indicates the dot product.
3. That formula is numerically unstable if the angle is small. In that case, it's better to use asin(||v1×v2||/(||v1||.||v2||)) where × indicates the cross product.

>>11939380
if you're still here I'll write something out. not going to put in any effort if you're gone
>>11940106
is entirely wrong. you're in the ultrarelativistic case, you absolutely cannot "assume classical physics"

>>11940403
You don't need to stop in philosophy before goint into science. What this post >>11940265 says is that you would never end if you choose to deal with the philosophical questions so you can simply avoid them and just go into science. You may not agree, but avoiding those questions is equivalent to assume you have them solved wether or not you care about the solution, because this philosophical answer will not change the scientific result.

Testing something real quick.
[math]\frac{2\pi}{2}[/math]
[math]\sin\frac{2\pi}{2}[/math]
[math]\sin(\frac{2\pi}{2})[/math].

One more test.
[math]\sin x=\sin x[/math]
[math]\frac{1}{1}=\frac{1}{1}[/math]
[math]0=\sin(\frac{1\pi}{1})[/math]

>>11940975
HMMMMMMMM.
[math]0=\sin0[/math]

>>11940977
Other one now.
[math]0=\sin(\frac{1\pi}{1})[/math]

>>11940573
Extremely relevant update.
https://imgur.com/a/FliqvF4

>>11940554
If I'm understanding this correctly, you're looking for the argument of u, so you can just do [math] \arctan \left( \frac{y_1-y_0}{x_1-x_0} \right) [/math].

>>11941062
>when you forget to test the obvious
https://imgur.com/a/LpgxGsz

crank this one out sci

>>11940638
Im still here my guy. Id appreciate a crumb of knowledge.

>>11932387
Hello, I'm an engy too. I think murricans take Calculus and such in HS, where they just learn methods and algorithms and stuff.
My math courses for engineering also went into a lot of proofs, but the problems weren't about proving stuff, for the most part, and we probably skimmed over some important results from a math major perspective.
This did lead to some funny stuff, like how an "Intro to Math" course that dealt with some geometry from a LA standpoint recommended Hoffman and Kunze as a course book.
>>11932423
>To improve critical thinking and problem solving.
I'm not quite sure that's how it works but hey. I did them because I found them neat, and to slack off on other work.

Currently 24, and will turn 25 later this year.
My question is: Do you think it's too late for me to learn any of this science and math stuff to actually pursue any of it as a fundamental career later in life? I 'graduated' with a GED at the age of 17, and have essentially sat on my thumbs doing nothing the entire time. Is it too late for me to go to college and strive to become something or someone that has the potential of working at NASA someday (perhaps something related to an Astronomer/Astrophysicist)? The biggest problem/fear that has plagued me is that I haven't 'figured out' what exactly I want to do with my life, but I've always found myself fascinated with space, and I've considered just going off of that. Are there any books you might recommend me reading or looking into that might set me in the right direction?

Hey fellas, I heard about a Joe Rogan podcast with Kelly Slater. Apparently he went on a water fast and shat out something that he thought was his colon after about 5 days. It was this huge black, serpentine mass, in the shape of a colon. I assume it’s some kind of lining that builds up from the trash we ingest. Can anyone shoot this down, or explain it from what I’ve provided? I can’t look into it right now, but it’s freaking me out.

>>11942015
I’m not very knowledgeable in this stuff, but a job at NASA would require some degrees. I would suggest finding an affordable 4-year university and getting a bachelors in something related. You don’t seem dumb, so a well-written essay and some favorable recommendations should get you into an alright school. That will give you time to think about it, and it will benefit you, regardless of what you choose to do. I knew a 32 year-old in undergrad, and guess what? He was just like anyone else, and perhaps at an advantage due to his maturity. There’s a bit of a decline after 20, but lifestyle and motivation outweighs that, by far. It’s not too late.
Try hard, have some fun, and you’ll leave with a useful title. If you do well, grad school is a step away. A graduate degree doesn’t guarantee a dream job, but it’s a real advantage.

I don't get it. Why are +1 and -1 at the sides?
In order to unify the real projective line with the surreals, where [math]\pm \omega[/math] replaces [math]\pm\infty[/math] at the top, shouldn't [math]+ \sqrt{\omega}[/math] and [math]-\sqrt{\omega}[/math] be at the sides?

>>11942015
shut the fuck up

>>11942015
go for it. you're definitely not the first person to do this. not sure if you use twitter but i know https://twitter.com/InertialObservr/ was in a situation pretty similar to yours, so it's probably worth asking him for help

what are one-forms and what is pullback?

>>11942090
but then using vertical parity of x, 1/x then 1/omega = 0
and sqrt(omega)=1/sqrt(omega)
sorry not massively familiar with surreals if these statements are ok

>>11942015
>Do you think it's too late for me to learn any of this science and math stuff to actually pursue any of it as a fundamental career later in life?
No, I don't think that.
>I 'graduated' with a GED at the age of 17, and have essentially sat on my thumbs doing nothing the entire time.
Same here, pretty much.
>Is it too late for me to go to college and strive to become something or someone that has the potential of working at NASA someday
That depends on a variety of factors. It's pretty unlikely, as these types of big name organizations can afford to really only look for the cream of the crop. Is that you? Be honest and adjust your expectations accordingly. If you happen to be a borderline genius, then you've probably got a shot even without any credentials at all. If you're just an average student at best, I think it's highly unlikely that you'd get hired by any well known company. Doesn't mean you couldn't get a job in your field. I'm not trying to dash your hopes or anything, just don't get your hopes too high about it.
>(perhaps something related to an Astronomer/Astrophysicist)?
I could see you getting a job in your field with effort, yes.
>The biggest problem/fear that has plagued me is that I haven't 'figured out' what exactly I want to do with my life, but I've always found myself fascinated with space, and I've considered just going off of that.
I don't see a problem with that.
>Are there any books you might recommend me reading or looking into that might set me in the right direction?
The only relevant things I could recommend are the Great Courses lecture series on Astronomy and Cosmology. I've never watched them personally, but I have watched many other series from them on Mathematics and they've helped me a lot.

https://www.thegreatcourses.com/courses/understanding-the-universe-an-introduction-to-astronomy-2nd-edition.html

https://www.thegreatcourses.com/courses/cosmology-the-history-and-nature-of-our-universe.html

>>11937617
Does anybody know of a software/program that will allow me to draw a shape and it will calculate the center of mass, it would mostly be composite shapes like triangle, rectangle, circle...

>>11942699
Solidworks

>>11942449
>what are one-forms
sections of the cotangent bundle
>what is pullback?
precomposition with the tangent map

>>11942449
A cotangent vector is a linear functional defined on [math]T_pM[/math]. A smooth section of the cotangent bundle, that is, a function that smoothly associates to each [math]p \in M[/math] a cotangent vector in [math]T_pM[/math] is a one-form.
In particular, when you have a function [math]f: M \rightarrow \mathbb{R}[/math], you can define a one-form [math]df[/math] through the evaluation map [math]df(X) = X(f)[/math].
In the case of the real line, de Rham cohomology vanishes (don't particularly concern yourself with this right now), so every one-form [math]\omega[/math] can be written as [math]\omega = df[/math] for a smooth function [math]f[/math] defined up to a constant, and you can then define integration of one-forms on the real line by [math]\int _a ^b \omega = f(b)-f(a)[/math] (that is, the fundamental theorem of calculus) (this isn't the usual definition, this is for intuition).
Consider the circle [math]S^1 = \mathbb{R} / \mathbb{Z}[/math] and the projection map [math]p : \mathbb{R} \rightarrow S^1[/math]. Not every one-form in [math]S^1[/math] can be written as the differential of a function (consider that every function on the circle has two critical points but there are everywhere non-zero one-forms, i.e. the one that just returns the coefficient of [math]\frac{\partial}{\partial x}[/math]). The pull-back of a differential form is defined by the adjoint of the tangent map, so [math]\langle d^* \omega , X \rangle = \langle \omega, dX \rangle[/math]. This lets us, for example, pull-back a differential form defined on [math]S^1[/math] to [math]\mathbb{R}[/math] and integrate it there with the fundamental theorem of calculus.

>>11942788
* [math]\langle dp^* ~ \omega, X \rangle = \langle \omega , dp ~ X \rangle[/math]

what is a manifold and what is a sheaf? explain without tex but explain rigorously for someone who only knows calculus

>>11941087
It was! Thanks a bunch! Pic included, another step on the way

>>11942834
>what is a manifold and what is a sheaf? explain without tex but explain rigorously for someone who only knows calculus
they're both something too complicated to explain to you, any other questions?

Hey guys my dad is a beekeeper and we found some information that lithium compounds work well against varrora destructor (a pest).
I've been trying to find some resources about plants that contain such lithium compounds, but I can't.

Do plants just not use lithium at all, or are there some species that use it?

>>11942834
A smooth manifold is a subset [math]M[/math] of [math]\mathbb{R}^n[/math] such that, for any [math]p \in M[/math] there is some [math]r_p> 0[/math] and [math]m < n[/math] smooth functions [math]f_1, \cdots , f_m[/math] such that [math]M \cap B(p, r_p) = N(f_1) \cap N(f_2) \cap \cdots \cap N(f_m)[/math] and, for every [math]p' \in B(p, r_p)[/math], the vectors [math]\nabla f_1 (p'), \cdots, \nabla f_m (p')[/math] span an [math]m[/math]-dimensional subspace of [math]\mathbb{R}^n[/math].
This is the brainletest definition I know of.
Tl;dr it's space that locally looks like euclidean space.
I'm not even gonna make an attempt with sheaves.

>>11937617
Why are the "Good charts" and "Shitty charts" imgur links in the wrong order? It should be reversed.

Tell me if I'm wrong and if I am, how I'm wrong. So, the (y) differential, (dy), in single variable calculus, can be interpreted visually/geometrically as the vertical distance (y-axis) between an arbitrary point on some curve, and a point on the line tangential to that curve at the initial point an arbitrary distance away in the horizontal direction (dx). The distance, (dy), is nearby the actual value of the curve when evaluated at the same argument and can thus be used to approximate the value of the curve at a given argument.

By similar logic, the (z) differential, (dz), in a function of two variables, can be interpreted as the vertical (z-axis) distance between a point on the solutions surface generated by the multivariable function and a point on the plane tangential to the surface at the initial point an arbitrary distance away in the (x) and (y) directions (delta x and delta y). Thus, (dz) can be used to approximate the value of the surface for a given (x,y) argument.

Is that right or wrong? I realize that trying to interpret multivariable functions in a visual way ceases being feasible once you have 3 or more variable arguments, but I'd still like to know if I'm in the ball park. Something I still don't fully understand though is that, according to Wikipedia, the differentials are supposed to be interpreted as infinitely small. Obviously, the margin of error between (dy) and (delta y) gets smaller as the change in x gets smaller, and the limit of this process yields the derivative, but I thought the whole point of such "linear approximation" was to approximate values that you couldn't normally calculate due to division by zero or something. I don't know.

>>11942735
That is not free

>>11943046

>>11942979
>A smooth manifold is a subset MM of Rn
stopped reading right here, very brainlet definition indeed

>Undergraduate GPA: Minimal pass
>Master's GPA: 3.7

Do I stand a chance at a PhD or will my shitty past pull me down. Just give it to me straight /sci/

>>11943081
shut the fuck up

>>11943081
PhD in what field?

>>11943190
geophysics

>>11943269
That's not my field, but what I'll mention when I was researching into grad programs for my field(pure math, USA) is that GPA acts as a filter. There are so many applications, that programs filter out people by GPA and GRE scores, just to reduce quantity. Now after that, they would look at your application and see what you would bring. So the question becomes whether or not the program will care about your undergrad GPA since you have a Master's. That will probably depend on the program, so I can't answer definitively. Maybe also depends on the country too.

why is every arithmetic operation sleek and efficient except the absolute retarded euclidean division
>muh remainder muh modulo
what the fuck

How the fuck am i supposed to solve this integral? It's wizard tier. Probably the teacher that wrote this stole the answer from somebody else

I'm a poor college student. Are there any longterm risks to selling plasma?

>>11943374
He's using basic vector geometry and the definition of the volume of a sphere, Gauss's law and Calc 3 to solve the surface integral your fucking retard.

>>11943751
>Surface integral
>sphere
>dV
>calls ME a retard

>>11943374
Off hand, I'd say that that is the wrong choice of angles to use. I would think it would be better to base your spherical coordinates with the y-axis as the pole, rather than the z-axis. That should represent the symmetry of the problem better. But I'm not going to do the problem for you.

>>11943839
I conjecture that that's where Gauss's law comes in.

How applicable are rat studies to humans?

I have the following exercise:

Consider functions [math]f : \mathbb{R} \ to \mathbb{R}[/math] with [math]f(x) = 1[/math] [math] \forall x \in \mathbb{R}[/math] and [math]g : [0,2\pi] \to \mathbb{R}[/math] with [math]g(x) = sin(x) \forall x \in [0,2\pi][/math]

find the preimage set of set [math]\mathbb{Z}[/math] for [math]f[/math] and the preimage set of the set [math]\mathbb{R}^+[/math] for [math]g[/math]

what exactly do i have to do here? i don't understand

>>11943986
do you know what a preimage is ?

>>11942788
will use this post to go through definitions carefully, ty anon

>>11944005
The subset of the domain in which the function is defined, i know what it asks for but i don't know how to solve it

>>11944005
is it [math](-\infty, +\infty)[/math] ?

>>11943883
probably not. i already tried it, and otherwise he would have done that

Who would win? ADHD or PhD?

What the fuck is [math]f(x) = min{-4,x}[/math] supposed to be?

What the fuck is [math]f(x) = min { -4,x }[/math] supposed to be?

>>11944387
the minimum of -4 and x

>>11944399
so if [math]x = -6[/math] then [math]f(x) = -6[/math] ?

>>11937617
In a module M over a ring R, is it possible to have nonzero elements r of R and m of M such that rm is zero? If yes, then what are the minimal conditions for the answer to be negative? Existence of identity? R being an integral domain? Commutativity?

>>11944445
yes
>>11944472
you could take the trivial scalar mutliplication on any ring couldnt you

>>11944472
Yeah, as anon pointed out.
The ring being an integral domain is obviously necessary, but also not sufficient, as anon pointed out (again) (for a less shitty example, [math]\mathbb{Z}_2[/math] is a module over the integers.)(inb4 something something p-adic integers no one gives a shit.)
Other than that, the condition is the same as the module being torsion-free.

>>11943839
fucking brainlet

How much worse is a math physics degree w/ a good github than a math/cs degree w/ a good github?

Can an economy work without money lending at compound interest? What about without interest at all?

>>11944663
be careful not to commit suicide man

>>11944600
Your employer will probably care about your github more than going physics over cs.

>>11944663
>What about without interest at all?
Japan has worked for a while with negative real interest rate, does that count?
In case you don't know (unlikely but possible), real interest is nominal interest (normal interest) adjusted for inflation.

>>11944674
I'd like to believe this meme but have a hard time

>>11942015
I'm in similar shoes at age 26 though. Worked a good job for the past 4 years and made too good of money to care about college. It was braindead and unfulfilling though, so I want to do something more fulfilling. Idk what you have done in your spare time, but it's going to be very hard to get the gears rolling inside your head to do school work again if you haven't done it for a long time. I burnt out in the middle of re-learning geometry and algebra 2. Very boring, lots of tedious rules to remember, don't want to practice it at all. I guess if you really have a passion it won't be as bad though. But you have to REALLY enjoy it like how I enjoy laying in bed and reading manga for 12 hours these days. Could only imagine bow far I'd be if I enjoyed something productive. That's my blog, hope it helps somewhat. I think you can do it if you got the autistic passion, can't be secondary to anything else.

>>11937617
Please don't post my second waifu as the OP to your threads. Thank you.

You have a stream of random bits (00101101001010 etc). For a moving window of size N, what is the probability after k window positions that all possible permutations of N bits have been seen in the window. For instance, if you had N = 2, the window needs to see 00,01,10, and 11.

What's going on here?

Making the obviously wrong assumption that the elements in the matrix are scalar, If I take the derminant of the matrix in (19) and assume the determinant is positive then I get [math] \alpha < G_1 [/math] and assume it is positive I get [math] \frac{ -F_v M(q)}[M^2(q)} [\math] which very similar to (21) and I'm about lost there.

What's going on here?

Making the obviously wrong assumption that the elements in the matrix are scalar, If I take the derminant of the matrix in (19) and assume the determinant is positive then I get [math] \frac{ -F_v M(q)}[M^2(q)} [/math] which is very similar to (21) except positive signs are max eigs and negatives are min eigs and I'm lost from there.

What's going on here? I would appreciate some pointers so I can understand why are minimum and maximum eigs showing up here.

>>11944728
2^N, right? for every bit, you have a binary choice of 0 or 1, so 2^N

>>11944728
oh sorry, I didn't read the full question, but the possible number of bit strings of length N is 2^N, ofc. but how is the window moving? incrementing left or right, or is it refreshing and displaying a new screen for each k?

>>11944834
moving over 1 bit at a time, so if the input was 011100, you would see 01, 11, 11, 10, 00

>>11944728
See http://oeis.org/A242206 and the crossrefs. I don't think there's a generalised formula for <N,k>.

>>11944691
>second waifu
Opinion discarded.
>>11944788
This is gonna be a two-parter, unfortunately. Blame the dots and the tildes.
First of all, we'll assume the following and presume that you forgot to mention it:
[math]F[/math] and [math]M[/math] are positive-definite and symmetric. Reasoning given here for positive-definiteness: https://en.wikipedia.org/wiki/Definite_symmetric_matrix#Block_matrices
I'll also assume that [math]\alpha > 0[/math].
Finally, I'll normalize [math]|| \tilde{q} || = || \dot{q} || = 1[/math].
We start by expanding the expression out to get [math]G_1 ( \tilde{q} , \dot{q} ) = \frac{1}{2} [ \alpha \langle \tilde{q} , F_v \tilde{q} \rangle + \langle \dot{q} , M(q) \dot{q} \rangle - \alpha \langle \tilde{q} , M(q) \dot{q} \rangle - \alpha \langle \dot{q} , M(q) \tilde{q} \rangle ][/math].
Note that [math]\langle M(q)( \tilde{q} - \dot{q} ) , \tilde{q} - \dot{q} \rangle = \langle M(q)( \tilde{q}) , \tilde{q} \rangle + \langle M(q)( \dot{q} ) , \dot{q} \rangle - \langle M(q)( \tilde{q} ) , \dot{q} \rangle - \langle M(q)(\dot{q} ) , \tilde{q} \rangle \geq 0[/math], so we get the bound [math]- \langle M(q)( \tilde{q} ) , \dot{q} \rangle - \langle M(q)(\dot{q} ) , \tilde{q} \rangle \geq - \langle M(q)( \tilde{q}) , \tilde{q} \rangle - \langle M(q)( \dot{q} ) , \dot{q} \rangle[/math].
Swap this into the old one for [math]\frac{1}{2} [ \alpha \langle \tilde{q} , F_v \tilde{q} \rangle + \langle \dot{q} , M(q) \dot{q} \rangle - \alpha \langle \tilde{q} , M(q) \dot{q} \rangle - \alpha \langle \dot{q} , M(q) \tilde{q} \rangle \geq \frac{1}{2} [ \alpha \langle \tilde{q} , F_v \tilde{q} \rangle + \langle \dot{q} , M(q) \dot{q} \rangle + \alpha (- \langle M(q)( \tilde{q}) , \tilde{q} \rangle - \langle M(q)( \dot{q} ) , \dot{q} \rangle)][/math].
We now use this: https://math.stackexchange.com/questions/1705386/showing-that-x-topax-is-maximized-at-max-lambdaa-for-symmetric-a

>>11946158
To get [math]\frac{1}{2} [ \alpha \langle \tilde{q} , F_v \tilde{q} \rangle + \langle \dot{q} , M(q) \dot{q} \rangle + \alpha ( - \langle M(q)( \tilde{q}) , \tilde{q} \rangle - \langle M(q)( \dot{q} ) , \dot{q} \rangle)] \geq \frac{1}{2} [ \alpha \lambda _{min} F_v + \lambda_{min} M(q) - 2 \alpha \lambda_{max} M(q) ] = \frac{1}{2} [ \lambda_{min} M(q) + \alpha [ \lambda _{min} F_v - 2 \lambda_{max} M(q)]] [/math]. If the term the alpha is multiplying is larger than zero, we're done. Otherwise, we use the inequality on the alpha to get that the previous equation is strictly(emphasis here) greater than [math]\frac{1}{2} \lambda_{min} M(q) +\frac{ \lambda_{min} F_v^2 \lambda_{min}M(q) }{\lambda_{max}M(q)^2} - 2 \frac{\lambda_{min} F_v \lambda_{min}M(q)}{\lambda_{max}M(q)}[/math]. Introduce [math]x = \frac{\lambda_{min}F_v}{\lambda_{max}M(q)}[/math] and isolate to get [math]\lambda_{min}M(q) [ x^2 -2x -1] \geq 0[/math], and done.
Overall disgusting proof, shouldn't have attempted to solve it, shouldn't have insisted on it, I wanna take a nap.
BTW, I really, really hope that the matrices are symmetric, because I have no fucking idea what you're supposed to do otherwise.

>>11946164
*[math]\lambda_{min}M(q) [ x^2 -2x
+1] \geq 0[/math] on the last line.

I remember my high school physics text book had a section where the student was supposed to naturally derive formulas from special relativity.
It was about some kind of analogy about swimmers in a river, where the speed of the river was somehow like the speed of light.
I have special relativity at uni now but I don't have the book anymore.
Does this sort of derivation sound familiar to anyone, does it have a name?

>>11946167
Thanks kindly partner, I got it.

>>11946164
And yes the matrices are symmetric positive definite

how are molecules directed on a cellular level? or are they not?

viruses bind to particular regions on a cell membrane, but do they just randomly float around until by chance they interact with membrane proteins?

or inside a cell, does tRNA just float around the cytoplasm until it happens to bind to an active ribosome?

maybe I'm misunderstanding the scale. is there an actual "attractive force" between ligand and receptor (analagous to a magnet sucking in metal)?

>>11942834
A smooth manifold is a space that when zoomed in on enough looks flat (or euclidean), but may have curvature when you zoom out more. A circle is a smooth manifold, when you zoom in enough it looks flat but globally it is not the same as the real line, the euclidean space of the same dimension.
A sheaf is a way to assign data to points on a manifold such that the data is as smooth as the manifold: when you move to a sufficiently nearby point, the data should only change slightly. This is a general concept which can be used to define many complex things like functions or operators over manifolds which have desired properties.

>>11946158
Yes, second. You didn't post my first waifu so I can forgive your transgressions this time

>>11947076
>do they just randomly float around until by chance they interact with membrane proteins?
yeah
>is there an actual "attractive force" between ligand and receptor (analagous to a magnet sucking in metal)?
not at the scale you're thinking. only w/i a couple angstroms

>>11938650
Nobody? Seems like such a basic question

>>11945371
thanks.

>>11947218
I'm gonna do it.

i need to calculate variance,

pic related is the solution we were given, i just dont understand wtf is going on

red is the expected value

pink is how he calculates variance

blue is how our book says to calculate variance

>>11948339
The definition of variance is
[math]\operatorname{Var}(X) = \mathbb{E}[(X-\mathbb{E}[X])^2],[/math] which is the blue formula. No one is going to use this to compute variance because it's annoying honestly. Expanding the square inside the expectation, and then applying linearity of expectation, another formula for variance, and the one you should always use to compute it, is
[math]\operatorname{Var}(X) = \mathbb{E}[X^2]-\mathbb{E}[X]^2,[/math] which is what that person did.

>>11938650
An unbalanced load in a 3-phase system results in a non-zero neutral current. If the neutral is disconnected, then the common point (where neutral should be connected) will have a non-zero voltage (it will move towards the phases with the highest currents), meaning that the voltages across the loads will vary, with lighter loads experiencing higher voltages and heavier loads lower voltages. If the imbalance is significant, the increased voltage on the lighter loads will be significant, possibly damaging them.

Talking about the "atomic level" is pointless.

>>11948293
Don't you dare homo. She is for me only. I love Remilia!

>>11937617
Is non linear dynamics useful in cutting edge physics research?

>>11937617
Hydrology and engineering related: what are the official /sci/ odds and metrics* for 3 Gorges collapsing?

*Like 95th percentile rainfall in the watershed for X days or something.

How do I realize my childhood dream of being a marine biologist. Don't understand why...but the yearning to the sea has existed since before I could remember. Do I become a deckhand or navy diver or something? How can I learn the sea? I am under the impression that I must work in the sea before I can contemplate what lurks beneath. I am quite disillusioned with academia, bio degrees, etc.... I want true marine wisdom, not panzy uni crap. Is there a way to become a marine biologist (that is, who studies the Logos of what the Creator has placed under the waves) without being a "biologist" grantcuck? Just looking at algae arouses me

>>11949088
There's a difference between being a marine biologist and being a mongoloid who likes to see weird ocean creatures and caress dolphins, what you're looking for sounds more like the latter.

Either go to uni and specialize in marine biology or get started on learning taxonomy with the aid of a couple of books, learn the generals of anatomy of vertebrates and invertebrates, then the specifics of anatomy for fish-like marine life and the specifics of all the kinds of common invertebrates in the sea. Then you can open a youtube channel and after a couple of videos regarding marine life in your nearest ocean, get to travel the seas with the help of your revenue while making educational videos about crabs and what not.

Get to work anon, if you want to make a name for yourself in the field you need to start studying first, documentaries on marine wildlife help a lot.

>>11942834
A manifold is a separated topological space that is locally Euclidean. Take the sphere. Around each point, it looks like flat like R^2. But globally it is not, because you can loop around on the sphere by travelling in a single direction.

A sheaf is a presheaf such that 1. sections that agree locally on a whole covering agree globally on it, and 2. sections defined on pieces of a covering which agree on the intersections can be glued together.

A presheaf is a contravariant functor from Top to Rng. Each open set is assigned a ring. Smaller open sets get larger rings. Take C(a,b), the continuous functions on (a,b). Obviously C(0,1) contains C(0,2).

>>11949403
hahahahahahahahahahahahahahahahahahahahahahahahaha holy fuck algebra fags hahahahahahahahahahahahahahahahaha

>>11949407
You think this is algebra? Funny.

>>11949412
Hwatever it is its fucking hilarious mate

>>11949415
I agree. Functors are pretty funny. I still can't believe how many people are scared of them. It shows up in real life too! I sometimes like to make fun of people by using them when I don't need to.

>>11949418
>I sometimes like to act like a massive faggot in front of other beta dweebs w/my algebraic and topological homofaggotry
I wouldn’t have guessed

>>11949420
I know friend. Maybe you can do it when you get older? I'd say to let me know but this is an anonymous board.

this converges surely

This high school level of rearranging formulas and inverse proportionality is a wall I can't seem to get past.
I am fucking retarded.

>>11949403
>you can loop around on the sphere by travelling in a single direction.
write this rigorously

What the fuck does he mean by "decimal digit"? He said the number of decimal digits in 2^n is 0.3n, which would give 1024 3 digits. Does he just mean every digit after the first one?

Am I going to become a brainlet from multitasking? I heard that it is bad! but will listing to youtube while playing games make me retarded?

Hypothetically speaking, would a bar blow up or at least experience a larger amount of destruction from a molotov cocktail than normal buildings considering the amount of alcohol available in the premises?
Also, would an alcohol molotov cocktail be at least moderately effective?

>>11949403
>A presheaf is a contravariant functor from Top to Rng.
Seeing this weirds me the hell out, because the only justification for this that I can think of is anon being in the beginning of a scheme-theoretic algebraic geometry course and not having seen that sheaves of modules are extremely important yet.
Also, please don't call the category associated to the space's topology Top.
>>11949581
Do you have any questions?

>>11949654
he said approximately you mong

>>11937617
I keep confusing Matrix pre and post multiplication
I know that one of the two means, that I do all transformations with respect to the reference frame that I start out with. The other means I transform my reference frame and then do the transformation with respect to my new reference frame.
But I keep forgetting which one is which.

>>11949943
its done right to left
so if you do A first and then B
youre doing B * A
changing reference frame first means do it on the right

>>11949943
(A.B).x = A.(B.x)
The transformation on the right is in the coordinate system established by the transformation on the left. e.g. if A is a rotation and B is a non-uniform scale, the scale axes have been rotated by A.

is there a math book that covers elementary topics (calculus, probability, combinatorics, etc) but is more of a handbook for reference than a pedagogical textbook?

like if I just need to remember the formula for a normal vector, I can just consult the index/ToC and find it, and it doesn't give any mumbo-jumbo educational stuff, just the info I need.

can someone explain how you'd immediately see this as a solution?

similarly, how would you recognize these graphs from the vector equations?

>>11950456
This book comes to mind, but I'm not sure if its exactly what you want.

>>11950594
thanks, I'll check it out. If all else fails I'll start making my own, shouldn't be _that_ unbearable especially if I start now and just keep adding shit as it comes up.

>>11950472
I know that the parametric form of a cylinder, where the axis of rotation is the z-axis, is
[math]\langle r\cos u, r\sin u, v \rangle.[/math]
If I wanted to have the [math]y[/math]-axis to be the axis of rotation, then I just permute the coordinates, so
[math]\langle r\cos u, v, r\sin u \rangle.[/math]
So here, the first thing I would do is shift the curve so the axis of rotation is the y-axis. Then I would get [math]\cos(y)-2[/math] as my radius, but this number is negative, so take its absolute value(you can get away by negating it here). So putting it all together, I get

[math]\langle (2-\cos v)\cos u, v, (2-\cos v)\sin u \rangle.[/math]

>>11950479
The very first thing I would do is get a sense of the cross sections. So to do that, I would just set [math]u=0[/math], and separately, [math]v=0[/math]. You don't always have to set them to zero, you just want to choose easy numbers, and usually that's zero, sometimes it's a different number.

>>11950636
>>11950656
thanks for the tips, fren

Anyone got any ideas what kind of function would fit this data nicely? I've tried fitting it in R with nls using negative exponential but had no luck.

>>11950820
1/x, possibly some higher power like 1/x^2?

>>11950829
that looks promising, thanks anon

I have this differential equation:
[math]y^\prime \ln (y) = 2x[/math]
Wolfram and our lecture says it isn't possible to give an explicit solution, so something must be wrong with what my solution is but I can't figure out what:
[math]y^\prime \ln (y) = 2x[/math]
[math]\left ( \frac{1}{y} \right )^\prime = 2x[/math]
[math]\frac{1}{y} = \int 2x \mathrm{d} x[/math]
[math]\frac{1}{y} = x^2 + c[/math]
[math]y = \frac{1}{x^2 + c}[/math]

Where is my mistake?

>>11950847
you mixed up the derivative and integral of 1/y
(1/y)' = (-1/y^2) y'

>>11950863
Thanks Anon. I have an exam soon and my brain is just mush.

if you're looking at a multivariable limit, and you're asked to find the limit along the x-axis, does this just mean you're supposed to find the limit of x as it approaches 0?

>>11950876
happens to everyone
>>11950906
youre asked to find the limit when y=0, since thats the x axis
where on the x axis should be in the question

>>11950847
y'ln(y)=2x
ENGINEERING SEPARATION!!!
Sln(y)dy=S2xdx
yln(y)-y=x^2+C
define myfun(t)=tln(t)-t
myfun(y)=x^2+C
define arcmyfun as inverse function of function myfun
y=arcmyfun(x^2+C)
note:x^2+C must be positive

I need to write a report where I need to plot the polarity of some paleomagnetic samples (reversed or normal) in relation to age or sample depth.
It would like pic related.
Anyone know of any software that does this for you or of a simple way to do this with a software like matplotlib?

can someone explain how he goes from that to this please help

>>11950919
thanks, obvious in hindsight.. How would you sovle this for y=mx?
[math] \lim_(x,y) \to 0 \frac{x^2}{2x^2 + 5y^2}[/math]

would the answer just be [math]\frac{x^2}{2x^2 + 5m^2x^2} = \frac{1}{2+5m^2}[/math]?

The maximum rate of change for a surface is just the magnitude of the gradient, and the direction of maximum change is just the gradient, right?

I'm really, really interested in stochastic calculus but I don't know where to start
I've taken up to and finished ordinary differential equations
is that enough to get me started? What resources are there to start with? Are there any that are more application/engineering oriented, rather than analysis/proof based?

>>11951102
>maximum rate of change for a surface is just the magnitude of the gradient
What?

>>11951080
yes

I know this is an optimization problem where I need to find the local minimum, but I don't know how to set up my function. Any help?

>>11951424
The box's dimensions are [math]x, y, z[/math].
Then the area of its sides are [math]xy, xz, yz[/math]. We can then proceed to consider the first side to be gold, the second to be silver and the third to be copper. Since there's two of each size, you want to minimize [math]2*120xy+2*40xz+2*10yz[/math] subject to [math]xyz=8[/math].
For this, we can introduce [math]a = xy[/math], [math]b=xz[/math] and [math]c = yz[/math], and consider that [math]abc = (xy)(xz)(yz)= (xyz)^2 = 8^2 = 64[/math], so we can minimize [math]240a + 80b + 120c[/math] subject to [math]abc = 64[/math].

>>11951497
the way I understand it, only two faces are gold/silver, while the other 4 are copper

>>11951544
this interpretation is correct, I believe. Top is gold, bottom is silver, sides are copper.

>>11951497
thanks, I was almost there! Incorporating the thoughts from above I have C(x,y,z) = 120xy + 40xy + 10*2yz + 10*2xz

>>11951497
>>11951544
so how do I proceed to solve this? I'm looking for stationary points (points where the partial derivatives are equal to 0), right? the thing is, they don't equal 0 unless x,y or z are negative, and that tells me I'm approaching this wrong.

ok so through some napkin math I've arrived at z=16, x=2,y=2. No idea how to verify if this is a solution though, but being it feels close at least

>>11951614
samefag, I think the answer is z=16, x=2, y=2, but I have no idea how to verify it unless I allow negative dimensions

if I were to want to find the sum from the upper RIGHT corner, would I just exclude the last row (like this one did) and the last column?

>>11951572
IOW, minimise 160a+20b+20c s.t. abc=64 => a=64/bc. Cancel the factor of 20 => 8a+b+c = b+c+512/bc. This is symmetric so put b=c=x => 2x+512/x^2. Differentiating gives 2-1024/x^3, minimum when 0 => x^3=512 => x=8.
b=c=8 => a=1 => xy=1, xz=8, yz=8 => xz/yz=1 => x/y=1 => x=y => x=1, y=1, z=8, total cost = 120+40+4*80 = $480.

>>11951711
sick thanks, I got this answer earlier as well but my math was a lot less coherent

so to find the answer to this and show my work, I'd have to sum 6*4 = 24 different inputs into f(x,y), right? this is crazy

what the heck prof

well, at least I use emacs calc with automatic latex output

>>11937617
Give me a book recommendation for a first course into numerical analysis.

>>11951737
its not really crazy, you can break it up and do the xs and ys on their own to make it easier

For any category [math]C[/math] there are two "projection" functors from its arrow category [math]s,t:C^I \to C[/math] whose behavior on objects is to send each C-arrow to its source and target, respectively.
My question is: can [math]s,t[/math] be characterized universally without reference to the definition of [math]C^I[/math], similarly to the characterization of the product as in pic related?

>>11951761
it's still 24 separate evaluations, that's a lot of work to show imo, almost done typesetting it though..

>>11941624
--- --- ---
| | X | |
--- --- ---
| | | |
--- --- ---
| | | |
--- --- ---

>>11941624
bottom middle maybe

>>11951711
can you expand on the 'this is symmetric' portion? I'm having trouble showing this implies b=c.

>>11951815
>>11951711
my issue is that when i take the partial derivatives and set them to zero, I have something like this
[math]8x + z = 0[/math]

but if 8x = -z the results get uggo. how do I fix this or do i just skirt it instead?

goldbox fag (me) on life support, dunno how to wrap it up

pls explain... I thought the answer was 0?
I've been trying to understand where the lone pairs would be?

>>11951815
Swapping b and c gives the same result, so you either have a single minimum on b=c or two minima symmetric about b=c. It's straightforward to prove that for a given height, the area of the top/bottom faces is fixed for a given volume, and the total area of the side faces is minimised for a given volume when the cross-section is square (i.e. the perimeter/area ratio of a rectangle is minimised for a square).

If you perform a 45° rotation of axes on b+c+512/bc, i.e. b=p+q, c=p-q => p=(b+c)/2, q=(b-c)/2 you get 2p+512/(p+q)(p-q) = 2p+512/(p^2-q^2). For any given p, q=0 (=> b=c) maximises p^2-q^2 and thus minimises 512/(p^2-q^2) and thus the overall expression. IOW, the minimum lies on b=c (xz=yz => x=y i.e. a square cross-section).

>>11951831
You're ignoring the constraint xyz=8. Without that, the minimum is at x=y=z=0 (for $0 total).

If you solve xyz=8 for one variable, substitute into f=8xy+xz+yz, take partial derivatives w.r.t. the two remaining variables, equate to zero and solve, you get 2 of the 3 and can calculate the third. E.g.:
xyz=8 => z=8/xy => f=8xy+8/y+8/x
=> ∂f/∂x=8y-8/x^2, ∂f/∂y=8x-8/y^2
∂f/∂x=0 => 8y-8/x^2=0 => y=1/x^2
∂f/∂y=0 => 8x-8/y^2=0 => x=1/y^2
=> y = 1/(1/y^2)^2 = y^4 => y^3 = 1 => y=1
=> x=1/1^2 = 1
=> z=8/(1*1)=8

>>11951975
BTW, I'm guessing that the partial derivative approach is the one they're looking for.

What does the e mean here?

>>11951975
I think i'm putting this together now, but why are allowed to just diivde our whole function by 20?

>>11951975
>=> y = 1/(1/y^2)^2 = y^4 => y^3 = 1 => y=1
>=> x=1/1^2 = 1
>=> z=8/(1*1)=8
also, final note, I don't understand these last few lines, where did they come from?

>>11951975
Use LaTeX if you are going to shit up the thread like this

>>11952019
oh wait, this is because we sub our points back into the original function right?

sorry super rushed now it's due in like 20 minutes, brain power fizzling

>>11951975
how did you justify y^4 = y^3?

>>11937617
How do you grasp math and physics concepts quickly say in summer school or in a short amount of time? Are there really just people who are quick learners and soak up knowledge like a sponge? How do you go about it

>>11952048
do it a lot, and when you do, do it well. i find i get a lot of benefit having a big session before bed and in the morning, where I really give it my all until I burn out. i know I'm doing well when I'm dreaming about the material, that's when you'll really start to sail imo.

>>11952048
>are there really quick learners
Yes, just as there are really natural athletes.

>>11952002
Because any minimum of f is also a minimum of k*f. df/dx=0 => k*df/dx=0 => d(k*f)/dx=0.

just dropping this before I go to bed, I have no idea how to approach any of it. Is the standard matrix for a) simply:
[math]\matrix{a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c} [/math]
?

not sure how to find the volume rn but that sounds pretty easy if the standard matrix is correct

>>11952065
forgot pic

>>11952067
wait is this seriously as easy as finding the determinant of the standard matrix, then multiplying it by the volume of the unit sphere?

>>11951926
Fuck I just realised what I did wrong
What a retarded mistake

>>11937617
is picking and choosing what to follow a kind of bias? e.g christians who choose to use some things set by the old testament but not others

Did Tooker finally take his meds? I've not seen him in a while.

>>11952072
Yes.

I did it.
I cracked formula rearrangement.
My knowledge now extends to the 7th grade.

>>11952072
yes

>>11951104
bump pls

What is the threshold for detecting weight/gravity?
I ask because, according to estimates, the total quantity of gold ever mined is roughly 171300 metric tons. This could form a cube of roughly 20.7 meters a side
Doing the math, if I were standing right next to it,
[math]\frac{\left(6.67\cdot 10^{-11}\right)\left(171300\cdot 10^3\right)\left(86.2\right)}{\left(20.7\right)^2}[/math]
the gravitational force would work out to .002 newtons.
I want to know if I would be able to feel that.

do one forms represent how a vector(tangent) deforms as you move around in a manifold? or is that something else

>>11953366
"20.7 meters a side" means r=10.35 m.
F/m = G.M/r^2, which works out at ~1e-4 m/s^2 or ~1e-5 g. Do you think you would notice the difference between 1 g and 1.00001 g? I doubt it.

>>11953449
ah fuck you're right, I forgot it's a radius. Thanks for clearing that up.

>>11953437
No, not at all.
For example, you can consider the one-form [math]dx[/math] and the vector field [math] \frac{ \partial}{ \partial x}[/math] on the real line.
Clearly [math]dx ( \frac{ \partial}{ \partial x} ) = 1[/math], but both of those are constant.
You might be thinking of the Lie derivative or of a connection.

>>11937617
Where should I start reading to improve my math skills? Any books to work from the fundamentals to the complex? Doesn't need to be practical, because I don't intend to study mathematics beyond self-improvement and expanding my understanding.

>>11953548
ignore me I am astigmatic I found the link to book recs I am sorry

>>11953486
>connection
thats the one, ty

What is a good way of determining the cardinality of quotient rings when dealing with polynomial rings?
E.g. Z_5[x]/<x^2-3>
I know that polynomial rings have infinite cardinality but it seems like workng over a finite field should allow me to form a finite number of additive cosets.

I don't know why I'm so retarded but my brain is just not working. halp please.

>>11953697
[math]Z_5 [x] / \langle x^2 - 3 \rangle[/math] is generated as a vector space over [math]Z_5[/math] by [math]1[/math] and [math]x[/math].
So the cardinality is [math]5^2=25[/math].

Wtf does the yellow part mean?

>>11953707
Hello, thank you! Really appreciated.

If you'll allow me to continue bothering you:
That makes sense but I'm having troubles corroborating that the choice of maximal ideal doesn't affect the cardinality of the quotient ring (when looking at basis elements, as you statede them, it seems like that should follow). Did you mean that it's generated with {1,x^2}?

With polynomial-absorption by the ideal, it seems strange to me. I guess that I'm only familiar with the argument that relies on ranging coefficients on more simple sets in e.g. Q.

Am I misunderstanding?

>>11953772
The amount of yarn used for scarves should be twice as much as the amount of yarn used for hats.

>>11953790
>the choice of maximal ideal doesn't affect the cardinality of the quotient ring
[math]x^2 - 3[/math] doesn't generate a maximal ideal.
>Did you mean that it's generated with {1,x^2}?
No. [math]x^2 - 3 = 0[/math] can be rearranged as [math]x^2 = 3[/math]. Adding in x squared is bloat, since it can already be given as a scalar multiple of 1 in the vector space.
>Am I misunderstanding?
Apparently.

>>11953801
>x2−3 doesn't generate a maximal ideal.
Wait, no, it does, my bad.
Still besides the point.

>>11953801
I guess that I have a fundamental misunderstanding somewhere then.

I'm considering [math](Z_{5},+,*)[/math] where [math]Z_5 = \{0,1,2,3,4\}[/math] under addition and multiplication [math](mod 5)[/math].

I'm looking at [math]Z_5[x][/math], which is an integral domain with unit. ([math]Z_5[/math] is a field since 5 is prime).

[math]3[/math] is not a quadratic residue of 5, so [math]x^{2}-3 = 0[/math] should have no roots in [math]Z_{5}[x][/math] and hence be irreducible.

It's also monic and primitive, etc. so I thought that [math]\langle x^{2}-3\rangle[/math] should generate a maximal ideal.

Thus [math]Z_{5}[x]/\langle x^{2}-3\rangle[/math] should be a field.

Where have I gone horribly wrong?

>>11953808
>>11953844

Oh, okay. Thank you!

So I know the standard matrix is just all 0s except the main diagonal is a b c, but how do I 'show my work' here? I keep loosing points like this.

is this scientifically accurate?

>>11954514

>>11954356
You do it the really, really dumb way.
We denote the matrix of expansion on the [math]l[/math]-axis by a factor of [math]k[/math] by [math]A_{l, k}[/math].
Then [math]T = A_{z, c} A_{y, b} A_{x, a}[/math], from what was said.
Compute [math]T[/math] by hand from that.

How difficult is it to learn Calc 1 in about three months?
I took a math placement test and made a perfect score, which I was very happy with considering I hadn't taken a math class in ~6 years. The problem is that the system somehow automatically placed me in Calculus 2. It doesn't make any sense, the test didn't ask any calculus questions whatsoever, I've never taken calculus, I can't differentiate myself out of a paperbag. The advisors aren't responding to my emails and the next phone appointments available are right before classes start. And the campus is closed because of Covid. I guess the best option, in time and money, would be to just skip a math class this semester, spend the time I need to learn differentiation, and take Calculus 2 in the spring but I would have preferred to take all my math classes with some guidance, especially calculus. Simultaneously, I also don't want to be a even more behind in my math than I already am and take Calculus I in my second semester while everyone else in my major is taking Calc 3 or DE.

>>11954686
It could not be more acheiveable. Three months is one semester and that is plenty for Calc 1.

These are notes for UK students, but it should be adequate preparation for more difficult college calculus, etc:

https://archive.uea.ac.uk/jtm/contents.htm

Try doing two units per week, minimum.

You can also find helpful notes for highschool courses such as:

http://www.hsn.uk.net/resources/Higher-Maths

https://tutorial.math.lamar.edu/classes/calci/calci.aspx

how do I calculate this series?

how come you can buy silicone spatulas and other utensils, but you can't buy teflon utensils?

Are animated gifs or short movies ever allowed inside a paper pdf?

>>11954898
I'm sure you'll find plenty of youtube videos.

https://www.youtube.com/watch?v=x3QxJnI9jNI

I didn't watch this by the way.

>>11954898
How about you rotate the fucking image so someone might actually be willing to help you

how do i get from left to right ;/

>>11955373
Use [math](j+1)! = (j+1)\times j![/math]
Then you get
[eqn]\dfrac{n!}{(j+1)!(n-(j+1))!} = \frac{n-j}{(j+1)(n-j)}\dfrac{n!}{j!(n-(j+1))!} = \frac{n-j}{(j+1)}\dfrac{n!}{j!(n-j)!} [/eqn]

What are some applications eigenvalues/vectors and multiplicity?
Taking LA this summer and a lot of this stuff seems pretty abstract

>>11955457
https://arxiv.org/abs/1907.02534

>>11955457
>What are some applications eigenvalues/vectors and multiplicity?
This inequality: >>11944788

>>11952424
cute dummy

how do you prove that [math]B-\bigcup A=\bigcap (B-A)[/math]?

>>11955564
am i retarded or does this notation not make sense

>>11955564
If [math]x\in B \setminus \bigcup A[/math], then [math]x\in B\setminus A[/math] for all A, so its in the intersection. If [math]x\in \bigcap(B\setminus A)[/math], then [math]x\notin A.[/math] Then [math]x\notin \bigcup A[/math].

>>11955573
those are unions and intersections over an indexed family of sets, i forgot the index notation
>>11955578
thanks anon

>>11955457
Matrix exponential. If Ax=λx then (A^n)^x=(λ^n)x. This extends to matrix polynomials and Taylor series.

>>11937617
I have basically no knowledge about math whatsoever, where should I start?

>>11955805
1+1=4

>>11955457
all of lagrangian, hamiltonian mechanics, etc.

>>11955805
https://www.youtube.com/c/njwildberger

Can someone check if my proof is correct?
[math]
\text{Let $f:A\rightarrow B$ and $g:B\rightarrow C$ be functions and let $H$ be a subset of $C$. Then we have $(g\circ f)^{-1}(H)=f^{-1}(g^{-1}(H))$}
[/math]
My proof:
[math]
(g\circ f)^{-1}(H)\\
=\{a\in A:g(f(a))\in H\}\\
=\{a\in A:f(a)\in g^{-1}(H)\}\\
=f^{-1}(g^{-1}(H))
[/math]

>>11956014
looks good to me

>>11953692
Where can I practice integrals and possibly diffeqs?
I want to feel confident in my integrating skills.

>>11956277
https://www.wolframalpha.com/problem-generator/?scrollTo=Calculus

>>11956014 = BASED

>>11956289
Sweet. Not too hard exercises though if I'm not mistaken, right?

>>11956405
They're piss easy.

>>11956277
>>11956289
>>11956435
When posting it on /mg/, I didn't think it would be so hard to answer. Is there really no good advanced integration practice book?

>>11956595
Oh, you wanted a book?
Apostol is the classical meme reference for piles and piles of brainless integration exercises. IIRC Alfohrs is good for contour stuff.
For DEs, there's the Historical Applications book that everyone likes.

Integration is a well-posed problem and there's literally no reason not to solve it numerically, don't be daft.

Could anyone explain to a brainlet why I must square both of these when cancelling this formula down to L?
I bracketed both sides and squared to remove the sqrt, leaving me with T^2g, but the answer has pi^2 as well.

Since white reflects and black absorbs, would a box painted white on the outside and black in the inside be the coolest, and black on the outside with white in the inside the hottest?
Hottest as in the possible combinations: black outside, black inside; black outside,white inside; white outside, white inside; white outside, black inside.

Could someone explain how to solve this? I guess it shouldn't be hard, I have found a solution but have trouble understanding.

Let [math]\mathbf{X} ~ U[0, 1], \mathbf{Y} ~ U[0, 1][/math]. Find the distribution of [math]Z = X + Y[/math]. Should a convolution function be used? In the end a triangle should be observed (if geometric interpretation was chosen), but I literally can't understand what steps should I take. Tips?

p.s. I have severe knowledge gaps in Calculus.

My retarded housemate wants to take schizophrenia medication recreationally. How bad of an idea is this?

>>11937617
Can anyone explain Wilson's rule regarding action variables (Intro to modern physics)? Not quite getting it

>>11956629
Squre both sides for [math]T^2 = 4 \pi ^2 L / g[/math].
Then you rearrange.
Honestly no idea what the fuck did you do.
>>11956855
>can't even find it on google
>can't find it on a classical mechanics book
At least give us a screenshot.

>>11955805
The basics

>>11956627
Thanks!
>literally no reason not to solve it numerically
I mean, ofc you are right, but as /mg/ said, one can't say he understands integration if he can't integrate.. and also it's a nice way of killing time - something like solving crosswords.
(not mentioning that Mathematica can't find integrals to functions that have close form integrals)

>>11956810
Does he thing the induced states will be enjoyable? That really is some retarded bullshit.

>>11956961
I don't know. Some fuckwit person he's communicating with on his phone told him it's fun. It doesn't sound like a good idea to me.

>>11956790
PDF is [math]f_Z(z) = \int_{-\infty}^\infty f(x)f(z-x)dx[/math] (convolution formula). The function [math]f(x)[/math] is a piecewise function
[eqn]f(x) = \begin{cases}1 & 0<x<1,\\ 0 & \text{otherwise.}\end{cases}[/eqn]
So you have to sit down and then ask what exactly is
[eqn]f(x)f(z-x),[/eqn] In particular, it is just another piecewise function taking values of either 0 or 1, but the region where it is 1 will depend the exact [math]z[/math] value, and this gives you the bounds for integration. You will have 2 cases, so you need to integrate 2 different cases, each giving you either the left side or the right side of the triangle. There is a third case, but it is 0.

I've done probability many times, and I really hate this example. You're probably using Ross too.

>>11957146
this formula doesn't work unless you assume something else

I constantly forget how to do long division, and I am not sure how to feel about that. Am I the only one that has to do a quick review to remember?

"if you're poor it's mental illness, if you're rich you're eccentric" is there any validity to this claim? anyone whos tested it by sending poor/rich "actors" to doctors to see if being rich leads to lower rates of diagnosis

>>11956810
If I remember right shizos take scopolamine which is a drug that inhibits you so much you don't even know you are high. Lots of cool storys on erowid

>>11937617
Is there a minimum (photochemical, or lower) frequency at which an electrocyclic reaction or light-dependent reaction can occur? Are there any biological processes or chemical reactions dependent on radio frequency waves?

how do wheels work? if you connect two wheels with an axle and then attach a carriage to the axle, wont the weight of the carriage prevent the wheels and axle from spinning?

test

>>11958022
only /g/ has code tags i think

I've spent fifteen minutes cleaning this, does anyone know have any good ideas to fill it in?

>>11958584
By the way, I was originally thinking of something like this, except this is just extremely rude.
And typesetting for those bubbles sucks.

With normal astronomical objects, a body that does a flyby will always leave with exactly the same speed (relative to the body) that it approached with, assuming it doesn't make contact or experience drag.
So what is it about a black hole's event horizon that makes a flyby impossible? Why can an object not swing around a black hole such that it dips just past the event horizon?

>>11958584
>>11958672
>And typesetting for those bubbles sucks.
Probably easier to just remove and redraw them entirely, at least for Miko (Seiga's bubble could support a short response like "Yes.")

>>11958770
I'm bad at typesetting, but I'm hot garbage at (evem this shitty level of) redrawing.
Feel free to compare with the original:
https://mobile.twitter.com/i/web/status/1286437105317552128

Also, pointless effort without a good idea.

US naval researchers found a range of organic compounds exhibiting superconductivity in 1975, most notably C24H40O2, with a transition temperature of 3.85 degrees C.
My question is, why aren't biological superconductors more of a big deal?

I still can't figure any of this out

>>11959381
To add to it I know that to find a proportionality constant you multiply the sides, so
9.8 x (6.37x10^6)^2 which equals 4x10^14
But I have no idea how to use it beyond that

>>11959390
Once you've found k, the formula gives you g for any d. So (ii) is asking for g at d=2*6.37e6 and (iii) at d=1e9+6.37e6.

>>11959406
Oh, it's 2*6.37e6 and not just 6.37e6? Because it's one radius above?
These word questions really trip me up if that's the case.

>>11959411
No that person was assuming d meant diameter. d means distance from the center of the earth (i.e. radius) according to the problem text

"You can't forget to do later what you've already done." - Anon the Wise.
There's the Latex meme image and three new charts btw.
On a side note, I have no idea if the finance chart is actually serious.
>ye brah, basic probability, stochastic processes and mathematical finance is all you need to dab on wall street

>what is /sqt/ for
Questions regarding math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc.
>books?
libgen.is (warn me if the link breaks)
https://stitz-zeager.com/
>articles?
sci-hub (you'll have to google for a link, unfortunately)
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
http://math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>how do I post math symbols?
https://i.imgur.com/vPAp2YD.png
>how do I succesfully post math symbols?
https://imgur.com/a/LpgxGsz
>a google search didn't return anything, is there anything else I should try before asking the question here?
https://scholar.google.com/
>where do I look up if the question has already been asked here?
>>/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

Question asking tips and tricks:
>attach an image
>if a question has two or three replies, people usually assume it's already been answered
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Stuff:
Meme charts: https://imgur.com/a/kAiPAJx
Serious charts: https://imgur.com/a/Bumj2FW (Post any that I've missed.)
Verbitsky: https://imgur.com/a/QgEw4XN
https://pastebin.com/SmBc26uh
Graphing: https://www.desmos.com/
Calc solver: https://www.wolframalpha.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

>>11937617
What book read if you want learn gooder english but not learned of the type speak that niggery people are?

>>11957547
yes to the first question. the energy of the light is the important factor in catalyzing the reaction, and there is a threshold
don't know about the 2nd q

why are the following expressions:

[math]f_1(x)=x^{-2}+3x[/math]
[math]f_2(x)=\frac{1/x^2+3x+1}[/math]
[math]f_3(x)=x^{\frac{1/2}}-5[/math]
[math]f_4(x)=x^\pi-x^2[/math]

NOT polyonmials, but:

[math]g_1(x)=3x^4-2x+\frac{1/2}[/math]
[math]g_2(x)=\pix^7+5x^2[/math]
[math]g_3(x)=3[/math]
[math]g_4(x)=8x+1[/math]

are polynomials? What makes [math]f_n(x)[/math] not polynomials and [math]g_n(x)[/math] polyonmials?

What makes a polynomial a polynomial?
i'm reading a book that says that expressions like this:

[math]f_1(x)=3x^4-2x+\frac{1}{2}[/math]
[math]f_2(x)=8x+1[/math]

are polynomials, but expressions like these ones:

[math]g_1(x)=x^{-2}+3x[/math]
[math]g_2(x)= \frac{1}{x^2+3x+1}[/math]

are not?

>>11960949
literally just the definition of a polynomial
"an expression of variables and coefficients that involves only operations of addition, subtraction, and ((NON-NEGATIVE)) integer exponentiation of variables."

what about [math]h(x)=x^{\frac{1}{2}}-5[/math] and [math]j(x)=x^\pi -x^2[/math] ?

how come these are not polynomials

>>11960982
sir are you aware of the definition of "integer"

>>11960988
ohh, sorry i misread. But shouldn't it be natural numbers only in the exponentiation then?

if [math]0 \in \mathbb{N}[/math] of course

>>11961008
non-negative integers is the same thing as natural numbers (if you say 0 is a natural number, which is grounds for debate)
saying non-negative integers is a more unambiguous way of saying it

>>11960949
Let [math]A[/math] be the set of all constant functions.
Then, the smallest set of functions containing [math]A[/math] and the identity function [math]f(x) = x[/math] that's closed under pointwise sum and multiplication is the set of polynomials.

the book says again that [math]s(x)=x^2- \sqrt{3x}[/math] is a polynomial, but an exercise says that [math]m(x)=x- \sqrt{x}+5[/math] isn't because [math]sqrt{x}[/math] is not a monomial, how come it's valid for [math]sqrt{3x}[/math] but not for [math]sqrt{x}[/math] ?

>>11961233
If I absolutely had to guess, you're reading [math]\sqrt{3} x[/math] as [math]\sqrt{3x}[/math].

When are they releasing the full version of GPT-3? Will it be available for the public?

Anyone help me with this problem? I tried substitution but got a nonreal solution. It says eliminate algebraically x but I can’t seem to figure out how to. Since the equation of the circle is 2nd degree and the other is linear I don’t see how I can combine the equations in a way that will eliminate x entirely.

Is a naive implementation of a password guesser an exponential algorithm? It seems like it should be (every unit increase in key length multiplies key space alphabet size) but it’s an NP problem which is strictly faster, to solve, than exp. so what am I misunderstanding?

>>11940481
The normal way us to take the dot-product and take arccosine, another anon mentioned using cross-product and arcsine for small angles.

Your vector difference would result in the third side of a triangle making Law of Sines and/or Law of Cosines possible to use but the normal way to do things is to use dot-product. The dot-product method works for both 2-d and 3-d coordinates.

If you don't like vectors and are working with 2-d, most programming languages have an atan2() function. Perhaps the coords of 2-d vectors could be interpreted as a complex number and divide one by the other (formula equalivant to trigometric angle difference equation).

Not all programming languages have vec2, vec3 builtin types but easy to implement. If you need to brush up on the math. https://www.youtube.com/watch?v=o5l_9QpYmhY https://proofwiki.org/wiki/Cosine_Formula_for_Dot_Product

>>11962391
[math]x+16 = 7y[/math] is the same as [math]x=7y-16.[/math]
Then [math]x^2+y^2 -4x+2y=20[/math] becomes
[math](7y-16)^2+y^2 -(7y-16)x+2y=20.[/math]

>>11962391
The circle can be expressed as (x-a)^2 + (y-b)^2 = r^2 where (a, b) are coordinates of the circle's origin.

Using the identy (a+b)^2 = a^2 + 2ab + b^2:

x^2 - 4x + [4] = (x - 2)^2
y^2 + 2y + [1] = (y + 1)^2

(x-2)^2 + (y+1)^2 = 20 + [4+1]
origin=(2,-1); radius=5

>>11962444
I don't think you know what NP means. I also don't think you know the distinction between the complexity of a problem and the complexity of a particular instance of an algorithm that attempts to solve that problem.

>>11962910
I don’t think you know what an sqt thread. I also don’t think you know the difference between being a smug faggot and answering the question.

Trying to git gud at math, is it bad if I probably don't put as much effort into applications problems as I should?

>>11966318
What exactly are application problems?

>>11966391
Word problems where you need to figure out how to set up the problem itself.

It's really more laziness than anything. Sometimes I'll just look up how to set it up and then solve it from there myself.

Got a final this week where this'll come up.

>>11966464
Well I've experienced many people who can solve problems that they've seen before, but cannot ever seem to solve a new problem which takes the things they should know and being able to apply it. Being able to read a problem and figuring out to set it up is a skill. If you can look up the answer and understand it, that's good. But remember no one is telling you that your answer is right or wrong on the exam until afterwards. Also, how can you solve a problem if you don't know how to set it up?

>>11966575
I think in general, I know how to solve it up but it usually takes a few minutes of thinking to figure it out and I've been feeling lazy the past week or so.