/sci/ - Science & Math

>>10980546
https://www.youtube.com/watch?v=JMz_PYnpJPY
Does he have >130 IQ?

Did I do this correctly?

I'm blanking out so hard right now. Must be the lack of food.
What is the piece wise function for this graph?
It's t/τ for 0 < t < τ
and
-t/τ for -τ < t < o , right?

>>10980685
The second term is correct. But the first term is wrong. Here's what you need to use
[eqn] \int_{-\infty}^{\infty} \delta (c t) f(t) dt = \frac{1}{|c|} f(0) [/eqn].

>>10980724
Where does that come from? All I know is that the dirac delta function needs to be 0, and e^j2pi(0) = 1, so it should just be 1.

if you got close enough to the sun and aimed perfectly could you theoretically cast shadow puppets over a spot on earth?

>>10980752
https://en.wikipedia.org/wiki/Dirac_delta_function#Composition_with_a_function

It follows from making the substation u = ct and the fact that the delta function is an even function.

>>10980847
No. From a viewpoint on the projection surface (screen), your hand would need to appear much larger than the sun in order to get clear shadows. Look up "penumbra".

>>10980752
[math]\int \delta(u)\,dt = \int \delta(u)\,{dt \over du}\,du[/math]
if u=ct => du/dt=c => dt/du=1/c

>>10980548
No, that's just what Finns are like

>if the matrix I+AB is invertible, prove that I+BA is invertible
what am I supposed to do here? set up an equation but solve for what?

>22
>dream about peeing
>wake up immedietly because I know I'm peeing irl
Is this normal? I mean, I didn't completely release everything in my bladder, just like a tiny bit. But still, weird.

>>10981093
Hint: Don't let the goyim fool you, this is true for all rings. Don't get distracted with matrix-specific arguments.

What's the secret to note-taking? Both during self-study and lectures? How do you take notes?

It's weird post-HS when all lecture slides are available in full online or you have a PDF of the textbook and there's zero reason to refer back to your hastily written notes. I know there are studies that show learning advantages to just note taking but I never felt they helped that much versus just problem-solving(and referring to the text/slides as needed)

Why isn't x = 1 also a vertical asymptote in this question? I thought any number that would leave a zero in the denominator is counted as a vertical asymptote.

Is it because the (x-1) in the numerator cancels the one in the denominator out?

I want a portable blacklight that can detect semen,urine, and blood
I got a cheap one from Aliexpress but it can't make any of those things light up.
what should I look for?

>>10980546
this is a really dumb question, but are you supposed to be able to have kept track of all the stuff proved? like this analysis textbook proves so many little corollaries and lemmas that pop up later, and a lot of them are intuitive too, so i have no idea how to keep track of all of them and know whether or not the author is assuming too much reading his proofs. is this bad? if it is i guess i am just going to keep a list of what notion has been proved.

>>10981430
i still take notes even as i read textbooks cause it helps me consolidate the information. if i don't, it's hard to focus and follow along. i eventually just get sleepy.

>>10981633
Are you retarded? You need a "BLB" black light for those uses. It also needs to be powerful enough to make stuff show up. Just search ebay chinks are less sleazy there.

>>10981524
I'm guessing nobody is responding to me because I answered my own question.

So whenever I am solving these, I should always factor both the numerator and denominator. Not just the denominator, right?

>>10981524
> Is it because the (x-1) in the numerator cancels the one in the denominator out?
Yes.

A vertical asymptote exists when either of the one-sided limits (below or above) at that point tend to ±∞. The function itself doesn't need to be defined at that point.

At x=-2, the numerator is -3 and the denominator is zero; the ratio tends to -∞ from below and +∞ from above, so you have a vertical asymptote. At x=1, the numerator and denominator are both zero, but the ratio converges to 4/3 both from above and below; there's no asymptote.

> I thought any number that would leave a zero in the denominator is counted as a vertical asymptote.
Not if it also leaves a zero in the numerator. If both numerator and denominator tend to zero at a point, there may or may not be an asymptote. E.g. (x-1)(x-2)/(x-1)(x-1)(x-2) has a vertical asymptote at x=1 while (x-1)(x-1)(x-2)/(x-1)(x-2) doesn't. Also, if the denominator is discontinuous such that it's equal to zero at that specific point but the limit approaching that point is non-zero, then there's no asymptote. The ratio will be infinite at that specific point but the function will otherwise be smooth.

>>10981821
Thanks a lot for putting it into words that I can understand better.

I was going to a community college for about a year and because of my good grades I got into this Phi Theta Kappa honors program. Shortly after that and because I got into that I was invited to a real university. It's Wrightstate University in Ohio.

Basically my question is, is there a point in going into physics degrees if I am not in some sort of super school like MIT? Like will I actually make it into some sort of decent position in the world or will I just become a teacher? And how do I know if this college is bottom of the barrel? I mean, its better than a community college and the honors program is practically going to pay for all of it anyways so it's still a bump up for me.

So yeah, tell me what you think /sci/?

I'm failing business statistics. Am I retarded?

So I just made a batch of cold porcelain. For anyone who doesn't know what that is, it's a type of home-made modelling clay based on mixing white glue and corn starch. The online recipes says that lemon juice is added to make it resistant to mold, but based on my very limited knowledge of polymer chemistry I think it's more likely that the lemon juice is there to snip up the polymer chains so they can then recombine with each other and mix the ingredients more thoroughly?

My understanding of the process:
> get two substances with long molecules with hundreds of carbon and hydrogen atoms (white glue and starch)
> add lemon juice, and mix until the acid has cut up the long chains somewhat
> add oil as a plasticizer (smaller oil molecules get between the chains and stop them tangling up too much)
> heat, stirring as long polymer chains get tangled up again, hardening the mixture

Do I have a basic understanding of the chemistry that's happening here, or am I way off? I know it's kind of stupid but it's going to bug me until I find out, and I couldn't think of anywhere else to ask.

Fun fact: as far as I can work out, no one has any idea who originally invented Cold Porcelain (hence my suspicion that the explanation given by the recipe may not be correct), but it may have come out of Argentina in the 1980s. Apparently when they couldn't grab clay in the Falklands, they decided to make some (ba-dum-tsss).

So, why exactly do we need the power set axiom?
Metamath doesn't use it for any actual theorems, and I haven't seen it used even once yet.

How do I get into meditation

What does [math]A^{2}=-\mathbf{1}[/math] mean in the context of [math]2\times 2[/math] matrices? The matrix with components all equal to 1?

>>10980717
correct
|1/t|

>>10981093
no, it's something about the column/row rank of that matrix.

>>10981996
short answer

yes

long answer

yes

source: I'm a statistician myself and I'm retarded and didn't fail that module

>>10982701
Nope, it means that you're going to obtain an identity matrix times the scalar -1

>>10982722
cheers

>>10982701
First row: 1 0
Second row -1 0
This is i in matrix form
Squaring it produces identity matrix times -1

>>10980546
What is the name of the statistical method that tries to predict the next few values in a line of already known values?

>>10982835
Forecast or trend calculation! How could I forget, shame on me.

>>10982772
1. That should be [[0,1],[-1,0]] or [[0,-1],[1,0]], i.e. a 90° rotation (in either direction). -I is a 180° rotation.
2. Those aren't the only solutions. The general solution is [[a,b],[c,-a]] where a=±√-(1+bc). For this to be real, bc<=-1, i.e. b,c need to have opposing signs and |b|.|c|>=1.

>>10980546
Why is Calculus generally regarded as being complex to the normal person, but is really just the beginning of a lot of STEM major curriculum.

>>10980546
How do you do equationy things in posts like this >>10980724 and this >>10980916

>>10981093
I think this is easier if you look at I - AB.
Think about it this way - what do you know about (1 - x)^{-1} for real x with |x| < 1? Think back to calc 2.
Now of course it makes no sense, but try rewriting (I - AB)^{-1} like this, and see what you can pull out. Can you find anything that reminds you of (I - BA)^{-1}?
Okay, now you'll have a guess for that the inverse of (I - AB) might be in terms of that of (I - BA). Now check that this formula ACTUALLY works as both a left and right sided inverse.
If you're not seeing it, that's alright. This is a devilish trick for finding great guesses.

>>10983111
Your statement is more of a generalization, as it depends on who you define as being normal. If you are an American, then the normal, average American would struggle with basic high school math. Almost a third of American high school graduates who took the Piacc could not spot incorrect data in a simple bar graph; a problem that most people in the world would label as being on an elementary school level.
https://qz.com/638845/americans-are-spectacularly-bad-at-answering-even-the-most-basic-math-questions/

Most STEM major curriculums do not tie themselves to the general population's math comprehension level. However, maybe someone else could explain why calculus is only the beginning of many STEM majors. As calculus I - III is actually the end of my math sequence.

>>10983111
Cause limits and integral signs look fancy, and it's the one thing a lot of people know about but never take.

Black holes
Has anyone every done the math to figure out how far it is (theoretically) from the physical black hole to the event horizon?
I ask because of that webm that shows black holes scaling up to the central black hole of the phoenix cluster, which apparently has an event horizon who's size dwarfs our entire solar system.
Of course this question supposes that gravity can't crush atoms out of existence and thus there is something physical (and incredibly dense) at the center of a black hole, but I don't know enough about anything to think otherwise.

>>10983111
Thank pop culture for making it sound scary when most people never take it.

And when they do take it their basic algebra skills are so shit they fail anyway

>>10983137
It's LaTeX. Use [math] and [./math] tags to do it (no period) or eqn instead of math for nice formatting.
You can use the little button in the top left of the quickreply box on desktop to test things out.
It's really easy to learn, and almost essential if you plan on doing any kind of STEM. It's how everything is written.

>>10983188
gotta wonder how many potential engineers got intimidated into taking calculus like their more prepared peers and got burnt out as opposed to swallowing their pride and taking a refresher course on algebra or precalc to nail down the basics after a shit HS education

>>10983137
>>10983193
You can also take a look at how people are writing what they're writing by right clicking the LaTeX typing and selecting "show math as >> TeX commands"

I'll be struggling with this one later, but I'm posting it now so any hints/tips will be very welcome.

The solution would also be apperciated

Any tips of solving these integrals?
Should I break it up into more integrals by using eulers identity?

>>10983305
> Any tips of solving these integrals?
d/dx e^kx = ke^kx
d/dx xe^kx = kxe^kx+e^kx
=> d/dx (kx-1)e^kx = k^2xe^kx
> Should I break it up into more integrals by using eulers identity?
No.

How do I find the fourier transform for this?
I first divided this into unit step functions:
e^(at) u(t) – e^(-at)e^(-a(t-T))u(t-T)
I can solve the left component with a table, but how would I solve the right?

No recap this time huh?
>>10983259
the hint gives you the solution.
>>10983429
Use faltung theorem.

>>10983429
> How do I find the fourier transform for this?
Direct integration. It's just the integral of e^-at.e^-2πiξt dt but over [0,T] rather than [-∞,∞].

> I first divided this into unit step functions:
> e^(at) u(t) – e^(-at)e^(-a(t-T))u(t-T)
Not quite (missing negative sign in the first term, t instead of T in the second):
e^(-at).u(t) - e^(-at).u(t-T)
= e^(-at).u(t) - e^(-aT).e^(-a(t-T)).u(t-T)
= e^(-at).u(t) - e^(-aT).[e^(-at').u(t')] with t'=t-T

> I can solve the left component with a table, but how would I solve the right?
Time-shift:
f(x)->F(ξ) => f(x-a)->e^(-2πiaξ).F(ξ)

Suppose [math]G[/math] is a group and [math]N,K[/math] are normal in [math]G[/math].
If [math]G/N\cong G/K[/math], is it true that [math]N\cong K[/math]?

>>10983698
yes
that's intuitive

>>10983468
>No recap this time huh?
Give me a break, I caught a cold.
>>10983698
Pretty sure I remember my textbook explicitly mentioning that doesn't happen.

>>10983939
See, I couldn't find it anywhere in my textbooks or even online (always end up getting stuff about the 3rd Iso Thm).

But also I was able finish my proof without needing that.

>>10981965
Nothing wrong with teaching anon

>>10983698
No, you can come up with a counterexample with just finite abelian groups

Can someone explain why a(t) is determined by the formula here, and not just by twice taking the derivative of r(t)?

>>10984076
Or is that the same thing, just in a different form? Then what is the point of having it as the sum of perpendicular vectors?

>>10984076
>taking the derivative twice in relation to r(t)
What do you mean lad.
a=dv/dt, it's literally right there.

>>10981965
In the information age your only limit is yourself.

So I failed my first abstract algebra exam, scored shite on the GRE, and my depression makes me want to kill myself. How do I get out of this hole? I used to be the golden student /sci/...

>>10984409
Leave this board and apply yourself

>>10984357
What is the point of formula (4)

>>10984592
You have a tangent and a normal component to the speed.

>>10984627
> You have a tangent and a normal component to the speed.
The velocity is solely tangential, as shown by (3). The acceleration has components which are tangential (caused by the speed changing) and normal (caused by the direction changing).

>>10984695
yes obviously but what is the use of this formula? why would you want to express it as the sum of perpendicular vectors?

Someone who's taken fluids pls help:
I don't understand this equation. I understand every part of its derivation, but it does not make sense to me.
For example, imagine a rocket ship in space with no gravity, no body forces. It turns on its engine, shooting a flow of hot gas behind it. This equation suggests that the force vector on the rocket would be parallel and pointing in the same direction as the velocity vector of the gas that is leaving the rocket. But this makes no sense. Why is there not a negative sign in front of this equation?
>>10984707
Because you don't always have to work with an arbitrary coordinate system that's fixed to the ground. If you have a_t and a_n, you can work with a coordinate system that is fixed to the body that is in motion)

Someone who's taken fluids pls help:
I don't understand this equation. I understand every part of its derivation, but it does not make sense to me.
For example, imagine a rocket ship in space with no gravity, no body forces. It turns on its engine, shooting a flow of hot gas behind it. This equation suggests that the force vector on the rocket would be parallel and pointing in the same direction as the velocity vector of the gas that is leaving the rocket. But this makes no sense. Why is there not a negative sign in front of this equation?
>>10984707
Because you don't always have to work with an arbitrary coordinate system that's fixed to the ground. If you have a_t and a_n, you can work with a coordinate system that is fixed to the body that is in motion)

Studying nonlinear dynamics and chaos. Are bifurcation points of ode's in normal form conserved? Say stable = +1 and unstable = -1 and partially stable = 0, the sum is always 0 or...?

>>10984409
why do you even want to study this shit
I have good grades but also "depressed". I'm planning an exit strategy.

>>10984823
Because it was the only thing that gave my life meaning. I thought I was in top of the world getting an A in Real Analysis and other higher level math classes. Abstract just proves to me that I am dumb as shit.

I am unable to concentrate on study due to a noisy upstairs neighbor. Earplugs can almost block out their incessant chatter and obnoxious laughter, but their constant stomping on the floor goes through my entire body and makes the fucking walls rattle. I feel like I'm in my own personal hell here. What can I do? My only alternative is the uni library and it's full of the exact same shit (ie. minorities acting with no consideration for the residents of the country they're guests in).

>>10983468
>the hint gives you the solution.
can you show me? i tried some stuff and ended up with pic related. I did some more attempts but i got stuck every time.

>>10985376
If f,g are real, |f+g|^2 = (f+g)^2 = f^2+fg+g^2 = |f|^2+|g|^2+fg. Also if f is real then, (F f)(-n) = (F f)(n)* (conjugate symmetry).

>>10985492
> (f+g)^2 = f^2+fg+g^2
(f+g)^2 = f^2+2fg+g^2

Is there a graphical representation of radius of convergence of power series? I don't get what is means tbqh. The wiki definition of it is: radius of the largest disk in which the series converges. Which means nothing to me

>>10985723
Take the series
[eqn]\frac{1}{1-x}=\sum x^i[/eqn]
The radius of convergence for this series is 1. This means the equality here holds only when -1<x<1. Did you want a picture or...? The mclaurin series for sine and cosine, on the other hand, converge for all values or x giving them an infinite radius.

>>10985749
Ohh I see thanks anon.

>>10985723
>radius of the largest disk in which the series converges.
dude what could be more geometric than this ?

>>10980546
Brainlet /sp/artan here, why does water hate oil and vice-versa? Keep it simple, friends

>>10985776
maybe this'll be up your alley:
https://www.youtube.com/watch?v=PVL24HAesnc

>>10985723
Note that a "disk" is a geometric disk in the complex plane. For real numbers, a disk of radius r about a point a means the interval a-r<x<a+r, i.e. the intersection of a disk of radius r with the real axis. In either case, it means |x-a|<r.

If you haven't encountered complex numbers (or you covered them as a distinct topic then promptly forgot about them), then a lot of post-HS math is going to confuse you, as it tends to assume complex numbers by default.

>>10984732
someone pls help

How does "will to life", or "holding on" affect a terminally ill person's ability to stay alive?
Is there anything empirical on this topic?

I got 2. Why does raising a number to the power of (i) change the real part?

Why are Asians so much more neotenous than other races?

>>10985776
>why does water hate oil
It doesn't, they technically do attract weakly. But since water forms such strong H-bonds with itself, it squeezes out any oil that might try and bond with it.
It's called the exclusion effect.

can i remove pulse width modulation pulses using a capacitor and/or a resistor???
>>10986629
thank you

>>10986070
> Why does raising a number to the power of (i) change the real part?
It essentially swaps the magnitude and argument:
z=re^iθ =>
z^i = (re^iθ)^i
= r^i.e^(i^2.θ)
= r^i.e^-θ
= e^(i.log(r)).e^-θ
=> arg(z^i)=log(|z|), |z^i|=e^-arg(z)

>>10986647
> can i remove pulse width modulation pulses using a capacitor and/or a resistor???
Not if you're actually trying to transfer power. For that case, you need an inductor and a diode so that you end up with a buck converter.

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

>>10983193
[math]test*sqrt(69)[/math]

[eqn]thank+you+anon[/eqn]

>>10983193
>>10986899
[math]jamal*tyrone = 0/0 + tan(90)[/math]

I have an analytic function defined somewhere, and I can extend its domain by analytic continuation.
Is there a name for when I have a continuous function and extend its domain by taking limits?

This should be banal, but I'm drawing a blank. How would you prove
[math]\sqrt6 - \sqrt5 > \dfrac{1}{4}[/math] ?

>>10987063
Disregard, I'm retarded.

>>10985376
1. Parseval on [math]h = f+g[/math].
2. Expand
3. Parseval on [math]f^2,g^2[/math]
4. ???
5. Paypal me $15 for doing your homework.

>>10987063
Add root 5 to both sides and square it

>>10983259
The Fourier transform sends multiplication to convolution.

The integral of f(x) = x from say -1 to 1 "seems" to increase as we move from -1 to 1 rightwards. We have "negative" area to the left of 0, and positive after it. However, the integral is x^2/2, who actually decreases first, and then increases. Why is this?

>>10987141
>The integral of f(x) = x from say -1 to 1 "seems" to increase as we move from -1 to 1 rightwards
It decreases initially.

[math]\int_{-1}^{-1}f(x)dx=0[/math]

[math]\int_{-1}^{-1/2}f(x)dx=-3/8[/math]

[math]\int_{-1}^0f(x)dx=-1/2[/math]

so im applying to grad schools soon (US citizen) and my goal is to apply for a phd and i have good grades and gre score for my target programs, but only one semester of research and not sure how good the other two letters of rec will be because of not really doing much extra to interact with professors so i fear i may have to do a masters first.
so because of this i was thinking of applying to one or two safety schools abroad (germany, switzerland) that would be cheaper and with scholarships would be much cheaper than the MS here, but would these be seen the same for phd admissions later on? or if i stayed there and got the full phd in europe would US industry and govt labs look at them the same as a domestic phd?
lastly, i could probably just do a MS at the school i want to do the phd at, would that make it much easier for phd admissions and maybe cost less or take less time?
thanks for any help

I can see computationally how, but as we move farther and farther left on the graph of f(x) = x, we get more and more "negative area". As such, I feel like its integral function should just become more and more negative. Surely, right? We're adding up more and more negative area. But it doesn't. It gets ever more positive.

>>10987285
That negative area is actually positive because to the left of -1 you're integrating the "wrong way."

>>10986732
thanks dudegonna chck on that

>>10986732
how can i use that without changing oltage though?

>>10987301
So how come that when I take the integral:
[math]
\int_{-x}^0 t dt
[/math]
it becomes more and more negative the larger x gets (i.e. we move further left) (which makes sense, we're summing up more and more negative areas), but its antiderivative gets more and more positive the further we move left?

>>10987322
Well now you've changed the function. That integral is -x^2/2.

>>10980546
thats a really cute 2hu

>>10980546
You know that effect when two gauge blocks stick together with nothing between them?
I dont know the name of the force doing this but is there a study or something that shows the effect on the thermal conductivity of the material during this event?

>>10987141
> The integral of f(x) = x from say -1 to 1 "seems" to increase
The integral of f(x) = x from -1 to 1 is zero. Zero doesn't increase (or even "seem" to increase) whatever you do.

>Show that signal g(t)cos(2pi*f*t) can be demodulated by multiplying it by 2cos(2pi*f*t) and passing the product through a low pas filter of bandwidth B Hz.

First I multiply the modulated signal by 2cos(2pi*f*t) and get 1+cos(4pi*f*t).

From this point, do I just consider this G(F) and find the inverse laplace? G(F) <=> g(t)?

>>10988940
fourier*
not laplace

How can i be smart like you guys?

Are traps gay?

How do in solve this problem with proportions? Book wants me to do unit rates from chemistry but I prefer proportions because I understand them better..

>>10988940
> From this point, do I just consider this G(F) and find the inverse laplace? G(F) <=> g(t)?
No. From there,
g(t)*cos(2πft)*2cos(2πft)
= g(t)*(1+cos(4πft))
= g(t)+g(t)*cos(4πft)
It remains to show that a low-pass filter will keep the g(t) term while discarding the g(t)*cos(4πft) term. If g(t) is a sinusoid a*cos(2πFt+φ) with amplitude a, frequency F, phase φ, then
g(t)*cos(4πft)
= a*cos(2πFt+φ)*cos(4πft)
= (a/2)*(cos(4πft+2πFt+φ)+cos(4πft-2πFt-φ))
= (a/2)*(cos(2π(2f+F)t+φ)+cos(2π(2f-F)t-φ))
i.e. multiplication gives you sinusoids with frequencies 2f+F and 2f-F. So long as B<2f-F, these will be discarded by the low-pass filter.

Dumb Question here.
I'm given this table of blood types in a population and they ask me to determine the probability of selecting 2 type Os.
But then they ask me, what the probabilty is for selecting 2 types that match.
What does match mean? Is that not the same as type O?

Stupid question but I wanna clear up some conceptual stuff before I move on
Say I have two subspaces of the plane [math](t,t),(-s,s)[/math]. By the most basic/common definition of a Direct Sum (Sum of all elements of both vector subspaces such that their intersection is just 0), the result would just be [math]\mathbb{R^2}[/math]. However, from a more generalized definition (which is used more in other categories I guess but it seemingly works here too, from what I read), the Direct Sum is the subset of the Cartesian product (and the respective operations) such that a finite amount of components of each element are non-zero. Since this sum is obviously finite, it's basically just the Cartesian product of two vector spaces. Which I guess is the reason why [math] \mathbb{R} \oplus \mathbb{R} = \mathbb{R^2} [/math].
Now, both direct sums give the same result, the plane. But if I do the first direct sum using the second definition, I'd get elements of the form ((t,t),(-s,s)), and if I do the second direct sum using the first definition, well I can't because the intersection is not only non-trivial, they are the exact same. So what gives here? Is this just the different between what's called an Internal Direct Sum and an External Direct Sum? And even if it was, from what I read they're supposed to be isomorphic, so why does the second sum exist for one definition of Direct Sum and not for the other?

>>10989545
Normally, I'd guess match means same blood type, in which case you need to calculate the probability of two type As, two Bs, two ABs and two Os and sum these up.
But this is blood type, so it probably means that one of them can't donate to the other, so the chance od getting an A and a B.

>>10989556
Internal direct sum [math]A \oplus B[/math] doesn't make sense unless there is some understood ambient space having both A and B as subspaces. You're right that [math]\mathbb{R} \oplus \mathbb{R} \cong \mathbb{R}[/math] as an internal direct sum, which is why it's understood to be external when written that way. In fact, almost every direct sum you see is assumed to be external unless you're explicitly writing out an example in a linear algebra class.

>>10989372
the car burns 4 gallons in 3 laps
so it burns 12 gallons in 9 laps
7 + 9 = 16

>Assuming that the phenotypes of two randomly selected individuals are independent of each other, what is the probability that both phenotypes are O?
I'm simply multipling (45/100) * (44/99) and get .2 however the answer is .1936
What am I doing wrong?
Should it be something like (99 nCr 44 / (45 nCr 100) + (98 nCr 4 / 44 nCr 99) ?

>>10989545
> What does match mean?
O donor matches O, A, B and AB recipient (i.e. anything)
A donor matches A and AB recipient (but not O or B)
B donor matches B and AB recipient (but not O or A)
AB donor matches AB recipient (only).

Given a 4x4 grid of donor/recipient pairs, 9 of the 16 possible combinations are matches, 7 aren't. Given the proportions of each of the 4 types, work out the probabilities of each of the 9 pairs which are a match (e.g. the probability of an AB donor and a B recipient is P(AB)*P(B)) and sum them. Also: you can simplify the calculations by summing before multiplying: a*b+a*c=a*(b+c). So the end result is:
P(O) + P(A)*(P(A)+P(AB)) + P(B)*(P(B)+P(AB)) + P(AB)^2.

>>10989590
Thanks, finally having that cleared up helps a lot. I'm actually studying about Direct Sums in modules, but since vector spaces are basically just a specific case of modules I was brushing up on the definitions used in Linear Algebra.
Now this isn't really part of what I'm studying since it's maybe more about categories than modules or vector spaces, but just out of curiosity, how does the isomorphism between external and internal direct sums work in this particular case? It's fairly easy to see that the element I mentioned in the first example [math]((t,t),(-s,s))[/math] could be mapped to the plane in a way that matches the concept of internal direct sum (componentwise sum), but isn't the case of the sum [math] \mathbb{R} \oplus \mathbb{R} [/math] a problem since it gets all messed up if you try to view it from the internal point of view? Is there a sort of workaround or extension for the definition of internal direct sum or is it really just an external sum with no "matching" internal sum?

>>10989673
It's as you said, the internal direct sum coincides with the external direct sum when the submodules have trivial intersection. The external direct sum [math]A \oplus B[/math] is defined to be the set of formal reduced R-linear sums of elements in the disjoint union [math]A \coprod B[/math] (reduced in the sense that their 0's are identified and a+a' evaluates according to the addition operation in A, for instance). It's clear that this is isomorphic to the internal direct sum when A and B have trivial intersection.

>>10989730
I think I got it, thanks a lot.

>>10981633
go to a thrift store and look for glass plates and cups etc that are a bright putrescent chartreuse green or yellowish green and use the uv light and then sell it to the russians

>>10982143
homemade modeling clay made out of bullshit
why would the lemon juice stop cutting up the chains if you think it does that? when does the citric acid get neutralized?

How should I address my lab instructor in an email?
Normally I start off with "Dear Professor," when talking to professors who actually lecture. In this case, he's literally some guy who earned his masters at the University I attend. He does this part time and has a "real" job elsewhere.

Best book for learning data science/data mining? Preferred if it has less to none business bullshit and tools shilling

>>10990165
Like you would address every other human being in a respectful manner?
Dear Mr. X

>>10984087
Why wouldn't you want that? The frenet frame (the basis {T, N, B}) is always the best place to work with space curves because it uniquely defines your curve and there are tons of relations between curvature, torsion, T, N, and B. Just in general, you always want to write things in orthogonal components. Here, a_T is acceleration along the path (speeding up/down) and a_N is acceleration perpendicular to the path (turning). Since these are such different effects, it is only natural to split them.

>>10985023
if you didnt do well in algebra and you did well in analysis, then keep doing analysis. they're just different ways of thinking.

>>10985303
Go tell them to quiet down you pussy ass bitch. They're not going to go crazy.
And if that doesn't work you can always tell the landlord that you're being disrupted constantly (assuming it's rented)

>>10986899
>>10986907
Use \sqrt{3} for square roots.
Use \tan for tangent.
Use \times for multiplication (I guess some use *)
Use either \frac{n}{k} or {n \over k} for fractions.
I think there's a basics guide in the wiki.

>>10985303
The university library in the morning is the best studying environment I have ever found.
But mine also has some small separate rooms where you can close the door so that others don't annoy you.

There also might be public libraries around you which you could check out.

>>10990901
I was in the same position as him and the people didn't give a fuck.
"No I do not care that we are celebrating an islamic Holliday at 1 in the morning with the entire family including constant shouting, stomping and crying children we refuse to bring to bed"
"No I won't turn down the volume of my TV to below Tinnitus inducing levels or stop shouting and stomping through the entire flat which doesn't even have rugs, just use headphones during the night or go to the library I am allowed to do what I want"
Good Lord I am glad that I know live below a girl which uses her flat as a skating park, never have I slept so well.

>>10991051
So you're saying you just went up and asked politely, and then said "okay" when they say no?
Tell them you'll call the police if they don't shut up.
Jesus christ. What is it like being such a pushover?

>>10991216
>So you're saying you just went up and asked politely, and then said "okay" when they say no?
I went up there and asked politely and when they basically said "I don't care, I do whatever I want" we had some stupid discussion which ended in them just saying "okay, I will turn it down", shutting the door and remaining as loud as ever.
This happened multiple times in some variation.

>Tell them you'll call the police if they don't shut up.
I called the police, they literally don't care saying something to the effect of "oh we currently don't want to sent anyone over for such a minor thing please call us back if something serious happens".
For the "landlord" option (the flat is rented by an organization) I would need to gather an actual documentation of this garbage including what when happened, etc. .
Which obviously was highly annoying and basically irrelevant since I was going to move out soon anyway.

Given u=(1,1,1) and v= (2,1,3)
1)Find the area of the triangle determined by these two vectors. (I think that it is sqrt6/2)
2) Find out if that triangle is isosceles.
I seriously can't do the point 2...

>>10991320
>I seriously can't do the point 2...
Have you tried drawing it?

(It's asking if the lengths of each side are equal you already know 2 of the sides, u, v the third is the line vector connecting u and v)

this is homework
how the fuck do I solve this
I cannot find a single equation to get me through the first part.

>>10991396
FOR ONE WEEK
FOR ONE FUCKING WEEK I THOUGHT THAT 1.3 WAS 13
FUCK THIS WORLD AND ITS DISCRIMINATION AGAINST THE LEGALLY BLIND

>>10989626
explain your logic like you would to a tard

>>10991396
>>10991427
and I still cant solve it FUCK

>>10991336
I couldn't.

Give me the quick rundown on topology pls.
Someone told me it could be very useful in economics but it all just seems like incredibly abstract and esoteric stuff to me.

I noticed that, upon a reflection from plexi glass, the first character of a spoiled text is greyed out. What is this?

>>10991538
>incredibly useful in economics
Economist here, you've been blatantly lied to.
Unless he didn't mean general topology, but specific things "within topology" like Morse theory or topological vector spaces, in which case yes, there is stuff.

>>10990820
>Mr.
Sounds awkward. I feel using his first name would he more approriate as opposed to this

>>10991606
youre right

start with "hey fuck face" instead.

>>10991538
What that person really meant was "someone far smarter than me mentioned some topological terms in a paper once."

H(j2πf) = 2π|f|/(2π5000), |f| < 5000 hz
H(j2πf) = 1, |f| > 10000hz
g(t) = 1.5cos(2π2000t) + 3.4cos(2π3000t)
g(t) is fed into this system and results in an output y(t)
Show that H(j2πf) causes amplitude distortion and no phase distortion of g(t).
I know that the requirements for there to be no amplitude distortion is the transfer function |H(j2πf)| must be a constant or 'k'.
For phase distortion, the phase of H(j2πf) must be constant.
But how do I show this? I'm having trouble showing H(j2πf) = 2π|f|/(2π5000) = ke^(-j2πft)

Why does coffee make me tired? It feels like I'm redlining then I just overheat and crash, I never actually feel more "alert" from it.

Also how to repair dopamine receptors after over a decade of porn abuse?

I put water on a 34 cm shallow flat bowl. I then poke one of the sides to produce a wave. How do I measure
>period
>frequency
>velocity
>amplitude
>lenth
of the wave?

>>10992642
>length*
Fixed.

Week out from exams on a general medicine exam. My current plan is to watch all of my lectures online at 1.5x speed and take notes into anki within the next 2 days, then pound anki for the 5 days after. Is there a more efficient way to do this or is it a solid plan?

Truth be told I could probably pass the exam without studying since I've sort of been paying attention but I want to spite all the Asian gunners by doing better despite not showing up to class due to have an actual JOB.

>>10992635
I'm pretty sure this means autism. I remember my co-worker saying this. Maybe not autism, but some shit like that.

>>10992769
Can't tell if you're memeing. Why would coffee making me crash be an indicator of autism?

>>10992635
I had this problem when I drank coffee all the time. Just quit cold turkey. Same for the porn thing.

>>10980546
Would anyone be able to explain to me what the asterisk (*) in the line that says g(v) = g(q) - g(p) means?

>>10993022
The asterisk is just used to denote that g* is a different (but related) transformation to g.

A rigid transformation has the form g(p)=R.p+t where R is orthonormal (i.e. a rotation). A rigid transformation preserves distances between points.

The corresponding transformation on vectors is g*(v)=R.v, i.e. it applies the rotation but not the translation. This can derived thus:
g*(v) = g(q)-g(p)
= (R.q+t)-(R.p+t)
= R.q-R.p
= R.(q-p)
= R.v

>>10993091
Thanks!

>>10980546
How do people like animators and manga artist work for so long and without rest for incredible periods of time? When I attempt doing that, I just end up either falling asleep or too energy exhausted to do anymore. Or am I? It’s more of a mental energy deficient, but is it really then too? Maybe it’s just a lack of focus and attention? There’s irritation too, not sure why that comes into play during tiredness or sleepiness, but hypothetically if you could ignore that feeling and just focus, you could get work done?

>>10993102
Also, I’m talking sort of about the concept of overwork. How can it be possible to overwork yourself when it’s so much easier to prevent it simply due to nodding off or such. People have overworked themselves to fatigue or to death? How? You would get so tired that you inevitably pass out, instead of collapse and other worse kinds of results. Is this what you call willpower? How can willpower bend and push the body and mind so far? Is it just that human limits are much further than we may anticipate? Or is having such a strong motive that much of a contribution to how chemicals react? In a way, it could potentially be interpretated as fear right? If you fear something enough, the body will probably react to counteract that and that’s quite possibly how soft limits can be pushed to the hard limits.

Brainlet relearning math here. Is that what the exercise wants me to do? How would I go about solving it if so?

>>10993397
I think so, do the same for b and c and solve each individual equation.

I'm not sure if it's my physics professor and physics textbook but boy do I really hate physics

It feels like nonsequitur after nonsequitur after nonsequitur. Stuff that supposedly builds off the previous stuff feels completely unrelated and not tied in at all with the old material.
Stuff that was supposed to be a symbol with no deeper meaning behind it is suddenly something with a value that I have to remember, and suddenly it can be algebraically manipulated

Whenever I'm in my physics lectures I feel so fucking lost. There's no intuition behind any of it all. It feels so hand-wavy and non-rigorous, especially coming from calculus. Is it supposed to feel this way? Be like this?

>>10991431
oh I thought I was already doing that...

After lap 4 there's 22 gallons left and after lap 7 there's 18 gallons left.
So the car burns 4 gallons in 3 laps.

After lap 7 there's 18 gallons left and we want to know how many more laps it will take until there are only 6 gallons left.
So we want to know how many laps it takes to burn those 12 gallons.
Since it takes 3 laps to burn 4 gallons, it takes 9 laps to burn 12 gallons.

Lap 7 + 9 laps = Lap 16

Okay /sci/ dumbass in intermediate algebra in college, and I am taking online classes. I am reviewing my quiz, and I missed a question and 66% of another (3 sub questions in a question)

>pic related

Is the question I missed, and I provided my process of getting my answers, can someone tell me what I did wrong or how I was suppose to approach it?

>>10994027
you need to add the equation 16x + 6y = 15 to the equation 12x - 6y = 6 to get 28x = 21
you subtracted some shit instead

>>10994027
You didn't add/subtract the equation correctly. Instead, you subtracted the x term and the result and added the y term. Instead, you should be getting 28x = 21.

>>10994046
>>10994057
oh man, wdf I did it correctly on the other questions, but this one I went full retard...

Thanks anons.

Does the axiom of choice force well-orderings into existing or does it prevent sets that can't have well-orderings from existing?

>>10991588
to be fair, when physics and other fields that apply mathematics throw the word "topological" around they often mean some weirdly specific topic like that, of which a particular example happens to be useful.

>>10994069
That's basically the same as asking if the axiom of choice is "forced" on every set or if there can be sets that don't obey the axiom of choice. We define the axiom of choice precisely because we believe it is a universal truth about set theory as a whole, so we declare that it applies to all sets. Ultimately the Well-ordering Theorem's proof follows as a consequence of Zorn's lemma, which is a consequence of the axiom of choice (and they are all equivalent so it's an even stronger relationship), so if the Well-ordering theorem wasn't true for a set you'd be saying that in that set the axiom of choice isn't true.
Note that if you don't want to assume the axiom of choice as a truth, there can be sets that don't have well-orderings. But if you then assume choice, nothing prevents you from defining those very same sets, and now they will automatically have a well-ordering. So even if I don't like the wording so much, the former is more accurate.

can anyone explain to me how to get this result:
[math]n(n-1)...(n-k+1) = \frac{n!}{(n-k)!}[/math]
thanks

>>10994879
n! = n(n-1)(n-2)...(n-k)(n-k-1)...
(n-k)! = (n-k)(n-k-1)...
=> n!/(n-k)! = n(n-1)(n-2)...(n-k+1)

>>10984732
Bumping for this

Am I allowed to do this? I continued and solved it then plugged it back in and it worked but it feels weird to me

>>10995258
You can't do absolutely anything that splits dy/dx into dy and dx, but it still usually works.

[math]
\exists x \; (A(x) \to B) \leftrightarrow (\forall x \; A(x) \to B)
[/math]
this was posted on a professor's site, is it wrong?

>>10995365
yes that's wrong

>>10995365
Yeah.
It's been a good while since I've last touched logic, but it depends on whether you fix x as you switch from A to A or not.
For a given A, then there is some x, obviously. But for all A, there is no single x that always works.
Since there's no for all A in the beginning, it's clear he's fixing A.

>>10995386
>Yeah
*No, it's not wrong. The formula is correct.

What did they do here? Multiply by conjugate? I don't understand this step in this example problem.

>>10995393
It's the difference of squares identity, goyim.

>>10995393
It's (1-a)(1+a)=1-a^2+a-a=1-a^2, lad. He just set [math]a= \sqrt{x}[/math]

>>10995395
>>10995410
ok thanks

>>10995393
to reduce the term in the numerator.
also I would have just used L'Hospital's rule.

Are calculus theorems universally numbered? This Early Transcendentals book just labels them theorem 1,2,3 etc. Is this how they are described universally? Same with limit laws. Like is limit "law 5" universally known as the quotient law?

why didn't you guys tell me mineralogy is so comfy?

>>10995611
lol, no anon. thanks for the wholesome chuckle

why does wolfram give a negative solution to y' = ty^3, y(0) = c ? It doesn't look like it works if you plug in, and gives y(0) = -c. Same thing with matlab
https://www.wolframalpha.com/input/?i=y%27%3Dt*y%5E3%2C+y%280%29%3Dc

>>10995810
nevermind

how do you go from left to right? I tried to solve the system for r, phi and rho but I can't get those expressions

>>10996371
Basic trigonometry

>>10996371
First check what x^2 + y^2 + z^2 is, try using your Pythagorean identities.
Then check what y/x is.
Finally, what is z/r?
If you're given a function and its inverse, and you're trying to show that the inverse is correct, you don't need to rederive it yourself. You just need to show that plugging in the outputs from one into the inputs for the other gets you the right thing.

Any good alternatives to Jewett's Physics for Scientists and Engineers, 9th ed? This textbook sucks.

>>10996385
Can you be more specific? I could get this far (I know it's stupid)

>>10996390
I don't want to show that the right one is correct, I want to find it from the left one. Because the left one is easy derive by just looking at a sketch, but I can't remember the right one

>>10996503
>>>10996385
>Can you be more specific? I could get this far (I know it's stupid)
Ok, I'll give you a derivation that will make you remember easily the right one. First take into account the Fundamental Theorem of Trigonometry (that's why I said that it's basic trigonometry): [math] \sin^2(x) + \cos^2 (x)=1 [/math]
With that look at x and y. Oh, their only difference is that one has a cos of phi and the other has a sin of phi... Why don't we use this theorem to simplify it?
Let me define then [math] \rho= \sqrt{x^2+y^2}=r \sin \theta [/math]. Look, we can do it again with this rho and with the z, and that's how you get the first equation.
The second equation is just dividing the definiton of y by the definition of x and solving for phi.
The third equations is just solving for theta in the last equation and then substituting the value of r.
I hope now you get it.

>>10996521
I got it, thank you

Has anyone done infrared therapy? Does this shit work?

please help out mathlet+brainlet here

In my east european country 1 kWh is about 1 euro cent, lets say now I use 1.56 kW per hour, and 6 hours a day (9.36 kW per day) and 30 days, 280 kW, how much am I going to pay at the end of the month?

>>10997016
280 euro cents.

>>10997027
this is actually what I got, but can that be right? I mean 1.56 kW for 180 hours sounds a lot and more expensive

>>10997037
1.56kW * 180 h=280.8 kWh.

>>10997037
Well, 1 cent/kWh is extremely cheap. In the UK, typical unit price is around 13p (~€0.15) +VAT per kWh, plus a standing charge of 20-25p (+VAT) per day.

>>10996486
this person here >>10993525
thank fucking god I'm not the only one who hates it. What's it done to you that you hate it so much, just so I can see if I'm not alone in what I've noticed.

I wound up finding a PDF of Young and Freedman's University Physics (ISBN 13: 978-0-321-69686-1)

>>10997467
>What's it done to you that you hate it so much
This is about the textbook, but it's all over the fucking place. I want to just focus on mastering one topic at a time and it switches to questions unrelated to what you just learned about. That and I wish it showed the work done to get to the solutions. I like seeing the path someone takes to get to a response. This book's explanations refer back to the dumb stories from the start of the chapter, and suddenly mention how theories can be used in totally different case scenarios that mess you up, then it simply refers to "use formula 1" when I want more of an understanding about solving the question.
I agree with this anon >>10993525 about feeling so dumb with physics. I've done calc and chemistry courses in the past but I feel like a brainlett with physics.
Thanks for the rec though anon.

>>10997733
I'm that guy, and we've been using Jewett Physics for Engineers as well.

The book doesn't even have problems worked out that you can practice on and learn from. Then the problems at the end of each section are always so ball-crushingly esoteric and difficult, they don't ramp up the difficulty and drill in the basic concepts before sending you curveballs. It's just trick shots one after another.

The solutions manual is even more fucked up. A lot of the solution methods for the problems are never even hinted at, let alone explained in the body of the text. I remember explicitly a problem from Physics 1 that used a formula which had never been introduced in the book.

This textbook blows ass.

>>10997758
>Then the problems at the end of each section are always so ball-crushingly esoteric and difficult
Fucking this too.
Sucks that most physics courses offered in my area use this damn textbook and its online assignment feature.

In the context of image processing, there exist convolution matrices or kernels that are used to manipulate the image in particular ways, according to what the user needs. There are multiple lists of the most common kernels, but how are they found or calculated? Do people just try out different matrices and see how they affect the image? Or is there a more scientific way to find useful kernels?

>>10998128
If you know what you want in the frequency domain, you can use an inverse Fourier transform to get the corresponding kernel.

how do you directly prove x^2+y^2=2k => x+y=2k for natural k

>>10998286
> how do you directly prove x^2+y^2=2k => x+y=2k for natural k
You don't, because that's wrong. Did you mean to say that both expressions are even? If so, you shouldn't have used "k" in both cases, because that implies that they're identical.

Assuming you did:
1. (2k+1)^2 = 4k^2+4k+1 => the square of an odd number is always odd => if x^2 is even then x is even.
2. (x+y)^2 = x^2+y^2+2xy. 2xy is always even, so if x^2+y^2 is even then (x+y)^2 is even and so x+y is even.

>>10998149
Thanks. In this particular case, how would I go about interpreting that for real number matrices instead of continuous real/complex functions (which is the case I'm the most familiar with)? I guess it'd be using the inverse discrete Fourier transform and analyzing the values in the matrix as a one-dimensional array of real numbers?

>>10998704
2D DFT.
https://en.wikipedia.org/wiki/Discrete_fourier_transform#Multidimensional_DFT

Whereas a 1D DFT gives you the coefficients for terms of the form f(t)=c[n]*e^2πi(n/N)t (a wave with period N/n), a 2D DFT has terms of the form f(u,v) = c[m,n]*e^2πi((m/M)u+(n/N)v) (a plane wave whose "period" is the vector [M/m,N/n]).

As in the 1D case, the product of DFTs of arrays is the DFT of their discrete convolution.

For real data, the DFT has conjugate symmetry. For a 2D DFT, this means that X[m,n] is the conjugate of X[M-m,N-n]. A DFT specialised for real data will typically return half the data of the complex case (i.e. the input and output will have the same overall size in spite of the output being complex), but exactly which half varies between implementations.

Anyone help me with this?

Is S&Z the best precalc book? The book itself is really good but exercises are too easy.

>>10998977
Thanks, I guess I'll have to do some reading on that then.

would this work?
(ignoring the orbital mechanics, force-to-move-stick and material-of-stick issues, unless those are the only reasons it wouldn't)

>>10999420
At such longs distances, the stick would act as a dampening spring. the material itself would absorb the force of the push so that it wouldn't ever actually move on the far end.

>>10999420
the pressure moves through the stick with the speed of sound of the material the stick is made of, so it would take much longer.

When spacetime is being created is there more energy being created and what about the second law of thermodynamics?

When space expands it can be argued that no new space is being created, that it is just being stretched. Ok. But what about time? Time is constantly being created, there is unarguably more of time since there was at the big bang. So at least one part of spacetime is constantly getting a larger numerical value. What happens to energy in these circumstances? Is there more energy being created or does it stay the same.

>>10999488
>the material itself would absorb the force of the push so that it wouldn't ever actually move on the far end.

So which is it? There's still force on the other end of the stick..

>>10999495

>the pressure moves through the stick with the speed of sound of the material the stick is made of, so it would take much longer.

Wood is not sound.

>>10999605
>So which is it? There's still force on the other end of the stick
>using newtonian mechanics to analyze lightyear sized objects
>wood is not sound
?

>>10999605
>So which is it? There's still force on the other end of the stick.
It bends.

>>10999804
surely the bending will transmit some movement to the other end which could be measured to communicate?

>>10999884
Nah, that would violate relativity.

How do i find the total reluctance? I’ve found the reluctances (or the resistors in the circuit) but don’t know where to go from there. Do I just do (R1+Rg1)||(R3)||(R2+Rg2)?

Why are distance-speed-time problems so common in math?

>>11000085
Because ambiguity of the matter provides lots of gotchas which as you know is the favorite way of one mathematician telling another that he is stupid.

Ive heard that if i want to go into industry after my phd in should try to work with professors with good connections to industry, but how would i got about finding the connections these professors have?

Any Mathematica experts around?

I need an explicit derivative of a very complex function that I'm currently writing. To better write the function I introduced some variables like a=..., but these variables have inside them the independent variable, like pic related. Theta would be the independent variable of beta. The function I want would be like beta(theta1) * beta(theta2) etc, so I was hoping the replace command would help me there.

Except it really didn't. I am very inexperienced with this software and I'm probably doing something really stupid. To get the complete expression I'm using Simplify (which takes a while), but the t from the a and b are still there even though I explicitly asked the beta function to substitute it with theta.

What should I be doing instead?

Trying to make a neural network myself. Let's say I have 2 batches of inputs, (x_1, x_2,...,x_i) and (x_i+1, x_i+2,...,x_n) with their corresponding outputs (y_1, y_2,...,y_i) and (y_i+1, y_i+2,...,y_n). If I use Feed Forward, so I have to take x_1 to x_i into the network, backpropagation them, and take x_i+1 to x_n into the network and backpropagation them again to count as 1 epoch, right?

Anyone take abilify before? I just got prescribed some and I'd like to know what I'm in for

>>10980546
How do instincts work?
Does the DNA just code pre-packaged neural connections?

In vector addition, is the second vector (the one connected from the head of the first) set as its coordinates + the offset? So if A = {2, 2} and B = {1, 1}, B would be connected to A from the offset of the head + its own coordinates?

In my multivar calc exam they asked us to solve the gaussian integral over the positive reals by integrating over these 2 sets:
[math]\mathfrac{A_1}=\{(x,y)\in \mathbb R^2 \, | \, x\in[-R,R],\, y\in[-R,R]\, , R>0\}\newline
\mathfrac{A_2}=\{(x,y)\in \mathbb R^2 \, | \, x^2+y^2\leq r^2\, , r>0\}[/math]

I just squared the gaussian integral and switched to spherical coordinates, no single idea how I was supposed to use the integral over these 2 sets. I kind of did use both of them if you assume r->infinity, and that e^-(||x,y||) is symmetric in regard to both 0xz and 0yz planes and and take some cuts but that's not rigorous. What was I actually supposed to do here?

>>11002150
That should have rendered. Here is the pic.

>>11001551
what is its chemical compound? amisulpiride? if yes then i am taking it and i think i see less delusions and less disorganised thinking because of it

Is it important that I learn how to code if I am to get a PHD in physics or mathematics?

>>11002173
Yes. Simple python scripts is the absolute minimum.

>>11002173
Yep. Just learn very basic python and read about those "data analysis" libraries.

>bio, Chen and math are really cool to do but are really difficult to learn
What do?

>>11002855
Chen is a very micro heavy hero

why is the finite condition required?

How do I not forget what I’ve previously learned after a lesson on a new topic? How do I remember everything?

>>11003480
>here's what I've concluded so far but it feels cheap:

summation simply isn't defined over an infinite set because a vector space isn't naturally equipped with a metric which would allow the use of limits

>>11000852
anyone?

>>11003480
>>11003590
Remember how a vector space was defined? For two elements a and b we have a+b?
From that, you induced sums of n elements by doing ((((...(a+b)+c)+d+....), that is, you exploited associativity to repeat sums of two elements until you've added them all up.
But, if you'll notice, you haven't actually defined any way of summing an infinite amount of elements. You can add a metric or a topology to your vector space, and then define some infinite sums, but a pure vector space only allows finite sum.

how should i put my undergrad "research project" on my resume for internships/grad school if all he is having me do is a small part of a research proposal? shouldnt i be vague so the idea isnt out but how do i be vague of such a small thing and how do i make such a small part look notable enough for a resume

I need help with understanding this. Does this mean that the outcomes are of the form CCLLSS or Could one such as CCCCCS exist? It doesn't seem obvious which one is the case from the question.

Is [math]|x^2| = |x|^2[/math] correct?

>>11004084
Obviously not, how can -(x^2) ever be x^2?

>>11004088
what the fuck am i reading

>>11004084
yes

>>11004088
fuck are you on about?
give me a number x such that the equation is false

This is indeed a stupid question.

66% of students study for 6 or more hours the day before the exam. If they do so, the probability of them passing the exam is .68, while if they study for less than 6 hours, the chances of them passing the exam is merely .5.

What is the probability a randomly selected student passes the exam?

So obviously we have [math]P( Pass \cap >6 hrs ) = .68 * .66 = .449[/math] and we have [math] P( Pass \cap <6 hrs) = .5 * .44 = .22[/math]

My assumption is that these are disjoint sets, so, we can just add the probabilities, [math].449 + .22 = .669[/math]. But this is wrong, apparently.

What am I doing wrong? I know the formula for conditional probability, but I don't see how it applies here.

>>11004084
What domain is x in?

>>11004210
You just used the formula for conditional probability, shit's correct.
Are you sure the question was asking what's the probability of an average student passing?

>>11004210
0.66+0.44=1.10

>>11004261
Actually, I've only noticed it now, but you're using .44 instead of .34.
>>11004262
What a lad.

>>11004269
>>11004262
oh wow i'm retarded

thanks lads

Need one more letter of recommendation for grad school (optics/photonics) and not sure who to ask between two professors:
>Got an A in the class, was pretty handson class with only 3 other students, in a related area (rf/antennas) but not in the exact area, he does some work with photonics, assistant professor
>Got a B+ .5 points away from A- mostly just from fucking up on one of the tests but finished strong, class was over photonics and optics, lab component that i did well in but was mostly supervised by the TA, not a professor but a Phd and Facility Director for a research center at the university

>>11004306
why would you not ask both

>>11004308
i only need three letters and i have two professors already doing them

So was it all just dust in the end? Or is there still some mystery to it and investigations going on?

>>11004306
Flip a coin.

>>11004466
t-thanks

I'm trying to show that the derivative of f_a = a * f(a) /(1+z).

However, when I differentiate term-by-term I get nothing that looks like it could be used to give me an expression of this form.

Wtf am I doing wrong?

Can I get some help with a homework question guys? This is busting my ass, I've tried everything but it's still not right. I understand the programming but it's the math that's fucking me up.

here's the question

>Linda is starting a new cosmetic and clothing business and would like to make a net profit of approximately 10% after paying all the expenses, which include merchandise cost, store rent, employees’ salary, and electricity cost for the >store.
>She would like to know how much the merchandise should be marked up so that after paying all the expenses at the end of the year she gets approximately 10% net profit on the merchandise cost.
>Note that after marking up the price of an item she would like to put the item on 15% sale.
>Instructions
>Write a program that prompts Linda to enter:
>The total cost of the merchandise
>The salary of the employees (including her own salary)
>The yearly rent
>The estimated electricity cost.
>The program then outputs how much the merchandise should be marked up (as a percentage) so that Linda gets the desired profit.

my code looks like this:

#include <iostream>
#include <iomanip>
using namespace std;
int main()
{
double cost;
double salary;
double rent;
double electricity;
double x;

cout << "Enter total cost of merchandise: " << endl;
cin >> cost;
cout << "Enter salary of employees: " << endl;
cin >> salary;
cout << "Enter rent: " << endl;
cin >> rent;
cout << "Enter Electric bill: " << endl;
cin >> electricity;
x = (cost + salary + rent + electricity);

cout << fixed << showpoint << setprecision(2);

double markup_percent = ((x * 1.1) / ( cost * 0.85) ) * 100.0;
cout << markup_percent;

return 0;
}


what the fuck am I doing wrong?

Can someone explain what Fourier transforms are in VERY simple terms? The textbook I'm looking at says that they 'separate a function into its frequency components'. That means fucking nothing to me since I'm a brainlet medfag.

Another source said it was a way to express a waveform as a weighted sum of sines and cosines. I still don't know what most of those words mean aside from waveforms.

>>11005347
>Can someone explain what Fourier transforms are in VERY simple terms?
There are two concepts here: Fourier Series and Fourier transforms.
1. Fourier Series: any periodic function F(x+L)=F(x) can be expanded in sum of sines and cosines with the same periodicity (this means the same frequencies or multiples of it). This is because sines and cosines form a complete basis of blah, blah, blah, you don't care about this.
What is the idea? Similar to a Taylor expansion: if you have F(x+L)=F(x), at first order you can say it's approx. A*sin(phi+2*Pi*x/L), with A and phi constants. It's better if we don't use the phi, so let's write it as B*sin(2*Pi*x/L)+C*cos(2*Pi*x/L), where B and C are constants you have to determine. This is the first order of your approximation, akin to f(x)=f(0) in a Taylor expansion.
This is a very poor approximation, so we can improve it adding the next term (like in a Taylor expansion we go from f(x)=f(0) to f(x)=f(0)+f'(0)*x). In this case the next term is D*sin(4*Pi*x/L)+E*cos(4*Pi*x/L), where again D and E are constants you have to determine.
You can continue and, in general, the nth term is given by Bn*sin(2*n*Pi*x/L)+Cn*cos(2*n*Pi/x).
2. Fourier transform: it's a continuous version of the Fourier series. When you take L to infinity, the sum over n becomes a integral and some wonderful properties appear.

>>11005347
A Hilbert space is a vector space equipped with an inner product and completeness, the latter being irrelevant right now.
You've probably learned that an inner product allows you to canonically decompose vectors in R^n into finite sums of orthogonal vectors. That's nice, but we'll use something a bit weaker: when you have a vector x and a vector y, <x, y> gives you the component of y in x. You'd normally use this to give x as a sum, but right now we're only interested in the value.
The space of Riemann-integrable functions defined from a to b admits the inner product [math]<f, g>= \int _a ^b f(x) \overline{g(x)} dx[/math]. You should have learned that the function [math]e^{it}[/math] spins around the complex unit circle. By taking [math]e^{ist}[/math], the extra factor s adjusts the speed at which it spins, that is, the frequency.
So we set up the Fourier transform as (some adjustment constants have been ommited) [math]F(s)=<f(t), e^{ist}[/math], that is, the component of f at a certain spinning frequency.

>>11005374
>>11005432
So I appreciate the detailed responses, but I'm purely looking at this from a 'words' perspective. I basically just need to explain what a Fourier transform does to a signal from a CT scanner's raw acquisition data. My mathematical knowledge only goes up to the basic integration I did in high school. Give me shit if you want but we are in the stupid question thread.

>>11005438
>the explanation in the book is too short, explain this to me
>wait no, those few paragraphs are too long
Lad, you either accept that it decomposes the function into frequencies or you demand to know how does it do that, in which case you'll need to suck it up and read a proper explanation.
There is no half understanding things.

>>11005438
>I basically just need to explain what a Fourier transform does to a signal
Ok, let's go back to the Fourier Series. There you have (in exponential functions instead of trig)
[math] f(x)=\sum_{n=1}^\infty a_n e^{2 \pi i n x/L} [/math]
when L goes to infinity you get the Fourier transform
[math] f(x)=\text{const.} \int_{-\infty}^\infty f(\omega) e^{i \omega x} [/math]
where f(\omega) plays the role of the a_n before.
What were the a_n before? They told you how much of each of the frequencies you had. The f(\omega) does the same, but now as a function of the frequencies instead of a discrete series.
The Fourier transform of a signal is this f(\omega), and tells you the different frequencies involved in it.

>>11005450
I think I might just accept I'm retarded and just spout the textbook question.
>>11005460
This sort of makes sense to me but you're definitely wasting your breath on me. Thanks for the help though.

I see the words "calculus" and "precalculus" thrown around a lot but I'm not sure what they mean, as in what kind of math they include (I'm European and I've never used these terms). Are limits and derivatives part of calculus?

>>11005577
yes, calculus 1 is mostly limits and derivatives while calc 2 is usually integrals and some series like taylor series. precalc is the class right before calc and i dont even remember what it covers, i think it at least covers trigonometry and then some more shit.
calc 3 is multivariable and partial derivatives

Let p be a prime > 2.
Show that
>pic related
is divisible by p.
I'm pretty sure I have to use Fermats little theorem but I don't understand how to apply it. Would appreciate some help lads

>>11005577
"Precalculus" really doesn't have much to do with calculus (analysis as I think you all call it) at all.

Precalculus is an introduction to a bunch of mathematical concepts and methods that don't really fit into College Algebra (basic algebraic manipulation, interpretation of graphs, function transformations) or Trigonometry.
Primarily, what would be covered in a Precalc course would be
>Introduction to Conic Sections and how they're derived
>Implicit functions
>The difference quotient
>Matrices and elementary linear algebra
>Introduction to Infinite Series (really just Geometric series, actual series analysis here is in Calc II)
>Introduction to complex variables (but not complex functions)
>Sometimes limits, but that's dependent on your college

Calculus I is typically a STEM/Engineering-oriented non-rigorous/non-proof-based course on
>Limits, their properties, and their evaluation
>Derivatives of elementary functions
>Properties of derivatives
>Chain, product, quotient rule
>Mean Value Theorem
>L'Hospital's Rule
>Rolle's Theorem
>Optimization using Derivatives
>Implicit Differentiation
>Related Rates
>Very basic intro on Integration
(continued)

>>11005779
>>11005577
Then, Calculus II is a bit of a mixed bag of concepts relating to the infinite. A lot of it is Integral Calculus, though
>Applications of Integrals to Science and Engineering (hydrostatic pressure, average value of a function, volume and surface area of a solid of rotation, arc length)
>Techniques of Integration (Integration by parts, trigonometric integration, trigonometric substitution, integration of rational functions by partial fraction decomposition)
>Integral/Differential Calculus of parametric functions
>Integral/Differential Calculus of polar functions
>Sequences and their properties
>Infinite Series and their properties
>Evaluation of series
>Rules for testing the convergence of infinite series
>Power Series
>Taylor/Maclaurin Series

Then there's Calculus III, which is pretty much all of the above, but in 3 dimensions, and also vector calculus
>Intro to the mathematical interpretation of a vector
>Vector functions
>Partial derivatives
>Lagrange Multipliers
>The Del Operator
>Divergence, Curl
>Green's Theorem
>Stoke's Theorem
>Line Integrals
>Multiple Integrals
>Vector Fields

is there any way to make textbooks remotely readable on an ereader like a kindle? I'd love to just have to carry it around rather than lug textbooks around everywhere

I have an exercise that asks to "show that the continuity equation is consistent with the maxwell's equations". The continuity equation should be [math]\partial_\mu J^\mu=0[/math] and maxwell's equations: [eqn]\partial_{\alpha}F^{\alpha\beta} = \mu_{0} J^{\beta}[/eqn]
[eqn]\partial_{\alpha}(\tfrac{1}{2}\epsilon^{\alpha\beta\gamma\delta}F_{\gamma\delta})=0[/eqn]
So what do they mean exaclty, and what am I supposed to do?

>>11005863
Derive first one and use that F is anti-symmetric.

I know this is a glorified homework thread but a dumb question just poped into my head while playing a game. Could there be any useful resources on foreign planets that couldnt be found on Earth? I dont mean like trees and stuff but like an unobtanium.

>>11005778
I gave it a shot despite never having seen this; consider:

[eqn]\sum_{k=1}^{p-1}k^p = 1^p + 2^p + ... +(p-1)^p [/eqn]. You can apply Fermat's little theorem by subtracting
[eqn]\sum_{k=1}^{p-1}k^p = 1^p + 2^p + ... +(p-1)^p - \sum_{k=1}^{p-1}k[/eqn] which is then divisible by p. Tinkering with the last sum (shifting the index etc.) you can show
[eqn]\sum_{k=1}^{p-1}k = \frac{p(p-1)}{2} [/eqn]. As this is divisible by p it follows that the original sum must also be divisible by p.

>>11005885
I understand the first and third equation but I don't see why you subtracted the sum
$$\sum_{k=1}^{p-1} k$$
I guess my problem is with the application of Fermat's little theorem.
Thanks for your help!

>>11005935
>i cant latex

>>11005881
It seems to be the case that all 'normal' material is just made out of atoms/molecules, and all stable atoms seem to exist on earth, albeit some more scarcely than others. Basically by virtue of being part of the periodic table everything is here or we can probably make it out of other elements.

There are things like metallic hydrogen, which is what you get under huge pressure and temperature, but that wouldn't be stable under normal earth conditions, so it's not that useful in the sense that making it is about as hard as storing it, probably. (Metallic hydrogen can probably be found on Jupiter and Saturn)

Then there is stuff like neutron stars and black holes, but again that wouldn't be stable in any way; a chunk of stuff that a neutron star is made out of would under normal conditions (not in the enourmous gravitational pressure of a neutron star) probably fly apart or radiate away.

>>11005875
Ok so you mean this?[eqn] \partial_\beta J^{\beta}=\frac{1}{\mu_{0}}\partial_\beta\partial_{\alpha}F^{\alpha\beta}=-\frac{1}{\mu_{0}}\partial_\beta\partial_{\alpha}F^{\beta\alpha}[/eqn] and then? How do I show that it's zero?

>>11005954
So "unobtanium" could exist on strange bodies as simply certain shapes and combinations of atoms? But they also wouldnt be of any use on earth really?

>>11005875
Ok so you mean doing this? (pic in case the rendering doesn't work)
[eqn]\partial_\beta J^{\beta}=\frac{1}{\mu_{0}}\partial_\beta\partial_{\alpha}F^{\alpha\beta}=-\frac{1}{\mu_{0}}\partial_\beta\partial_{\alpha}F^{\beta\alpha}[/eqn]
then how do I show that it's zero?

>>11006009
>Ok so you mean doing this?
Yes

>then how do I show that it's zero?
Remember now that [math] \partial_\alpha \partial_\beta=\partial_\beta \partial_\alpha [/math].

>>11006009
>>11006033
Also, don't forget that you can freely relabel summed indices, i.e. [math] \partial_\beta \partial_\alpha F^{\alpha \beta}= \partial_\alpha \partial_\beta F^{\beta \alpha}[/math]

>>11006033
Alright I got it, thank you. What about the second maxwell equation though? Does the excercise mean only the first one?

>>11006077
I think you don't need the second one in this case.

>>11005942
I subtracted that to be apply to apply Fermat's little theorem, as far as I can claim to understand it. You need those factors to show [math]a^p-a[/math] is divisible by p, I think. Err, should be on the LHS too as I just noticed.

>>11006101
To clarify:
[eqn]S = \sum_{k=1}^{p-1} = 1^p + 2^p+...+(p-1)^p[/eqn]
We can subtract
[eqn]S - \sum_{k=1}^{p-1}k= \sum_{k=1}^{p-1} = 1^p + 2^p+...+(p-1)^p - \sum_{k=1}^{p-1}k [/eqn]
such that
[eqn]S - \sum_{k=1}^{p-1}k = (1^p -1) + (2^p - 2 ) +...+ ((p-1)^p - (p-1))[/eqn]
which should be divisible by p by Fermat's little theorem. Showing the sum is a multiple of p then implies the original sum is also a multiple of p.

>>11006126
Got it, thanks!

>>11006126
[eqn]S - \sum_{k=1}^{p-1}k= 1^p + 2^p+...+(p-1)^p - \sum_{k=1}^{p-1}k [/eqn]
This should be eq. 2.

>>11005942
>can`t Tex
Gotchu lad.

>>11006228
Damn getting spoonfed today, appreciate it man.

>>11001137
Collect everything in a single Module.
>>11003519
You are correct. The "for all finite collections of [math]X[/math]" type of statements are how one extends finite-dim notions to infinite-dim cases formally without any additional assumptions.
Without a norm (hence a Banach space) you cannot make precise the notion of convergence. Even with the slightly weaker notion of seminorms, we still directly work with finite subsets of the family for convergence/uniformity statements.
>>11005347
The Fourier transform is a morphism [math]\mathcal{F}:X \mapsto \operatorname{Hom}_\mathbb{C}(X,U(1))[/math] into the space of irreducible characters of a compact Abelian group [math]X[/math]. Pontrjagyn duality then states that [math]\mathcal{F}[/math] is idempotent.
>>11005863
Apply [math]d\ast [/math] to Maxwell's equation [math]d\ast F = J[/math] to obtain [math]d\ast d \ast F = d\ast J = d \delta F[/math] as [math]\ast d \ast = \delta[/math] is the codifferential. However since [math]F[/math] is exact with [math]dA=F[/math], [math]dF = 0[/math] hence [math]d\delta F = (d\delta + \delta d)F = \Delta F[/math], where [math]\Delta[/math] is the Laplacian. The Lorentz gauge then implies that [math]F = F_\text{harm}[/math] is harmonic hence [math]\Delta F = d\ast J = 0[/math].

>>11006321
>Apply d∗ to Maxwell's equation d∗F=J to obtain d∗d∗F=d∗J=dδF as ∗d∗=δ is the codifferential. However since F is exact with dA=F, dF=0 hence dδF=(dδ+δd)F=ΔF, where Δ is the Laplacian. The Lorentz gauge then implies that F=Fharm is harmonic hence ΔF=d∗J=0.
Why doing that when you can just apply d instead of d∗ and get it instantly using that d^2=0?

>>11006340
Because [math]dJ[/math] is not [math]\operatorname{div}J[/math], [math]d\ast J[/math] is. Remember, [math]J[/math] is a 1-form and [math]d[/math] is a graded differential of degree 1, so [math]dJ[/math] is a 2-form while [math]d\ast J[/math] is a 4-form. On orientable 4D spacetime, [math]\Omega^0 \cong \Omega^4[/math] where the isomorphism is given by multiplicaiton by the volume form [math]d\operatorname{vol}\in\Omega^4[/math] so [math]d\ast J (d\operatorname{vol})^{-1}= \operatorname{div}J[/math] is an actual number.

Why is [math] \left( \matbb{C}, \mathbb{R}, + \right) not a complex vector space?

Why is [math] \left( \matbb{C}, \mathbb{R}, + \right) [/math] not a complex vector space?

>>11006361
Because it's over the real numbers.

>>11006369
Then [math] \left( \mathbbR , \mathbbC , + \right) [\math] is a complex vector space?

>>11006379
>>11006369
Then [math] \left( \mathbbR , \mathbbC , + \right) [/math] is a complex vector space?
i suck at TeX

If the probability of A is 1/n, what is the probability of A happening given n chances for A to happen?

>>11006385
It would be, if it existed.

>>11006401
1-(1-1/n)^n.

>>11006425
How did you come up with this?

>>11006425
Also, what number does it approach as n goes to infinity?

>>11006425
And what about the formula for kn trials where k is an integer.

>>11005778
1^p+2^p+3^p+...+(p-1)^p
≡ 1+2+3+...+(p-1) (mod p) # by Fermat's little theorem: a^p≡a (mod p)
≡ p(p-1)/2 (mod p) # sum of an arithmetic series
≡ 0 (mod p) # if p is a prime >2 then p-1 is even and (p-1)/2 is an integer => p(p-1)/2=np for some integer n

>>10995810
Lol if you cube a negative what do you think will happen