/sci/ - Science & Math

Unanswered questions from the previous thread:

Math questions:
>>11853133
>>11854162
>>11854515 [It kinda resembles an unanswered question.]
>>11858039

Physics questions:
>>11839453
>>11846098
>>11846892
>>11857109 [Technically maths, but a physicist is more likely to know the ins and outs of this particularity.]

Materials science questions:
>>11854016 [Protip: just ask the fucking question.]

Engineering questions:
>>11854191
>>11856695
>>11857648

Probability and statistics questions:
>>11837029
>>11863154 plus >>11863162

Biology questions:
>>11841412
>>11859450

Chemistry questions:
>>11838903
>>11840335 (Followed up by >>11840627 )
>>11858851

Stupid questions:
>>11839360
>>11839708
>>11840377
>>11847916
>>11850467
>>11863150

Rrrrrrrrrrr!! Why are mouths bigger than buttholes? I'm having a hard go.

fuse : fusion :: ??? : fission

>>11840377

I am practicing on you. I share your Reee.

>>11846098
Just use Gauss's law. The electric field is only impacted by the charge enclosed by your gaussian surface (assuming the spheres are concentric).

>>11863805
fizz? fiss? fise? fize?

>>11863805
it's fission

>>11863805
Fissure.

i was reading this https://pdfs.semanticscholar.org/85dc/4510613c4a14f6e77e1022bc4aa6fcd28090.pdf

basically it says
"The best currently available evidence suggests that prolonged clinical
supervision is probably the best of the three options for the reduction of stress and burnout among mental health nurses"

my question: Do you think the people who treat/observe these "mental health nurses" will burn out too?

I think they will, and that doesnt sound sustainable, so isn't that a huge flaw with the mental health industry?

I posted this question on /ic/ first and then on /g/ but didn't get any worthwhile replies, so you guys are my last hope. Here's my post from /g/:

I just got a new drawing tablet (one with a screen), and when I hold my bare foot to a radiator and touch the tablet's metal backplate, I sometimes get electric shocks that are strong enough to be a bit painful. I realize that the backplate is used to ground the internal circuit, can that high of a potential difference between it and the radiator be normal? It seems strange to uninformed me, but I'm kind of worried about the courier bill if I send it back to be replaced and they find nothing wrong with it

>>11863470
Any good puzzle games to buy during the steam sale? I've already played the witness and baba is you. I was considering stephens sausage roll but I'm still not sure. Looking to buy 2-3 games

ESL here. is there such thing as strength of proof or something like terms or some scale that describe how possible a theory is?
let's say we have 5 different hypothesis
1. just states a plausible idea/explanation
2. states an idea/explanation and provides correlation as proof
3. states an idea/explanation, provides correlation as proof and provides a plausible theory
4. states an idea/explanation, provides correlation as proof and provides a plausible theory that is also supported by statistics and experiments
5. states an idea/explanation, is statistically valid and provides an also proven theory that works all the time and explains tangentially related ideas/questions
is there words that describes each stage or are they all equal (except first one)?
it seems to me that people ambiguously refer to all of these as theory or fact or scientific proof

What's the difference between applied mathematics and mathematical physics?
There's a definition for each of them? Everywhere I look I get the impression that mathematical physics is just a branch of applied mathematics.

>>11864772
Anything from Zachtronics really.

You will probably like Opus Magnum.
There's no right solution for the puzzle, you might like to try to get the "optimum" solution, be it area, cost or speed categories.

Stretching the term puzzle, I can also recommend factorio, which fall into the "optimization" genre.
Satisfactory is similar, but I never played.

Can a function be infinite at some point but have a finite integral?

>>11865216
https://math.stackexchange.com/questions/2304098/can-an-unbounded-function-have-a-finite-integral
in general, no

wtf is this i dont understand

aside from burning your skin with the metal head of a lighter after you heat it up what other relatively low risk ways are there for a prostitute to cause pain to you and your genitals?
trauma to the testicles is too risky for me and burning my dick is worrying when it comes to infections
face slapping would hurt their hand too much, I need something simple and low effort for her and low risk for me but which causes a lot of pain

what power does r1 disipate?

>>11865750
https://www.purplemath.com/modules/factrthm.htm

>>11865075
Applied mathematics studies abstract computational methods for solving and approximating solutions of mathematical problems, which are practically motivated.
Mathematical physics studies physics with mathematical methods.
For a weird example, I'd consider von Neumann's axiomatization of QM to be a part of mathematical physics, but not a part of applied maths.

>>11865276
if f(a) - lim x->a f(x) = 0 and f(x-a) is even and lim x->infinity f(x) = 0 then there is a finite integral.

>>11865216
>>11865276
if f(a) - lim x->a f(x) = 0 and f(x-a) is even and lim x->infinity f(x) = 0 then there is a finite integral

>>11865216
>>11865276
fuck me, ok last time

if f(a) - lim x->a f(x) = 0 and f(x-a) is even and lim x->infinity f(x) = 0 then there is a finite integral

I'm having trouble with an inequality. I believe there is an error in the solutions for the book I am using. I have: [math] | \sum_{j=1}^na_j|^2 = | \sum_{j=1}^na_j^2 + 2\sum_{i\neq j} a_ia_j |[/math]. But the author claims that it is equal to [math] |\sum_{j=1}^na_j^2 + 2\sum_{(i,j) \in S} a_ia_j|[/math] where [math]1\leq i <j \leq n[/math] and S is the set of all pairs such that i+j is even. I don't agree with this because there are terms in my answer that has i+j odd which are ignored in the book solution. Can anyone give some explanation for what is happening here?

>>11866418
Set [math]a_1 = a_2 = 1[/math].
Then, [math]| \sum _{j=1}^2 a_j |^2 = 4[/math].
Also, [math]| \sum _{j=1}^2 a_j ^2 + 2 \sum _{(i, j) \in S} a_i a_ j| = 2[/math].
So clearly, you're either misinterpreting something (i.e. [math]S[/math] isn't just the pairs with i+j even, but just those with [math]1 \leq i < j \leq n[/math], in which case the sum is correct) or it's a typo.

>>11866418
>>11866458
Also, your formula is fucked, it's either [math]\sum _{j=1}^n a_j^2 + \sum _{i \neq j}a_ia_j[/math] or [math]\sum_{j=1}^n a_j^2 + 2 \sum _{1 \leq i < j \leq n} a_i a_j[/math]
Kept thinking about how I should tell you this yesterday in /mg/ but kept forgetting to actually do it for some reason.

Complex Analysis

Want to evaluate integral from -inf to inf of (x^4+1)^-1 dx.
I know the method where you draw a halfcircle and show that the half-circle part goes to zero but I'm left with an integral in z that I can't evalute.
Is there any way to evaluate this WITHOUT the residue theorem? (Res. th is introduced in chapter 9 in this book, this exercise is given in chapter 5).

>>11866483
>>11866458
I masterbated and figured out where I was going wrong. Indeed, the lower index should not be [math] i\neq j[/math]. So here is the sum: [math] |\sum_{j=1}^na_j|^2 + |\sum_{j=1}^n(-1)^ja_j|^2[/math]. If we expand the first sum, we get [math]|\sum_{j=1}^n a_j^2 + 2\sum_{1\leq i < j \leq n} a_ia_j|[/math]. If we expand the second sum, we get [math]|\sum_{j=1}^na_j^2 + 2\sum_{1\leq j < j \leq n} (-1)^{i+j}a_ia_j[/math]. The absolute values drop away so now we are adding all of the sums together. [math]2\sum_{1\leq i < j \leq n}a_ia_j + 2\sum{1\leq i < j \leq n} (-1)^{i+j}a_ia_j[/math]. So when i+j is odd, it subtracts out the terms in the first sum. The answer in the book is correct. The final answer is: [math]2\sum_{j=1}^na_j^2 + 4\sum_{(i,j)\in S : 1\leq i < j \leq n} a_ia_j[/math] where S is the set of all (i,j) such that i+j is even. Thanks everyone.

>>11866503
It's been a while but I think you can evaluate this integral using winding numbers.

'()' = 99!, do you agree?

Which law says that if i have [math]-ax-bx=-8-5a[/math] then i can just multiply everything by -1 and that would be valid?

>>11867045
No, you can do it in way less.
You can check manually, for example, that for three, it's 2.
For an n-product, you can separate it into two chucks, one with m terms and one with n-m, with two parenthesis. By iterating this, I think that we get 2(n-2), by induction.

>>11867175
this is how it is given for 4 terms = 5

if '()' means order of prority isn't it effectively a permutation without changing the order of the elements thus n!/n? instead of counting brackets we can perhaps move elements to the left thus giving them priority and then devide by the number of elements so that we don't count the actual permutations but it still should give the actual answer? im not too sure but i think that might be the way.

>>11864772
not a puzzle game but the smartest people here seem to have a fixation with touhou. Whether the play the games or not, I do not know. However you might want to consider them.

I'm playing a puzzle game (shenzhen IO). I tried to be cheeky with one of my answers but wound up stumping myself with a relatively simple math problem that I'm starting to think isn't solvable.
I believe the answer lies in modular arithmetic but I don't know enough about it to solve it myself.

There is a clock that goes from 0 to 95 (so modulo 96 I think). There are also two external timers and a microcontroller.
The microcontroller should output logic TRUE between 93 and 37, and logic FALSE between 38 and 92.
The microcontroller only supports an extremely limited instruction set and instruction memory, so I want to use as few operations as possible.

My naive solution was to break it into an inequality, FALSE for all x such that 38<x<93. Since the clock resets to 0, I thought it could be simplified to only one inequality of FALSE for all x such that x<55.

No matter how I try and implement it, it's always off by 2 which I think arises from the difference between 93 and 95. I can't find a way to eliminate this extra 2, which leads me to believe it's not possible to do this in only one comparison. I have no idea how to prove this. Does anyone have any ideas?

>>11867250
>if '()' means order of prority isn't it effectively a permutation without changing the order of the elements thus n!/n?
I have genuinely no idea what you mean with that.
Anyhow, proving by induction is simple, even if it's kinda shitty. Setting [math]n[/math] as the number of terms in the product, the cases [math]n=1[/math], [math]n=2[/math] and [math]n=3[/math] clearly follow the formula [math]max[2(n-2), 0][/math] for the number of necessary parenthesis. The induction step is done by noticing that there's a "final multiplication" between all the terms up to some [math]i[/math] times all the remainder to the right, so by parenthesising one of the two chunks (note: you need to parenthesize the one that has more than one element, this is the only rule), you'll get a product with [math]m[/math] terms inside the parenthesis, and a product with [math]n - m +1[/math] terms obtained from the original expression by treating the full parenthesis as a single term. Then induction gives that we need [math]2 + 2(m-2) + 2(n-m-1) = 2(n-2)[/math] parenthesis.

I'm playing a puzzle game (shenzhen IO). I tried to be cheeky with one of my answers but wound up stumping myself with a relatively simple math problem that I'm starting to think isn't solvable.
I believe the answer lies in modular arithmetic but I don't know enough about it to solve it myself.

There is a clock that goes from 0 to 95 (so modulo 96 I think). There are also two external timers and a microcontroller. The timers define when the microcontroller should switch logic output states.
In the given puzzle, when the clock is equal to 38, the microcontroller should output logic FALSE. When it reaches 93, it should switch to logic TRUE.
The microcontroller only supports an extremely limited instruction set and instruction memory, so I want to use as few operations as possible.

My naive solution was to break it into an inequality, FALSE for all x such that 38<x<93. Since the clock resets to 0, I thought it could be simplified to only one inequality of FALSE for all x such that x<55.

No matter how I try and implement it, it's always off by 2 which I think arises from the difference between 93 and 95. I can't find a way to eliminate this extra 2, which leads me to believe it's not possible to do this in only one comparison. I have no idea how to prove this. Does anyone have any ideas?

>>11867063
>law
If you want, like, a name of a "law", I don't think there is one, but it's purely logical (equal things multiplied by the same thing must be equal).

>>11867335
for n=4 it doesn't work because as the picture shows there are 5 ways.

This is probably an extremely simple question but I just want to double check.

My first thought was to set the origin at one end of the ladder (the one that contacts the ground) and define the distance s from this origin going up the length of the ladder. The position vector can then be written in terms of the angle,
[eqn]\vec{r} = s(\cos\theta \hat{x} + \sin\theta \hat{y})[/eqn]
The kinetic energy is then
[eqn]dT = \frac{1}{2}\dot{\vec{r}}\cdot\dot{\vec{r}}dm = \frac{1}{2}s^{2}\dot{\theta}^{2}dm = \frac{1}{2}s^{2}\dot{\theta}^{2}\frac{M}{L}ds[/eqn]
Integrating from s=0 to s=L gives
[eqn]T = \frac{1}{6}ML^{2}\dot{\theta}^{2}[/eqn].

Does this check out?

>>11867379
It's not asking how many ways, it's asking how many parenthesis symbols you need anon.

>>11867387
oops, i accidentally conflated 2 questions.

>>11867387
i was thinking of 31 and answering for 32, but for 31 it is (n-1)! right?

>>11867408
>(n-1)!
That doesn't work for n=4, tho, you get 6 instead of 5.
I got a disgusting recursion relation by doing the exact same trick from earlier, want me to post it?

>>11867063
youre applying the function f(x) = -1 * x
to both sides of the equation
so youre going from
a = b
to
f(a) = f(b)
which is just a statement that f(x) is a coherently defined function
ie, you cant have i = j but have f( i ) =/= f( j )

>>11867440
sure

I'm an American that's been given an opportunity to complete a PhD in Italy, fully funded (60k EUR/year). Are European PhDs worth it for an American, will I be discriminated against when it comes to jobs, even if I come back to do a post-doc?

>>11867491
[math]f(n)= f(n-1) + \sum_{i=2}^{n-1} f(i)f(n-i+1)[/math] , where [math]n[/math] is the number of terms in the product.
Checked manually and it works for [math]n=3[/math] and [math]n=4[/math]. Returns [math]19[/math] for [math]n=5[/math].

>>11867514
Nevermind, it returns 6 for n=4. I am going insane.

>>11867507
It depends on the reputation of the school, but I wouldn't ever think of going to Italy for a PhD. There isn't a program even in the top 75 for what I do.

>>11867545
Yes, the school's global rank is complete trash, but I never really cared about rank. I work in pharmaceutical research, and intend to go into industry. The more I think about it, it would just be best to stay here in the US.

>>11867552
All that matters is how well-equipped the school is for getting you in the position you want. If Europe has pharma research and this is a good pipeline, then go for it. Rank is like IQ in then it tells part of the story but you never know what sort of connections the school has, or the group you want to work in.
However, in my experience American research is miles ahead. But then you'd have to stay here for 6 more years or so.

>>11867382
Looks good.

t. Someone who hasn't done any physics since high school over a decade ago.

I don't understand what it's even asking for. The inverse point?

>>11867577
Thanks anon. My advisor is actually from here and I've been interning with startups and companies here through his connections, it's just that he also lives in Italy and has another lab there as well. Once I get the full project details I'll mention to him that I want to be able to come back and work in the US and I'll see what he says. I don't want to permanently live in Europe to be honest. By the way, the school will be Polytechnic University of Turin.

>>11867592
[math]f^{-1}(y)=x[/math] means [math]f(x)=y[/math].

>>11867531
what if:
(n! - (n-1)! - (n-2)! - ... - 3! - 2! - 1!)/(n-1)

>>11867609
Check marks across the board. Thank you anon.

Does anyone have experience with exploding dice in probability? I'm making a tabletop game that uses exploding d10s as the primary game mechanic, but I'm too retarded to develop an equation for how to determine the probability of a result if they have a given number of dice they roll.

For those unfamiliar, exploding dice are rerolled when their highest face value is rolled. In my game, for example, a player could roll anywhere between 1 and 5 10-sided dice. If any of those dice land on a 10, it's recorded and that die is rerolled.
Does the probability spread evenly between all possible results? Or is it broken up so 1-9 still have a 10% chance, but 10's probability is split between the probability of rerolling into a 1-9, repeating ad infinitum?
An example roll might look something like: A player rolls 3 dice, of which he needs two to show at least a 6 on their face. If any dice land on a 10, it counts as a successful die, and can be rerolled, possibly resulting in another 6 or higher, or even another exploding die.

This might be way more trouble than I understand, but I figured I'd ask.

>>11867693
because you can theoretically keep getting 10's, I don't know if there's a good closed form for this probability. Let's see.

probability of getting a 1, for example, would be 1/10 (from rolling a 1)
+1/10*1/10 (from rolling a 10 then rolling a 1)
+1/10*1/10*1/10 (from rolling 10, 10, then 1)
so this series converges to (p being the probability of rolling a specific number besides 10):
[math]\sum_{i=1}^{\infty} p^i=\frac{1}{1-p}-1[/math]
I guess it does have a closed form, since it's just a geometric series. Oops.

>>11867725
>>11867693
this would be the probability given you use just one die. since dice are independent you would just manipulate the probabilities like you would for standard dice, but with the probabilities of rolling a certain number given by the expression I gave in my last reply instead of just [math]p[/math].

let's say i have a vector X and 5 other vectors, how can i determine which of these 5 vecotrs is the most similar to X?
i feel like if i subtracted X from each of these vectors and then calculated the length differences, the most similar one would give the smallest length but i'm not sure

>>11867693
>Or is it broken up so 1-9 still have a 10% chance, but 10's probability is split between the probability of rerolling into a 1-9, repeating ad infinitum?
Yes.
Any other questions?

>>11867725
I'll finally clarify that [math]p=1/n[/math] in the case of a n-sided die, since I was a little unclear about that.

>>11867734
If by "similar" you mean closest, and by "calculate the length differences" you mean calculating the norm of the differences, then you're doing it right.

>>11867621
Bro if you plug in n=3 it doesn't even return an integer.

>>11867771
yep, that's what i meant, thanks
i'm still not used to the english nomenclature

>>11867725
>>11867732
>>11867741
Alright, thanks! This really helps a lot

>>11867777
fuck it i'll think about it more thoroughly another time, the answer's gotta involve a factorial though it feels like it

>>11867812
Anon...
Judging from the way the question was written, there isn't a closed form.

As a 19 year ols anon who might catch corona soon, how fucked am I? Am I going to die?
/sci/ rarely talks about it and /pol/ info is accurate but scary

>>11867846
does recursion constitute closed form? it might be a slightly different formula depending if n is odd or even.

>>11867856
start writing your will, anon...

>>11867862
Quite possible.
I think that if I autistically threw myself into computing examples by hand I'd figure out why the formula from earlier didn't work and could correct it, but that sounds like a pain in the ass.
>>11867856
Bro quit being a little bitch.

>>11867875
Oh come on, it's not fair
>>11867883
Huh?

>>11866131
V^2/(25*R).

The voltage at the junction is (4/5)*V, the voltage across R1 is V/5, the current through R1 is V/(5*R), so the power is V^2/(25*R).

You don't even need Kirchhoff's laws to find the junction voltage. It's a voltage divider with R/2 at the top and 2*R at the bottom.

>>11867045
You need 97 pairs. The outer-most multiplication doesn't need parentheses, three numbers needs one pair of parentheses (A*(B*C) or (A*B)*C), each additional number needs an additional pair, so N-2 sets for N numbers. And you have N=99.

>>11867925
i somehow mixed the questions up, the max number of parantheses should be n-2 yes

why must there be a difference of 2 after the prime modulus? Whats the point

>>11867856
death rate for 19 year olds is minimal, quit being a little bitch
i had it last week and it gave me a bitch of a migraine and body aches for days but im still here
its literally just a bad cold

Why we only use x to divide? What happens when we also include -2?

>>11868555
youre already including -2, thats why you subtract off [math](5x^3 - 10x^2)[/math]
instead of just [math](5x^3)[/math]

>>11868568
Thanks

can you turn triglycerides into glucose with just some chemistry and enzymes? doesn't have to be same way the body does it, just the shortest and easiest way possible. i couldn't find anything other than how the body does it (too complicated to be replicated by a retard like me) and useless diet advice. i prefer if the sugar is edible but if it's too complicated then it's ok

What do we think of COVID and behavioral changes, neurotoxin like.
There's been a rise on incidents and madness

>>11866131
Just spam kirchhoff and solve the system

https://youtu.be/5vZ4lCKv1ik
Why doesn't this work? Shouldn't the bullet travel like pic related?

>>11869113
I don't understand your drawing

As a physicist, recently I have realized that I don't understand entropy and that I know jack shit about the concept of information in general. I know understand it a bit better in terms of probability theory, but there are two other areas where I see "information" being discussed without seeing the deeper rigour, if any exists. If what I say makes any sense whatsoever I'd love to be pointed to a place where I can learn more about it.
1) I have the idea that an isomorphism can be seen as a map that preserves information. Is there a mathematical theory of the information-content of functions?
2) It is sometimes said that in special relativity things can move faster than light if they don't carry information (e.g. shadows can move faster than light but can't be used for signalling). Can this be understood from a theoretical perspective?

>>11863470
extremly stupid question
i wanna reach for summa cum laude, starting uni next year

how do i make sure i'll nail every exam with highest mark possible?

t. wannabe chemfag

Is there a way to minimize length or curvature of cubic splines as the 2 free conditions? I don’t like it when they wiggle.

>>11869170
Why doesn't bullet go like the ball on this video:
https://youtu.be/-VJzr_aSSE4

So, let me get this straight. Electricity is generated by spinning magnets near a circuit because the generated electromagnetic field causes valence electrons in the highly conductive material to jump from atom to atom in one direction? That's It? At the simplest and largest levels? Fundamentally, all you're doing is spinning magnets over conductive coils or spinning conductive coils over magnets?

>>11869945
yep, or separated ions forcing electrons to go through your circuit.

Typing this was a pain, so i hope you also make some effort to finally help me solve this.
How do i get from

[math]p_{w_{k+1}|x_k,u_k}(\bar w_{k+1}|\bar x_k,\bar u_k)=[/math]
[math]\sum_{\bar x_{k+1}\in S_{k+1}}\sum_{\bar u_{k+1} \in U_{k+1}(\bar x_{k+1})} p_{w_{k+1}|x_k,u_k,x_{k+1},u_{k+1}}(\bar w_{k+1}|\bar x_k,\bar u_k,\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}}(\bar x_{k+1},\bar u_{k+1})=[/math]
[math]\sum_{\bar x_{k+1}\in S_{k+1}}\sum_{\bar u_{k+1} \in U_{k+1}(\bar x_{k+1})}\frac{p_{w_{k+1},x_k,w_k,x_{k+1},u_{k+1}}(\bar w_{k+1},\bar x_k,\bar w_k,\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}}(\bar x_{k+1},\bar u_{k+1})}{p_{x_k,w_k,x_{k+1},u_{k+1}}(\bar x_k,\bar w_k,\bar x_{k+1},\bar u_{k+1})}\ =[/math]
[math]\sum_{\bar x_{k+1}\in S_{k+1}}\sum_{\bar u_{k+1} \in U_{k+1}(\bar x_{k+1})}\frac{p_{x_k,w_k|w_{k+1},x_{k+1},u_{k+1}}(\bar x_k,\bar w_k|\bar w_{k+1},\bar x_{k+1},\bar u_{k+1})p_{w_{k+1}|x_{k+1},u_{k+1}}(\bar w_{k+1}|\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}}(\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}}(\bar x_{k+1},\bar u_{k+1})}{p_{x_{k+1},u_{k+1}|x_k,w_k}(\bar x_{k+1},\bar u_{k+1}|\bar x_k,\bar w_k)p_{x_k,w_k}(\bar x_k,\bar w_k))}\
[/math]

to this
[eqn]p_{w_{k+1}|x_k,u_k}(\bar w_{k+1}|\bar x_k,\bar u_k)=\sum_{\bar x_{k+1}\in S_{k+1}}\sum_{\bar u_{k+1} \in U_{k+1}(\bar x_{k+1})}p_{w_{k+1}|x_{k+1},u_{k+1}}(\bar w_{k+1}|\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}|x_k,u_k}(x_{k+1},u_{k+1}|\bar x_k,\bar w_k)=p_{w_{k+1}|x_{k+1},u_{k+1}}(\bar w_{k+1}|\bar x_{k+1},\bar u_{k+1})\ [/eqn]

Typing this was a pain, so i hope you also make some effort to finally help me solve this.
How do i get from

[math]p_{w_{k+1}|x_k,w_k}(\bar w_{k+1}|\bar x_k,\bar w_k)=[/math]
[math]\sum_{\bar x_{k+1}\in S_{k+1}}\sum_{\bar u_{k+1} \in U_{k+1}(\bar x_{k+1})} p_{w_{k+1}|x_k,w_k,x_{k+1},u_{k+1}}(\bar w_{k+1}|\bar x_k,\bar w_k,\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}}(\bar x_{k+1},\bar u_{k+1})=[/math]
[math]\sum_{\bar x_{k+1}\in S_{k+1}}\sum_{\bar u_{k+1} \in U_{k+1}(\bar x_{k+1})}\frac{p_{w_{k+1},x_k,w_k,x_{k+1},u_{k+1}}(\bar w_{k+1},\bar x_k,\bar w_k,\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}}(\bar x_{k+1},\bar u_{k+1})}{p_{x_k,w_k,x_{k+1},u_{k+1}}(\bar x_k,\bar w_k,\bar x_{k+1},\bar u_{k+1})}\ =[/math]
[math]\sum_{\bar x_{k+1}\in S_{k+1}}\sum_{\bar u_{k+1} \in U_{k+1}(\bar x_{k+1})}\frac{p_{x_k,w_k|w_{k+1},x_{k+1},u_{k+1}}(\bar x_k,\bar w_k|\bar w_{k+1},\bar x_{k+1},\bar u_{k+1})p_{w_{k+1}|x_{k+1},u_{k+1}}(\bar w_{k+1}|\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}}(\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}}(\bar x_{k+1},\bar u_{k+1})}{p_{x_{k+1},u_{k+1}|x_k,w_k}(\bar x_{k+1},\bar u_{k+1}|\bar x_k,\bar w_k)p_{x_k,w_k}(\bar x_k,\bar w_k))}\
[/math]

to this
[eqn]p_{w_{k+1}|x_k,w_k}(\bar w_{k+1}|\bar x_k,\bar w_k)=\sum_{\bar x_{k+1}\in S_{k+1}}\sum_{\bar u_{k+1} \in U_{k+1}(\bar x_{k+1})}p_{w_{k+1}|x_{k+1},u_{k+1}}(\bar w_{k+1}|\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}|x_k,u_k}(x_{k+1},u_{k+1}|\bar x_k,\bar w_k)=p_{w_{k+1}|x_{k+1},u_{k+1}}(\bar w_{k+1}|\bar x_{k+1},\bar u_{k+1})\ [/eqn]

Typing this was a pain, so i hope you also make some effort to finally help me solve this.
How do i get from

[math]p_{w_{k+1}|x_k,w_k}(\bar w_{k+1}|\bar x_k,\bar w_k)=[/math]
[math]\sum_{\bar x_{k+1}\in S_{k+1}}\sum_{\bar u_{k+1} \in U_{k+1}(\bar x_{k+1})} p_{w_{k+1}|x_k,w_k,x_{k+1},u_{k+1}}(\bar w_{k+1}|\bar x_k,\bar w_k,\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}}(\bar x_{k+1},\bar u_{k+1})=[/math]
[math]\sum_{\bar x_{k+1}\in S_{k+1}}\sum_{\bar u_{k+1} \in U_{k+1}(\bar x_{k+1})}\frac{p_{w_{k+1},x_k,w_k,x_{k+1},u_{k+1}}(\bar w_{k+1},\bar x_k,\bar w_k,\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}}(\bar x_{k+1},\bar u_{k+1})}{p_{x_k,w_k,x_{k+1},u_{k+1}}(\bar x_k,\bar w_k,\bar x_{k+1},\bar u_{k+1})}\ =[/math]
[math]\sum_{\bar x_{k+1}\in S_{k+1}}\sum_{\bar u_{k+1} \in U_{k+1}(\bar x_{k+1})}\frac{p_{x_k,w_k|w_{k+1},x_{k+1},u_{k+1}}(\bar x_k,\bar w_k|\bar w_{k+1},\bar x_{k+1},\bar u_{k+1})p_{w_{k+1}|x_{k+1},u_{k+1}}(\bar w_{k+1}|\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}}(\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}}(\bar x_{k+1},\bar u_{k+1})}{p_{x_{k+1},u_{k+1}|x_k,w_k}(\bar x_{k+1},\bar u_{k+1}|\bar x_k,\bar w_k)p_{x_k,w_k}(\bar x_k,\bar w_k))}\
[/math]

to this
[eqn]p_{w_{k+1}|x_k,w_k}(\bar w_{k+1}|\bar x_k,\bar w_k)=\sum_{\bar x_{k+1}\in S_{k+1}}\sum_{\bar u_{k+1} \in U_{k+1}(\bar x_{k+1})}p_{w_{k+1}|x_{k+1},u_{k+1}}(\bar w_{k+1}|\bar x_{k+1},\bar u_{k+1})p_{x_{k+1},u_{k+1}|x_k,w_k}(x_{k+1},u_{k+1}|\bar x_k,\bar w_k)=p_{w_{k+1}|x_{k+1},u_{k+1}}(\bar w_{k+1}|\bar x_{k+1},\bar u_{k+1})\ [/eqn]

>>11870222
>[math]p_{a|b} (c|d)[/math]
Mind telling me what book you're using for me to look up the notation?

>>11869590
Place the control points at 1/3 and 2/3 between the end points. Then the quadratic and cubic terms disappear and you have a straight line.

If you're matching derivatives at both ends, you don't have any free conditions. If you're matching the the direction but not the magnitude, then reducing the magnitude will make them closer to straight lines.

Ultimately, you need to decide what your constraints actually are and exactly what you want to minimise within those constraints.

>>11870231
use this
https://ethz.ch/content/dam/ethz/special-interest/mavt/dynamic-systems-n-control/idsc-dam/Lectures/Optimal-Control/Lecture%20Notes/Appendix.pdf
last page

>>11867856
If you're 19yo with no pre-existing conditions, it's probably not even in the top-10 list of things that might kill you.

>>11869760
they both go the same way

>>11870222
>>11870243
The first equality in the last line seems to be something like [math]p(x|b) = \sum_{possible ~ c} p(x|c)p(c|b)[/math].
The last one is magic and I have no fucking idea where does it come from.

Is cryptography a good field to get into?

is it normal to feel like your progress/speed of acquisition of materials drops of dramatically the higher up in your courses you go? I'm afraid that I'll reach a point where it takes me so long to learn new material I won't be able to do it fast enough and I'll start failing classes

>>11870335
I understand how the last term comes about. But where do the terms in the sum come from?

Okay, why do TI calculators require you to set an equation to y= before graphing? Considering the current year, shouldn't we have handheld calculators that are able to solve a linear equation and graph it at the same time? I feel like there is a simple answer to this that I'm just not seeing.

For instance, say I'm graphing 35x+10y=1500, why do I need to set it as y=150-3.5x to input it into a TI 84

>>11870476
Just use a CAS and stop whining that you don't know linear algebra

>>11870441
You have the probability of an event [math]A[/math] at time [math]t[/math] given an event [math]x_{t-1}[/math] at a time [math]t-1[/math], and the event [math]A[/math] only depends on the state of the system at time [math]t[/math].
Then you had something like [math]p(A | x_{k-1} ) = \sum_{x_t ~ in ~ the ~ state ~ space ~ at ~ time ~ t} p(A |x_t ) p(x_t | x_{t-1})[/math].
That is, the probability of [math]A[/math] given [math]x_{t-1}[/math] is the sum of the probabilities of the system evolving into some state at time [math]t[/math] and then the event happening.

The formula looks a lot like something like this, at least.

>>11870484
I'm not whining, I just want to know why TI calculators have this limitation lol. No need to be so aggressive

>>11870489
it depends on your calculator, my TI-89 from 1997 can solve and graph linear equations like no one's business

>>11870486
OK, I think I get it. But how do you determine whether A depends only on [math]x_t[/math]. And when you do what happens to the extra variables conditioned on A. Do they disappear, do they jump into some other pdf function? I'm trying to find a way to extend this concept with the marginalization and total probability theorem rule so that it could be possible with the attempt I first posted I could come to your conclusion.

>>11870486
OK, I think I get it. But how do you determine whether A depends only on[math] x_t[/math]. And when you do what happens to the extra variables conditioned on A. Do they disappear, do they jump into some other pdf function? I'm trying to find a way to extend this concept along with the marginalization and total probability theorem rule so that it could be possible with the attempt I first posted to come to your conclusion.

>>11868650
Nope. glycerol is easy if you make soap and skim it off the top, but converting that/fatty acids to glucose is ridiculously impractical, if not impossible

>>11870569
>But how do you determine whether A depends only on x_t.
It's usually obvious.
Or, you have a Markov chain.

I'm teaching myself high school math. Should i finish algebra before starting plane geometry or can i start both at the same time?

>>11870621
Thanks man I think I've figure it out.
I'd forgotten about the nature of markov processes. When you introduce a conditional variable you use this rule [math]p(x|y)=\sum_{z \in Z}p(x|y,z)p(z)[/math]. You basically multiply by the pdf of the introduce variable. But, when you remove it, then you have to divide it out.

So the first line of my attempt becomes

[math]p(w_{k+1}|x_k,w_k)=\sum_{x_{k+1}}\sum_{u_{k+1}}\frac{p(w_{k+1}|x_{k+1},u_{k+1})p(x_{k+1},u_{k+1})}{p(x_k,w_k)}=[/math]

[math]\sum_{x_{k+1}}\sum_{u_{k+1}}\frac{p(w_{k+1}|x_{k+1},u_{k+1})\sum_{x_k}\sum_{w_k}p(x_{k+1},u_{k+1}|x_k,w_k)p(x_k,w_k)}{p(x_k,w_k)}=[/math]

[math]\sum_{x_{k+1}}\sum_{u_{k+1}}p(w_{k+1}|x_{k+1},u_{k+1})p(x_{k+1},u_{k+1}|x_k,w_k)\sum_{x_k}\sum_{w_k}\frac{p(x_k,w_k)}{p(x_k,w_k)}=[/math]

[math]p(w_{k+1}|x_{k+1},u_{k+1})\sum_{x_{k+1}}\sum_{u_{k+1}}p(x_{k+1},u_{k+1}|x_k,u_k)=p(w_{k+1}|x_{k+1},u_{k+1})[/math]

[math][/math]
Thanks for your perspective man, I've been trying to figure this out for more than a week now.

>>11870621
Thanks man I think I've figure it out.
I'd forgotten about the nature of markov processes. When you introduce a conditional variable you use this rule

[math]p(x|y)=\sum_{z \in Z}p(x|y,z)p(z)[/math].

You basically multiply by the pdf of the introduce variable.
But, when you remove it, then you have to divide it out.

So the first line of my attempt becomes

[math]p(w_{k+1}|x_k,w_k)=\sum_{x_{k+1}}\sum_{u_{k+1}}\frac{p(w_{k+1}|x_{k+1},u_{k+1})p(x_{k+1},u_{k+1})}{p(x_k,w_k)}=[/math]

[math]\sum_{x_{k+1}}\sum_{u_{k+1}}\frac{p(w_{k+1}|x_{k+1},u_{k+1})\sum_{x_k}\sum_{w_k}p(x_{k+1},u_{k+1}|x_k,w_k)p(x_k,w_k)}{p(x_k,w_k)}=[/math]

[math]\sum_{x_{k+1}}\sum_{u_{k+1}}p(w_{k+1}|x_{k+1},u_{k+1})p(x_{k+1},u_{k+1}|x_k,w_k)\sum_{x_k}\sum_{w_k}\frac{p(x_k,w_k)}{p(x_k,w_k)}=[/math]

[math]p(w_{k+1}|x_{k+1},u_{k+1})\sum_{x_{k+1}}\sum_{u_{k+1}}p(x_{k+1},u_{k+1}|x_k,u_k)=p(w_{k+1}|x_{k+1},u_{k+1})[/math]

[math][/math]
Thanks for your perspective man, I've been trying to figure this out for more than a week now.

>>11870800
>blind leading the blind somehow worked out
Nice.

>>11870692
You should finish algebra.

>>11870621
>>11870621
Thanks man I think I've figured it out.
I'd forgotten about the nature of markov processes. When you introduce a conditional variable you use this rule

[math]p(x|y)=\sum_{z \in Z}p(x|y,z)p(z)[/math].

You basically multiply by the pdf of the introduced conditional variable.
But, when you remove it, then you have to divide it out.

So the first line of my attempt becomes

[math]p(w_{k+1}|x_k,w_k)=\sum_{x_{k+1}}\sum_{u_{k+1}}\frac{p(w_{k+1}|x_{k+1},u_{k+1})p(x_{k+1},u_{k+1})}{p(x_k,w_k)}=[/math]

[math]\sum_{x_{k+1}}\sum_{u_{k+1}}\frac{p(w_{k+1}|x_{k+1},u_{k+1})\sum_{x_k}\sum_{w_k}p(x_{k+1},u_{k+1}|x_k,w_k)p(x_k,w_k)}{p(x_k,w_k)}=[/math]

[math]\sum_{x_{k+1}}\sum_{u_{k+1}}p(w_{k+1}|x_{k+1},u_{k+1})p(x_{k+1},u_{k+1}|x_k,w_k)\sum_{x_k}\sum_{w_k}\frac{p(x_k,w_k)}{p(x_k,w_k)}=[/math]

[math]p(w_{k+1}|x_{k+1},u_{k+1})\sum_{x_{k+1}}\sum_{u_{k+1}}p(x_{k+1},u_{k+1}|x_k,u_k)=p(w_{k+1}|x_{k+1},u_{k+1})[/math]


Thanks for your perspective man, I've been trying to figure this out for more than a week now.

Does this inequality have a name? Both are R^n vectors.

>>11870843
shitty vector inequality #155
its a special case of shitty vector inequality #53, #77, and #122

>>11870843
Never heard of any.
If you're just looking for a proof, it pretty much just goes [math]\langle u-v, u-v \rangle > 0[/math] .

>>11870489
You can play video games on them in class

How can I think of homotopyäquivalence in R^2? It's a weaker from of homoemorphism, so you can extend/inflate or shrink/reduce certain parts?
For example, which letters of the alphabet in R^2 would be:
i) homotopyequivalent to [math]S^1 \vee S^1[/math]
ii) homotopyequivalent to [math]S^1[/math]
iii) contractable, i.e. homotopyequivalent to a single point.
My guesses are:
i) B
ii) A D O P Q R
iii) the rest.

>>11870862
>>11870873
Seems like a simple enough inequality, was just searching for a more formal name. Thanks

>>11871004
one reasonable intuition is: X and Y are homotopy equivalent if and only if they're deformation retracts of the same larger space Z. check this on ii) of your exercise.
I think one needs to understand some stuff from homotopy theory, e.g. Whitehead's theorem, in order to *really* understand in what sense are homotopy equivalent spaces equivalent.

Hello, something like professor leonard for physics 101?

pic unrelated

>>11871097
Forgot to say, preferably calculus based so I use what I learned with Prof L.

>>11871066
I think I don't really understand what you mean with "they're deformation retracts of the same larger space Z". Can you give an example or something?

>>11871229
do you know what a deformation retract is ?

>>11871240
sadly no, and google doesn't help much

I'm a math senior that has only really taken pure math classes like algebra, analysis, topology. I took an applied ODEs class for retards in high school forever ago at a community college, where I basically learned nothing, not even variation of parameters or reduction of order (LOL).

I need an ODE book that goes into all the cookbook techniques as well as the theory. I checked out Tenenbaum and Pollard and it was too brainlet and routine, Arnold's had no cookbook techniques. I don't want to read several 800 page books, so please, give me a good mathematically mature book that teaches the monkey techniques as well as the theory and is concise.

>>11871645
I'll shill this one:
https://www.maa.org/press/maa-reviews/differential-equations-with-applications-and-historical-notes

I just passed Calculus 3 and have one more math mandatory math class to take called "advanced mathematics for engineers." The fuck is that?

>>11871680
read the syllabus
it's not a real class, it contains whatever the fuck your department has decided to put in it

>>11871680
shot in the dark: basic ODE's methods, very primitive fourier analysis, basic lin alg mashed into the ODE's, probably a bit of stats+probability (heh)

Definitely not a well thought out class, and you'd be better served using Schaum's Outlines or some stupid shit like that desu

>>11863470
how do you apply for a course that you dont meet requirements to

>>11871645
Used this for grad school in engineering, it is quite straightforward.

>>11871871
You email the professor for permission. Either they can add you themselves or your department aide will (with approval from the professor)

>>11871871
You e-mail the department asking how to do it, mention that you have firm knowledge of the pre-requisites, and claim to be fully willing to do a test on it if they actually need you to.

>>11863470
How do you get into stem if you just got passing marks in pre calc and physics? (50% in phys btw)

Sup /sci/ I'm a csfag I don't have the best grasp on mathematics but I believe I know the fundamentals. Could you please suggest some books/courses for me to understand the mathematics required for starting out in ML? I'd prefer them being a bit 'involved' because I've been through a couple of coursera/edx courses and a lot of them just tell you about applying results rather than how they were derived

>>11872346
just import a library a smart person wrote

>>11872404
That doesn't help me understand shit tho

>>11871871
Just ask very politely and be ready to demonstrate you are at least as knowledgable and competent as the typical student who registers for that class. In my case the person I asked this of was already teaching me in one of their classes so they knew ahead of time how competent I was. But, if this is not the case for you there is a chance they may need to see actual evidence of your abilities depending on the difficulty of the course and your major.

why is lim x -> infinity x + 1 = infinity allowed, but not 1 + infinity = infinity

>>11872446
think carefully about what a limit implies and what passing to the limit also implies. the answer is in the very name of the concept anon

Someone for the love of god please explain to me how transistors work and why they are important. I can't wrap my smooth-brain around it. I'll explain what I think so far. The transistor is essentially two diodes sandwiched with each other. In the middle is the Base which is P-Type. It has an atom that allows electrons through and on either side is the N-Type which only flows towards a P. So to me, a transistor just seems like a fork in the road, where two one way streets meet and continue in the same direction. But all the animations and illustrations I have seen show the current going through the entire transistor. How is this possible if the N-Types don't allow a current through? And why is the design of the transistor so important and what causes it to amplify and switch?

>>11872346
Any help? Any one?

>>11872346
The prerequisites are Linear algebra and multi variable calculus, some other mathematics (even quite complex ones) are involved on the side. If you know those you should be able to jump into basically any rigorous textbook on the subject.
I have no suggestions on books, just make sure that if you look at one that it derives what a FNN is and is nice to read.

>>11863470
Can someone help me design a D-latch counter that counts 00, 01,01,10,10,01,01, etc pls?
I need it for a pump alternating system

>>11865216
Absolutely, the dirac Delta function is +infinity at t=0 and it's integral over the reals is 1

>>11872611
lmao is this seriously what they're teaching kids these days? Vbe~0.63V and hfe are all you need to know. Get a breadboard, go on spice, build a curve tracer and learn how to bias these fuckers. They amplify current.

also, the base is only lightly doped from what I'm reading, and really thin too.
>Having a lightly doped base ensures recombination rates are low. In particular, the thickness of the base must be much less than the diffusion length of the electrons.
Even good diodes will conduct some current backwards, shitty diodes more so

>>11865216
>Can a function be infinite at some point
If it is, how would the integral be defined?

>>11872715
Not a function. The Dirac measure also is not "infinity" at 0, that is a very shitty way to talk, as it misses the essential point.

>>11867300
Bless the touhou posters

>>11872715
wrong and misleading

>>11867300
>the smartest people seem to have a fixation on touhou
you are not in a position to judge this nor are you capable of discerning attention seeking autistic fags from productive intellectually superior individuals. There are many people past and present on this board who have no interest in such things that are smarter than avatarfagging niggers that you’re referring to.

>>11872715
Kek.
>>11872906
>If it is, how would the integral be defined?
As an improper Riemann integral?

>>11873008
>>11872906
Lebesgue integral works perfectly well for functions with values in [-inf,inf], with the convention

0*inf = 0
a*inf = sgn(a) inf

Integral of the function which is infinity at x=0 and zero everywhere else with respect to the Lebesgue measure is zero. With respect to the Dirac measure (for example) it's infinity.

>>11873049
Yes, but you don't actually need to do any of that, [math]\int _{-1}^1 |x|^{-1/2}dx [/math] already makes sense as an improper Riemann integral.

>>11873109
>∫1−1|x|−1/2dx∫−11|x|−1/2dx already makes sense as an improper Riemann integral.
how is it relevant ?

>>11873121
[math]|x|^{-1/2} = \frac{1}{\sqrt{|x|}}[/math] goes to infinity at 0, anon.

>>11873049
>Lebesgue integral works perfectly well for functions with values in [-inf,inf], with the convention
It does?
Take the function which is -inf on [-2,0) and inf on [0,1].
What is it's integral? By definition it is -inf*2+inf. Which is, by your definition inf-inf.

The only sensible answer you can give is inf-inf= -inf, since else linearity is instantly broken. But I can give the exact same example mirrored and you are forced to say inf-inf=inf.

I see no way to define it without completely tearing apart everything.

>>11873008
>As an improper Riemann integral?
See >>11873239 and tell me what the integral is.

>>11873239
>What is it's integral?
undefined. "it works" was not supposed to mean that every function is integrable in this sense.

>>11873277
You said "it works perfectly well", if it's just a zero set it works for very obvious reasons, else it really does not.

>>11873290
the usual construction of Lebesgue integral for functions X -> R works in the exact same way for functions X -> [-inf,inf]. in both cases there are functions which are integrable, and functions which are not integrable.

>>11873290
>You said "it works perfectly well"
The Lebesgue integral works perfectly well for real-valued functions, but this doesn't mean that every real valued function is integrable. Don't be unreasonable.
Also, the original anon asked for infinite at a point.

>>11871004
any help?

>>11873349
The classification seems correct (I got the exact same result), so your current intuition should be alright.

>>11873349
>>11871240
deformation retraction is a homotopy equivalence between a space X and its subspace A where the map A -> X is the inclusion and it stays the same through the whole homotopy. it's literally shrinking X onto A.
to illustrate the theorem, for example 1-dimensional Q and O are homotopy equivalent because they're both deformation retracts of a thickened (2-dimensional) O. Hatcher some illustration in his book.

Explain ODE and PDE to me like I'm 5. What are they?

>>11873320
>in both cases there are functions which are integrable, and functions which are not integrable.
Is every function with a non-zero set where the function is not real valued not integrable?

>>11873362
You are trying to find a function where you just know how the derivative behaves.

>>11873378
Yes.

What would the difference in explosions be like if you were to theoretically detonate a single, one megaton nuclear bomb versus ten 100-kiloton nuclear bombs strapped together?

>>11863470
Why does the lamp on the "path" with less resistance on it shine brighter than the lamp with more?

If electrons is a current, going from negative pole to positive, surely the electrons would split up evenly at the lamps and only at the actual resistors would they voltage change, right?

Or in other words: how can the electrons "know" that the path ahead has more resistance and therefore chose the path of less resistance, before the information about the resistance has even occurred?

>>11866381
Did you mean to ask whether what you said is true in general? Because it isn't if you meant the integral to infinity. Maybe you tried to said something different to what you actually wrote?

>>11873530
>how can the electrons "know" that the path ahead has more resistance and therefore chose the path of less resistance, before the information about the resistance has even occurred?
they don't. this is the steady-state solution, the transient behavior of the circuit is not even being considered here. and in steady-state, an electron current is already flowing throuh both resistors.

>>11873563
i made a bunch of mistakes in the image, but in general i see no reason why you can't find an integral if you chop up the function and use the inverse function like this

>>11873378
that depends on whether your definition of "integrable" allows the integral to be infinite. usually it doesn't.

How does diffraction work?
According to Huygen's model, shouldn't there be no "blind spots" when a wave diffracts through a slit?
How does the size of the slit interact with how much diffraction occurs, and how does the wavelength play in this?

Any resources that explain this in more detail? Thank you in advance.

>>11873580
Ofc, thank you

>>11873351
>>11873359
cheers

>>11873682
Yeah, I didn't even try to understand your drawing but now I see what you're thinking, and it does work.

Anyone got references for taking the derivative of a set of data points? I know you can do it analytically with cubic splines but I want to know if there is just a straight up formula.

>>11873916
not sure of the exact formula but if the data points are evenly-spaced you just interpret the derivative literally as the "rate of change"
that is, set up a table of values containing points [math](y_{i+1}-y_{i})/(x{i+1}-x_{i})[/math]
If they're not evenly-spaced this works I think but is a worse approximation. You'd probably just want to do splines. Or, if you know your data should be modeled by a simple function, then just curve-fit the function and then differentiate that.

>>11873932
>>11873916
that should obviously read
[math](y_{i+1}-y{i})/(x_{i+1}-x_{i})[/math]

>>11873936
fuck it I give up, I have no idea what's going wrong I definitely put all the curly brackets that time

>>11873916
http://web.media.mit.edu/~crtaylor/calculator.html
I love wikipedia.
God bless wikipedia and God bless America.
>>11873932
Good effort on that unilateral approximation.

>>11863470
Hello sci I have decided I want to take learning seriously what are the steps I can take If I want to get into STEM if I was just an average student in highschool?

>>11872712
> 00, 01,01,10,10,01,01, etc
What is "etc"? You want something that starts with 00 but then alternates between 01 and 10 every other tick?

>>11873932
>>11873936
>>11873962
Thanks

>>11872712
just use a uC for arbitrary shit mane

https://www.youtube.com/watch?v=98TQv5IAtY8
Is the solution to this puzzle totally flawed or am I just an idiot?

>>11870242
i don’t think I understand. What do you mean with control points?

I had something that looked similar to e^-x or 1/x, a natural spline made wiggles and interpolation pointless (got a negative mass).
Is there a way to force the 2nd derivative >0 or something similar?

>>11873686
This was in the context of the standard Lebesgue integration theory.

I should know how to do this but I've managed to forget my statistics class.

How do you handle a probability distribution of a random variable which has its own distribution?
For example, say you have a process that follows a normal distribution, but the argument you're passing into this distribution is also a distribution rather than a discrete value. How do you write the form of the final distribution? Is it as simple as replacing the random variable with its distribution in the expression for the process distribution?

I want to find a homotopyequivalence between [math] S^1 \vee S^1[/math] and a θ-like looking thing with [math]θ = S^1 \cup \{ (x,0) | x \in [-1,1] \} \subset R^2[/math].
It's obvious I map "arcs" to "arcs" and the other way around, the problem comes with mapping [math](0,0) \in S^1 \vee S^1[/math] to single point on the middle section of the θ... It can't be in the middle of it like (0,0), because the preimage (0,0) isn't open in [math] S^1 \vee S^1[/math]. So maybe on the side of the θ, but then pic related happens: If a have a open subset of θ going over the point in the middle (blue), it's preimage isn't open in [math] S^1 \vee S^1[/math] at (0,0).
Is the map just completely wrong or am I retarded?

Does higher voltage mean faster current? I mean how can 100V and 1A have the same power as 10V 10A.

what's the best, most gentle introduction to analysis book there is, for an electrical engineering student looking to broaden their math background?

>>11874837
Abbott's Understanding Analysis and Spivak's Calculus (intro to intro analysis book disguised as a Calculus book).

>>11874812
I=V/R buddy
voltage means there's a *potential* for higher current. It all depends on what the resistance is.

For your second question, it's like getting hit by a baseball bat at 10 miles an hour or a wiffle bat at 100 miles an hour.

>>11874855
you can have any current at any voltage

>>11872718
Okay. So I learned a lot more about transistors last night and today and I pretty much completely understand how they work. But I still don't understand why they are useful. The two common things they are used for is switching and amplification. Well, when it comes to switching, what is the benefit of using a transistor rather than just using a physical switch. Every diagram I have seen so far of a basic transistor switch still requires some kind of manual physical connection to complete the circuit. What is the point of having a transistor, it just seems like a useless middle man to me. The other thing it's used for is an amp which I still don't even remotely understand.

>>11875077
a transistor can switch several million times a second
how fast can your finger flick a switch

the "amplifier" thing is a bit of a red herring. It took me a while to understand as well.
Whatever is done to the base/gate of a transistor is mimicked by the collector and emitter, or gate and source. However, you've presumably hooked the collector/drain to a much higher line voltage than is being supplied to the gate/base.

Since the (fuck it I'm just going to use one) collector-emitter path mimics what's being done to the base, it will do the exact same thing that's happening to the base but it will instead use the higher line voltage for its signal.

Imagine you work at a dam. You have a button you can press that will open up the sluice gates of the dam when you hold it down.
When you press the button, it only requires a tiny bit of force. But by pressing the button, you've unleashed a huge torrent of water. Your tiny little button press was, in a sense, amplified into a huge torrent of water.

As another example, when you turn the steering wheel in a car, are you yourself pushing the entire car into a new direction? No, of course not. However, your comparably small force turning the steering wheel still has the effect of turning the entire car. Your turning force was amplified into a force that moved the entire car. The same could be said about the accelerator.

Thinking about amplifiers like this (at least for me) was a "Well fuck, I mean I guess..." moment. It turns out "I guess..." moments come up a lot in electrical engineering.

If gravitons can't escape a black hole then how does information about its mass get transferred out, it shouldn't affect/be affected by anything i.e no planets orbiting black holes?

>>11875210
That was a pretty good explanation on the amplification aspect but as for the switching. How does it actually switch that fast without a physical input? I drew this up in MS paint, the symbols are probably wrong because I'm really new to this. Is this how the transistors are able to switch so fast without a physical input or am I missing something?

>>11875288
>How does it actually switch that fast without a physical input?
Well, that's the *actual* answer as to why transistors are used. They don't *need* a physical input.
Since transistors are electrical devices that switch when there's an electrical signal on their base/gate, *anything* that outputs an electric signal can be used as a switch.

For example, If you've ever looked at an ethernet port on a computer and seen the little flashing LEDs - those are using transistors. The ethernet cable alters between 0 and some V+ voltage.
Whenever there's a V+, the transistor acts like a switch and turns the LED on. The end result is that the LED flashes along with the data moving through the ethernet cable.

Another good example would be a solar powered street light. At night, the light turns on. But, if it's solar powered and there's no light, how can the light turn on?
Well - there's gotta be an external power source. But, then how does the external power source turn on? A switch. An electronic switch - the transistor. When the solar panel goes dormant, the transistor turns on, switching power into the street light's lamp.
(cont.)

>>11875372
As far as how the transistors are able to switch that fast, that would require some intense physics stuff I don't think you're ready for yet.
The truth is, transistors ARE limited in how fast they can switch. Their limits are just really fucking fast compared to what a human can accomplish.
Unfortunately your schematic doesn't make much sense, but I see what you're trying to get at. As it is, it wouldn't do much of anything since the emitter (which should be the collector) of the transistor of the left isn't connected to the V+ side of the circuit. That's where your voltage comes from - you've essentially left one of your metaphorical wires dangling, unconnected to anything.
Assuming a corrected circuit, what you've drawn would turn both transistors on at effectively the same time. It wouldn't oscillate. This has the effect of amplifying the amplification - it's called a Darlington Pair.

The darlington pair essentially uses a smaller, weaker transistor to trigger a much larger transistor. The small transistor wouldn't be able to handle the currents required through it, so it instead triggers a much larger transistor.
https://en.wikipedia.org/wiki/Darlington_transistor

Conceptual thermodynamics question:
Under what conditions on the experimental setup (i.e. state of each subsystem, type of exchange permitted by each separator) would the final state be independent of the order in which the separators are removed?

>>11875077
>Every diagram I have seen so far of a basic transistor switch still requires some kind of manual physical connection to complete the circuit.
no, what the fuck
the base detects a current, which makes it turn on. This current can come from a microcontroller, or a pulse generator, or from an physical probe (temp, pH, magnetic field) that generates a current

>>11863470
i'm working on a card game that runs in the command prompt as a simple project
as is, i have the program clear the screen each turn, and at the beginning of each turn i display the user's hand at the top. however i feel this is inadequate because the user's hand will change after they make their play, and potentially after other players make their play. is there a way to write over previous lines so that i could have the user's hand update in real time?

>>11875938
Yes, there is.
To save yourself a lot of trouble you should look into ncurses, which is a library to create terminal interfaces.

Alternatively, you can just update the screen after each action manually.

>>11875372
>>11875383
Thanks. This really helped me understand a bit better.

Spivak vs Stewart? I have taken up to multivariable in college. Wanted to relearn calculus. Want a more intuitive understanding again as opposed to "plug and chug"

>>11876424
Also does the edition matter? There are some cheap stewart books in my local bookstore

>>11876354
you're welcome. Transistors and all of their intricacies and gotchas can be a lot to wrap your head around.
I still get turned around trying to think about enhancement mode ("normally off") N-channel and P-channel MOSFETs and depletion mode ("normally on") N-channel/P-channel MOSFETs
in fact that's another good tip - there's actually 4 types of MOSFET, not 2.

>>11876424
stewart is more of an engineering/applications-of kind of book. You're not going to get a deeper look into calculus by using that book

>>11875938
cout<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl<<endl

>>11863470
Is there a book that describes all properties of liquids?(Wikipedia calls it fluid dynamics)
For a person with high school knowledge of physics.

How do I understand Bayes' Theorem?

>>11877824
>Is there a book that describes all properties of liquids?
No, basically nothing is known about the properties of liquids.

>For a person with high school knowledge of physics.
I doubt there is anything interesting to learn at that knowledge level. Fluid dynamics absolutely requires PDE theory.

>>11878497
k then i will just go and play in the dirt

>>11876424
Spivak if you have done some calculus before, absolutely. Do not waste your time with Stewart.

>>11876434
>Not using a pdf you find online
They're everywhere for free. It's really not hard to read electronically.

>>11873362
If you know how something changes in terms of what it is, and you know what it is at the start, you want to find what it is at all times.
For example, the more people there are, the more they reproduce. This relationship is approximately proportional. So if P(t) is the number of people at time t, and we start with p people, the differential equation is dP(t)/dt = k*P(t) for some number k that you can pick. You can solve this equation to show that P(t) = p*e^(kt), which tells you population growth is exponential.
PDEs are the same idea except now instead of just changing in one direction, you can change in other directions too. So how much the temperature of something changes depends on the temperature of the points all around it, not just the temperature in front or in back.

>>11873362
shitposting with calculus

>>11878532
Just learn PDE's and pick up a book on fluid dynamics, learn about Navier-Stokes, have a time of it

>>11877920
do you understand conditional probability?

>>11879013
barely....

>>11879059
Likelihood of A and B happening is the likelihood that B happens and that A happens given that B has happened.

>>11877920
The likelihood of A and B happening is the likelihood of A happening times the likelihood of B happening given that A happened.
It also equals the likelihood of B happening times the likelihood of A happening given that B happened.
In math speak, [math]P(A ~ and ~ B) = P(A)P(B|A)[/math] and [math]P(A ~ and ~ B) = P(B)P(A|B)[/math].
But [math]a=b[/math] and [math]b=c[/math] implies [math]a=c[/math], so [math]P(A)P(B|A)=P(B)P(A|B)[/math]. You can then rearrange this into your preferred form.

>>11879059
think of it this, when you know something about the event that happens your sample space adjusts accordingly

Need a distributor for shopping for science materials, specifically magnets but also non kid stuff like solenoids
Amazon is run by BLM so that's out of the question

If I have a ring [math]R[/math], can the additive group [math](R,+)[/math] ever be isomorphic to the multiplicative group [math](R^{\times},\cdot)[/math]? I know this is never the case for fields, but wondering if it can ever happen for other rings.
By order considerations alone [math]R[/math] must be infinite, and it must also be commutative. Any further ideas?

>>11863470
Any ideas.?

>>11879967
C. Because I have a 50% chance of choosing the correct answer which is A or D.

>>11865216

>>11879782
I don't think so. In a ring the additive group has to be abelian, and if it is isomorphic to the multiplicative semigroup then it must also be an abelian group and thus you end up with a field, which you already know can't be the case.

Having some issues understanding this proof, mostly just the part that's highlighted.
>and thus has a prime ideal
I assume that is just because [math] S^{-1}A [/math] is a ring with identity and every ring with identity must have a maximal (and thus prime) ideal, right? Or is there some other reason/some other prime ideal they could be talking about?
>which corresponds to the prime ideal P of A
I read that this comes from the ring homomorphism [math] \varphi : A \longrightarrow S^{-1} A [/math] defined by [math] \varphi (a) = \frac{a}{1} [/math], and I assume it's just cause the preimage of a prime ideal under a ring homomorphism has to be a prime ideal. But I don't see how that would be helpful without surjectivity here, isn't it possible that the other elements besides 0/1 in the prime ideal simply have an empty preimage and therefore the preimage of the prime ideal is just (0)? Or would that not be a problem?
>with [math] A \setminus P \subset S [/math]
I just don't get why this is true, probably because I'm not too sure about the questions above

Anyone has any pointers?

>>11863470
>books?
>libgen.is (warn me if the link breaks)

Recently libgen.is tends to redirect to libgen.lc

According to 'no-hair theorem' black hole's got only three properties: mass, charge and angular momentum.
What happens to baryon number, lepton number and spin when atom of hydrogen falls into black hole?

What is this kind of regression called:

y = x^n + b (n and b are constant)

Also, what's the best way of finding n if I have data about the value of y from x=0 to 50 and that I know that b=21?

>>11880250
Polynomial regression, in general.
I doubt there is a special name for monomial + constant, but I wouldn't know.

>Also, what's the best way of finding n if I have data about the value of y from x=0 to 50 and that I know that b=21?
Just try it for n=0 up to n=?.
And use the best one.

>>11880276
Is it still polynomial if n is not an integer, but a number between 1.28 and 1.38?

Can someone explain to me Enderton's proof at page 153? Wouldn't a restriction of a model by removing the infinitely large constant make those statements for which it is true unprovable in the model itself. How would it be in the universe of said structure, when it can't be either true or false in it?

Trying to prove the convolution theorem for finite abelian groups. Let [math]\chi[/math] be a character of [math]G[/math], and let [math]f,g: G \to \mathbb C[/math].

I've shown that [math]\widehat{f*g}(\chi) = \frac{1}{\#G} \sum_{x\in G} f(x) \overline{\chi(x)} \cdot \frac{1}{\#G} \sum_{y\in G} g(yx^{-1}) \overline{\chi(yx^{-1})} = \frac{1}{\#G} \sum_{x \in G} f(x) \overline{\chi(x)} g(x^{-1}) \overline{\chi(x^{-1})} \hat{g}(\chi)[/math]. How do I get rid of that extra [math]g(x^{-1}) \overline{\chi(x^{-1})}[/math] factor?

>>11879782
Take the ring [math]\mathbb{R} \oplus \mathbb{Z}_2[/math]. Define [math]f: \mathbb{R} \oplus \mathbb{Z}_2[/math] by [math]f(a, b) = ((-1)^b \exp (a), 1)[/math].
I think that works.
>>11880235
>right?
Yes.
>would that not be a problem?
It wouldn't. Telling you that the zero ideal is prime is very useful data in and of itself, since it tells you you have a domain.
>I just don't get why this is true, probably because I'm not too sure about the questions above
Because the elements of [math]S[/math] gain inverses with the localization, so they can't belong to any ideal of A other than the entirety of A.

Is R^2\({(1/n, 0) | n natural} and {(0,0}) homeomorphic to R^2\{(n,0) | n integer}?

>>11880684
circle inversion ?

if electrons move cm/hour speeds then how do capacitors charge in a fraction of a second?

Can you guys point me the way for proper reference to scientific research methods for communications and journalism? I'm planning to write some stuff and I want to make it proper scientific research material instead of ideological shilling. I'm from Brazil and the best word to define scientific research methods for journalism is "pauper", not to mention old, or incomplete, or pozzed, or made by chair teachers with zero commitment to anything but to kiss ass of politicians. Help?

Picture merely ilustrative.

>>11880302
No.

how does pressure in an enclosed vessel relate to usable work?
in the sense of a fluid-filled piston (water) compressed to 1000 PSI. i open a valve with a 1 in*in area.
what sort of things do i need to know in order to model this behavior? like, does the flow-rate depend on the volume of fluid behind it, or only the Delta P across the orifice?

i imagine the flow rate drops off logarithmically. all the work is going to be done by the kinetic energy in the fluid molecules right? so orifice size doesn't change the net work, but a smaller orifice would take longer to drain the reservoir.
how would you determine flow rate? it would be viscosity limited right?

>>11880736
it really doesn't take much to charge a cap, just the few e-'s at the end of the wire usually does the trick

might be a question for /his/, but:
What is the name for this fallacy?
>women are less likely to choose or excel at technical professions
>therefore, all women are inferior in technical professions
it's not slippery slope, is it?

>>11881205
sounds like a faulty generalization

>>11881205
Ox before the cart

>>11881205
I'd frame it as 'absence of evidence isn't evidence of absence', since the logic seems to go "If women were as good as men in technical professions we'd have more women in technical professions".

>>11880681
Awesome, thanks a lot, I actually get the proof now

>>11881205
Non sequitur. The conclusion does not follow from the premise.

>>11881205
Two fallacies in one. First, "appeal to probability" (because something is probably the case then it's definitely the case). If you downgrade "all women are inferior" to "on average ...", then you're left with the "base rate fallacy" (because something is likely in general it's therefore equally likely in a specific case, ignoring prior probabilities i.e. selection bias).

Do any of you guys know of a circuit simulator that uses real elements? As in you get a thing that looks like a breadboard and things that actually look like capacitors etc, not a SPICE looking thing.

I have to determine if a compound is a good conductor of electricity in water based on its freezing point depression.
It seems like a simple enough problem but when I calculate the van't Hoff factor it is greater than the number of atoms in the compound.
Am I being fucked with or is this possible?

>>11880736
because you're not charging it with the electrons that start at the switch. You're charging it with the electrons that start right in front of the capacitor

Am I doing this right?
[eqn]\int_0^2 \sqrt{4t^2 + 4t^2 + 36t^4}dt [/eqn]
[eqn] \int_0^2 \sqrt{8t^2 + 36t^4}dt [/eqn]
[eqn] \int_0^2 \sqrt{4t^2(2+ 9t^2)}dt[/eqn]
[eqn] \int_0^2 2t\sqrt{(2+ 9t^2)}dt[/eqn]

And then my answer is just that indefinite integral?

>>11881554
Yes.
Substitute y = t^2 btw.

>>11881583
*y = 2 + 9t^2

>>11881224 >>11881234 >>11881237 >>11881316 >>11881336
none of that is catchy or memorable though

Can someone explain how to go from the first to the second?
I know that (n-1)! can be expressed as n!/n
And (m-n+1)! can be expressed as (m-n)!*(m-n)
But I don't know how to get that common denominator

>>11881554
> And then my answer is just that indefinite integral?
No. It's [math]\frac {4 (19 \sqrt {38} - \sqrt 2)} {27}[/math]
The antiderivative is [math]\frac {{2 (9 t^2 + 2)}^{\frac 3 2}} {27}[/math]

>>11881638
> And (m-n+1)! can be expressed as (m-n)!*(m-n)
It's (m-n)!*(m-n+1). The factorial is the product of the highest term and the remaining product: (n+1)!=(n+1)*n!.

>>11881586
thanks! also, I meant 'definite integral', not indefinite (obv)..

>>11881661
Okay got it, thanks.

>>11880681
Just checked, the isomorphism works. Thanks a lot, this was a really interesting answer.

>>11881723
>Just checked, the isomorphism works.
Very good to know, thank you for checking.

how can i represent [math]\pi[/math] in a cartesian graph? just something between 3 and 4?

>>11882022
Christ..

what the fuck is porosity

explain it to me like i'm a retard, please

>>11863470
When i turn a monoid into a one object category, the monoid itself becomes the collection of arrows, but what are the objects? If i take the collection of objects as just any arbitrary thing, as long as is only one, will suffice?

>>11882022
Take half of the unit circle and unrroll it from the origin.

>>11882164
a measure of how much not stuff is in a given volume over how much stuff is in a given volume

Is it possible to be a successful scientist even after humiliating yourself in the 6th grade by mixing up Michael Jackson and Michael Jordan?? I called the famous basketball star a pedophile at this age and was laughed out of the lunchroom.

>>11882317
when I was in 6th grade science class, I wound up answering a question in front of the entire class
"Does anyone know what the space telescopes such as the Hubble Telescope were named after?"
"They were named after former presidents!"
I meat to say astronomers
but I still said presidents

>>11882332
lol what a fucking retard

>>11882334

>>11863470
If the universe is mathematical and science is the pursuit of understanding universal truths. Why do I see math treated like a distracting waste of time and physics be treated like it isn't just math? Even if certain mathematics aren't useful now wouldn't they be later?

>>11882317
theres still no evidence of that all these years later

>>11882492
don't think he was a pedo desu
I just think it was tabloids looking to snipe an easy target and what better target than an eccentric, confused, emotionally lost and isolated black man

Say i have a random set of points, how can i calculate entropy of the set?
How can i make sure if i were to have a regularly spaced cube/tetrahedral/hexagonal/whatevergonal lattice of points it would have an entropy of 0?
What if small subset of points are repeated regularly? What would the entropy of the set be then?

>>11880745
Please?

so how come theres more matter than antimatter anyway

>>11882231
IIRC you usually use the set of elements of the monoid as the group.
This has the advantage that morphisms can be interpreted as actual functions on the category's single object (action from the left, that is [math]f_a : M \rightarrow M[/math], for any [math]a \in M[/math], is defined by [math]f_a(x) = ax[/math] ) and also because Cayley's theorem.
You can absolutely use whatever the fuck as object, tho.
>>11882317
I too mixed up Michael Jackson and Michael Jordan when I was little. I also remembered someone saying he was half black, so I literally pictured him as having the entire left of his body that of a white man's and the right of a black man until I saw him on Space Jam. Great movie.

>>11883642
>as the group
*as the object.

Is the image of an element of the domain always part of the range?

How can i be faster at resolving math problems?
i don't consider myself bad at math, but i am slow as fuck when i'm solving a math problem, i don't remember the last time i have done the whole exercises in a test because of the lack of time

>>11884419
Read math books in your free time and solve provided exercises that are challenging.

what does it mean for x to not belong to x? how is this possible if x is an element of A and not its own set? what does it even mean?

How the fuck can you determine the order of reactant [B]? There are no two experiments where [A] and [C] remain constant but [B] changes. The answer key says it's 0 order, but I have no idea how they found that.

>>11884880
What? [math]x \not\in x[/math] means exactly that, i.e., x is not an element of itself. For example, [math]\emptyset \not\in \emptyset[/math].

>>11884407
Yes.

BTW, the term "range" is ambiguous; it can refer to either the codomain (the set to which the function's values are defined to belong) or the image (the set of possible values). E.g. for f : R->R, f(x)=x^2, the codomain is the reals while the image is the non-negative reals.

But that doesn't affect the answer to your question. The value lies in both the image and codomain, as the former is a subset of the latter.

>>11884965
other examples?

>>11863470
if sodium hydroxide is very soluble in water then why during electrolysis with small separated containers with a salt bridge does my sodium hydroxide form on crystals on the cathode and refuse to drive the solution over 5 - 7 % even after 14 hours ?

is there to much gas production and its oxygenated and hydrogenated the water to such a degree that there isnt any more room in suspension?

im making sodium hydroxide and its only forming on the cathode after 5 - 7% pretty much and at a point i think it dropped to 3% and stuff in solution crystalized on the cathode. i can get it to like oxypad level where it kind of bubbles on the skin but doesnt do much else then it drops lower and only is on the cathode

>>11884907
find the order of A (exp 1&2). Now starting with data from exp4, calculate the rate you'd get if A was doubled (from 0.012 -> 0.024) (call this exp5).
To find B, compare exp5&1.
To find C, compare exp5&3 (once you know B)

>>11884994
Probably anything you know. Natural numbers, the set of natural numbers, [math]\mathbb{R}[/math]... Maybe you need to think about a set that belongs to itself to clear your doubts.

>>11884994
[math]\{ \emptyset \} \notin \{ \emptyset \} [/math].

>>11885036
so it applies to sets and not elements? I guess elements are sets anyway... I don't understand how for example [math]1 \not\in 1[/math], but [math]1 \in {1}[/math].

>>11885073
sorry meant 1 belongs to {1}

>>11885075
You just do a \{ and a \}.
Like so: [math]\{ \}[/math]

>>11885073
Yeah, in set theory everything are sets. [math]\in[/math] is a binary relation between sets. Don't think too much about it; [math]x \not \in x[/math] just means x does not appear as an element of itself.

>>11863470
How do you guys achieve dopamine from studying?

>>11863470
I got an offer to study mathematics at St Andrews, should I take it? I'm from a third world country, my main "goal" of studying in Scotland was to get a degree in Europe so that it'd be easier to then continue my work or further studies there, making connections and c. I heard good things about the department so that's the main reason I applied to St Andrews.
So, would it be worth it to pay full tuition for 3 years rather than attend a cheaper university at my home country? How is a degree in Maths from St Andrews generally seen by employers/etc. I don't really care about clubbing, or that the weather is damp, etc.

>>11885300
I feed on the nervous tissue of healthy fellow high iq's in the late evening right before I do my cog heavy lifting.

Could i be consider a smart person if i learned a language just by watching subtitled movies/series? does that say something about my IQ?

>>11885369
no, infants do that all the time
just cuz you picked up the meaning of Ohayo from watching anime doesnt mean youre a savant or some shit
everyone does that

>>11885374
wasn't anime and i wasn't a kid

>>11885338
depends on the country, what your future plans are (grad school vs industry, where you want to work)
it'll be much much easier to continue work in Europe with a European degree

OK GUYS HI HOW WE DOIN TODAY UH HUH YEAH GREAT OK WELL YEAH SO TODAY WE GOT A REAAAAAAL LITTLE STINKER FOR YA!

WHAT WE HAVE HERE IS A SOLUTION TO A SYSTEM OF EQUATIONS - _BUT_ - WHAT WE DON'T HAVE HERE IS THE PARAMETRIC REPRESENTATION OF IT!! UNBELIEVABLE!

MAN IF I WASN'T SUCH A [math] \mathbb{R} \sum \mathbb{T} A\mathbb{R}D [/math] I'D DO IT MYSELF BUT HEY HAHA THAT'S WHY I GOT YOU GUYS!!

>>11885571
Bro literally rewrite the first four equations there with [math]x_3[/math] and [math]x_4[/math] swapped on the right (ONLY on the right sides of the equations) by [math]t_1[/math] and [math]t_2[/math].

>>11885687
it's the syntax of the entry I'm really having trouble with

>>11885766
[math]A = [[3 r + 7/9 s], [-2r + 4/3 s], [r], [s]][/math]
Also, you typed in 9/7 instead of 7/9.

>>11885766
Your pic says 7/9 but you entered 9/7.

>>11885786
>>11885790
yeah, i swapped those around awhile based off what i had on paper, forgot to switch them back. I've tried every varient i could think of, including the one just provided (which didn't work, even after removing 'A = ')

>>11885786
>>11885796
wait FUCK it worked

gentleman and a scholar, thanks!!!