/sci/ - Science & Math

>Personal version: Maple or Mathematica?

>I have a better impression of Maple for reasons that have nothing to do with mathematics.

Looking for more anon's opinions.

>>9516210

>>9516230
What do you plan on doing?

how much linear algebra can i learn in 14 hours
i have an exam tomorrow

>>9516893
you're fucked lel

>>9516898
please dont say that

>>9516795
mostly I tinker with algebra, fields, etc. No analysis.

>>9516893
>Learning the day BEFORE th exam
Brainlet detected

>>9516915
I've gone to class but I've really just not thought about it outside of that time

>>9516225
Where can I get a shit ton of genetically identical peanut seeds

>>9516893
>how much linear algebra can i learn in 14 hours
>i have an exam tomorrow
how to drop out

I'm helping a friend design a user payout system (cryptocurrencies) for a sort of social network site and would like input for some questions posed.

https://youtu.be/FEZXDUy6YCU

>>9516893
y=mx+b b is y intercept m is slope start there buddy good luck :)

>>9516893
I hope you know what a matrix is

>>9516926
buy yourself a peanut tree

>>9517065
This bait is very tasty.

>>9517065
I need the immediate ancestor seeds. And like 200 or so genetically identical ones.
>>9517134
Peanut trees are real. It's a tree native to Australia that has a fruiting body with 8 to 10 edible black seeds that taste like peanuts

How do I show that the cross-ratio is invariant under projective transformations of the line [math]\mathbb{F}P^{1}[/math]?

>>9517057
yea, the movie?

Do you guys use solutions to study?
I often don't get how to solve a problem, then I look at the solutions and understand the strategy to solve it. The textbook have a lot of exercises so similar problems are common.
I feel anxious because the professor says we should try to solve the problems by ourselves.
There is no graded homework here.

>>9516230
Mathematica is the best CAS, period. But the Wolfram Language is rather... uncommon. You have to learn it to truly understand Mathematica capabilities.
If you want to get the work done without thinking about programming, try Maple. Is Java-based and a bit slow, but it works.

Repeating my question from last thread because nobody was able to help me:

How do I prove that that f(x, y) = x^2y + 1 is continuous in (0,0) using the epsilon delta proof?

I know that in order to prove this I need to prove that f(x,y) reaches its limit in (0,0) which is pretty clear from intuition, but I'm having a real problem proving it using the epsilon delta definition.

>>9517428
>How do I prove that that f(x, y) = x^2y + 1 is continuous in (0,0) using the epsilon delta proof?
>I know that in order to prove this I need to prove that f(x,y) reaches its limit in (0,0) which is pretty clear from intuition, but I'm having a real problem proving it using the epsilon delta definition.
What have you tried? It follows immediately by making use of easy lower bounds for |(x,y)-(0,0)|.

>>9516893
Good luck, we believe in you.

>>9517472

I think I got it actually.

|x^2y+1-1| = x^2|y| < ||(x,y)||^3 < 𝛿^3 = ε


So if you take ε>0 and 𝛿=ε^1/3 for x: 0<||(x,y)-(0,0)||<𝛿 the above equation holds, proving that lim of f(x,y) approaching (0,0) equals f(0,0) and thus the function is continuous in (0,0).

>It follows immediately by making use of easy lower bounds for |(x,y)-(0,0)|.
I'm not sure what you mean by that. How would you write out the proof?

>>9517490
>I'm not sure what you mean by that. How would you write out the proof?
Essentially the same way you did (I meant the |x|<|(x,y)| and |y|<|(x,y)| bounds).

Is the angle for the slanted surface 90?
Also, how do i find the area of that surface when I’m given only 2 lenghths?

>>9517311
You are learning how to solve them, not the concept behind. If you managed to grasp the fundamentals you would not be having so much trouble. Personally i just think you are not studying right.

>>9517052
if you're in Australia, use
q + xw = λ

Any help with part b? The conclusion I'm supposed to verify is the statement on the bottom

>>9516225
Fuck your feelings. Stop feeling feels and start thinking logically, newfag.
>>>/r9k/

>>9517780
>Any help with part b?
Use the hint.

>>9517311
If you're truly lost, look at a few lines at a time and try to do the rest on your own. Then go back a few days/week later and try to solve it again cold.

But try to solve it completely on your own for at least an hour before giving up. And speak to your professor for guidance in his office hours.

>>9517760
Probably

>>9517780
∮_γ dz = ∫ i*e^iθ dθ from 0 to 2π
z -> e^iθ

>>9517760
>Is the angle for the slanted surface 90?
nah it's 60, the angle is between the e vector and the vector perpendicular to the plane
>how do i find the area of that surface when I’m given only 2 lenghths?
you have a 60 30 triangle and are given a side, solve for the hypotenuse

I remember downloading a collection of all the books recommended on the /sci/ wiki a while back. Now my hard drive is dead and I lost them all. Anybody got a link or torrent for them?

>>9517961
Just download few books at a time and actually fucking read them.

>>9517961
http://4chan-science.wikia.com/wiki/Recommended_material

>>9517964
>Just download few books at a time and actually fucking read them.
Do you need to swear?

>>9517966
oh it was right there the whole time. I'm glad I posted my question in the right thread.
>>9517964
no

>>9516225
how do i figure out this problem? corresponding slide in next post

>>9518068

>>9517770
>>9517824
Thank you. It's not like I don't try to understand the concept (I try to demonstrate almost every equation by myself), but some questions are tricky.
I will try to not rely that much on solutions.

guys i need school advice.

I got in to u of Arizona for their optical science program and UIUC for their EE photonics track. These are both awedome schools that i didnt think id ever get in to. Where would you go?

>>9518068
>>9518071
Use Green's theorem and derive the Jacobian from the Hamiltonian.

>>9518128
Where do you live? I got into UIUC but didn't go because I live in California and I'm a greedy fucking Jew who prioritizes saving a few shekels over personal gratification. I regret it.

>>9518145
p-pls no memes

im just a brainlet anon

>>9518151
>>>9518128 (You)
>Where do you live? I got into UIUC but didn't go because I live in California and I'm a greedy fucking Jew who prioritizes saving a few shekels over personal gratification. I regret it.

I live in Arizona phoenix area. So like 90 minutes from u of arizona

>>9518158
That's really not very far. Both seem equally appealing. How about this: If you feel more comfortable at home, go to UoA; if you're rich and don't mind travelling alone, go to UIUC.

what's a good linear algebra book

>>9518217
Gilbert Strang or whatever his name is for introducing LinAlg is okay plus you get his funny lectures

>>9518217
I know these are shallow as fuck but I still love having them around.

>>9518217

shit guys i really screwed up
i need to learn all of symplectic geometry by tomorrow and all i know is remedial college algebra
any good resources out there for quickly learning the intermediary material?

>>9518580
I'VE GOT TO LEARN ALL OF SYMPLETIC GEOEMTRY IN 1 HOUR 30 MINUTES.

What’s likely to be wrong with Sminem, medically?

Is there some genetic developmental disorder at play?

>>9518602
marfan syndrome

FOURIER TRANSFORMS

I know a shift in the time domain corresponds to a linear phase in the frequency domain....

But what does a shift in the frequency domain correspond to in the time domain?

>>9518602
He looks like an Elder Scrolls Oblivion NPC. Maybe he was downloaded and has no genes at all.

>>9516225
Let G be a group. If a topology on G is such that all left- and right-translations are homeomorphisms then it is called a homogenous topology. It is clear that a homogenous topology is determined by its system of neighborhoods at 1.

Does every system of neighborhoods at 1 determine a homogenous topology? You could just say that all left- and right-translations of all the things in the system of neighborhood of 1 are open but I'm having difficulty completing the proof. A 'paper' I was reading seems to use this without proof and there is probably something ridiculously simple I am missing.

How much (modern) algebra do you need to know in general as a mathematician?

>>9518609
anons pls this is urgent

>>9518217
hoffman&kunze

is there anything interesting that uses the golden ratio, which isnt a putting-golden-spirals-over-pictures-of-plants type thing?

>>9516225
Can someone explain how exactly we get 3l/4 and -5l/4 please? I can't really hazard a guess as to how those limits were retrieved and its kinda bugging me.

>>9518694
>How much (modern) algebra do you need to know in general as a mathematician?
None at all.

>>9518694
>mathematician as a job
bruh

either your field of study demands it or it doesn't, what the hell kid

>>9519012
>posts the solution, not the question
my guess is it's obvious from the question

>>9519092
Sorry, here's the question.

Should I be worried about Coronal Mass Ejections?

>>9519108
>total length is 2L
>midpoint is L
>midpoint +/- L/4

Hi did they get from a to b ?

>>9519181
How*

Sorry, I’m phoneposting.

>>9519181
need more context phonefag

>>9519181
>>9519182
Pic related seems to be the most obvious method in my eyes. But I am not sure what postulate/theorem they used for the initial transformation in the example i posted previously.

>>9519189
Sorry. This is two-valued Boolean algebra.

>>9519195
I can see how it is done algebraically to go from b to a and therefore to conclude that a is just (x+y) but I don't understand how to just directly infer the transition from a to b. Sorry m8.

>>9518217
http://4chan-science.wikia.com/wiki/Mathematics#Linear_Algebra

>>9518609
You should be able to guess it since the Fourier Transform is its own inverse.
https://en.wikipedia.org/wiki/Fourier_transform#Basic_properties

>>9519002
sin(18°) = 1/2φ
Fibonacci(n) = [φ^n - (-1/φ)^n]/√5 ≈ φ^n/√5
Since the worst case input of Euclid's gcd method are obviously the Fibonacci numbers, the max number of steps is n ≈ log_φ(√5*a).

>>9518694
2 years worth. One at the level of Artin/Herstein and another at the level of Lang/papa Hungerford.

Shitter schools that use lower books -> you're never getting tenure.

>>9519326
>Since the worst case input of Euclid's gcd method are obviously the Fibonacci numbers, the max number of steps
this is also (not coincidentally) related to the worst possible bound on approximation of irrational numbers by rationals, basically everything else is much better approximated (transcendentals especially so)

>>9519012
Because x=0 is set to where the axis meets the rod which is apparently l+l/4 = 5l/4 down it. as shown on the figure. The whole rod is 2l.

>>9519181
>>9519191
>x = x + 0 = x + xx'
>x = x + x
>x = xx
>x = x*1 = x(y+y')

x+x'y = x + x + 0 + x'y
= xy + xy' + x + xx' + x'y
= xy + x(y' + 1) + xx' + x'y
= xy + x + xx' + x'y
= xy + x + x'(x + y)
= xy + xx + x'(x + y)
= x(x+y) + x'(x + y)
= (x+y)(x+x') = (x+y)(1) = x + y

alternatively
>1 = 1 + y
>x = xx
>0 = xx'
x -> x*1 -> x(1+y) -> x(x+y)
x'y -> x'y + 0 -> x'x + x'y -> x'(x+y)
x+x'y = (x+x')(x+y) = x+y

2nd alternative
DeMorgan
x'(x+y') = x'y'
DeMorgan back
x+y

Could someone point to a resource where I can understand why for example taking a derivative of lnx=1/x, but of lny=1/y*y'? Also would like to understand taking a derivative of something with respect to something. I'm 100% those two concepts are connected, but my "teacher" never explained any. We just learned the rules. And I'd like to understand these through usage of Leibniz notation.

Also in pic related is the second one a second derivative and why is it written as such? I've only ever learned y', y", y"' etc. in school and this is new to me, but the teacher randomly started using d/dx, dt/dy/dx/dt and similar shit without even explaining the concept behind it. Fuck I hate my school.

>>9519452
>Could someone point to a resource where I can understand why for example taking a derivative of lnx=1/x, but of lny=1/y*y'?
That's just the chain rule (when y is y(x) and you're taking the derivative of lny with respect to x)

Okey, so I'm trying to show that Maxwell's equations (without sources of field) are not invariant by means of galilean transformations but invariant under Lorentz transformations. In the examples I've seen, they take some weird liberties on the chain rule, so I decided to try it defining everything properly. A time varying Electric field can be represented as a vector function [math]\vec{E}:\mathbb{R}^4\to\mathbb{R}^3[/math] and the same for a time varying magnetic field [math]\vec{B(t,x,y,z)}[/math]. So I just defined a composition of these fields with a galilean boost defined simply as [math](t,x-vt,y,z)[/math] and then applied the chain rule and found out all the partial derivatives are same except for [math]\frac{\partial\vec{E'}}{\partial{t}}=\frac{\partial\vec{E}}{\partial{t}}-v\frac{\partial\vec{E}}{\partial{x}}[/math]. With this extra term it was clear that the curl of the new [math]\mathbb{\vec{B'}}[/math] isn't the same as the one before the boost so I assume I was done. But then I did the exact same procedure for Lorentz transformations and I got a contradiction with Gauss's law as other terms appeared out of no where. Searching online I found out that People use also the Lorentz force and show how the fields transform under galileo/Lorentz, but I'm in a situation where I have no sources, so the Lorentz force shouldn't even come in this case.

>>9519460
I get that it's a chain rule, I just don't understand why there's a chain rule for lny but not for lnx. I guess I don't grasp the derivative of "1st" with respect to "2nd".

>>9519486
>>9519486
>I get that it's a chain rule, I just don't understand why there's a chain rule for lny but not for lnx.
x' = dx/dx = 1

>>9519341
>>9519147
Oh, Christ sorry I skimmed the thing. Thanks a ton for the help. Apologies for my thickness.

>>9519452
>Could someone point to a resource where I can understand why for example taking a derivative of lnx=1/x, but of lny=1/y*y'?
Only the second is correct.

However, by convention x is not a function of something else, so we can say that dx/dx is 1 and ignore it. If, for instance, both y and x were a function of t then we'd have d/dt ln(x) = x'/x.

>>9519486
> I just don't understand why there's a chain rule for lny but not for lnx.
In both cases, you're differentiating with respect to x, so the two aren't equivalent.

d/dx ln(x) = 1/x
d/dy ln(y) = 1/y
d/dx ln(y) = (dy/dx)/y
d/dy ln(x) = (dx/dy)/x

How in the fuck am I supposed to prove this?

[math]A \cup \bigcap B = \bigcap \{A\cup X \,|\, X \in B \}[/math]

Here's what I tried so far
[math]x \in (A \cup \bigcap B) [/math]
[math](x \in A) \lor (x \in \bigcap B) [/math]
[math](x \in A) \lor (x \in \bigcap B) [/math]
[math](x \in A) \lor \forall b\,(b\in B \land x\in b) [/math]

Wtf now. I get a feeling that my definition of [math]\bigcup B[/math] is probably broken

>>9519329
I don’t think the intro book matters so much. Personally I like Gallian and Pinter. And Hungerford is much better than Lang to learn from.

>>9519326
> since the Fourier Transform is its own inverse.

No

My question is math related, but not homework related.
I graduated with a bsc in math from a no name program a little over two years ago. I would like to get a PhD in math so I can teach at a college level, but I'm not sure if I should pursue a master's degree first.
My undergraduate program was small and didn't offer many courses (pic related plus a few electives and an independent study in FEM). Would it be worth while to get my shit together at a master's program before going on to a PhD? The Big 10 in my state offers TA-ships for master's students. Cost wouldn't be an issue, just time.

>>9519452
dx / dx = 1

You take a derivative with respect to a variable.
If you do d/dy[ln(y)] = 1/y.
If you do d/dx[ln(y(x))], you use the chain rule. d/dx[f(g(x))]= f'(g(x))*g'(x) -> 1/y(x) * y'(x)

>>9518648
Bump for interest

>>9519486

This is the chain rule:
[math]\frac{df}{du} \times \frac{du}{dx} = \frac{df}{dx} = f'(x)[/math]

Notice that [math]\frac{df}{du} = \frac{f'(x)}{\frac{du}{dx}}[/math]

which translates to

[math]\frac{df}{du} = \frac{f'(x)}{u'(x)}[/math]

Let f(x) = ln(x) and u=y and you get exactly what you asked for

I learnt this through Calculus Made Easy, and now the chain rule is 100 times easier.

>>9519465
> as other terms appeared out of no where

That's what should happen.

>>9519643
But how to I discern between terms that leave my equation invariant and those which don't?

>>9519607
>How in the fuck am I supposed to prove this?
Unpack the definitions of both side.

a∈A∪∩B ⇔ a∈A OR ∀X∈B a∈X ⇔ ∀X∈B (a∈A OR a∈X) ⇔ ∀X∈B (a∈A∪X) ⇔ a∈ ∩{A∪X | X∈B}

>>9519615
>Gallian and Pinter

They're really written and intended for future high school teachers and others who won't be heading to graduate school in STEM. You really just fuck yourself over by taking algebra or analysis for brainlets and delay everything by a year.

>>9519625
>TA-ships for master's students

That's a bit unusual. I would go for the masters. Maybe read up on topics you missed in undergrad.

>>9519645
Their effects on a test particle?

need to learn partial fraction decomposition and need a shit ton of practice problems
anyone have links to worksheets or book problems on this?

>>9516225
Why is science falsifiable, but claims that it will someday discover the truth and unify Einstein's and Quantum theories?

>>9519779
I will never understand why people have trouble with partial fraction decomposition. It's like saying, "I get division, but how do you multiply?"

>>9519827
it's not that i have trouble with it, i just have never learned it in a classroom and keep forgetting the process since i haven't done any practice

>>9519656
Thanks. I don't really get the ∀X∈B (a∈A∪X) ⇔ a∈ ∩{A∪X | X∈B} part. Why is that so?

Also, I got stuck again :( how can I prove that [math]P(\bigcup A) = \bigcup (P(X) : X \in A)[/math] ?

Also, where can I get more of these exercises? I can easily do all of the problems in Enderton's chapter 2 but these kind of exercises (regarding arbitrary unions and intersections) are really hard for me.

>>9519952
That was meant to be arbitrary intersection, not arbitrary union

>>9517780
Is this complex analysis?

>>9520093
Not really, it's pretty simple.

I'm a brainlet that just bombed my first linear algebra exam. The computations are easy but it's impossible for me to visualize what's going on in a problem

Any tips?

I'm interested in learning algebraic geometry but I don't have a mature enough math background to take on even entry level books right now. I took linear algebra, calculus 1, and discrete math in university 5 years ago, did okay - good in them. Is pic related a good entry point into the subject? I'd like to refresh and start self learning.

>>9519952
>Thanks. I don't really get the ∀X∈B (a∈A∪X) ⇔ a∈ ∩{A∪X | X∈B} part. Why is that so?

a is in the intersection iff if a is in all the sets being intersected. Now read that backwards.

>Also, I got stuck again :( how can I prove that P(∪A) = ∪{P(X) | X∈A}
Unpack the definition and follow your nose

x∈P(X) iff x ⊆ X
X ⊆ A iff x∈X ⇒ x∈A

a∈P(∪A) iff a ⊆ ∪A iff α∈a ⇒ α∈∪A
a∈∪{P(X) | X∈A} iff (∃X∈A) a∈ P(X) iff (∃X∈A) a⊆X iff (∃X∈A) α∈a ⇒ α∈X

now α∈∪A iff (∃X∈A) α∈X so
[ α∈a ⇒ α∈∪A ] iff (∃X∈A) α∈a ⇒ α∈X

And we've met in the middle of an iff chain, therefore a∈P(∪A) iff a∈∪{P(X) | X∈A} so P(∪A) = ∪{P(X) | X∈A}.

NB: Book proofs will stylistically reverse the iff chain and have one long sequence from one end to the other to look slick.

>>9520153
>>9519966
Bah, you can more or less mindless De Morgan it by replacing ∪ for ∩ and ∃ for ∀

>P(∩A) = ∩{P(X) | X∈A}
Still unpack the definition and follow your nose

>x∈P(X) iff x ⊆ X
>X ⊆ A iff x∈X ⇒ x∈A

a∈P(∩A) iff a ⊆ ∩A iff α∈a ⇒ α∈∩A
a∈∩{P(X) | X∈A} iff (∀X∈A) a∈ P(X) iff (∀X∈A) a⊆X iff (∀X∈A) α∈a ⇒ α∈X

now α∈∩A iff (∀X∈A) α∈X so
[ α∈a ⇒ α∈∩A ] iff (∀X∈A) α∈a ⇒ α∈X

And we've met in the middle of an iff chain, therefore a∈P(∩A) iff a∈∩{P(X) | X∈A} so P(∩A) = ∩{P(X) | X∈A}.

>>9520145
This is the most entry-level AG book I know of

>>9519782
>Why is science falsifiable

It's not. Stop reading popper's garbage.

>>9520145
You are not really at a level to have actual mathematical reasons for wanting to learn algebraic geometry.
I don't know if people jump at it because it has a reputation for being hard and abstract or something but you're not going to succeed trying to learn a field that relies entirely on abstract algebraic tools before you learn any abstract algebra.

Keep it as a goal if you want but learn some ring/field theory first.

>>9520161
That looks interesting and approachable. Thanks, I'll keep it in mind.

>>9520171
I think I didn't phrase my question correctly. I do have that as my end goal and am interested in learning the necessary background topics to get there. Do you have any textbook recommendations for ring/field theory?

>>9520182
I like MacLane's Algebra (not Survey of Modern Algebra, which is anything but modern nowadays). It has all the basic algebra stuff but also doesn't hide from categories (fundamental to the modern version of algebraic geometry) and even includes (I think) some stuff on affine and projective spaces, which is nice and related too.

Literally anything would work though. Just use what you can find.

>>9520197
Thanks. My university has a used book store so I'll see what I can pick up for cheap.

>>9520145
Finish learning calculus

>>9520171
>mathematical reasons for wanting to learn X field of math
What do you mean? What "mathematical reasons" does one need to start learning something interesting?

>>9520208
There is no need to infect your brain with garbage when you're just starting out.

I'm going to office hours for the first time in my university career because of a Calc III problem i've spent around 6 hours on now
This makes me more nervous than it should. How do I not embarrass myself

>>9520233
>How do I not embarrass myself
Put on a nice fresh dress shirt, get a haircut, walk in confidently and give a firm handshake to him/her in charge of office hours

>>9520226
By mathematical reasons I mean being motivated by the actual technical content of the subject.
You cannot say you are (seriously) interested in algebraic geometry if you do not know what a ring is. It makes no sense.

>>9520235
>motivated by the actual technical content of the subject
I still don't get fully get your message. Are you saying that you have to be interested in problems algebraic geometry can solve to be interested in starting to learn it?
>You cannot say you are (seriously) interested in algebraic geometry if you do not know what a ring is. It makes no sense.
This is obviously true, but it's unrelated to your earlier comment.

What the everloving fuck am I supposed to do with implicit differentiation? I've been watching the Khan Academy video and it just doesn't click. What are some good resources

>>9520278
APEX had a pretty good explanation of implicit differentiation afaik.
http://www.apexcalculus.com/downloads
What is it that you didn't understand, anyways

>>9516225
what would happen if, say, superman punched the earth. would it shatter into pieces, or would it be pushed out of orbit? what are the factors that would cause the one thing or the other?

>>9520233
Don't be and go to office hours more often

Probability distribution for black iq, please.

http://aristocratsofthesoul.com/average-iq-by-race-and-ethnicity/

>>9516225

do quantum computers use supersymmetry?

>>9520503

seriously i need a response...I thought quantum entanglement and suppersymmetry were the same.

>>9520144
You probably don't get what the matrix is telling you about the system, take a simple square matrix and list off ~20 things about it.
If you can't do that, read the book again.

>>9520233
Just be honest.
Hopefully you bring your attempts with you so they can point out the issue.
Just don't say shit like "I have no idea" because you wouldn't be in that class in the first place, or "I've tried everything" because then you wouldn't be having issues.

can i learn pre algebra / basic algebra in five months, startint fr i just need to prep for college algebra.

>>9520714
starting from the beginning.

i plan to study for an hour each day

>>9520714
Yeah, totally.

Hey m8s

Physics dept is getting about 30 new pcs and Im helping out with them. They want to use a linux distro so I want to ask you all if you guys have ever used it, which distros have you used and which did you find met all your needs & was easy to use?

>>9520714
No.

>>9520808
debian stable

help pls

Can anybody write out the proof for an intersection of two closed sets being closed in lR^n real quick? It would be much appreciated

>>9520685
thanks, thats a good idea

I WILL NOT FAIL, DIDNT COME THIS FAR TO BOMB ON LA

>>9520937
>Can anybody write out the proof for an intersection of two closed sets being closed in lR^n real quick?
What have you tried?

>>9520943
Take two closed sets V and W
lR^n \ V is open because V is closed
lR^n \ W is open because W is closed
lR^n \ intersection V,W = union lR^n \ V, lR^n \ W
so lR^n \ intersection V,W is open and thus intersection V,W is closed

would be my proof, but I don't know if it's rigorous enough

>>9516225
How do I find the reference number and terminal point determined by t = 19pi/6? I think i'm missing something. The way I tried to solve it is subtracting 2pi to get 7pi/6, which is in the 3rd quadrant. I thought that means the terminal point should be, (-sqrt(3pi)/2,-pi/2), but apparently that is wrong. And to find the reference number, since i'm in the 3rd quadrant, i'm supposed to subtract 180 right? which gives me pi/6.

How many clowns would it take to shield the Earth from an asteroid impact. Assume the one that killed the dinosaurs

>>9521089
Only 1, if he's a big guy

why is 2/5 .4 and not .3?

>>9520808
Debian has the most documentation for when something goes wrong.

>>9518596
You've got no chance mate.
Do you know what a differential form is? And a symplectic matrix?

>>9521127
>why is 2/5 .4 and not .3?
Why would it be .3?

What's the best classical mechanics lecture series?


>>9520808
I would recommend NixOS since you need to likely deploy similar configs en masse, but it's not mature enough yet, so I'm going to have to say Gentoo is exactly what you want.

I need some help anons. I have to choose two to three of the following math courses for my next semester:
Discrete maths
Differential equations
Equations of mathematical physics
Statistics and probability
Numerical analysis
Selected chapters of real and complex analysis (basically Fourier and z transform plus a bit more detailed complex analysis than we've already done in the previous semsster)
What are the most useful courses if I'm an electrical engie going into the fields of automatic and control systems, signal processing, adaptive learning and similar areas?

>>9521842
sucks to only pick 2

personally I think fourier+z and diffy-q for engineering, but stat and numerical analysis are pretty fucking important too

>>9521842
Discrete maths + probability and statistics can be learned by yourself if need be. Equations of mathematical physics sounds a bit unorthodox to me so I would avoid it for now. So take numerical analysis, real/complex and diff eq.

>>9521870
>Discrete maths + probability and statistics can be learned by yourself if need be.

So can I all of it, but I understand the sentiment and agree with your selections.

Construct a holomorphic function on the open unit disk that takes all values of the complex plane
>How do
Idea: use sth like e^(1/z^2+2). But I don't think this is surjective
Any ideas?

I need a good fluids book. I don't liked the Cegala one recommend by the wiki (explanation not so clear and bad examples), and the other one is actually too advanced for me.
Good lectures would help too.

>>9521095
for you

>>9520669
>I thought quantum entanglement and suppersymmetry were the same.

>>9521986
Use Picard's little theorem.

>>9522037
hmm Picard only applies to entire functions. So i will have to "stuff" [math] \mathbb C[/math] into the unit disk.

An idea: Take an entire function f whose range is the whole of [math] \mathbb C[/math] . (such function exist by picard)
Define [math] f_n(z):= f(nz)[/math]. For large enough n, this gives the original function f, while still remaining in the unit disk

Am i on the right track or is there some flaw in my argument?

>>9520159
I don't understand why
[math]a\in \bigcap \{P(X) : X\in A\} \iff (\forall X \in A)\,\,a \in P(X) [/math]

Using the definition of the arbitrary intersection:
[math]a\in \bigcap A \iff (\forall s\in A)\,\, a\in s [/math]

Using that definition, the equivalence should be as it follows:
[math]a\in \bigcap \{P(X) : X\in A\} \iff (\forall s \in \{P(X): X\in A \}) \,\,a \in s [/math]

Help please

>>9517777
sick get
also kek

>>9522154
What are the s'es? They are exactly the sets P(X) such that X∈A. So all the s'es are all the P(X)'es from all X'es in A.

a∈∩{P(X) | X∈A} ⇔ (∀P(X)∈{P(X) | X∈A}) a∈ P(X) ⇔ (∀P(X)∈{(∀X∈A) P(X)}) a∈ P(X) ⇔ (∀X∈A) a∈ P(X)

>(∀y s.t. y∈{(∀x) x}) = (∀x)
>for all elements that are in the set S = for all elements in S

>>9521842
>Discrete maths

Math department or EE/CS? Does the math department offer an honors version?

>Numerical analysis
>Selected chapters of real and complex analysis (basically Fourier and z transform plus a bit more detailed complex analysis than we've already done in the previous semsster)
>What are the most useful courses if I'm an electrical engie going into the fields of automatic and control systems, signal processing, adaptive learning and similar areas?

Literally the 2 course right above. Also if you've done a real and complex analysis course, then you've done an "intro to proofs"/discrete math course already so definitely don't do Discrete Math.

>Statistics and probability

Don't all EEs already do a Probability and Stochastic Processes course(s)?

>Differential equations

What EE program doesn't require DE1/ODEs? Are you referring to a Partial Differential Equations course, a Dynamical Systems course, Numerical DE/FEM, or a theoretical ODEs course?

>>9520144
The columns of the matrix are where each dimension gets transformed to. Take a vector decompose it into it's dimensions (basis) and combine the columns of the matrix in proportion to the vectors dimensions, this is your result. Matrix * matrix multiplication now becomes obvious if you follow this logic.

>>9520714
Just speed watch Khan videos

>>9520808
It doesn't matter what you use. Just pre-install:
Python & NumPy, SciPy, Sympy, Matplotlib, Pandas, IPython/Jupyter, Spyder, + anything else frequently used
Clang++ & Boost, Eigen3, Armadillo, + anything else frequently used
VS Code / Atom
GFortran
IDL (if you have Astro faggots)
Matlab*
Maple*/Mathematica*
Labview*

*Assuming your school has licenses. Otherwise don't pirate them yourself. Let the kids pirate it themselves.

>>9522283
not the guy who asked but thanks these looks cool

>>9522227
>Take a vector decompose it into it's dimensions (basis) and combine the columns of the matrix in proportion to the vectors dimensions, this is your result.
That's assuming a basis exists.

>>9520937
Assume not, then there is a limit point not in the intersection so every neighborhood of it contains at least one point of the intersection. But the intersection is part of the closed sets being intersected. So both set must have the limit point as members from being closed. Thus it's in the intersection of both sets. Contradiction and QED.

>>9521994
I've heard good things about White.

Thanks for the input, anons. I go to a non-burger uni so that's why the courses may seem oddly arranged. In the last three semesters we've covered calc I, II and III, group and field theory, linear algebra, diif-eqs, complex analysis, Laplace transforms and just briefly brushed over Fourier transforms, graph theory, combinatorics and Boolean algebra (although we did Boolean algebra from like 3 other subjects already). These courses are either supposed to expand what we already know or supplement what we didn't cover but may be important for further studies but since i can only pick three I wanted to know what would be the most useful combination.
>>9521858
>>9521870
>>9522216
>Math department or EE/CS?
I'm EE
>Does the math department offer an honors version?
I don't think we have an honors class here if I correctly understood what it represents but we can pick courses outside of what we already selected in accordance with the student service and it won't count in our credits
>Also if you've done a real and complex analysis course, then you've done an "intro to proofs"/discrete math course already so definitely don't do Discrete Math.
I have done that and this course is more focused on the mathematics surrounding algorithm and computational complexity and optimization. All the replies say that it's skippable so definitely I'll have that in mind.
>Don't all EEs already do a Probability and Stochastic Processes course(s)?
Yea we have that next semester this statistics course was recommended as a more mathematically rigorous intro so we can learn Stochastics and Estimation processes more easily,
What EE program doesn't require DE1/ODEs? Are you referring to a Partial Differential Equations course, a Dynamical Systems course, Numerical DE/FEM, or a theoretical ODEs course?
Yea we already did the basics in diff-eqs, this course just expands on that with an accent on solving systems of diff-eqs,

In a linear expression with two variables, when replacing an ordered pair in it, it yields a positive number for points above the line and a negative numbers for points below the line. why?

>tfw bored with nothing to work on.
How do you stay motivated when you're out of ideas /sci/?

Oy niggers what’s an good IQ test to partake?

Does the difference between things determine their shape? Where can I find a girl who understands me? Is everything waves? How do radios receive information?

so I know the FDC theorem states that I can find one of the anti derivatives of the function or a specific one if Im given a bounded interval.

Its easy to find the antiderv if Im given the function, but my text book only states it as f(x)

So I have this: integral f(x)dx = 10 between 0 to 4. It then asks me to evaluate the integral of f(2x)dx between 0 to 2. (the answer is 5). (pic related)

Now I would have gotten the result long ago if I was given the goddamn function and not just f(x). I imagine its related to the first theorem. (which Ive done many exercises but I was given a function and I just had to plug in x or do some variable substitution.

Basically, is it possible to find the anti derivative, without the function, if only given the area and/or the bounded interval?

Btw is my description of the FTC-Theorem right or am I wrong? Thanks.

If I don't remember falling asleep or not and it fell like I fell asleep, does that mean I fell asleep for once?

I'm reading up on the RK4 variation of Runge-Kutta. Can anyone tell me why the four separate slopes for each step are weighted as 1:2:2:1? What's the idea behind that?

Please help. I’m trying to do pic related with the Direct Comparison Test to determine the divergence or convergence of each series. But I don’t understand how to.

>>9523555
Bump please

[math]a(b-c)=ab-ac[/math]
How do I prove something like this, using field axioms?

>>9523759
(b - c) is shorthand for (b + -c). And x(y + z) = xy + yz for all x, y, z is an axiom; substituting x = a, y = b, z = -c yields what you want.

>>9523774
Thanks! It clicked finally

Can someone recommend a good and easy to follow self-teaching calculus book without retarded confusing mathematical definitions not even the ones who made them up can't understand?

I feel I'm not learning dogshit in my uni class, I can solve functions but I have no clue why it works, I just learned how to solve. I want to understand in depth but my math teacher doesn't appreciate that.

I don't want to solve something through sheer memorization of the process without knowing what the fuck I'm doing in the first place.

In class we literally went from y(x)=x^4 ==>y'(x)=4x^3 to fucking alien chinese moonrunes in pic related. I'm so frustrated.

>>9523555
[eqn]0\leq\sum\limits_{n\geq 1}\exp(-n^2)\leq\sum\limits_{n\geq 1}(\exp(-\log(n^2))=\sum\limits_{n\geq 1}n^{-2}\,,[/eqn]which converges.
Therefore [math]\sum\limits_{n\geq 1}\exp(-n^2)[/math] converges and so does [math]\sum\limits_{n\geq 0}\exp(-n^2)[/math]

My mouse broke, and now I wanna inspect its circuitry. What's the safest way to crack this thing open?

>>9524226
hammer time

>>9524226
The fuck you mean "safe", it ain't gonna explode.
Just don't force anything, get something to pry and it should start popping open. Chink shit isn't exactly quality.

need help deciding between thesis, development, and course tracks for grad school.
http://www.strawpoll.me/15095091

the upside of the course option would be that i'm risk averse and it's low risk of failing a thesis defense. development seems interesting but also has the same problem of risk as the thesis track. the upside of thesis is that i would be better able to continue to a phd. but idk if i even want to get a phd. so decide for me

>>9523339
It's literally just change of variables nigger
let y=2x; then dy = 2dx

[eqn]\int_{x=0}^{x=2} f(2x) dx = \int_{y=0}^{y=4} f(y) dy/2
= \frac{1}{2} \int_{y=0}^{y=4} f(y) dy = \frac{10}{2} = 5 [/eqn]

>>9524053
>fucking alien chinese moonrunes in pic related
Derivatives are linear
D(f(x)+g(x)) = D(f(x)) + D(g(x))
D(af(x))=aD(f(x))
y' = D(y)
y'' = D(D(y))
y^(n) = D(... n times altogether... D(y)...)))))

>Can someone recommend a good and easy to follow self-teaching calculus book

>short
https://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/dp/0312185480/
https://www.amazon.com/Manga-Guide-Calculus-Hiroyuki-Kojima/dp/1593271948/

>long
https://www.amazon.com/Calculus-Lifesaver-Tools-Princeton-Guides/dp/0691130884/
https://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536/

>>9524548
>nigger
Why the racism?

How do i multiply a matrix and a vector again?
t. brainlet and it's been 3 years since i took linear algebra

>>9516893
Let us know how you do.

I don't understand what the fuck they want me to "show"? They've already fucking shown it.

>>9524935
You're supposed to make it really obvious. Like show the individual steps.
It should be so obvious that an 8th grader can see that the equations are true, basically. Because that's what you are.

>>9524958
It's a stock take test for Engineering. I just wasn't expecting something so fucking retarded. I don't remember the last time I had to "show that."

>>9524958
So I don't need to calculate n I just need to basically "simplify" it?

>>9524972
n doesn't need to be calculated. The propositions hold for any n

>>9524935
[math] \dfrac{2^{n+1} 4^{n}}{8^{n-1}} = 2^{n+1} 4^{n} 8^{-n+1} = 2^{n+1} 2^{2n} 2^{-3n+3} = 2^{n+1 + 2n - 3n + 3} = 2^4 = 4^2 = 16 [/math]

>>9524979
Oh, no shit, that makes so much more sense.

>>9524935
>I don't understand what the fuck they want me to "show"?
Use induction.

>>9519607
What class is this?

On a side note, was thinking of taking the 'set theory' - 'foundations of math' sequence of electives at my school. how hard are they?

So I want to change to either psy or soc.
I had 2 semester of psychology, without beeing inlisted in psy.
Are there any sociology guys here?
I am interested in how to build societies, thus I would have an interest in the difference in societies (from a historical point of view aswell).

I think this is a big chunk of sociology. Can someone confirm / give their expierience with soc.?
I just fear the SJW stuff, althought from what I can tell there is no reason to.
What would the career paths be in this case?

>Please help

>>9519621
>F(F(f(t))) = f(-t)

Close enough.

>>9519607
A first order logic axiom is you're allowed to add or remove "for all" to statements that don't depend on it.

[math](x \in A) ~or~ ((\forall b\in B) x\in b) \\
((\forall b\in B) ~ x \in A) ~or~ ((\forall b\in B) ~ x\in b) \\
(\forall b\in B) ~ x \in A ~or~ x\in b \\
(\forall b\in B) ~ x \in A \cup b
[/math]

>>9525063
It's basically addition and subtraction for people who want to feel smart.

>>9525075
>goes on /sci/ board
>doesn't want to do sci
why are you even here?
You'll probably have more luck asking >>>/lgbt/

>>9525086
I know, right? absolutely crazy.
But really, I think it would be a good field for me.
Also I study in german. we do actuall math in curses, even if they arent math/phi

>>9525094

>>9525097
...I used to be in computer science...

>>9519452
For the notation, it depends on what variable you differentiate with respect to. d^2y/dx^2 just means taking the derivative of y twice, both times with respect to x. Later on, you do partial derivatives, where you might differentiate with respect to x the first time and then y the second time, such as: d^w/dydx.

>>9519486
There is a chain rule for both x and for y. However, the derivative of x is simply 1, so they omit it. The derivative of y, on the other hand, is still a function, so they include it.

>>9525101
Well I suggest you skip over sociology and go to psychology. Just keep moving down until you realize the only worthwhile field is Engineering. If you believe in God you've gone too far.

>>9525103
[math]\frac{d^{2}w}{dydx}[/math]

>>9525117
fuuuuck man i didn't know you could use [math]\LaTeX[/math] on this
>newfagging

is functional analysis an actively researched field?

been teaching myself math/physics and came across it. im not that interested in proofs or calc analysis but i found some analysis of physics equations like the schroedinger wave equations. very interested in it

>pic unrelated. some random image off googz

do Americans seriously not learn calculus until university?
you have stacy and chad doing this shit in year 11 in normal countries

>>9525149
>is functional analysis an actively researched field?
https://arxiv.org/list/math.FA/recent

I don't fucking understand this shit.

Isn't it supposed to be a/b/c = a*c/b?

>>9525211
The full question is: (ax^(-2) + a^(-2)x) / (a^(-1) + x^(-1))

>>9525211
2/3/4 = 2/12 there's really not a lot of room for interpretation here even in common core destroyed minds

These nested fractions are doing my fucking head in.

>>9525219
But then why does (ax^(-2)) + a^(-2)x) / (x + a) / ax become ax(ax^(-2)) + a^(-2)x) / (x + a)

>>9516225
can somebody please tell me wtf a Gaussian surface is?

>>9525211
(a/b)/c != a/(b/c)

>>9525226
Okay I get that but I can't tell where the fuck the brackets are supposed to be anymore. There's probably some way to infer it but my mind is fucking friend right now.

>>9525229
fried...

>>9525075
sociology is 100% interesectional postmodern garbage.

>>9525112
>If you believe in God you've gone too far

>>>/reddit/

i'm in physics 2 and finding it way easier than physics 1. i hated physics 1 so much.

i even made an A on the first exam and the average was barely passing

is this normal? i always heard people say physics 2 was the worst class of their life

>>9525252
>>>/x/

>>9525251
so....is there anyone with a degree in soc. or that's currently studying it?
I start to get the feeling that most people on sci have never seen an university.

>>9525225
A "closed" metal surface. So like the surface of a hollow sphere of steel.

>>9525258

I don't know either anon, I did horrible in General Chemistry 1 (Got a B) and I am dominating General Chemistry 2 while everyone else is failing hard.

>>9525075
I can tell you about psy. Your career prospects are most likely fighting for below minimum wage pseudo-scientific research positions or carting loonies between hospitals. Only the very best get to go on to counselling and PhDs and shit. Sociology I have no idea but I think it might be the better option.

In what order should I be studying mathematics?
Which should I study first, analysis or number theory?

>>9525364
>Which should I study first, analysis or number theory?
Whichever you're more interested in.

>>9525394
If I'm interested in applying what I learn in electrodynamics semiconductor physics, which branch should I study?

>>9525364

>>9525415
can I skip calculus for analysis?

>>9525474
No.

Why does altering frequency at a constant amplitude increase the perception of loudness?

how do i tell by inspection whether a function, say like [math]f\colon C\to C\,;\ f(z)=|z|[/math], is complex differentiable?
for real functions, most of the time, you can visualise the graph to see if there are any discontinuities or 'sharp' points (for example, with [math]f\colon R\to R\,;\ f(x)=|x|[/math] it's almost obvious that it is not differentiable at 0) but i can't think of a good analogue for complex functions

>>9525496
Human ears suck

>>9525502
>for real functions, most of the time, you can visualise the graph to see if there are any discontinuities or 'sharp' points

Nope.

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

>>9525502
f(z0+h)-f(z0)/h = |h|/h = e^-i*argument(h)

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

>>9525482
but isn't analysis just calculus with set theory

>>9523462
Pls respond

>>9525507
>Nope.
>or 'sharp' points

>>9524548
Thanks mate, cheers cunt

>>9525520
Then how the fuck are you going to do in analysis if you dont or barely understand calculus

>>9525547
perhaps if you're autistic enough

>>9525554
I have yet to see this.

Is this a good book about Automata and Grammars? It's recommended reading for my course.

J.E. Hopcroft, R. Motwani, J.D. Ullman: Introduction to Automata Theory,
Languages, and Computations, Addison–Wesley

>>9525647
>The first edition of Introduction to Automata Theory, Languages, and Computation was published in 1979, the second edition in November 2000, and the third edition appeared in February 2006. Since the second edition, Rajeev Motwani has joined Hopcroft and Ullman as third author. Starting with the second edition, the book features extended coverage of examples where automata theory is applied, whereas large parts of more advanced theory were taken out.
>https://en.wikipedia.org/wiki/Introduction_to_Automata_Theory,_Languages,_and_Computation

It's for brainlets.

Can someone enlighten me as to the transformation used to get from the second to the third formula? The goal is end up with a well-formed formula containing just ~ and ->.

>>9525713
it's just an expansion, and re-factorization of the 2nd line.

>>9525770
Makes sense, thanks.

What are good youtube videos/channels about maths?

>>9525812
1brown3blue

>>9525824
Others? I've already got that one.

>>9525812
Numberphile was fun, with professor Chad Grimms, they touch many branches of maths in an intuitive way

alright lads not /sci/ here, my doctors are trying to force me to try some first generation anti psychotics but iwas thinking this time it would be useful to track some data then i can evaluate what anti psychotic has the least negatives, here's what I plan on tracking

>cognition
>reasoning
>memory
>verbal fluency
>blood glucose levels
>blood pressure
>heart rate
>blood oxygen levels
>breathing
>side effects
>quality of life

anything else I could/should monitor?

I need to program an FSM in C, and I want my loop to end after I pass through each state and loop back to my initial state. How do I implement this?

Can someone help me with this analysis question. Question 5. Thanks

>>9516893
I'm in the same boat,

But it's differential equations.

I'll be alright, good luck anon

how can I show x/3(e^(3x)) converges to zero as x approaches infinity? If you're too lazy to do it out for me, point me in the right direction please.

>>9525994
exponentials win against polynomials

>>9525994
the quickest way would be using l'hopital's rule

Math newbie here.
Natural numbers are iterations of the successor function on the empty set; integers, equivalent classes on the naturals; rationals equivalent classes on the integers; reals, Dedekind Cuts on the rationals; and complex, ordered pairs of reals. So what do we actually mean when we say that [math] \mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset \mathbb{C} [/math] ?

>>9525987
write down like 10 numbers that are contained in the sets, and see if you discover a pattern. For example for (b), calculate the numbers for n=1 through n=10.
then it should become somewhat obvious what the supremum is.
it doesn't say you have to prove it, so a short explanation should suffice.

>>9526020
>>9526065
I think there was something about l'Hopital's Rule deep down in my notes, I'll track it down. In the mean time would pic related be appropriate or is the concept of multiplying zero by infinity not clearly defined? It doesn't feel right.

Would a gamma ray burst destroy the sun?
Would the sun shield us from a supernova?

>>9526166
Infinity times zero is not defined, but you can get around with a trick.

>>9526204
Thanks a million anon

>>9525994
L'Hopital's rule:
-x/(3e^(3x))=-1/(9e^(3x))
The result will be -1/inf which is zero. But to be honest, you can obviously see it's going to converge just by looking at the thing.

>>9526132
oh yeh for b I got 1/2, but i can't do a

>>9526328
the largest number in A is 0.8 repeating. why isn't the supremum 0.89?

Someone please explain why 0.999... = 1 like I'm a retard

>>9526380
a) It's just a consequence of how we define the "sum" of an "infinite series."
b) it's just another symptom that as we make more kinds of numbers (naturals->integers->rationals) we may not have a unique representation, so [math]\frac{4}{8} = \frac{2}{4} = \frac{1}{2}[/math]
c) it is a consequence of polynomial division
d) they aren't "equal" it's that we identify the real number 0.999... with the natural number 1 due to how real numbers are defined

>>9526367
oh right yeh, id forgotten the supremum can be in the set. Thanks man, my bad

>>9526431
*the supremum doesn't have to be in the set

>>9526367
Because if a set has a largest element, then it must also be its supremum (it's obvious from the definition, but check it if you don't see it). You have identified an element greater than all others, hence it is also the supremum, which tells you.
To see specifically why the supremum is not 0.89, you can see that the interval of radius 0.001 around 0.89 contains only numbers the decimal expansion of which contains an odd number (the decimal expansion of the numbers on the left is of the form 0.889.... and it is of the form 0.89.... for those on the right)

>>9526470
which tells you that 0.89 is not*

Is Architecture considered part of STEM, even if only tangentially? Asking purely out of curiosity.

>>9526476
>Is Architecture considered part of STEM, even if only tangentially?
No, since architects do not use the scientific method.

>>9526480
Fair enough. So could it be considered related to just engineering, but not considered related to STEM as a group?

>>9526480
Neither do engineers.

>>9526072
After having constructed C, you have a natural way to construct copies of N, Z, Q, R inside C: N is the additive submonoid of C generated by 1, Z is the subgroup generated by 1, Q is its fraction field and R is its closure of Q wrt the topology of C.
These are different from the ones you constructed C with, but we can choose to work with them

>>9526380
writing 0.9999999.... in rational form is 1

>>9526473
Am I right in saying 8/9 is the supremum?

How am I supposed to solve second one?

>>9526545
yes

>>9526550
[math](\tan 2x)^{\tan 3x} = \exp\left((\tan 3x)\ln(\tan 2x)\right)[/math]. Moreover, [math](\tan 3x)\ln(\tan 2x) = \left(\frac{\tan 3x}{3x}\right) 3x\ln x + \left(\frac{\tan 3x}{3x}\right) 3x \ln\left(\frac{\tan 2x}{x}\right)[/math]. Since each term goes to 0 with x, we conclude that the initial limit is 1

>>9526380
[math] 0.9 = \frac{9}{10} [/math]
[math] 0.99 = \frac{99}{100} [/math]
[math] 0.999 = \frac{9}{1000} [/math]
....
The distance to 1 is
[math] 1 - 0.9 = \frac{1}{10} [/math]
[math] 1- 0.99 = \frac{1}{100} [/math]
[math] 1 - 0.999 = \frac{1}{1000} [/math]
....
As you can see, the distance towards 1 keeps getting smaller and smaller.
In fact, the distance is [math] \frac{1}{10}^n [/math]
Now let n go towards infinity, and you have
[math] \frac{1}{\infty} = 0 [/math] as a distance
and [math] 1 - 0 = 0 [/math]

>>9526380
1/3 = 0.333...
2/3 = 0.666...
3/3 = 0.999...

of course this just shifts the problem to why 1/3 = 0.333... but for some reason many have no problem accepting that and therefore accept this explanation

>>9523462
>>9525534
part of the derivation for RK4 writes:
[math] y_{t+h} = y_t + a\cdot hf_t + b\cdot \frac{h^2}{2}\frac{df_t}{dt} + c\cdot hf_t + c\cdot \frac{h^2}{2}\frac{df_t}{dt} + c\cdot \frac{h^3}{4}\frac{d^2f_t}{dt^2} + d\cdot hf_t + d\cdot \frac{h^2}{2}\frac{df_t}{dt} + d \cdot \frac{h^3}{2}\frac{d^2f_t}{dt^2} + d\cdot \frac{h^4}{4}\frac{d^3f_t}{dt^3} + O(h^5). [/math]

We match this with the taylor series:

[math] y_{t+h} = h_t + hf(y_t, t) + \frac{h_2}{2}\frac{d}{dt}f(y_t, t) + \frac{h^3}{6}\frac{d^2}{dt^2}f(y_t, t) + \frac{h^4}{24}\frac{d^3}{dt^3}f(y_t, t) [/math]

which gives us:

[math]
\begin{align*}
a + b + c + d &= 1\\
\frac{1}{2}b + \frac{1}{2} c + d &= \frac{1}{2}\\
\frac{1}{4}c + \frac{1}{2}d &= \frac{1}{6}\\
\frac{1}{4} d &= \frac{1}{24}
\end{align*}
[/math]

which gives the coefficients as
[math]
a = \frac{1}{6}, b = \frac{1}{3}, c = \frac{1}{3}, d = \frac{1}{6} [/math]

how do i solve this?

>>9526589
>and 1−0=0

How do I make myself more employable/stand out from the rest?

Right now I am a sophomore at a community college (45 credits). My program is three years long which also includes an internship the final semester. I do work part-time in an unrelated job to my field, but I am thinking long-term for my career.

When I look at the type of people who get employed at the companies I'd like to work for, they have extensive research experience, masters, and Ph.Ds. The people my age usually have life stories like "I got sick once when I was younger and that is why I am passionate about this industry and have been involved in it since I was a kid"; these people will inevitably become the scientists that are in charge I bet.

My parents aren't intelligent, let alone have any bit of curiosity. So, I was never introduced to anything scientific as an adolescent to even gain an interest until I started college. I'm behind af and the people in my classes are people with great experience already because they've been involved for a long time.

>>9516225
Ok I have a dumb question I know nothing of science, is the temperature cooler inside a closed esky/ice chest etc cooler then room temperature , there is no ice in the esky

>>9526702
Find a way to learn Python, R, and algorithms.

>>9526702
Certs

How am I supposed to find the equivalent capacitance of this?
I tried making c3 and c4 in series, and then c2 and c34 in parallel, and then c1 c234 and c5 be in series, but I got it wrong
I seriously can't figure out how its supposed to be, help please?

>>9526804
>but I got it wrong
well that's the right method

>>9517428
Nigga just look at a graph lmao you can see it right there hahahaha

why does my calculator say that cos(PI/2)=.9996... when it actually equals 0

>>9526852
Degrees vs radians, probably

>>9526804
That's the right method my man just check on your algebra.

Get up, get a cup of coffee, and come back to it. You'll probably see what's wrong.

>>9525713
ANDs(*) and ORs(+) distribute into each other
(a+b)(c+d)=ac+ad+bc+bc
(ab)+(cd) = (a+c)(a+d)(b+c)(b+d)

second follows from the first by applying deMorgan twice

>Protip: ~C & (A xor B)

>>9525982
>FSM in C,
Why not C++?

enum state{ init, /* ..., other states, ... */ final};
enum input{ signalA /*, signalB, signalX, ....*/ }; //or using input = std::string;
const std::map<std::pair<state, input>, state> transitions = { {{init, signalA}, final} /*... the transition diagram ... */ };
const std::vector<input> inputs = {signalA};
state current = init;
for(const auto& in : inputs){
current = transitions[{current, in}];
}

>and I want my loop to end after I pass through each state and loop back to my initial state. How do I implement this

enum {init, /*...*/ final};
int state = init;
int i = 0;
do{
state = get_next_state(state, input[i++]);
}while(state != init);

But it sounds like you just want a simple ring FSM with no input so

int state = 0;
const int num_states = 42; //or w/e
while(1){
state++;
if(state == (num_states+1)){
state = 0;
break;
}
}

>>9525987
a) 8/9
b) 1/2

>>9526072
>rationals equivalent classes on the integers
No, it's an equivalence class on pair of 2 integers. Z/nZ are equivalence classes on the integers.
>reals, Dedekind Cuts on the rationals
No, it's an equivalence class on pair of an integer and an infinite sequence of digits in {0, ... r}. Or equivalence class on Cauchy sequences.

>So what do we actually mean when we say that
Short answer: They're isomorphic to subsets so we define new N, Z, Q, R that are subsets of the construction of C and play with them since mathematics almost never depends on the underlying construction.
Long/autistic answer: http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf

>>9526804
=(C3||C4 + C2)||C1||C5
[math]
= \dfrac{ C_1 C_5 \left ( \frac{C_3C_4}{C_3+C_4}+C_2 \right ) } { C_1 \left(\frac{C_3C_4}{C_3+C_4}+C_2\right) + C_5\left( \frac{C_3C_4}{C_3+C_4}+C_2\right)+C_1C_5 }
[/math]

>>9526672
ma = kq^2 / x^2
x^2 x'' = kq^2 / m
let kq^2 / m = c
let v=x'
x^2 v dv/dx =c
v dv = c/x^2 dx

v^2 / 2 = - c/x + c/d
dx/dt = sqrt(-2c/x + 2c/d)

[math] t = \dfrac{\sqrt{ \frac{2c x^2}{d} -2cx }}{2c/d} + \dfrac{2c \log \left (2\sqrt{2c/d} \sqrt{ \frac{2c x^2}{d} -2cx } + 4cx/d - 2c \right ) }{2(2c/d)^{3/2} } |_{x=d}^{x=2d} [/math]

plug and chug.

(b) ma = kq^2 / x^2 - Gm^2 / x^2
x^2 x'' = kq^2 / m - Gm

repeat but with c = kq^2 / m - Gm

>>9527022
Idk, I did use the computer
Here's the function
(defun ceq-series (&rest cs) (/ (apply '* cs) (apply '+ cs)))

>>9526496
Neither do scientists

>>9527244
thanks senpai, ill check my answer against this

>>9516225
Is the brainlet meme meant to be ironically stupid? I would think factors such as neuron density, neuron connections, brain structure, and brain to body mass ratio have much more to do with intelligence than brain size.

can parallel plate capacitors be circular?
__d
O----O
like instead of it being a rectangle, they're both just a disc

Do I go to a brainlet university?