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/sci/ - Science & Math


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9189751 No.9189751 [Reply] [Original]

This thread is for questions that don't deserve their own thread.

Tips!
>give context
>describe your thought process if you're stuck
>try wolframalpha.com and stackexchange.com
>How To Ask Questions The Smart Way: http://www.catb.org/~esr/faqs/smart-questions.html

Previous thread: >>9180375

>> No.9189752 [DELETED] 

I need some assistance with residues: Assuming a>0, how do you compute
[math]\int\limits_{0}^{\pi}\frac{\cos(\theta)}{a+\cos(\theta)}d\theta[/math]? I keep on getting caught in a mess of work.

>> No.9189755

Imagine I had a brick of mass 1kg that was drifting in space. If 1 Newton of force was applied on the brick for 1 second, would that increase the velocity of the brick by one 1m/s?

>> No.9189758
File: 62 KB, 1117x483, Untitled.png [View same] [iqdb] [saucenao] [google]
9189758

pic related. I need to find the voltage inside the box using excel (numerical method of laplace equation). i was thinking of doing the thing on the right except i'd replace 300, 100, and 20 with 0V and i's use 100V instead of 140. Also, it would be 12 cells across and 10 cells down. is my train of though correct?

>> No.9189772

>>9189755
yes

>> No.9189909

How do I calculate residues?
I have a function
[math]f(z)=\frac{\pi\cot (\pi z)}{z(z+1)}[/math]
With poles at [math]z=0,\quad z=1[/math]
How do I find the residues in these points?

>> No.9189910

>>9189909
Small error, z is -1, not 1 obviously.

>> No.9189936
File: 8 KB, 192x256, 1506185005266.jpg [View same] [iqdb] [saucenao] [google]
9189936

Hello /sci/,
brainlet here.
I am having an embarassing problem... why the hell is the derivative of y=62x-2x^2=50 if x is equal to 3 but 62*3-2*3^2-(62*2-2*2^2)=52?
I have literally no idea. Can someone give me an illuminating explanation? thank you.

>> No.9189945

>>9189909
>How do I calculate residues?
https://en.wikipedia.org/wiki/Residue_(complex_analysis)#Calculating_residues

>> No.9189947

>>9189936
>y=62x-2x^2=50
Is y=62x-2x^2 or y=50?

>> No.9189949

>>9189947
it's 50 if x=3 is what I meant. Sorry for being unclear.

>> No.9189952

>>9189949
Well then what does 62*3-2*3^2-(62*2-2*2^2) have to do with anything? It's just f(3)-f(2)?

>> No.9190001

>>9189952
For some reason I thought it should be like the derivative.

>> No.9190006

>>9190001
>For some reason I thought it should be like the derivative.
It's not.

>> No.9190025

Hypothetically, what is the legality of writing a research paper about CP, and including links to actual CP in the paper? Strictly hypothetically of course.

>> No.9190028

>>9190006
thanks

>> No.9190340

>>9189909
cot(πz) has a pole of order 1 at 0, since it is cos/sin and 1/sin can easily be seen to have pole of order 1 at 0 (see its series expansion).
The denominator makes the order of the whole thing 2.
Therefore the residue at 0 is the limit of the derivative of z^2 f(z) as z goes to 0.

Now for the pole at -1. It's obvious that the pole of order 1, therefore the residue is the limit of (z+1) f(z) as z goes to -1.

>> No.9190388

>>9190340
actually my bad, the pole at -1 is of order 2, so you have to do the same as for 0

>> No.9190422

What are the implications of a vector space not necessarily being naturally isomorphic to its double dual in the infinite dimensional case?

>> No.9190430

Given that x,a,b are between -1 and 1, how do I find the maximum of |(x-a)(x-b)| ?
I have absolutely no clue.

>> No.9190437

>>9190430
x=1,a=b=-1
>how do I
split the terms and maximise both (semi)independently

>> No.9190438

>>9190430
|(x-a)(x-b)| =
|(x-a)||(x-b)|<=
2*2=
4

>> No.9190513

Is their an approach for finding a bijection between [math]\mathbb{N}[/math] and some set [math]A[/math]? For instance, for [math]a,b \in \mathbb{R}[/math], [math]a<b[/math], find a bijection from [math](0,1)[/math] to [math](a,b)[/math]. So just looking at this, I know that I don't need 0 or 1, so I'm thinking a decreasing function with vertical asymptotes at 0 and 1. Maybe [math]\frac{1}{x^2-x}[/math], but this isn't bijective on the interval, so moving it over to the left a bit I can get [math]\frac{1}{(x+1)^{2}+\frac{1}{4}}[/math]. Is this a correct answer and line of reasoning?

>> No.9190530

>>9190513
>Is their an approach for finding a bijection between N and some set A?
depends on the A

> For instance, for a,b∈R, a<b, find a bijection from (0,1) to (a,b).
f(x)=bx+a(1-x)

>> No.9190534

>>9190513
if you don't deal with unbounded sets you can just use a linear approach
lets say f(x) = mx+n and you want f(0) = a and f(1) = b, you'll get a set of 2 equations.
0*m+n = a
1*m+n = b
which you can solve and get n=a, m = b-a, so
f(x) = (b-a)x + a
has the properties you want.
you only have to involve more complex functions, when you want to find a bijection from a subset of the reals that includes infinity

>> No.9190555

>>9190530
>>9190534
Ah, I see. Thank you.

>> No.9190559

>>9190530
I prefer looking at that formula this way:
α + (b-α)x
you start at α and add a scaled version of x by he length of (a,b) so that it can manage to reach b in time.

>> No.9190790

I'm trying to remember some proof from a while ago

Consider a hilbert space [math] \mathcal{H} [/math] and a linear operator [math]A [/math] on [math] \mathcal{H} [/math]. Lets say for some [math] b\in \mathcal{H} [/math] there exists an [math] x\in \mathcal{H} [/math] such that [math] \left \| Ax-b \right \|_\mathcal{H} [/math] is minimised.

I want to prove that [math] (Ax-b)~ \bot ~im(A)[/math] or [math] \left \langle Ax-b,Ay \right \rangle = 0~~ \forall y\in\mathcal{H}[/math]

I want to prove least squares on general hilbert spaces, so I cant use that [math] A^* (Ax-b) = 0 [/math]

>> No.9190802

>>9189751
Best Calculus textbook? I'm looking at Thomas Early Transcendentals.

>> No.9190929
File: 135 KB, 1166x847, Καταγραφή.jpg [View same] [iqdb] [saucenao] [google]
9190929

>>9190790
Haven't studied functional analysis. but if the theorem in pic works for infinite dimensional Hillbert spaces, then it proves what you want, since the minimum would be achieved by the projection of [math] b [/math] to the subspace [math] Im(A) [/math] and [math] Ax-b [/math] .

>> No.9190933

>and [math] Ax-b [/math]
ignore that

>> No.9190992

>>9190790
|| A(x + t y) -b||^2 is quadratic in t and must vanish at t=0 for all y because it has a minimum there. This gives <A x-b, A y> =0.

>> No.9190996

>>9190992
I mean the derivative must vanish.

>> No.9191025

>>9190929
that should do the trick, thanks.
>>9190992
>>9190996
I remember doing something like that in numerics, but isn't
[eqn]\left [\frac{\mathrm{d} }{\mathrm{d} t}|| A(x + t y) -b||^2 \right ]_{t=0}=2\cdot\mathfrak{Re}(\left \langle Ay,Ax-b \right \rangle) [/eqn]
which doesn't exactly give the result in complex hilbert spaces

>> No.9191054

>>9191025
>that should do the trick, thanks.
Are you sure though? Cause I googled and found this:
https://math.stackexchange.com/questions/275391/orthogonal-projection-on-the-hilbert-space
and an operator's image isn't always closed

>> No.9191061

>>9189751
ARE YOU SMART ENOUGH TO FIGURE OUT THE GREATEST PUZZLE OF ALL TIME?
>>9191052

>> No.9191087

>>9191054
oh you're right, the orthogonal projection doesn't exist if the subspace isn't closed.
I guess my question only really makes sense for operators with closed image, because you couldn't otherwise guarantee a minimum

>> No.9191112 [DELETED] 
File: 349 KB, 639x480, bearlain.png [View same] [iqdb] [saucenao] [google]
9191112

I've got a BS in biology and 4 years experience as a technician in academia. Can I get a decent paying job in industry without any further education/certifcation bullshit? I really don't want to get a PhD, and I want to get a Master's even less since I feel like a lot of Master's degree programs are horseshit money grabs.

>> No.9191169

>>9191112
> 4 years experience as a technician in academia

Whytho

>> No.9191183 [DELETED] 
File: 2 KB, 189x66, hm.png [View same] [iqdb] [saucenao] [google]
9191183

>determine the maximum domain of convergence for the Laurent series, justify your answer etc etc

I am 99% sure I am not supposed to use any convergence tests, like the root test and all those things from calculus. What do then?

>> No.9191207
File: 1 KB, 183x63, fixd.png [View same] [iqdb] [saucenao] [google]
9191207

shit, fixed.

maximum domain of convergence for this laurent series, without using any convergence tests from calculus?

>> No.9191211

>>9191169
thought i was gonna go to grad school, got to last year of undergrad and decided fuck school. lab i was in offered me a job, so i took it. then another lab was moving and offered me another job for more money so i took that.

>> No.9191228
File: 2.17 MB, 1920x816, Important_Scientific_Question.png [View same] [iqdb] [saucenao] [google]
9191228

IMPORTANT SCIENTIFIC QUESTION:

How far out were they? Assume the following:

-The galaxy depicted is their home galaxy - the one far, far away.

-This spiral galaxy is equal in size to our own spiral galaxy, the Milky Way.

-The humanoids depicted in the films are 1-1 scale with real human beings (specifically, the actors who portray them), and aren't self-contained in sci-fi-fantasy logic where everything is really twice as big or five times as small as its earth-counterparts. So both Luke and Leia are approximately 170cm tall, give-and-take their true heights (that is, the actors' heights).

-Thus, that window is about the size of a big picture window in a nice living room on Earth, say roughly 3M x 5M.

>> No.9191287

>correlation isn't causation

How else do we prove causation other than doing a bunch of experiments and saying "well the two events correlated a whole bunch"?

>> No.9191292

>>9191287
natural science doesn't provide proofs

>> No.9191314

So I'm an idiot that never did much math in high school. I'm trying to learn some math now on my own time, and I have started to use Khan Academy but I've been quite confused.

There seems to be no way that I can see to do the World of Math mission without trudging through gradeschool math. I know I'm dumb, but I'm not exactly "can't count to 10" dumb.

How do I skip/complete that shit quickly?

Related to this, I'm trying to go through it with Mastery Challenge, and it'll give me like 90 gradeschool math problems then drop a quadratic equation in between "count the pictures of beetles" and "name this angle".

tl;dr how khan difficulty curve

>> No.9191325

>>9191025
Yes. Didn't think about complex spaces. If the inner product has no real part, it's pure imaginary, and you can replace y with i*y and get pure real, and so zero. Is that right?

>> No.9191352

Find all funcs G(t) such that u(x,y) = G(x^2+y^2) is harmonic, shid pls help :-DDDDDDD

>> No.9191403

>>9191352
Calculate the laplacian of u

>> No.9191507

What's the most recommended book on artificial intelligence, according to /sci/? I am reading artificial intelligence a modern approach, but I also want to try my skills with Deep learning by Ian Goodfellow.

What do you think /sci/? P.S. I would ask /g/, but they're retards.

>> No.9191549

are there any journals/textbooks for learning more about current thought about abiogenesis?

>> No.9191590

Basic statistics question:
I've got a sample exam, with 12 questions on it. 8 of these exact questions will be on the real exam. on the real exam, i have to answer 5 out of the 8. how many questions, of the 12 on the sample exam, can i choose to ignore?

>> No.9191591

Will AIs ever replace scientists?

>> No.9191619

>>9191590
is the real exam also 12 questions?

>> No.9191624

>>9191619
the real exam is 8 questions

>> No.9191630
File: 10 KB, 1063x538, sjhgdfhjsdfg.png [View same] [iqdb] [saucenao] [google]
9191630

QUICK

is this right

i'm too tired to think

>> No.9191639

>>9191630
nigga is you high

>> No.9191642

>>9191639
yyyyyyyyyyerteyru tert i'm gonna sleep thanks my dude

>> No.9191643

>>9191590

You can ignore 3. Then if you get the three you ignored, you can answer the other 5.
If you ignore more than 3, you might get all the questions you ignored on the exam.

If you want only a high probability of only getting questions you studied for you might be able to ignore more.

>> No.9191645

>>9191228
I'd say they were pretty far out, bro

>> No.9191648

>>9191643

For example if you only study 8 and neglect 4 then you have a 86% chance of being able to choose 5 questions you know.

>> No.9191650

what are all the domains where f(z) = |x^2-y^2| +2i|xy| is analytic? z = x+iy, ofc

>> No.9191672
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9191672

>>9189751
Is the hairline pictured there normal for a 27 year old?

>> No.9191794

>>9191650
u(x,y) = |x^2-y^2| , v(x,y) = 2|xy|
check cauchy riemann conditions

>> No.9191797

>>9191325
that works, yes

>> No.9191818

>>9191207
let's check for absolute convergence.
The series from -infinity to 0 behaves differently then the series from 0 to infinity, so we split them up.

case n>0: We have
[math] \left | \frac{z^n}{3^n+1} \right |<\left | \frac{z}{3} \right |^n [/math],
which means, this part is bounded by a geometric series for |z| < 3.

case n<0: In this case we see that the denominator tends towards 1, so for convergence we need |z|>1

so now we have the condition 1<|z|<3 for absolute convergence

>> No.9191940

Not really a stupid question, but don't feel like it deserves its own thread.

Does anyone know of any online accredited college courses on artificial intelligence? Not a whole major, just a single introductory class.

>> No.9191948

If I have a limit where the denominator is not going to be 0, can I do this?
[math] \lim_{x\rightarrow 0} \frac{f(x)}{x+1} =\frac{\lim_{x\rightarrow 0}f(x)}{\lim_{x\rightarrow 0}x+1} = \lim_{x\rightarrow 0} f(x)[/math]

>> No.9191955

>>9191948
https://en.wikipedia.org/wiki/Limit_of_a_function#Properties

>> No.9191957

>>9191948
yup
if [math] \lim_n a_n = a [/math] and [math] \lim_n b_n = b [/math] exist, [math] \lim_n \frac{a_n}{b_n} [/math] also exists and is equal to [math] \frac{a}{b} [/math]

>> No.9192017

Am I correct in saying that, given [math]A=\{1,2,3 \}, B = \{2,4,6 \}[/math], the subset of [math]A\times B[/math] [math]: C = \{ (1,2),(2,4) \}[/math], is not a function, since f(3) isn't defined?

>> No.9192024

>>9189936
I'd also like to know. Really bad at derivatives

>> No.9192026

>>9192017
it is a function, but it's a not a function from A to B

>> No.9192028

>>9190025
Go work for a magazine if you want that

>> No.9192034

>>9192026
In the context though, is it not obvious that the function's domain/codomain is A and B, since a function is defined as a subset of the Cartesian product.

>> No.9192038

>>9192034
> is it not obvious that the function's domain/codomain is A and B, since a function is defined as a subset of the Cartesian product.
the issue is that a set can be a function for different codomains, i.e. {(1,2),(2,4)} is a function from {1,2} to {2,4}, it's also a function from {1,2} to {2,4,6}, and in general it's a function from {1,2} to any set containing {2,4}. the set making up the function makes no reference to where the elements 'came from'

>> No.9192055

How does one show that the integral [math] \int_{1}^{\infty} \frac{1+e^{-x}}{x} [/math] diverges?

>> No.9192059

In probability, how do 3+ mutually exclusive events work?
From the description I've read, if it's for every event A1, A2 ... An, every two events cannot happen at the same time.
So if you have A1 A2 and A3, does that mean they're mutually exclusive if A1^A2, A1^A3 and A2^A3 = O?

>> No.9192061
File: 7 KB, 427x385, necklace beads.png [View same] [iqdb] [saucenao] [google]
9192061

Hi /sci/, recently an interesting question come up while im studying combination and permutation. I can't get the right answer so I hope we can discuss about this.

There are 5 big beads, each of them is different and unlimited amount of 5 different types small beads.

How many ways can you arrange them into a necklace so that
-there are 5 any type of small beads between every big beads
-all big beads is used

So far, I've only find out that there must be more than 4! ways of arranging them since the 5 big beads is a circular permutation (5-1)!
Pic related, I will try to clarify some things if the question is not clear enough. I'm thinking of making a thread about this but this might be just a stupid question.

Thank you

>> No.9192063
File: 70 KB, 595x335, eeg-headset-595x335-c1.jpg [View same] [iqdb] [saucenao] [google]
9192063

Anyone familiar with any research groups focussed on finding higher-bandwidth methods of getting information to a brain?

>> No.9192066

>>9192061
I'm thinking the answer would be the number of way the big beads can be arranged in circular permutation multiplied by the number of ways the 5 different types of small beads to 25 places.
Any thought?

>> No.9192073

>>9190025
I think including a link to an actual CP content or forum or somekind is a form of sharing it so it may be against the law.

>> No.9192080

>>9192055
Man, you are so lazy. I immediately graphed your curve and noticed it looks like [math] \frac{1}{x} [/math] but bigger. So all you have to do now is prove that [math] \frac{1 + e^{-x}}{x} > \frac{1}{x} [/math] which is trivial because [math] 1 + e^{-x} > 1 [/math]. Then remember that integrals preserve inequalities so:[math] \int_{1}^{N} \frac{1 + e^{-x}}{x}dx > \int_{1}^{N} \frac{1}{x}dx [/math] and by comparison it diverges.

I hope you take this as a lesson. The difference between a good analyst and a bad analyst is that the good analyst has memorized hundreds of curves and knows immediately when to compare a curve with another. I recommend trying a similar problem now. Train your intuition. Rise above good man. Analysis is better than algebra or topology, everyone knows that.

>> No.9192084

>>9192059
yes

>> No.9192088

If [math]f^{-1}(f(x))=x[/math] does is follow that [math]f(f^{-1}(x))=x[/math]?

>> No.9192090

>>9192088
yes, by definition of an inverse function

>> No.9192092 [DELETED] 
File: 2.89 MB, 3600x4000, 1502854778426.jpg [View same] [iqdb] [saucenao] [google]
9192092

Hi, I'd like to go to university and wonder which STEM field(s) to choose.
I'm OK with math, not particularly good but obviously willing to make an effort and learn.
I'm somewhat proficient in Biology and also interested, but the other fields are also cool.

Which field has the best job opportunities and what can I expect from each field?

Thanks in advance.

>> No.9192094

>>9192092
>STEM meme
unless you really enjoy it with a passion forget it. Ching zing Tang is already studing 25 hours a day and will out class you in everything.

>> No.9192099

>>9192094
Are you being serious? What am I supposed to do else, history? I don't want to do an apprenticeship to be honest, I did very well in school and want to learn more.

>> No.9192103

>>9192080
thanks!

>> No.9192106

>>9192099
from personal experience you have the chinks, poos, and literal 500IQ autists who will make you work like a fucking horse to keep up to the top echelon.

>> No.9192107

>>9192106
>>9192099
>>9192094
>>9192092
You can go into STEM but aim for getting lab time. If you can get involved in some research projects and have some experience in you CV by the time you finish your undergrad you will be just as viable as the academically top students, if not more so (hell, I got two separate offers for post-grad placements in my third year of undergrad from groups that I did some work with).

>> No.9192154
File: 102 KB, 421x307, 1498013264299.png [View same] [iqdb] [saucenao] [google]
9192154

>>9192080
>Analysis is better than algebra or topology

>> No.9192177 [DELETED] 

http://www.scienceforums.net/topic/59514-calculating-the-luminance-of-the-sun/
>Sun subtends about 0.5 degree on earth surface solid angle Omega becomes = 2pi (1- cos (0.5/2)) = 5,98e-5 steradians
>At bright day light and at 90 degree normal incident, illuminance of sun at earth's surface is around 10.000 lux = lm/m2
>Luminance = illuminance / Omega = 10.000/5,89e-5 =1.67e9 cd/m2
how does this calculation make any sense??

how do you explain the wild discrepancy vs e.g.
>The average luminance B of the sun, observed outside the atmosphere, is a fixed quantity having a value of about 200 000 candles/cm2 . The values of B found in the literature are usually those calculated from the measurements of Bo, the only reference to its direct measurement being that by Teele, who compares his value of 190 000 candles/ cm2 calculated from the normal insolation observed during the 1935 stratosphere flight to "a directly measured value of 200 000 candles/cm2 reported by Worthing"
https://webcache.googleusercontent.com/search?q=cache:GRKFNJ2KT4MJ:https://www.osapublishing.org/viewmedia.cfm%3Fid%3D51094%26seq%3D0+

>> No.9192180 [DELETED] 

fucking retarded sites like wikipedia and others just parrot the same 1.6 Gcd/m^2 without any explanation

http://www.schorsch.com/en/kbase/glossary/luminance.html

>> No.9192202
File: 666 KB, 619x771, dumb maths.png [View same] [iqdb] [saucenao] [google]
9192202

>>9189751
Is there a typo here or something? Why is the answer in terms of "N" if x is approaching positive infinity? I know the limit itself equals a negative value, but isn't that irrelevant? The definitions seem to imply that the behavior along the x-axis is what determines the answer.

Top portion of the picture is the definitions, middle is the problem, and bottom is the book's answer. Sorry about the shitty lighting.

>> No.9192205
File: 42 KB, 857x622, derivatives graph.png [View same] [iqdb] [saucenao] [google]
9192205

A bit baffled by this one. It's derivates-related.

>> No.9192209

>>9192202
if x is bigger than N, then the difference between f(x) and it's limit at infinity is smaller than epsilon
basic definition of convergence

>> No.9192215

>>9192205
r'(x) = g'(x)*f'(g(x))
r'(1) = g'(1)*f'(g(1)) = g'(1)*f'(4) = 0 *5/4 = 0
now try it for s

>> No.9192237

>>9192202
>Why is the answer in terms of "N" if x is approaching positive infinity?
N is the number that x has to be greater than to guarantee that f(x) falls within epsilon of -3 man
Think about it, if f(x) has a limit at x going to positive infinity, you can always find some interval for x where f(x) is within an arbitrary fixed value of the limit. This problem is about finding N (and thus a satisfactory interval for x) as a function of the distance, epsilon, from -3, thus showing there's a satisfactory N for *every* distance from -3, proving the limit

>> No.9192290

>>9192205
g(1)=4
f(g(1))=f(4)
f'(4)=?

>> No.9192329
File: 687 KB, 984x805, mathbff.png [View same] [iqdb] [saucenao] [google]
9192329

>>9192290
It's 5/4 because that's the slope. I'll solve s'(4) then. Thanks!

>> No.9192336
File: 3 KB, 310x104, derivatives graph - solved.png [View same] [iqdb] [saucenao] [google]
9192336

>>9192215
>>9192290
Got 'em.

>> No.9192343

What the fuck is algebra used for? Like what is the point of solving 4x^2+20+16?

>> No.9192347

>>9192343
That's not algebra. It's what we call "engineering".

>> No.9192353

>>9192209
>>9192237
>N is the number that x has to be greater than
The definition says that x has to be *less* than N. The book uses M for positive values.

>> No.9192394

>>9192353
yeah that's a typo then. make it M=sqrt(1/epsilon -2) and it should fit in with your definition.

>> No.9192399

If Jack won 462 of the 832 card games played, how many more wins than losses did he have?

How the fuck do I answer this question? I don't even understand it.

>> No.9192409

>>9192399
number of wins = 462
number of losses = number of games - number of wins
difference between wins and losses = number of wins - numbers of losses
are you in elementary school?

>> No.9192410

>>9192399

nvm I got the answer 92

832-462 = 370
462-370 = 92

I don't understand the wording of this question oh well...

>> No.9192419

>>9192394
Sweet. I was going crazy over this thinking I was turning retarded. Thanks for the help!

>> No.9192425

>>9192409

I'm not in elementary school I just don't understand the "how many wins than losses did he have?" part until I found out it meant finding the difference.

Thanks for the help.

>> No.9192549
File: 28 KB, 599x563, 17918090_1855685004691926_1777495618_n (copy 1) (copy 1).jpg [View same] [iqdb] [saucenao] [google]
9192549

good god how do I reparameterize the curve
[eqn]\vec{r}(t) = a\cos^{3}(t)\hat{i}+a\sin^{3}(t)\hat{j}+2\cos(2t)\hat{k}, \hspace{0.3cm}0\leq t \leq \frac{\pi}{2} [/eqn]
in terms of the arc length measured at a point where t=0?

>> No.9192551

>>9192549
should be [math]b\cos(2t)[/math], not 2.

>> No.9192613

>>9192549
>>9192551
I keep getting the integral
[eqn]s(t) = \int_{0}^{t}\sqrt{ \sin^{2}(t)\cos^{2}(t)\left( 9a^{2}\cos^{2}(t) + 4a^2 + 4b^2 \right)}[/eqn]
which I'm stuck at

>> No.9192674

>>9192613
I am getting this integrant:
[eqn] ( \frac{9}{4} a^2+4b^2) ( \sin (2t) )^2 [/eqn]
Use the facts that [math] ( \sin (t))^2+( \cos (t))^2=1 [\math] and [math] \sin (2t)=2 \sin (t) \cos (t) [\math].

>> No.9192678

>>9192674
I mean the square root of it.

>> No.9192690
File: 328 KB, 1920x1080, Snapchat-1384650750_01.jpg [View same] [iqdb] [saucenao] [google]
9192690

>>9190430
is this what you needed?

>> No.9192730

>>9192061
is the answer 5625000?
I took each group of 1 big bead and 5 small beads as a single unit, and found number of different permutations of the units (5P5)
Then I found number of different possible units (For Unit 1, 5 (big bead possibilities) * 5^5(number of possible combinations of small beads). For unit 2, number of big bead possibilities becomes 4 etc...)
Am I right?

>> No.9192867

>>9192088
[math]f \circ f^{-1} = y \implies f^{-1} \circ f \circ f^{-1} = f^{-1} \circ y \implies f^{-1} = f ^{-1} \circ y [/math]

Notice that this implies that y is the identity, denote that by [math] I [/math]. Then, as desired you can conclude [math] f \circ f^{-1} = I [/math]

>> No.9192887

>>9192867
what a horrible post

f f^{-1} = y already implies y is the identity by definition of f^{-1}, you don't need to do any of the bizarre implications you went through

>> No.9192894

>>9192887
Autist. What I am doing is proving that y is the identity without assuming it is. Notice that he was asking just that.

You say "Oh it's by definition" but that's no proof, you fucking brainlet.

Also notice that you are a fucking faggot who cannot appreciate the beauty of being able to prove y is the identity just from knowing that
1) The right identity and left identity are the same in function composition
2) Function composition is associative

God damn man. Learn to appreciate algebra. It's fun when you get that huge stick out of your ass and just appreciate the arguments.

>> No.9192911

>>9192894
>What I am doing is proving that y is the identity without assuming it is
but you did assume it is when you cancelled out f f^{-1} by replacing it with the identity when you wrote
f^{-1} f f^{-1} = f^{-1} y => f^{-1} = f^{-1} y,
brainlet

>You say "Oh it's by definition" but that's no proof, you fucking brainlet.
definitions don't require proofs, brainlet

>Also notice that you are a fucking faggot who cannot appreciate the beauty of being able to prove y is the identity just from knowing that
>1) The right identity and left identity are the same in function composition
Wrong, a function f:X to Y has right identity I_X and left identity I_Y, not the same functions.
>2) Function composition is associative
trivial

>God damn man. Learn to appreciate algebra. It's fun when you get that huge stick out of your ass and just appreciate the arguments.
You should try learning algebra in the first place before trying to 'appreciate' it

>> No.9192917

>>9192911
You faggot, I assumed what >>9192088 gave me.

He gave me that [math] f \circ f^{-1} = I [/math] and I applied that. You do realize that it is not the same right? Composition monoids are not commutative.

>>9192911
>definitions don't require proofs, brainlet
You must be fun at parties.

Then you go on to nitpick my comment and then call it trivial. All I am saying there is that you should just appreciate what the argument is saying. Also of course my proof is only valid for endomorphism monoids, that should be self evident. I don't know why you need to nitpick me like anyone was implying otherwise.

>You should try learning algebra in the first place before trying to 'appreciate' it

Sure man. I will.

>> No.9192940

>>9192917
>You faggot
Why the homophobia?

>He gave me that f∘f−1=I and I applied that.
There's no reason to apply anything, the notation f^{-1} already implies f f^{-1} = f^{-1} f = I by definition.

>Composition monoids are not commutative.
No one said otherwise.

>Also of course my proof is only valid for endomorphism monoids, that should be self evident. I don't know why you need to nitpick me like anyone was implying otherwise.
Considering the rest of the statements in your posts have been incorrect, nothing should be considered 'evident' at all

>> No.9192951

>>9192940
>>9192917
Also the only reason you can say that 'f^{-1} = f^{-1} y implies y is the identity' is because you know f^{-1} is injective (by definition of f^{-1}).

For a generic function g, the statement 'g=g y' does not imply y is the identity, consider y(x)=-x and g(x)=x^2.

>> No.9192967

>>9192940
You are just repeating yourself now.

>>9192951
Well, at least now I know you don't know shit about algebra. f is not a specific function, it is an arbitrary element of the composition monoid.

Saying [math] g = g \circ y [/math] in the context I was using does not say "Using a very specific g, this is true". It is saying [math] \forall g, g = g \circ y [/math] which does imply y is the right identity. Learn to algebra mate. I know I've told you this like 3 times now but you will enjoy it. Stop trying to sound intelligent by trying to nitpick what was a quick interesting argument that used only the inherent properties of monoids instead of resorting to definitions. Get real. Learn to enjoy life. Learn to enjoy math. LIVE.

>> No.9192968

Where does your belly button go? Also, why is there blood on my qtip after I stick it in my belly button?

>> No.9192971
File: 11 KB, 184x187, 11716028.jpg [View same] [iqdb] [saucenao] [google]
9192971

WHERE DO I EVEN START WITH THIS?

What date is the fourth Monday in June, if May 4th falls on a Friday?

>> No.9192987
File: 19 KB, 861x215, Screenshot_2017-09-26_19-31-31.png [View same] [iqdb] [saucenao] [google]
9192987

is this a valid proof of surjectivity for the collatz algorithm? what about odd numbers? why is it satisfactory to just check an arbirary even number?

>> No.9192988

>>9192967
>f is not a specific function, it is an arbitrary element of the composition monoid.
Invertible elements are not 'arbitrary' in a monoid.

>Saying g=g∘y in the context I was using does not say "Using a very specific g, this is true".
No, but it's only true when f^{-1} is injective, which it only is by definition, not by any 'inherent property of monoids'.

>> No.9192990

>>9192987
>is this a valid proof of surjectivity for the collatz algorithm?
Why wouldn't it be?

>what about odd numbers?
The proof was for arbitrary c in N.

>why is it satisfactory to just check an arbirary even number?
c was never specified to be even.

>> No.9192995
File: 127 KB, 601x508, 1499816625812.png [View same] [iqdb] [saucenao] [google]
9192995

>>9192990
ah yes, at last I truly see. thanks

>> No.9193014

>>9192967
dude, you are so wrong.
consider [math]f \colon X \to Y[/math]. the original question can be interpreted in two ways:
either you take [math]f^{-1}[/math] to be an arbitrary map [math]g \colon Y \to X[/math] which is just (for whatever reason) denoted [math]f^{-1}[/math] and he's asking whether [math]f \circ g = id_Y[/math] implies [math]g \circ f = id_X[/math]. this is of course not true in general.
or you take [math]f^{-1}[/math] to be what it usually is, i.e. an inverse for [math]f[/math], i.e. the mapping which BY ITS VERY DEFINITION satisfies OP's implication, I mean it's LITERALLY half of the definiton. and so the question is really the same as "let [math]G[/math] be a group. is the operation associative?" and the only sane answer is "yes, BY DEFINITION".

>> No.9193016

In the book Lie Algebras by Georgi, can anyone tell me of the factor 2 in equation 8.63 is incorrect?
Using an SU(2) raising operator gives me sqrt(2) using Georgi's formula. The same mistake was made in deriving the matrices 3.32.

>> No.9193026

>>9193016
>In the book Lie Algebras by Georgi, can anyone tell me of the factor 2 in equation 8.63 is incorrect?
post the equation

>> No.9193029

>>9193016
one sec, let me access the book from my photographic memory banks

>> No.9193036

How do I solve the integral
[math]\int_{-\infty}^\infty\frac{dx}{x^2+x+1}[/math]
By extending to the complex plane?

>> No.9193038

>>9193036
first thought is to use a big semi-circle contour (the integral of the arc hopefully tending to zero as the semi-circle gets infinitely large), have you tried that?

>> No.9193051

>>9193038
I know that works if we have a function [math] e^{iax}, \quad a>0 [/math] in the numerator by Jordan's lemma, does it work similarily without it?

>> No.9193064

>>9192971
Alright I managed to figure it out myself I was hoping there would be an easier way but counting seems like the only option..

May has 31 days
June has 30 days

So the question states 'if May 4th falls on a Friday'

So 4th May is the first friday

4+7 = 11th Friday (second)
11+7 = 18th Friday (third)
18+7 = 25th Friday (fourth)

F, S, S, M, T, W,TH
25,26,27,28,29,30,31,

Now starting to count into the month June
F,S,S,M
1,2,3,4

Alright so 4th June is the first Monday

4+7 = 11th June (2nd Monday)
11+7 = 18th June (3rd Monday)
18+7 = 25th June (4th Monday)

That means 25th June is the solution. Wow that wasn't so hard after all..

>> No.9193070
File: 47 KB, 820x598, Capture.png [View same] [iqdb] [saucenao] [google]
9193070

>>9193051
see page 3 on http://www.thomashulse.com/notes33.pdf

>> No.9193076
File: 31 KB, 555x629, georgi.png [View same] [iqdb] [saucenao] [google]
9193076

>>9193026
>>9193029
Forgot to mention the full pdf is freely available as the first hit on google. Pic related

>> No.9193080

This is a really stupid question so buckle up.
What sort of jobs go with just plain mathematics? Why is it differentiated from science, tech, engineering, etc?

>> No.9193081
File: 212 KB, 1246x1010, TooManyPigeons.jpg [View same] [iqdb] [saucenao] [google]
9193081

Suppose we have two finite sets, A and B, with size m and n respectively, then suppose [math]f : A \to B[/math] is a function.

Proof: if f is injective, then [math]m\leq n[/math]

by contrapositive, m > n [math]\implies[/math] f is not injective. by the PHP there exists [math]x_{1},x_{2} \in A [/math] such that, for [math]y\in B[/math], [math]f(x_{1} )= y = f(x_{2})[/math]. So f is not injective.

Proof: if f is surjective, then [math]m \geq n[/math]

by contrapositive, m<n [math]\implies[/math] f is not surjective. by the PHP there exists [math]y\in B[/math] such that [math]y \neq f(x) [/math], so f is not surjective.


how'd I do?

>> No.9193083

>>9193070
thanks anon

>> No.9193090

>>9193036
>>9193051
Yes of course it does work.
The integral is bounded by constant/(radius of semicircle)^2 which goes to 0 as radius-->infinity.
It works in general for integrands P(x)/Q(x) when P,Q polynomial functions with the degQ-degP>=2 and with Q having no roots on the real line.

>> No.9193091

>got a C- on my first calc 2 exam
Am I just a fucking retard?

>> No.9193096

I have a physics problem that basically says "as a particle passes through the region x=0 to x=d, it experiences acceleration a = axi^ + ayj^ where ax and ay are constants"
(I can't be assed to figure out latex code but the in axi^, x is subscripted and i^ is an "i hat", also the first a has a vector line over it).

it gives m/s^2 values for axi^ and axj^ and asks for the position of the particle at x = .01 meters.
My question is just, what does "position of the particle" mean? like does it want it as x,y coordinates? because obviously the x is already given, it's .01. It also wants velocity and speed and direction of travel, and for those I guess I would just fuck around with the given kinematic equations till something seems to sort of work right.

>> No.9193105

what do you tell someone who likes mathematics but more so the numerical aspects of it rather than the abstractions behind it? where should they focus their studies (in which field) ?

>> No.9193108

>>9193105
dont study mathematics

>> No.9193121

>>9193105
What do you mean by "the numerical aspects"?

>> No.9193126

>>9192107
This is excellent advice.
One long project is fine but the more the merrier. Just ask your professors. They probably have something you can assist with.

>> No.9193135

>>9193126
>Just ask your professors. They probably have something you can assist with

I'm a sophomore and I've heard people say you should do this many times but I don't even know how to approach this especially considering I sort of suck. What the hell could I possibly "assist with"?

>> No.9193156

Does matter have an infinite amount of detail (ie quarks are made of shit and that shit is made of shit etc)? I can't think of a more logical explanation.

>> No.9193187

>>9193156
>infinity
>nature
anon, I...

>> No.9193300

I have to obtain the real solution of a damped and driven harmonic oscillator using a given complex solution and I have no fucking clue where to even start
So I'm told this is the complex solution
[math]x(t) = \frac{F_0 e^{i\Omega t}}{m(\omega^2_0 - \Omega) + ir\Omega}[/math]
and i have to use this to get the real solution, im so fucking lost
somoene please point me in the right direction

>> No.9193307

>>9193300
dude just take the real-part lol

>> No.9193315

>>9193307
AAAAA

>> No.9193532

>>9193300
>>9193307
>>9193315
FUCK
I JUST REALISED IM RETARDED
this truly qualifies as a stupid question
i watched 2 hours of anime and i figured it out, sorry

>> No.9193564

>>9193121
Double and triple integrals and volume of revolution problems

>> No.9193591

How do you find alpha for the moment of inertia of a barrel if you know the length to radius ratio?

>> No.9193593
File: 1.70 MB, 250x194, 1505201193819.gif [View same] [iqdb] [saucenao] [google]
9193593

>>9189751
These questions are still too smart for me. I truly have a stupid question:

Why is bandwidth cap a thing with ISP? Is it exhausting on their cables? It's not like it's a reservoir or water.

>> No.9193606

>>9193593
their infrastructure is built too weak especially on mobile. when they first built 3g/4g networks they didn't think people would use so much bandwidth on their phones. but even if they could handle it they want to cut costs and to make more money whenever they can get away with it by having people pay extra for more bandwidth.

>> No.9193615
File: 1.42 MB, 300x300, 1505499697374.gif [View same] [iqdb] [saucenao] [google]
9193615

>>9193606
Okay, but my question is more about what is so exhausting about bandwith? Isnt it just information through light moving at light speed, which is how my brainlet brain sees it?

>> No.9193651
File: 291 KB, 259x137, 1287387212244.gif [View same] [iqdb] [saucenao] [google]
9193651

>continuous random variable
>impossible to assign a probability to any given result, as there are infinitely many of them
>one of them gets selected anyway

>it literally doesn't matter whether you include the end points, because they're one of infinity other possibilities, and therefore also have 0% chance of being selected
>just like everything else
>one of which is selected

>> No.9193657

I've always heard the main difference between plants and other life forms is the cell wall. Are there any instances of non-plants with cell walls or plants without it?

>> No.9193663

How would one find bounds for this?
[eqn]\prod_{n=1}^N (p_n+1)[/eqn]

>> No.9193669

>>9192088
if f^{-1} exists, then yes

but f(g(x))=x does not imply that g(f(x))=x

>> No.9193676

>>9193615
The problem is not the flow of information itself but the processing power used to relay the information from the servers to all access points and the actual power consumed to transmit signals in all the required mediums and frequencies.

>> No.9193692

>>9192867
>Notice that this implies that y is the identity

no it doesn't, unless f^{-1} has a left inverse, which is what you are trying to show

>> No.9193765

https://www.cs.ox.ac.uk/admissions/undergraduate/how_to_apply/sample_interview_problems.html

Where can I find more problems like these? Also, how would you categorize these types of problems? Logic? Combinatorics?

>> No.9193788

>>9193156
Eventually you will reach some particle that can be thought of as a monad, in that it is composed only of itself and cannot be decomposed any further.

>> No.9193799

>>9191228
Assuming that the galaxy occupies 10 degrees of their total field of view and they are perpendicular to the disk (i.e widest point ~100 000ly) you get ~283 564 ly, or somewhere in the galactic halo

> t. someone who took astro 100

>> No.9193852
File: 20 KB, 606x129, dc.jpg [View same] [iqdb] [saucenao] [google]
9193852

Can the union of any number of Dedekind Cuts, as defined by Rudin, equal Q?

>> No.9193864

Is there a more rigorous formal definition of what the fuck a limit actually *does* in calculus besides the epsilon-delta proof of restricting the domain that I can read up on without too much extra work?

Or is it similar to the situation of trig functions in that it takes me years struggling with my shitty math teachers until I realize they're transcendental and the unit circle definitions are provisional until we get to infinite series?

As far as I can tell they're 'linear functionals' but I haven't the slightest idea what a vector space is.

>> No.9193866

>>9193852

If you mean finitely may Dedekind cuts, the answer is no.

A Dedekind cut is of the form
{ x in Q | x < r } for r Real.

So the union of finitely many Dedekind cuts is not all of Q.

If you allow infinitely many you can get Q with countably many cuts.

>> No.9193879

>>9193864
what is it exactly that you want ?

>> No.9193886

Explain to me Mach's Principle

>> No.9193905

>>9193879
I want a definition of a limit that doesn't use the word 'arbitrary'.

>> No.9193916

What's the deal with master's of science of engineering? They don't need ABET. So what's the point of it?

>> No.9193926

>>9193866
Ok, so I suppose I'm wrong in assuming that given a family of cuts, the union of the family will be one of the cuts? Could you point me to a place where I can read more about this?

>> No.9193959

>>9193905
so you just want a definiton of limit without the universal quantifier ? no such thing

>> No.9194152

What's the easiest way to git gud at deriving equations for rate of change questions?

>> No.9194241

How do I go about finding people to study together with?

>> No.9194268

>>9193905
Why exactly would such a thing exist?

>> No.9194274

>>9193663
any information on the p_n?

>> No.9194298

>>9189751
Can water purifiers be modify to purify air?

>> No.9194306
File: 32 KB, 628x438, question.png [View same] [iqdb] [saucenao] [google]
9194306

How would you formulate this question correctly? pic related is my attempt. I made the objective function the formula for the plane, then my constraints were that, when the points from the first set were inserted into the plane equation it was greater than or equal to zero and the other set were less than or equal to zero. My thinking is that when you substitute points into the plane equation, the sign of the result will be the same if the points on are on the same side, so I figured this would constrain my function enough to get any feasible solution, but all I get is 0.

halp pls

>> No.9194366

>>9194306
the constrains make sense, but what exactly is the optimalized function ? it feels like it should be something like "empty function"

>> No.9194420

Hey everyone I'm new here.

>>7734126

>> No.9194472

>>9193096
Yes.

>> No.9194481

>>9194306

doesn't make much sense to write it as a linear program, but I i
[math] f = (1,1,1,1) [/math]
[math] A= \begin{pmatrix}
1 & 3 & 2 &-1 \\
3 & 4 & 2& -1 \\
5 & 6 & 7& -1 \\
0 & 3& 1& -1 \\
3 & 3 & 2& -1 \\
-1 &-2& 1& 1 \\
-3& -1& 1& 1\\
-3 & 0& 3 &1\\
-1 &-1 & 1 & 1\\
-2 &-1& 1& 1
\end{pmatrix} [/math]
[math] b = (0,0,0,0,0,0,0,0,0,0)^T[/math]

[math]\min f * (a_1,a_2,a_3,\beta)^T [/math]
subject to [math] A*(a_1,a_2,a_3,\beta)^T \leq b [/math]

f is kind of random
the problem is, that those coefficients aren't unique, since the plane that is defined by [math] \alpha^Tx = \beta [/math] is also defined by [math] \lambda \alpha^Tx = \lambda \beta [/math], so if you want to solve this via simplex it won't terminate

>> No.9194591

>>9194274
It's the nth prime, for example: [math]p_3 = 5[/math]

>> No.9194601
File: 30 KB, 316x202, pepe enough.jpg [View same] [iqdb] [saucenao] [google]
9194601

Last year at uni I didn't study properly and now it's backfiring me. I did only 4 / 7 exams for the past years and now 4 more added, nothing per se is difficult but I'm seriously struggling to keep up to the sheer amount of things to learn.

How can I make my brain work at its maximum biological efficiency?

>> No.9194603

>>9194601
Invent a time machine anon


Then go back in time and abort yourself, so you will not grow up to be a moron who did not manage his time properly

>> No.9194609

>>9194603
Brainlet kill themselves as it's the easiest route to all problems

>> No.9194617

>>9194601
>maximum biological efficiency?
For a frogposting subhuman such as yourself that wouldn't be much, so I wouldn't even bother.

>> No.9194636

>>9190422
The category theoretic implication is that you don't get a natural transformation between the two categories. Thus you can't apply a lot of theorems you would be able to apply in the finite dimensional case, you also can't associate monads naturally either. I don't know of any consequences pertaining to the structure within the vector spaces though, sorry.

>> No.9194645

>>9193081
Correct

>> No.9194674

>>9193081
Well, it's ok, but the essence of the proof is proving the pidgeonhole principle.

>> No.9194684

Why isn't there a much bigger push for psychiatric programs to help autists like us function passably as members of society?

>> No.9194685

>>9194684
>autists like us
Speak for yourself.

>> No.9194704

>>9194601
Try taking a legal amphetamine like Ritalin or Adderall or Vyvanse, personally I use Ritalin NVR20's and they make me more productive

>> No.9194710

>>9194674
could you elaborate on this?

>> No.9194714

>>9194704
Good lucking with killing off your brain power.

>> No.9194727

>>9194714
>Nonsense

What are you talking about, no source, nothing

>> No.9194733

>>9194684
psychiatry is a scam. what are they going to do. just don't be retarded. autismbux help a lot. learn a skill or something. realize that most normies are top pleb. just because you have a diagnose doesn't mean you must have a worse life than a normie.

>> No.9194772

Is the probability of events A^B basically saying the probability that both events happen at the same time?

>> No.9194793

Can someone check my proof here?

If a function ,[math] f : A \to B[/math] ,is a bijection then there exists a function [math]g : B \to A[/math] such that:
[eqn]g(f(x)) = x , \hspace{0.3cm} \forall x\in A[/eqn]
and
[eqn]f(g(y)) = y, \hspace{0.3cm} \forall y\in B[/eqn]

Proof: [math]f[/math] is a bijection thus [math]f^{-1}[/math] exists. Let [math]g: B \to A[/math] be defined as [math]f^{-1}[/math]. Thus [math]g(f(x))= f^{-1}(f(x)) = x[/math] and [math]f(g(y)) = f(f^{-1}(y)) = y[/math]. QED.

>> No.9194817

not a very good proof imo

f^{-1} is usually defined to be the function g satisfying those properties, using it sort of seems like cheating

>> No.9194823

>>9194817
I see. How else could I go about proving it? I'm not too sure how to proceed.

>> No.9194832

>>9194823
define such a g using the fact that f is bijective

>> No.9194848
File: 56 KB, 645x773, 1503241219948.jpg [View same] [iqdb] [saucenao] [google]
9194848

>>9194832
how should I determine g based on that information?

>> No.9194859
File: 1.31 MB, 3264x2448, IMG_6072.jpg [View same] [iqdb] [saucenao] [google]
9194859

>>9194817
Wrong. You can't say f^-1 exists when that is what you want to prove.

You need to construct it and prove it works. See pic related for rigor.

>> No.9194865

>>9194859
Ah, I see.

>> No.9194876

>>9194859
Are you a CS-tard by any chance? The notation is barely readable.

>> No.9194881

>>9194859
how is g(b) validated by property 2?

>> No.9194884

>>9194876
I'm a math major that has been in the library for 3 hours as my classes finished just that much ago reviewing complex analysis. I am too tired to keep thinking so I decided to refresh the SQT to do a little charity. I shat out that doodle in less than 30 seconds. If you want me to type it out in latex and add diagrams then that will be 50 bucks.

>> No.9194893

>>9194881
g(f(a)) = a is only well defined because f is injective (property 2). Imagine f was not inyectice. Lets say f(c) = f(v) but c not equal to v

Then g(f(c)) would not be well defined as it could equal either c or v. That is why property 2 validates that definition.

>> No.9194897
File: 210 KB, 645x968, 1503241345483.jpg [View same] [iqdb] [saucenao] [google]
9194897

>>9194893
right on. sucks being a brainlet. many thanks.

>> No.9194905

Is time just the universe in flux?

>> No.9194912

>>9194884
>analysis
It's garbage, no wonder you come off as a CS-tard.

>> No.9194914

"Your boss randomly assigns everyone an extra 2 hours work between 4 and midnight."
[math]|S| = 8 [/math]
but shouldn't it be 7 because of the possible two hour time slots between 4 and 12?
So shouldn't it be:
[math]S = {4-6, 5-7, 6-8, 7-9, 8-10, 9-11, 10-12}[/math]
or am I looking at this stupidly? That makes more sense to me.

>> No.9194919

>>9194914
shit
[math]S= {4−6, 5−7, 6−8, 7−9, 8−10, 9−11, 10−12}[/math]

>> No.9194956

when I apply the Euler-Lagrange equations to $\int \ln f(x) dx$ so to find the function that minimizes the functional I obtain that $\frac{1}{f(x)} = 0$ but this is not what I am expecting at all since $\ln f(x)$ explodes as $f(x)$ gets larger, am I not applying the Euler-Lagrange theorem correctly?

>> No.9195267

>>9194793
>Theorem:
>if f is a bijection, f^-1 exists
>Proof:
>f is a bijection, thus f^-1 exists. QED
outstanding work!

>> No.9195332
File: 79 KB, 874x684, brainlet 2.jpg [View same] [iqdb] [saucenao] [google]
9195332

can your IQ permanently decrease if you spend an entire year playing vidya / on 4chan?
I was pretty smart before, I don't want to become a complete brainlet because I fucked around for a year lmao.

>> No.9195370

>>9195332
Not likely, but your IQ probably wasn't high to begin with.

>> No.9195389
File: 17 KB, 746x600, 1505585106740.png [View same] [iqdb] [saucenao] [google]
9195389

>>9195370
ok, thanks anon.

>> No.9195436

Find the volume V of the described solid S.
The base of S is an elliptical region with boundary curve 25x^2 + 16y^2 = 400. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.

I can't even visualize what it's talking about.

>> No.9195449
File: 3 KB, 364x348, Unbenannt.png [View same] [iqdb] [saucenao] [google]
9195449

>>9195436

>> No.9195554
File: 322 KB, 450x455, 1497353420856.gif [View same] [iqdb] [saucenao] [google]
9195554

>>9195436

>> No.9195560

>>9192063
Victor Chondria University has quite a reputation for that kind of research, check them out.

>> No.9195633

>>9193651
>continuous random variable
>impossible to assign a probability to any given result, as there are infinitely many of them
>one of them gets selected anyway

this. can someone clear this up for us?

>> No.9195647

>>9189751
when am i able to call an organism a new species? you know what i mean idk how to ask it but

>> No.9195654

>>9192347
FUCK OFF STUPID ENGINEER CUNT

>> No.9195657

>>9195654
I'm not subhuman though, "we" as in "mathematicians".

>> No.9195662

how do i use this ∫

Just give me a simple integral problem and tell me how to solve it please

>> No.9195702

>>9195662
integrals are the opposite of derivatives. do you know how to solve derivatives?

>> No.9195710

>>9195702
No :(

please someone teach or you teach i will be forever in your favor

>> No.9195722

do class conditional probabilities not need to sum to one?


>>9195710
what do you want to know

>> No.9195726

>>9195722
how to find the derivative and then how to do integrals

>> No.9195727

>>9195726
of what function?

>> No.9195731

>>9195727
f(x)

idk you give me an example please

>> No.9195733

>>9195727
just give me like an easy example, how to solve it, another easy example, and ill solve that

>> No.9195743

>>9195733
>>9195731
?? just look up a youtube video or just read the wiki page and if you have a question, then come back
whats ur deal lol

>> No.9195749

>>9195743
i want to learn it from a /sci/entist.

I need the personal maths connection with someone. please

>> No.9195856

>>9195449
ILLUMINATI

>> No.9195890

>>9195662
https://www.youtube.com/watch?v=rjLJIVoQxz4

>> No.9196037

>>9195727
f(x) = x + x + 3

>> No.9196074

Niggas tryna tell me that {1, x, x^2} is a basis for Q(x) over Q(x^3), but how do I generate 1/(x+1) from this?

>> No.9196188

>>9196074
1/(x+1) = px^2 + qx + r, multiply both sides by x+1 (beware x=-1), you do the rest.

>> No.9196200

I'm new to LaTeX. I write \section{} before my text and the equation are numbered like (1.1) (1.2) and so on.

How do I get them numbered just as (1) (2)...
?

>> No.9196277

>>9196037
f(x) = 2x + 3
f'(x) = 2
int(f(x)) = x^2 + 3x + c

>> No.9196279

>>9196200
https://www.sharelatex.com/learn/Sections_and_chapters
documentation is really your best friend here

>> No.9196282

if I have multiple lemmas, am I allowed to use the same dummy variables for each one or should I use different variables. For instance, in lemma 1 I'd use m and n, so should I use m' and n' in lemma 2? or are these numbers exclusive of what goes on inside the lemma?

>> No.9196341

>>9196282
you can use the same variables

>> No.9196350

Best linear algebra lectures? On youtube?

>> No.9196371

>>9196282
You use the same variables. It's how everybody does it. Sometimes you use the same letters inside the Same proof, if there is not much room for confusion.

>> No.9196375

>>9196350
Axler made some videos where he essentially reads his book out loud:
https://www.youtube.com/channel/UCtHp0WNe3OaSXAr1C_Oi0AQ/videos

>> No.9196419
File: 198 KB, 539x309, Screenshot_2017-09-28-09-40-41~01.png [View same] [iqdb] [saucenao] [google]
9196419

PROOF QUESTION

My friend (who is a very bright individual just recently broke up and hates all men) she found this funny and posted this on her instagram. I'm trying to figure if these assigned values are in fact true.

On literary connotation, all three words have a negative meaning.

The initial problem (up left) is

Niggas+shit=aint.
The next (visible top left) is aint+shit=niggas.

The first maybe true. The second implies it cannot at the same time. Based on the divison problems, we can assume there is no 0 in the equation.

Really gets my noggin joggin. Help.

>> No.9196469

can someone tell me if i get it yet on derivitives?

so a derivative is the instantanious rate of change at a given point on a slope, right? and there are multiple known functions used to extract this value (Power Rule, Product Rule, Quotient Rule, and Chain Rule), right? suppose i dont exactly have the best understanding of non-linear algebra, where could i go for a plain english explanation of each of these methods and their advantages?

ive been at this on and off for a while now and i still dont quite feel like i know how to properly pull off backpropagation in a neural network.

>> No.9196482

>>9196469
>so a derivative is the instantanious rate of change at a given point on a slope, right?
yes
I think it is better to interpret it as the best linear approximation of the function around a point x0, i.e. for x close to x0, f(x) is almost f(x0)+ax where a is the derivative of f at x0.
Same goes for higher dimensions as well (a becomes a matrix/linear transformation)
We care about the derivative because linear stuff are simple and we know how to do things with them.

>> No.9196602
File: 49 KB, 1714x142, Screenshot_20170928-124143.png [View same] [iqdb] [saucenao] [google]
9196602

I'm trying to prove by induction that 7^n-2^n is divisable by 5, for all natural numbers n.

The first step is fine:

f(1) = 7^1-2^1 = 5 (divisable by 5)

The second step, I can't work out. This is as far as a got:

f(n+1) = 7^(n+1)-2^(n+1)
= 7*7^n-2*2^n
= 5((7/5)*7^n-(2/5)*2^n)
= 5((35*7^n-10*2^n)/25)

Can anyone help me out?

>> No.9196606

>>9196602
hint:
f(n+1) = 7^(n+1)-2^(n+1)
= 7*7^n-2*2^n
= 5*7^n + 2*7^n-2*2^n

>> No.9196610

>>9196602
7*7^n - 2*2^n = 5*7^n - 2*(7^n - 2^n)

>> No.9196613

>>9196469
>right?
Wrong. It's the slope OR the instantaneous rate of change
>right?
Wrong. These aren't functions but rules to apply when differentiating.

Non-linear algebra is pretty much the same thing as algebraic geometry so I don't see how that is relevant to calculus.

>> No.9196614

>>9196606
Thanks, will look into that after class!

>> No.9196672

>>9194793
Just wondering how I'd do the converse of this.

So, If there exists a function [math]g : B \to A[/math] such that:
[eqn]g(f(x)) = x , \hspace{0.3cm} \forall x\in A [/eqn]
and
[eqn]f(g(y)) = y, \hspace{0.3cm} \forall y\in B[/eqn]
then [math]f : A \to B[/math] is bijective .

haven't a clue how to proceed

>> No.9196674

>>9196613
sorry, ive a programming backround, not a maths one. by slope i meant the curve of the function, and in the second bit i meant function as in the kind i might write to do these tasks.

well curves are non-linear algebraic functions, right?

>> No.9196683

>>9196672
injective:
f(x) = f(y)
<=>
x = g(f(x)) = g(f(y)) = y

surjective:
let y \in B,
then there exists x = g(y), s.t. f(x) = y

>> No.9196701

>>9196606
>>9196610
Thank you, I figured it out!

>> No.9196702
File: 13 KB, 225x225, 1503247350492.jpg [View same] [iqdb] [saucenao] [google]
9196702

>>9196683
fuck this question, it's so simple but my iq is too low. t-thanks for the quick response

>> No.9196712

>>9196702
believe in yourself anon.
we're all gonna make it.

>> No.9196724

what's an 'offset'? Don't need in-depth explanation, we haven't covered 'poisson regression' yet

>> No.9196795

>>9196724
consider an array, A, which contains abcdef. We say "d" has an offset of three from the start of A.

>> No.9196809 [DELETED] 

>>9196602
[eqn] a^n - b^n = (a-b) ( a^{n-1} + a^{n-2} + \cdots + a b^{n-2} + b^{n-1} ) [\eqn]

>> No.9196811 [DELETED] 

>>9196602
[math] a^n - b^n = (a-b) ( a^{n-1} + a^{n-2} + \cdots + a b^{n-2} + b^{n-1} ) [\math]

>> No.9196813

[eqn] a^n - b^n = (a-b) ( a^{n-1} + a^{n-2} + \cdots + a b^{n-2} + b^{n-1} ) [/eqn]

>> No.9196817

>>9196809
[eqn]a^{n} - b^{n} = (a-b)( a^{n-1} + a^{n-2} + \cdots + ab^{n-2} + b^{n-1} ) [/eqn]
>>9196811
[math] a^n - b^n = (a-b) ( a^{n-1} + a^{n-2} + \cdots + a b^{n-2} + b^{n-1} ) [/math]

watch the direction of the slash on the closing tag lads

>> No.9196818

>>9196602
>>9196813

>> No.9196821

>>9196817
I somehow was completely sure that it was [\math] .

>> No.9197161
File: 9 KB, 411x269, 1505792378664.jpg [View same] [iqdb] [saucenao] [google]
9197161

A professor made a passing comment in class that sometimes you can say the supremum of an infinite set of points can be infinite.
Is it possible to do this without changing the definition for supremum and what would be the use since as far as I know you could just say the set has no upper bound?

>> No.9197176

>>9197161
>Is it possible to do this without changing the definition for supremum
sure just define the range as [math] \mathbb{R} \cup \{\infty\} [/math]
>what would be the use
you wouldn't have to define the domain of your supremum function in an akward fashion i guess

>> No.9197207

>>9197176
>sure just define the range as [math] \mathbb{R} \cup \{\infty\} [/math]
Huh, didn't think of that for some reason.

Thank you, anon.

>> No.9197209

>>9189755
yup \bigtriangleup v=\frac{F \bigtriangleup t}{m}

>> No.9197212

>>9189758
WTF is this shit?

>> No.9197255

>>9193663
Would anyone know how to find the bounds on [math]p_n\#[/math], at least? It's the primorial function.

>> No.9197264

>>9193663
prod (p_n+1) >=
prod (n+1) =
(N+1)!

>> No.9197277

>>9197264
I was hoping for something more close, but thank you.

>> No.9197480
File: 584 KB, 1400x2700, 1501182066623.png [View same] [iqdb] [saucenao] [google]
9197480

How are polynucleotides made if it's thermodynamically unfavorable to form phosphodiester bonds via dehydration?

>> No.9197482

>>9197449

>> No.9197488

quick, prove to me that [math]x^2 - y^2 = (x+y)(x-y) [/math] using only elementary math

>> No.9197491
File: 6 KB, 426x408, generator.png [View same] [iqdb] [saucenao] [google]
9197491

Why wouldn't this work?
Would you be able to actually get net power out of it?
>Electromagnet attached to a generator
>Spins from Earth's magnetic field
>Keep switching the polarity
>The generator powers the electromagnet

>> No.9197496

My girlfriend bought me Principia Mathematica. What do?

>> No.9197499

>>9197496
Wife her.

>> No.9197500

What the fuck is a perfectoid space?

>> No.9197501

>>9197488
FOIL / first outer inner last. multiply x (first parenthesis) by x and -y (both second parenthesis), multiply y (first parenthesis) by x and -y (both second parenthesis)
X x X = X^2
X x -Y = -YX
Y x X = YX
Y x -Y = -Y^2

X^2 + (-YX) + (YX) + (-Y^2)
-YX and +YX cancel out
X^2 + -Y^2

>> No.9197505

>>9197491
look up an "earth battery"

>> No.9197643
File: 12 KB, 468x92, discrete.png [View same] [iqdb] [saucenao] [google]
9197643

Guys am I going crazy or wut. Question D is false right? The textbook says the answer is true tho..

But put any negative number and 3n>4n

>> No.9197666

>>9197488
Okay, but how about only using [math]x^2-y^2[/math]?
Because later I ask me to prove that [math]x^n - y^n[/math] and for that I can't multiply each term

>> No.9197726

(a) Given n boys and n girls, how many ways are there to break
them into n pairs?


Thoughts: is the answer just n!?

(b) Given 2n girls, how many ways are there to break them into n pairs?

Thoughts:
Would it be 2n! or is it more complicated.

I'm just thinking the first male would have a choice of 2n women, the second male would have a choice of 2n-1 women, and the third would have a choice of 2n-2 women, etc etc...

>> No.9197777
File: 12 KB, 550x405, dht.png [View same] [iqdb] [saucenao] [google]
9197777

>dihydrotestosterone
>Only one hydroxyl group

Can someone explain?

>> No.9197880

>>9197726
>I'm just thinking the first male would have a choice of 2n women, the second male would have a choice of 2n-1 women, and the third would have a choice of 2n-2 women, etc etc...

but what would the last man have a choice of?

>> No.9197900

If I have a business-related degree and graduated with a decent GPA, how feasible is not spending a lot of money (given potential scholarships, core classes being out of the way etc.) if I wanted to pursue a STEM major (math or computer related [not CS])

>> No.9197907

>>9197777
hydro- has nothing to do with hydroxyl groups. the prefix indicating that is hydroxy-

>> No.9197929

>>9197726
>Thoughts: is the answer just n!?
Yup.

>(b) Given 2n girls, how many ways are there to break them into n pairs?
This one is trickier.

Let's order the girls from 1 to 2n. There are 2n-1 possible partners for girl 1; afterwards, the number of possible matchups for the remaining 2n-2 girls is the same as the total number of matchups for 2n-2 girls in general. If I am not mistaken, this yields [math]1 * 3 * 5 * 7 * ... * (2n-1) = \prod_{i=1}^n (2i-1)[/math].

>> No.9198093

>>9197900
Continuing onto this, realistically I'd look into something IT-related. My current major pays a good amount but jesus christ work life looks bleak

>> No.9198125

>>9198093
What work life looks interesting to you, or at least less bleak? I have parlayed STEM degrees into jobs at big pharma companies and smaller business outfits, but it was mostly due to data science skills. If this kind of thing interests you, you need to get comfortable with data and scientific, data-driven decision-making.

>> No.9198139

>>9198125
>What work life looks interesting to you, or at least less bleak?
Work weeks that don't arbitrarily jump to 50-70 hours and not taking my work home with me are the big ones. I'll probably an hero if my day is work, get home, do more work because companies are understaffed, obsess about work, sleep, repeat

>> No.9198150

>>9198139
You're best bet might be moving to Europe then. Americans (and to a lesser extent Canadians) in the white collar labor force get all kinds of fucked up on the long hours and productivity mousewheel. It's better as you get promoted, but it's a grind. If that's not an option, and you aren't interested in blue collar (ie, union) work, then you're best bet is to try to get into a BIG company. The bigger the better. Small companies are like you think--not enough folks, so work is omnipresent. Bigger/huge megacorps have enough staff, and while you'll be monitored for project completion and all that, they aren't going to make you stay all hours. You might get into this stuff though, and not mind it so much. Some of my work ends up like puzzles, and I do that shit for fun. Except now I collect mad stacks for it.

>> No.9198161

>>9198150
Europe for various reasons is a non-option at the moment. I have considered looking into trades, though, they seem to pay reasonably well with minimal waste in terms of time and money as barriers to entry.

What do you even do?

>> No.9198163

>>9198161
Also I'm extremely sleep deprived and might be speaking complete nonsense

>> No.9198168

>>9198161
Big companies generate big data and they don't know how to effectively consume all of it. I work with (here, scientists) to figure out how to reduce and display their data so they can make decisions. But you can apply these skills to sales numbers, bioinformatics, sports stats, polling, whatever the hell. The skills are portable.

Trades are great though, I don't knock those at all. I was watchign some dude cleaning my carpets and thought, that's it. This guy cleans carpets, gets paid, goes home and fucks his wife. He doesn't need to think about how he's going to clean a carpet tomorrow.

There's a mental load that comes with white collar work that is hard to shed in the States, because you never get enough vacation and time to reset. Unless you get fired, and then your job becomes panicking.

>> No.9198172

>>9198168
You pretty much described my issue with white collar work. I really can't make up my mind on trades, part of me sees it as incredibly monotonous, part of me sees it as a lot of varied work in different places but I'm worried about requiring an expensive degree to actually make money off it. Again, I'm sleep deprived and might be rambling but I appreciate the replies.

I also feel like a bit of a retarded spending god knows how much on my degree then abandoning it

>> No.9198181

>>9198172
It's teaching you how to think. Just because your degree is in finance or whatever doesn't make you unemployable in other fields. It might even make you interesting in the resume pile. If you can be thoughtful and contribute, what your degree is in isn't that huge a deal.

And don't succumb to sunken costs fallacy. You spent a lot on the degree, so you need to use the degree to pay yourself back? Or something? That's BS and will make you miserable. Rest up and think about things. You'll be OK.

>> No.9198183

>>9198181
Marketing, not finance. Basically you're not a manager/director and making 60k or you are and are making 120~ while being stressed the fuck out at all times with little free time. Anyway again, the responses are appreciated

>> No.9198508

>>9197880
n+1 women?

So it would be 2n, 2n-1, 2n-2,...., n+1?

since the last man will be exhausting the nth woman?

Is there a nicer way to write this then?

>> No.9198653

>>9198508
>Is there a nicer way to write this then?

you noticed that 2n! is too big, and specifically that it is too big by a factor of n!, so simply divide out n!. It might seem a bit wasteful to include all these terms that cancel out, but at least it's a simple way to write the expression.

>> No.9198793

>>9189751
It's summer. It's humid. There's no wind. But I have a 100m tall tower. The tower is 3m x 3m at the base, slowly tapering upward. On each face of the square tower a large fan is fixed towards the "front" of the face (front being the direction the fan is blowing in). This continues upwards for the entire 100 meters.

If I turn on the fans will I generate a high pressure system and bring comfort to my area?

>> No.9198916

Anyone can help with this? >>>/wsr/390064 In short, my question is what's the angle between the triangle base and pentagon, because it's not 90 degrees. Evidence of this is that if you place both pentagons like that and look them from above, you will see that the vertex protrudes from the edge of the other one. So the triangle is in an angle a little bigger than 90 degrees. How to know?

>> No.9198973

>>9198916
A pentagon has 5 sides. 360/5=72. 72/2=36. So the centre of the triangle base is at a radius of R*cos(36) ~= R*0.809 while the apex is at R. So the horizontal distance is R*(1-cos(36)) ~= R*0.191.

The length of the triangle base is 2*R*sin(36) ~= R*1.176. The altitude is half the base times tan(60) = R*sin(36)*tan(60) ~= R*1.018.

The cosine of the angle you're after is the ratio of these: R*(1-cos(36))/R*sin(36)*tan(60) ~= 0.188, so the angle is ~79.19 degrees.

>> No.9199015

Bump limit reached.
Someone make a new thread.

>> No.9199023

I need to show that the series [math]\sum_{n=0}^{\infty}\frac{z^n}{n!}[/math] converges and is infinitely differentiable using (also) the fact that the even and odd subsequences of [math]\frac{z^n}{n!}[/math] converge to the same value (or at least that's what I understood from the problem).
The problem is that I have no idea on how to show this. The sequence converging does not imply that the series will converge. I have that if the series converges then the sequence converges to zero.
What am I missing?

>> No.9199028

>>9199023
>infinitely
No such thing.

>> No.9199029

>>9199028
?

>> No.9199038

>>9199029
Huh?

>> No.9199041

>>9199038
Can you say more than "No such thing"? That really doesn't help...

>> No.9199042
File: 230 KB, 934x503, hxbDc0O.png [View same] [iqdb] [saucenao] [google]
9199042

Professor sent us the quiz answers.
Where it says A(y) = Area of Square he uses the formula "A = 4s" which is wrong right? The area of a square is A=s^2
And using s^2 I got 1/2 as the answer. Someone tell me if I'm retarded

>> No.9199052

>>9199023
ratio test gives you absolute convergence of the series
do you have any theorems for derivatives of power series already?

>> No.9199057

>>9199041
So-called "infinite" things can't be shown to exist. So your request already doesn't make sense mathematically.

>> No.9199063

>>9199052
>do you have any theorems for derivatives of power series already?
Yes, we've gone through that already.

>ratio test gives you absolute convergence of the series
That's what I thought I should do. But the problem is asking to use the fact that if the odd and even subsequences of a sequence converge to the same value, then the sequence converges to such value.
My problem is that I have no idea on how to apply this fact to this situation...

>> No.9199066
File: 118 KB, 768x1024, 1490552510279.jpg [View same] [iqdb] [saucenao] [google]
9199066

>>9199057

>> No.9199078

>>9199063
>But the problem is asking to use the fact that if the odd and even subsequences of a sequence converge to the same value
that's weird. as far as I can see, you know exactly as much about the convergence of your original series as you would about its even/odd subsequence.
maybe it means splitting the series into even and odd parts, and getting convergence through absolute convergence of sin and cos power series (if you have proven those).
Those are not subsequences of your sequence of partial sums though

>> No.9199087

>>9199078
Well, I think I'll dismiss that part for now and send my professor an e-mail asking wth he meant by that.
Thank you!

>> No.9199251

Im looking for a book that was suggested to be read after how to prove it by velleman. I think it was written by two russian guys and it is essentially a compendium of everything an undergrad math major should know, or at least that was how it was described.

>> No.9199466

NEW THREAD
>>9199462
>>9199462
>>9199462