/sci/ - Science & Math

>>9952775

My boss uses me as a punching bag at work but the job pays hourly $35. At this point its assumed any work I do is wrong and he will redo it. Even if I fully followed him to spec I am blamed for the failures.

But interestingly I am never fired leading me to believe I am just a punching bag.

Any reason I should leave this company? It's really just free money.

>>9952795
You kind of answered that one yourself. Good pay, job security even though you are berated, win win.

The only thing, if you start to accept it and take it very well, do you run the risk of your boss realizing it isn't hurting you anymore and firing you because the fun is gone? How replaceable are you realistically?

Any texts for pre-calc, algebra, trig that provide an analytic commentary not just the rules of high school math?

>>9952797
Well I wish I had meaningful work. It sucks knowing whatever I do will be called out as shitty. For reasons unknown to me I'll never get fired unless an economic recession occurs. I am definitely replaceable but this company does not fire you for unknown reasons.

I've started learning Python in my free time and I workout consistently. So just staying sharp outside of work.

So would you stay knowing your work was not meaningful?

>>9952775
I'm getting a minor in math (I'm an EE grad/undergrad student, with a focus on controls/signal processing), and I need one more elective for my minor. Which of these do you think I should take?
>Numerical Analysis
>Abstract Algebra
>Real Analysis
>Complex Analysis
>PDE's and Fourier Analysis
>Applied Statistics
>Mathematical Programming
>Mathematical Modeling

>>9953137
Real and Complex Analysis

>>9952795
I wonder if this can be fixed by matching the mode of communication your Boss utilizes/expects?

>>9952819
>So would you stay knowing your work was not meaningful?
If your work was meaningless you would not work there anymore.

>>9953137
>>9953171
Funny. I thought "Real Analysis couldn't hurt."

>>9953137
In order:
>applied statistics
>complex analysis
>pde/fourier
>math programming

Stats is a MUST have. I'm shocked it isn't already in your curriculum. Engineers also need a knowledge of complex variables so definitely that one next. You can get away without having taken fourier analysis and programming but I'd suggest studying it on your own then.

>>9952775
>No
>No
>No
>No
>Yes
>More irrational numbers

>>9953336
>>No
Wrong, since odd integers exist.

>>No
Wrong, since composite numbers exist.

>>No
Wrong, since there are non-integer rational numbers.

>>No
Wrong, since irrational numbers exist (in b4 wildberger)

>>Yes
Correct.

>>More irrational numbers
Why?

I've got a bunch of data points in the form of "Number - Tuple", where the tuple represents a cell in a 2D grid (ex. 10.98 - 1,2). Every cell has the same number of measurements

What kind of plot(s) do you recommend to illustrate de data?

I was thinking about recreating the grid, but each cell is color coded according to its average

(Context: This is about electric field)

>>9953330
It is, I had stats and I have another class for stochastic processes coming up
This other stats class is a different and more advanced class I guess
Thanks for the suggestion though, I was leaning toward complex analysis or PDE's, since my boss suggested it.

>>9953355
incredibly wrong

>>9953355
Retard

>>9953355
Hint: The trick is that you have infinitely many discrete Labels.

>>9953355
And here I thought this wasn't a "stupid answers" thread.

>>9953364
How many of the measurements from each cell must be conveyed? Must the sequence of cells be shown (ex. each cell represents a different point in time, so you want to show the progression over time).

You can have a 3d graph so that there are 2 independent variables shown by position. Data points can be different colors, (or on a spectrum from one color to another), and can be different sizes. That's 4 independent variables right there.

>>9953465
>>9953399
>>9953388
>>9953388
>>9953373
>>9953373
t. brainlet

I need to statistcly analyze a real-time temperature vs time graph and send out an alarm if the trend goes out of a tolerance limit and don’t know where to start.

what would be the correct/best method to start looking into?

Would just averaging all points together to form a basis graph, then give it a 5% tolerance range before an alarm is triggered be correct?

I have several years worth of data and I have minitab at my disposal, but I am not really familiar with it or statiscally analysis besides basic standard deviation.

Thanks

taking calculus 3, 3rd semester of calculus. What is calculus, even? What should I get out of it? When can I apply this?

>>9953771
>What should I get out of it? When can I apply this?
If you're in any STEM field calculus will be everywhere
Even bio needs calc for stats and some other topics

What branch of biology studies prions?

If I have to do a research project, of which the final product is a journal-quality article for a class, do I own the rights to publish it in journals by myself?

>>9952795
Ask yourself what ratio of your life you spend at work and how important your work is to you. If the answers to either of those indicate that your work is more important than your social life then bail and get a better job, all the money they pay you will only benefit your social life and if that sucks then it's not worth it.

>>9953355
>>9953678
b8

How often will an EE use math in the real world? What should one study?

The answer is "No" to every question, Now can you tell me how to fuckin destroy my pilonidal cyst without going to the hospital (I am fuckin tired and don't wanna spend 45€ for the treatment) instead of talkin' about this math shit for kids?

>>9953908
Retarded and unreasonably angry at those smarter than he is: quite a combo.

Anyway, you're wrong. The cardinality (size) of the reals is greater than that of the integers (countables). The following question is left as an exercise to the reader.

Now go be an arrogant brainlet elsewhere you acne-ridden troglodyte.

>>9953316
child

>>9953771
calculus is the study of sufficiently good approximations

>be me
>ABSOLUTELY TRIGGERED by numerical solutions
>PDE course in my uni is all about numerical solutions
>Some of the more advanced courses I'm interested in require it

How do I deal with this?

What are the actual possible limitations of parallel universes?
Could they actually contain every conceivable reality or would they still need to abide by certain rules?

Currently on chapter 8 in Spivaks calc. Everything went fine up to here and then it started to fall apart and I found myself referencing the answer book more and more on these problems. I even felt a little shaky on some of the previous chapters but kept going on just because I could comprehend the next batch of stuff. So my question is, should I try to complete all of the problems I couldn't do in the previous chapters, or just keep going on, returning to them later?

Where can i find full pdfs of iso standards?

>>9953355
Is that njwildburger?

>>9953316
>>9952797
>>9952795
I've read studies that a large percentage of the workforce believe their jobs are meaningless, and they probably are. If you're certain the job isn't having an adverse affect on your mental, social or physical health then what's the problem? Are you looking at working up to a higher/better job and if so is this helping it?

>>9954220
An infinite number of possibilities within some parameters obviously does not imply every conceivable possibility among those parameters. Actually OPs questions demonstrate the same principle.

The fundamental issue with naively hypothesizing these sorts of parallel universes is that if you model them in such a way such that they can never, even in theory, have any interaction with our own universe, then asserting their existence is largely meaningless. There do, of course, exist models which do have interaction between "nearby" parallel universes. However, you will find that these allow for relatively narrow parameters compared to all "conceivable" realities.

tl;dr the popsci meme of "every possibility I can think of is a parallel universe that exists" is retarded

How brain electricity became feelings?

>>9954213
just call them numerical approximations

>>9952775
Damn people really ask these questions they are pretty obvious.

Yes
Yes
Yes
Yes (twice as many see below)
Same amount. Take any rational number .75 for example and just add an irrational suffix to it
.75767778798081...

>>9954392
for every irrational number you can create new irrational numbers by dividing it with arbitrary rational numbers

For mercurial projections, if i wanted to shift the entire thing so that for example antarctica were centered exactly in the middle, what would that be in rotation?
Im converting LLA to spherical XYZ and that works great. So what, 90° around the right hand axis?

>>9952775
I heard again today that electrons are aligned in a magnet, and one thing about that has been bugging me since high school: do the electrons in a magnet point north or south?

>>9954534
Electrons in free space have their spin point along the magnetic field.
In a material, it depends on the material's gyromagnetic ratio, which is usually positive, so there the spins also align with the field.

How does gravity keep the atmosphere stuck and spinning to the earth when the air has no solid bond to the earth and itself?

>>9953137
Do the PDE course

>>9954594
it just werks

>>9954598

>>9954221
Never read Spivak so I can't give you particular advice

But it depends on what your goal and situation is. If you have the time and want to understand the material, to answer your question: yes. If you are a student who needs to keep their grades up, you probably don't have the time.

>>9954594
If I jump in the air, I am not bonded to the earth but gravity still affects me. That's not an answer, just pointing out this is not a weird scenario.

To answer your question: we don't know. It is undecided and there are lots of theories about it. GR is the most popular one although I'd argue that it's, at the least, incomplete at answer how gravity works. It offers more of a map of the amusement park rather than how the rides function.

>>9954626
So the atmosphere isn't "dragged" along with the rotation due to friction? Because I've read people saying that.

I haven't really had much experience with proofs, can anyone help me get started on this? I'm pretty sure I understand what's going on, like if you factor out constant in a function you'll still get the same answer when you plug in numbers, and then multiply by the constant at the end.

I can prove that numerically by factoring out the constants(or constant if I need to find the common denominator), and plugging in values for x1, x2, and x3, but I don't know if there's another way I should go about it. This is similar to a homework question I have, I made this one up just to get an example of how I should go about this.

Probably super brainlet question, plz no bully

>>9954659
That equality isn't true for that particular function.

>>9954702
fuggg

If it's not too much trouble, would you mind posting an example of a function which is true, or at least explaining why the equality isn't true? Or would it be true if the addition sign was changed to a subtraction sign?

>>9954221
Skip those exercises. That is a complex subject if you've never read something alike before, and it's used again in chapter 13.

The topic of chapter 8 is a basic one in set theory, and is part of the concept of order. I suggest you to read A book of set theory, by Charles C. Pinter. Reading at least two books on set theory (a naive approach and an axiomatic one) is desirable as it is a basic theory anyone studying maths must know.

Finally, don't consult an answer books, because if you do so, then you will never develop your ability to solve problems.

Sup guys
Could one of you explain what happens in the part in red?
Wouldn't the answer to z'=z^2 just look like exp(exp(s)) ?

>>9954727
He just replaced the xi by cxi's and checked if it was the same than multiplying the whole thing with c.
Why not take the identity function?
Or F(x,y,z)=x+y+z

>>9954648
I'm not sure how that addresses your original question. Friction doesn't cause things to be dragged.

Serious question: what do all you mathfags here do when you're out of school with a math degree?

There is no way you're all professors and there's basically no math beyond undergraduate applied math courses used in any jobs except math research. Do you all work in applied math and study theoretical math on your own?

>>9954760
>Why not take the identity function?
>Or F(x,y,z)=x+y+z


Oh shit, thanks anon!

Why do we know that R(z) is a polynomial? I can't find a source for that. Is the real part of a polynomial always a polynomial?

>>9954727
> would you mind posting an example of a function which is true

It's true for a *linear* function, as that's one half of the definition of linearity, which is:
f(c*x)=c*f(x)
f(a+b)=f(a)+f(b)

So it's true for any function of the form:
f(x1,x2,x3) = k1*x1+k2*x2+k3*x3
where the ki are constants.

But I'm wondering whether this is supposed to be about *homogeneous* functions, which satisfy:
f(c*x1,c*x2,c*x3)=(c^n)*f(x1,x2,x3)
for some n (not necessarily equal to one).

Note that the first term is homogeneous with n=1 (i.e. linear) and the second term is homogeneous with n=2 (you get a factor of sqrt(c)^6 = c^3 in the numerator and a factor of c in the denominator, giving c^2 overall). But adding a linear term and a quadratic term gives a non-homogeneous function regardless of the scale factors of the individual terms.

> Or would it be true if the addition sign was changed to a subtraction sign?
No. The structure of the terms is wrong. If the second term was ^4 rather than ^6, then it would be true, and you could change the constants or swap variables arbitrarily and it would still hold (you'd basically have factors of c^2/c=c for both terms). Similarly, if the first term was e.g. x1^2*x3/x3 it would be homogeneous with n=2.

>>9952807
Bumping for answer

>>9954810
I agree, I've just heard people saying that.

What also doesn't make sense is how the moon's gravitational pull doesn't appear to affect anything else other than the tides.

>>9954855
nvm I got it. It is a polynomial but only locally. It should say that. Makes me angry.

>>9954885
BAD GOY! STOP ASKING QUESTIONS! BELIEVE IN THE MOON! THE THEORY THAT (((WE))) JUST PROJECT A MOON HOLOGRAM AND SAY IT AFFECTS THE TIDE TO COVER UP OUR UNDERWATER NUCLEAR BOMB AND MASS DESTRUCTION WEAPONS TESTING PROGRAMS IS A VILE ANTI-SEMITIC, RACIST AND SEXIST CONSPIRACY THEORY. NOT TRUE. CEASE YOUR INVESTIGATIONS.

>>9952795
Ultimately to me fulfillment from work is quite important. I would not work somewhere where my work isn't valued even if it pays well. I'd use my position as a leg up to apply somewhere else instead.

>>9952775
I'm just a physishit but
>no
>no
>no
>yes
>irrational, because the set of the reals minus the rationals is still uncountably infinite (and the same cardinality as the reals) whereas the rationals are a countable infinity

>>9954897
"Jews" are goys whether they know it or not. The moon and sun are electromagnetic you buffoon.

>>9954213
You need to confront your brainletism face-to-face, anon.

>>9954885
>how the moon's gravitational pull doesn't appear to affect anything else other than the tides

It does affect things other than the tides. The moon actually has it's own, tiny atmosphere. It doesn't look like the earth's because the moon doesn't have the chemistry (to create clouds n shit) to create what we envision as an atmosphere. But there are small rocks and such orbiting the moon.

>>9954933
>It does affect things other than the tides.
LIKE WHAT.

I just started taking an Astronomy class mostly online but with a lab at the school once a week. The pre-lecture assignments we are supposed to complete by tonight are kicking my fucking ass though because of the math and physics. I haven't done any math or science since I took basic algebra in my first year of highschool 7 years ago. Can I going to make it through this class?

>>9954749
Foud the solution! I just had to integrate

How can you prove that an elementary function does not have an elementary anti-derivative? Like x^x and 1/ln(x)
I know that they don't have one but how can you prove it?

>>9952775
how would i find out how much force 2 rare earth magnets exert at 10 cm distance

I need to generate a force of about 5 newtons with this device

>>9955054
https://math.stackexchange.com/questions/265780/how-to-determine-with-certainty-that-a-function-has-no-elementary-antiderivative

EE student here.
What exactly do they do after collegfor? I’m sure they don’t calculate circuits all day since there should be automatic calculators for shit like this.

Help me with my topology HW.
I need to prove that if [math]X[/math] is an infinite set and [math]\tau[/math] a topology on [math]X[/math] and every infinite subset of [math]X[/math] is in [math]\tau[/math] then [math]\tau[/math] is the discrete topology on [math]X[/math]

>>9954948
Its atmosphere and orbiting rocks, like he said. In addition to water tides, there are atmospheric tides it affects.

It technically affects everything, but it's far enough away that the effect is really only measurable with very large, relatively free moving objects (like lakes, oceans, and atmosphere). It also is causing the rotation of the Earth to slow - very slowly. (Couple of hundred million years ago we had 9 hour days.)

>>9954648
>>9954594
The atmosphere does revolve with the earth due to the viscous drag of the surface of the earth on the air. If there was a stationary outer shell to the atmosphere, this would generate a shear in the velocity versus height so that the tangential velocity on the outer surface would be zero as well. However, there is no such bounding layer to the top of the atmosphere, so it is all dragged into rotation with the earth. There are many subtle features to this "solid body" rotation, though. First is the fact that the velocity of the surface of the earth varies with latitude, so there is shear as one goes north. The rate of change of velocity with latitude is low enough that the atmosphere can still be in local equilibrium with the earth's velocity, but it leads to a "stirring" motion of the atmosphere, causing global circulation cells to form, such as those in the Tropic of Cancer and the Tropic of Capricorn. Additional effects of the rotation "Coriolis forces" are visible in the flow of air around low and high pressure zones in the atmosphere, and affect any large-scale circulation of air, causing it to divert from straight-line motion to curved motion. Nevertheless it is true that on average, the atmosphere rotates with the earth at that latitude.

>>9955128
Take an proper infinite subset, split it and using said split show that a single point is an intersection of open sets

>>9952775

Meaningless questions because there is no infinite pigeon hole principle

I know modern time keeping is based of Greenwich mean time, but how did we decide what GMT would be? What I mean is, solar noon isn't the same day to day, so we had to decide on a "noon" that would be noon for Greenwich. How did they decide it? On that note, how the hell would I keep accurate time without modernity? Like say I had a mechanical watch, how would I set it? I could wait until the shadows are shortest in the day, but as I said, solar noon shifts through the year.

pls help timekeeping is confuse

is anyone able to help with part b) here, i know n is 12 but dont really know how to start

>>9953708
What methods do they want you to use? Would a rolling Average do? In what timeframe should the trend stay within bounds? Or does it react to the derivative trend (trend of speed picking up)?

>>9953771
Calculus is the Study of how a specific (Real number) input range is transformed into a (Real number) output range.
Aka. Behavior of Functions

For what it can do: Simply Google "Calculus Applications" or "Calculus $subtopic Applications" or something.

>>9953985
They would have already fired him.

Do futa balls produce testosterone?

>>9954933
>The moon actually has it's own, tiny atmosphere.

>Until recently, most everyone accepted the conventional wisdom that the moon has virtually no atmosphere. Just as the discovery of water on the moon transformed our textbook knowledge of Earth's nearest celestial neighbor, recent studies confirm that our moon does indeed have an atmosphere consisting of some unusual gases, including sodium and potassium, which are not found in the atmospheres of Earth, Mars or Venus. It's an infinitesimal amount of air when compared to Earth's atmosphere. At sea level on Earth, we breathe in an atmosphere where each cubic centimeter contains 10,000,000,000,000,000,000 molecules; by comparison the lunar atmosphere has less than 1,000,000 molecules in the same volume. That still sounds like a lot, but it is what we consider to be a very good vacuum on Earth. In fact, the density of the atmosphere at the moon's surface is comparable to the density of the outermost fringes of Earth's atmosphere where the International Space Station orbits.
Neat.

>>9954953
Talk with your TA / Prof about this. Then brush up your Math.

>>9955209
There is a place in each time zone where noon/midnight *are* (or maybe were) the same each day. That is, the clocks were set so that noon would be at precisely midday.

This used to be how it was done everywhere until the invention of trains necessitated a unified system so that trains could run on devised schedules and wouldn’t run into each other.

>>9955209
More politics than science. It used to be every capital of every major nation was considered its own prime meridian - so if you think timekeeping is confusing now...

Suffice to say, the Brits started using it just before the empire peeked, so it caught on. It's an entirely arbitrary designation, and even it is subject to some leeway (actual noon in Greenwich being +/- 12 minutes GMT). Then you get into time zones, daylight savings time, UT, and all that jazz... Time is truly relative. Gonna get a whole lot worse if we ever start colonizing the system - and then the galaxy.

I've bought the book I've attached in my image. The writer says that this book is for people with knowledge of classical physics and calculus.

I've got some experience with the latter (bought a book to brush up still), but do any of you guys have any book recommendations on classical physics?

>>9955209
Search for "equation of time".

"Mean time" is the average noon over a year. Measuring the number of seconds lost/gained between consecutive "sundial" noons (when the sun is directly north or south) gives you the derivative. Summation gives the equation up to a constant of integration, which is chosen so that the mean error is zero.

>>9955251
Young and Freedman is the gold standard but any university physics 101 text will do.

>>9955234
> There is a place in each time zone where noon/midnight *are* (or maybe were) the same each day.
This is incorrect, assuming that you're using "noon" to mean something you can observe with a sundial.

The point where the sun is due north/south varies by ~15 minutes from "mean" noon over the course of a year, due to a) the inclination of the earth's axis and b) the eccentricity of earth's orbit.

When accurate clocks were a new thing, there were clocks which would calculate "sundial time" based upon the day of the year, as sundials were the de facto time standard.

>>9955275
Cheers.

Also, I don't go to any university and I study at home. Now, I buy second-hand books and I don't have access to solutions. Is there any loophole to get them? I've tried searching online, but to no avail.

>>9955280
I wonder if any knowledge regarding sundial making got lost.

>>9955295
Library genesis (libgen) sometimes has solution manuals.

There's a classic physics text by Giancoli. The 4th edition is the one I used in university and the solution manual is definitely available on libgen. Although the text itself isn't that great.

http://libgen.io/

why do people with dark green eyes always have dark brown hair? or is this just my subjective observation?

>>9955305
Thanks. Downloaded your suggestion.

Unfortunately couldn't find what I needed. Maybe I'll come across it one day.

I got a warning for posting a topology question here, is this an _all time low_ of sci?
(Hey mods, that's a stupid question that doesn't deserve its own thread, hope that this time you don't give another warning) sorry for my bitter ass

>>9955337
It probably looked like a homework question

>>9955210
a-anyone

>>9955210
Can you use. Sylow's theorem?

>>9955305
>Giancoli

LMFAO

Stay away from this book.

Young/Freedman or Tipler if you like harder problems.

>>9954392
this is bait, but very wrong.

these are some of the first things you learn/discuss in real analysis with the introduction of cardinality, which will be the first thing that comes to mind when talking about relative sizes of infinite sets (there are other ways to go about this but when you hear clops think horse not zebra etc etc).
>>9953336 is correct
as for why: https://math.stackexchange.com/questions/180550/why-is-the-cardinality-of-irrational-numbers-greater-than-rational-numbers

>>9953336
>Math thread
>Post with 5 questions
>You gave 6 responses

>>9954892
>It is a polynomial but only locally.
Wrong.

>>9954855
>Why do we know that R(z) is a polynomial?
P(z) =
sum_{k=0}^{deg P} w_k * z^k
sum_{k=0}^{deg P} (a_k+b_k * i) * z^k =
sum_{k=0}^{deg P} a_k * z^k + sum_{k=0}^{deg P} b_k * i * z^k =
R(z) + i * Q(z)

>>9955210
>i know n is 12
Why?

>>9955751
should have expanded z^k = (x+iy)^k, but the idea is there

>>9952775
>are there more integers than even integers
Yes. There is double the amount of integers as compared to even integers.

>are there less primes than integers?
Yes, because whenever you add 100 new integers, 100 of them will be integers, but you will get less and less primes over time.

>are there more rational numbers than integers
yes, because for every integer you can create a, for example, rational number that is integer+1/2 integer

>are there more real numbers than rational numbers
yes, because real numbers include every rational number plus something more like pi and e

>are there more rational numbers or irrational numbers
i dont know this one

>>9952775
> are there more integers than even integers
No. For every integer n, there's an even integer 2n, and vice versa.

> are there less primes than integers?
No. There are infinitely many primes, so for every positive integer n there's a corresponding nth prime. And there are as many positive integers as integers:
f(n) = 1+2n if n>=0
f(n) = 2-2n if n<0

> are there more rational numbers than integers
No. Rationals are enumerable: enumerate all positive rationals whose numerator and denominator sum to 1, then those which sum to 2, 3, etc. Thus for each positive integer n, there's an nth positive rational, likewise for negatives.

> are there more real numbers than rational numbers
Yes. See Cantor's diagonal argument.

> are there more rational numbers or irrational numbers. Why?
Irrational. There are uncountably many reals but only countably many rationals, so there are uncountably many irrationals.

>>9955210
how can n be 12 if the order of G is not even?

>>9955295
i used young and freedman and there is a solutions manual and i'd know because i used it to cheat on my assignments

https://libgen.pw/item/detail/id/1283568

here is one for some edition, but of course they'd probably change the label of the exercises to fuck shit up, but just ctrl f that shit

>>9955921
>>9955210
>>9955763
in fact i just calculated it (in less than 10 seconds...) that the largest subgroup is of order 63

it's trivially true from the theorem of fin gen abelian groups. The order of Aut (Z/315Z) is clearly 315 = 5*7*3*3, so if G is not cyclic, then the only possible decomposition is Z/3Z x Z/63Z. So it remains to show that there is no element of order 315.

Part b is also quite clear, you just need to realize Z/63Z as a Sylow 5-, 7-, 3^2-subgroup, use the second to show the other subgroups are conjugates of it and then use the third sylow theorem until submission (numberings may vary across books/lectures but you can surely point them out)

>>9955932
***use the second sylow theorem***

>>9955932
The order of Aut(Z/315) is actually (5 - 1) * (7 - 1) * (9 - 3) by the Chinese Remainder theorem.

>>9955932
fuck also another correction: it shouldnt be 63, it should be 3*5*7 = 105, i just messed up the multiplication

>>9955934
>every group is a ring

>>9955937
Aut(Z/315) = (Z/315)* = (Z/7)* x (Z/5)* x (Z/9)*

>>9955939
>the automorphism group is the group of units
nigga you're embarrasing yourself, just stop. It is well known that Hom(Z/aZ, Z/bZ)=Z/gcd(a,b)Z

>>9955940
It is the group of units lmao. For any automorphism, 1 must be mapped to an integer coprime to n.

>>9955940
>nigga
Why the racism?

>>9955945
Don't be upset by the word nigger, it's just a word

I'm implementing a little 'calculator' operating on sets. Is there an established convention for ASCII character set operators for set theoretical operations? I'm thinking of just using:

union: A | B (maybe A + B ?)
intersect: A & B
relative complement: A - B (maybe A \ B ?)
exclusive disjunction: A ^ B
complement: ~A

>>9954858
>But I'm wondering whether this is supposed to be about *homogeneous* functions, which satisfy:
>f(c*x1,c*x2,c*x3)=(c^n)*f(x1,x2,x3)
>for some n (not necessarily equal to one).

>>9954659 here, I think you're right. I went ahead and got the textbook, even though class doesn't start til next week and in the "math needed for this particular class (intermediate microeconomics)" section, homogeneous functions are one of the topics covered.

>>9954858
>>9955987

If the second term was ^4 rather than ^6, then it would be true, and you could change the constants or swap variables arbitrarily and it would still hold (you'd basically have factors of c^2/c=c for both terms). Similarly, if the first term was e.g. x1^2*x3/x3 it would be homogeneous with n=2.

Just saw this part, and in the original problem the second term is ^4, and it's being subtracted rather than added. Thanks!

>>9955992
Actually looks like it's most likely a homothetic function

>>9955976
Don't use + for union if you use - for difference.

>>9952775
Okay, so i'm studying the motion of a marble on a wire on the surface of a cylinder (a helix if you will) and i want to write the equations of motion in intrinsic coordinates. The position vector is (in cylindrical coordinates):

[eqn] \vec{r} = a \hat{\rho} + z \hat{k} [/eqn]
where [math] \hat{\rho} = \cos \theta \hat{i} + \sin \theta \hat{j} [/math] and [math]a[/math] is the radius of the cylinder.
The motion is one dimensional and therefore should be expressed by one parameter, lets say the angle [math]\theta[/math]. Why is the height [math]z[/math] of the marble written like this?
[eqn]z(\theta) = \frac{h}{2\pi} \theta[/eqn]


where [math]h[/math] is the step of the helix.

Okay, so i'm studying the motion of a marble on a wire on the surface of a cylinder (a helix if you will) and i want to write the equations of motion in intrinsic coordinates. The position vector is (in cylindrical coordinates):

[eqn]\vec{r} = a \hat{\rho} + z \hat{k}[/eqn]

where [math]\hat{\rho} = \cos \theta \hat{i} + \sin \theta \hat{j}[/math] and a is the radius of the cylinder.
The motion is one dimensional and therefore should be expressed by one parameter, lets say the angle [math]\theta[/math]. Why is the height z of the marble written like this?

[eqn]z(\theta) = \frac{h}{2\pi} \theta[/eqn]

where [math]h[/math] is the step of the helix.

>>9956065
[math] \theta [/math] actually represents time. The height of the marble is increasing linearly as it goes around the cylindrical surface.

>>9956079
shouldn't it be [math]\theta = \omega t[/math] where [math]\omega[/math] is a constant?

>>9956085
Yes, that would be more accurate.

>>9956088
i just don't get where on earth [math]z(\theta)[/math] (or if you want [math]z(t)[/math]) came from

>>9956096
It's just the definition of a helix
https://en.wikipedia.org/wiki/Helix#Mathematical_description

>>9952775
Where can I find a quick basic overview of manifolds, tangent spaces and vector bundles?

I've done a course on differential geometry but only in the context of n-surfaces in [math]\mathbb{R}^{n+m}[/math]. A course I want to follow now lists those three things ("a basic understanding of...") as prerequisites and I want to do some reading to prepare.

How much time would be needed to make this timelapse photo, judging from the stars' movement?

life started with some some self-replicating molecula, what is the reason and what is the reason of self-replication on the microlevel?

>>9956171
I'd eyeball about an hour and a half aimed at a celestial pole. That looks like 20-something degrees with the stars rotating a15 degreees per hour.

What is the best way to learn a programming language? I feel like all the YT tutorials just start blathering out commands without any context so when I go to apply them I have no idea what I'm doing

>>9956186
What exactly are you aiming to achieve? What do you want to program?

>>9956178
Got it. Thank you, anon!
Now the real question is why did that guy stand on a Raptor for about one hour.

>>9956204
isn't that just a game screenshot / rendered promotional image?

>>9956208
It is, I think they released that pic back in late December/early January.

>>9954213
you sound like a retard.
>waah waah numeric methods are bad
>muh purity
If you knew 2 shits about math you'd knew you can only solve these numerically as of now save for a very select handful of trivial cases (and in some cases these trivial cases have a very difficult solution).
Acknowledge the utility of numeric approximations to gain insights and move on, brainlet.

I'm not really /sci/ and I'm not in university just yet, so I don't have more than high school education right now.
What the fuck is the deal with Zeno's paradox? Specifically Achilles and the tortoise.
How is it anything other than Zeno being a smartass? even if we don't know about the Planck length (which in itself shits on the idea of dividing distance into infinity) we clearly see the real world doesn't behave like that, and that made up bullshit "paradox" would be a non issue if you just use subtraction instead of division.
Am I missing some sort of bigger picture? failing to read between the lines? am I just being a dumbass?

>>9956202
i want to get into using it for like mathematical modeling and data analysis if that makes any sense; i'm not so much interested in making a vidya game or web development which seems to be where most tutorials are geared towards.

>>9956221
Well can you describe it mathematically for us?

>>9956221
In the standard model of physics spacetime is not discrete, not in terms of Planck units or anything else. Planck units aren't a physical limit, so much as they are an analytical one, beyond the fact that it represents the minimum wavelength.

The fallacy in Zeno's paradox is in the assumption that an infinite sum always results in an infinite number, so would take an infinite amount of time to complete. Given a finite distance and a finite speed, it can be shown that the time to completion is finite, even within the framework of Zeno's paradox.

The other usual mathematical solution is to use convergence between infinities, not that it's perfect under all circumstances.

Nonetheless, the paradox can still be taken as a proof that reality cannot actually be broken into the discrete and the continuous as we so conveniently like to model. In reality, the world lies between these two extremes. At the lower bound, it is almost broken up into the discrete. At the upper bound, it is almost relativistically smooth and continuous. So it is almost dualistically broken. But not quite. Instead it seems it actually exist just within the bounds, the event horizons indeed, of these modelled extremes.

>>9956226
what language are you eager about learning?

>>9956251
Matlab

>>9956251
I figured I'd learn python since most places seem to be adapting to it as a more user-friendly language

>>9956226
I think you're best off starting with Python if you're a beginner. Especially with it having MatPy: https://github.com/MattCocci/Python-MatPy..

Afterwards when you think you're confident enough and know 'how to think' like a programmer (because it's a shift of thinking in a sense) then, for performance, you could always switch to C++. Others will argue you use C, but C++ is more user-friendly and will already have plenty of libraries for you to use.

>>9956254
http://greenteapress.com/thinkpython/thinkpython.pdf This has some great material that should cover most things.

>>9956268
most importantly it has some exercises each chapter which are probably the best way to learn

is there any way to simplify this expression? maybe getting a and b in the same absolute value?

>>9956186
get a book on data structures in c++
study the first half of it so you get a feel for the basics of programming

then get a book on modeling in matlab (the only math language worth using) and go through it. you can use matlab for free by downloading gnu octave. it's pretty much the same.

if you dont want matlab then theres a famous book called numerical recipes in C that you can use

dont do java, its useless. python is okay, fortran is dead, julia is a meme

>>9956483
>matlab instead of R

Why does a fluid traveling at higher speed result in a lower pressure? I know it's because of Bernoulli's equation, but I want a deeper reason behind it.

>>9956474
you can just do it by cases. you'll get 4 cases depending on whether a or b are >1 or <=1. there's no other way since you can't separate the absolute values

>>9956483
> julia is a meme
Julia is a perfectly good language, but the 1.0 release was a couple of weeks ago, whereas the other options have been around for a couple of decades. The utility of a language is determined less by the language itself and more by its "ecosystem" (books, tutorials, libraries, tools, user base).

Personally, I'd suggest Python (with NumPy/SciPy for numerical stuff) over e.g. Matlab. Mainly because knowledge of a general-purpose language will be far more useful in the long run than knowledge of a specialised tool such as Matlab. If you ever need to learn another language for any reason, that language will be more similar to Python than to Matlab.

why do schools teach math the dumb way instead of as a function of logic?

>>9956493
be gone, datafag

>>9956667
python is for short scripts not the type of dense programs encountered in math/science

>>9956493
I love R my brother, but the domains of R and matlab are quite different and I wouldn't interchange them.
Though the OP wanted to just learn programming, and in this case, matlab is a really stupid answer, and R is also pretty bad.

>>9956254
honestly python is widely used but as far as programming goes, it teaches some horrendously shit habits.
I don't know why python won that domain, over ruby. For a high-level prototyping language, ruby is excellent and much less idiosyncratic than python. You'll end up learning more "python" than you will "programming."

what's a good way to tutor earlier math (like, lin alg and "lower"), for a guy with a rusty math degree who wants to rebuild his confidence and make sure his fundamentals are in place?
community colleges tend to only hire in-house, students and faculty, right?

>>9955796
For the first three, you're wrong because you're using finite logic on infinite sets. You're right on #4 for the wrong reason. And the answer to #5 is #irrationals>#rationals

>>9955945
Shut up, nigger.

>>9957242
read "A Mathmatics Lament," a short essay
The PDF is the top result in Google

>>9957342
I really want to crush your head with a rock

>>9957347
The kind of violent response to words that I'd expect from a nigger. Thank you for proving me right, nigger.

>2.1772 posts per user
any stats nerds care to weigh in on how to get meaningful analysis from a unique user count that resets every 24ish hours
I mean, unique ip is pointless early in the thread so what do you do about that

>>9957477
Maybe 4chan really uses a unique "user GUID saved in a cookie" count by thread?

I'm a 28 year old boomer who wasted his life doing retarded jobs instead of finishing college. I have like 2 semesters completed so basically nothing.

I really love physics and will sometimes help people I know with their physics homework or problems.

Is there any sort of hope or point for someone like me to go back to school?. I would want to do research not teaching but I don't want to saddle myself with debt and struggle through college while working if nobody is going to take some loser in his 30's over a young face fresh out of college.

Honest answers please.

>>9957817
>I don't want to saddle myself with debt
Why don't poor Americans just study abroad? I lived with 300€ a month (less than 0€ after the gibs) as a student in a small French city, and it must be even cheaper in Eastern Europe.
You don't need to go to a prestigious school for your bachelor's degree

>>9952775
3(u^2)v + 3u(v^2) - 24u - 24v
u(3uv + 3(v^2) - 24) - 24v

If you can arrive here: (u+v)(3uv - 24),
can you show me how you do step by step please from the second line.

>>9957837
[math] 3u^2v + 3uv^2 - 24u - 24v = 3uv(u + v) - 24(u + v) = (u + v)(3uv - 24) [/math]

>>9957826
For the purposes of this question let's just assume that to be off the table.

>>9957837
Thanks!
So this way u(3uv + 3(v^2) - 24) - 24v
(factorizing by u) it's a dead end, we have to go backward and factorising by 3uv?

>>9952775
why dont we just communicate FTL with quantum entanglement by using morse code? how come they say you cant use quantum entanglement to communicate?

>>9957874
It's possible to consider it as a quadratic in u (or v) and solve it by the quadratic formula. I don't see how that particular factorization can help though.

>>9957875
Say I have two coins, magically linked, and when you flip one coin to heads, the other turns tails. However, you can't determine if either is heads or tails until you catch them. Until then, these magical coins are constantly spinning and the outcome unknown. You can't decide to pin the coin into a particular state, the result is always totally random and outside your ability to control. Further, you can never tell if either magic coin has been flipped, you can only read the random result and report it.

So I give you one, and you magically teleport to a galaxy far, far away, while I have the other.

So we decide, adjusting for relativity and the distance between us, that I'll catch my coin at a predetermined synchronized time, at which point you'll catch yours, and see the result.

But... As the result is random and you can't even confirm if or when I've flipped the coin, we've no way to communicate anything this way.

While it's entirely possible to violate the speed of light in a number of ephemeral ways, it's impossible to transmit information at faster than the speed of light (which is, really, just the speed of information propagation) lest you start warping or bypassing the distance somehow. These magic coins, thus, do not violate this law, and this is the same fashion in which quantum entanglement respects it.

But you could send sealed messages all over the world, and just have everyone open theirs at UTC midnight. (Okay, still not a violation, assuming the sealed messages with the information arrive via UPS Air - but fun at geek parties.)

Anyone here ever use Octave? I can’t get the GUI to launch on Ubuntu 16.04 and I’m frustrating myself

If each male of a pair of identical twins has a baby with one woman, would the babies show up as brothers in a DNA test? What if each male has a baby with a different woman but the women are identical twins themselves?

>>9956158
Someone answers

Turbobrainlet here

Can anyone explain entropy to me without using "it's a measure of randomness" shit?

Can I think of it as the likelihood of distribution of energy (wherein an increased distribution of energy is favored)?
Thanks

I started growing some CuSO4 crystals two weeks ago using the method in this video https://www.youtube.com/watch?v=FKCS1DvORug . I prepared a saturated solution and then I placed it into different containers, some in plastic flasks and the rest in glass jars, in which I placed the seed crystals. I left everything unattended until recently. The crystals have grown, including the ones that have formed at the bottom, and most of the water had evaporated, so the CuSO4 had started to form on the walls of the containers. Now my question is, how did the crystals start forming on the outside of the jars as well, while the holes were covered with cardboard? Can the vapors of the solution pass through the cardboard? I noticed only a little CuSO4 on the cardboard and this only happened to the glass jars. Also, why is it easier for crystals to form on glass than on plastic? I noticed that when using a glass jar, the crystals formed much faster, which I guess is why this didn't happen to the plastic flasks.

>>9952775

How to we measure the mass of black holes if the singularity has an infinite density?

>>9952775
I'm having trouble getting this (from Spivak, chpt. 1, problem 19a). I can post problem 18 on request, but it's basically

I understand that it's a quadratic equation of the form [math] ax^2 + bx + c [/math]. Of course, I can factor out a and complete the square, leaving me with [math] a((x + \frac{b}{2a})^2 + (\frac{c}{a} - \frac{b^2}{4a^2])) [/math], where x is \lambda, b is [math] -2(x_1 y_1 + x_2 y_2) [/math].

I have read the wikipedia pages on completing the square, quadratic equations and schwarz inequality and even studied the answer supplied and those I could find on the triple w, but cannot close the gap on this problem just yet. I think I'm supposed to somehow derive the quadratic formula here, but I'm not sure how.

>pic 1/2

>>9959056
anyway, this follows my line of reasoning pretty well

https://www.physicsforums.com/threads/spivaks-calculus-4ed-1-19-schwarz-inequality.585714/

>>9957894
I'm assuming that this is related to Cardano's method for finding the roots of a cubic polynomial.

Any such problem can be easily reduced to the form x^3+p*x+q=0. The next part is to set x=u+v:
=> (u+v)^3 + p*(u+v)+q=0
=> u^3+3u^2*v+3*u*v^2+v^3 + p*(u+v) + q=0
=> u^3+v^3 + 3*u^2*v+3*u*v^2 + p*(u+v) + q=0
=> u^3+v^3 + 3*u*v*(u+v) + p*(u+v) + q=0
=> u^3+v^3 + (3*u*v+p)*(u+v) = -q
Without loss of generality, we can add the constraint 3*u*v=-p
=> u^3+v^3 = -q
Also:
=> u^3*v^3 = -p^3/27

Put U=u^3, V=v^3:
U*V=-p^3/27
U+V=-q
=> V=-q-U
=> U*(-q-U)=-p^3/27
=> U^2+q*U-p^3/27 = 0
Solving the quadratic gives
U = (-q ± sqrt(q^2+4*p^3/27))/2
(by symmetry, V is the other root)
Take cube roots to get u and v, back-substitute into x=u+v.

Minor complications:
1. The above gives 6 solutions (two solutions for the square root and 3 for each cubic), but only 3 of them satisfy 3*u*v=-p.
2. If all 3 roots are real, q^2+4*p^3/27 will be negative and U,V will be complex (they'll be a conjugate pair; their cube roots will form 3 conjugate pairs for which x=u+v will be real).

>>9957817
>I'm a 28 year old boomer
Do people not know what boomers are anymore? Is this a meme?
>the demographic cohort following the Silent Generation and preceding Generation X... demographers and researchers typically use birth years starting from the early- to mid-1940s and ending anywhere from 1960 to 1964.

>>9959056
>>9959065
>https://en.wikipedia.org/wiki/Quadratic_equation#Completing_the_square

ok so I just followed the alogorithm above and I now I'm looking at inequality with lambda being greater than the the quadratic formula. Still not sure how to get t schwarz

>>9958926
Event horizon radius.

Density doesn't increase gravitational reach, in and of itself. A planet the size of Mercury has the same gravity, whether it's packed into the ball of mostly nickel and iron it is, or spread out over an area the size of Jupiter. Similarly a black hole doesn't start with anymore gravity than the core of the star it's made out of. However, as nothing can escape the event horizon or edge there of, it's only going to gain mass after that. (Save the Hawking radiation bit, which isn't really a thing for macro black holes, picking up more background radiation than they lose that way.)

If the Earth or the Sun were to suddenly magically become a black hole, the orbits of the planets wouldn't shift, as the objects involved would have the same mass.

Anyone here works or knows about semiconductors? I have a few questions I'd like to ask.

I'm stuck on this: https://math.stackexchange.com/questions/147515/help-understanding-proof-of-schwarz-inequality

can anyone help? the answers were not sufficient for me. Why is the discriminant 4(x_1 + y_1), shouldn't it be x_1 + x_2, with the discriminant on the whole being b^2 - 4ac? I also don't understand how to show that it (the discriminant) will always be negative.

>>9959233
By no means am I an expert, but the short answer is that you make it so that a single electron can either be liberated from or fall into a valence shell when other electrons are added to a lattice (this either causes a "traveling hole" or a game of electron tag between atoms).

There are n and p type semiconductors that exhibit each respective effect.

>>9959268
My question is: what is the meaning of the Fermi level? I know that it's supposed to be the chemical potential of the electrons in the system, but why is it inside the band gap? I thought no energy states are allowed in that region. So if it isn't an electronic state, then what is it?

>>9959150
>>9959260
>>9959065
>>9959056
nvm I got it

How do I get my divorce attorney to fight for me to get me into Princeton University to divorce some girl that isn't loyal?
I want to go to Princeton. Not Lexington.
Actually, Columbia University would be a better choice.
You see, I would be so happy in a program that is extensive in the fields of mathematics and computer science.
The college I'm in offers like 10 math classes.
It really do be like that sometimes. Entertain me /sci/

UK poster applying for computer science at:

Cambridge
Imperial College London
Warwick
York

Wtf do I put as my 5th?

>>9959337
Nottingham.

>>9959339
I know it's meant to be decent but what about something like Southampton or Durham?

Given a convex quadrilateral of sides [math]a, b, c[/math] and [math]d[/math], is there a general formula for calculating its area? Diagonals' length, and angles are unknown.

>>9959523
Yeah.
Hint: a b sin ga

>>9959523
> Diagonals' length, and angles are unknown.
Then the area is unknown. In general, given the 4 side lengths there are infinitely many quadrilaterals with those lengths, with differing areas.

You need at least one angle or one diagonal length in order to identify a specific quadrilateral for which an area can be calculated.

>>9952775
>yes
>yes
>no
>yes, but the set of "real" numbers is bullshit
>there are more rational numbers. the set referred to as "irrational numbers" is in fact empty.

>>9959600
Thanks, anon.

>>9959605
>yes, but the set of "real" numbers is bullshit
Fuck off, Wildeberg

>>9959605
go to bed wildeberg

i'm unironically a brainlet who somehow managed to get into an european law university and I am starting in a month, how do I fake being smart and finish this? I have issues with my native language grammar because I spent a lot of time speaking english online and I got no idea what cultural trends/figures are in this country or anything related to literature I studied in highschool. Please help

>>9959717
>>>/adv/
literally, unironically just bee yourself
people are pretty nice in general and often will be your friend if you don't show serious insecurities. you'll be that guy who knows a lot of internet pop culture and can speak english really well and is pretty weird but in a cool way, you know?

I remember when I was in college I was terrified of anyone finding out I browsed 4chan and one day I went to some (somewhat weird, but in a cool way) guy's dorm room and he was sitting their browsing /o/ and pumping EDM like the most typical channer as if it was nothing. my normie friends didnt even skip a beat, they became fast friends.

Material and geographical limitations aside, would it be technically possible to slow or speed up the rotation of the planet using thrusters along one or more entire longitudinal line?

>>9959743
Thanks.I don't really care about the other students all I want is to give the teachers a good impression so they don't think I am very dumb because i have grammar issues (it's stuff like the equivalent of you're/your mistake in my language). i've stopped playing all videogames this summer and I will just focus on law and gym hopefully, I kind of look like a primitive man thanks to the steroid cycle i've been on so I dont know how it will be like in a law classroom as I heard most guy are really skinny and small

>>9959116
I wasn't referring to Cardano's method while making that post as there is no cubic term in the equation after all.

It's possible to consider the polynomial as a quadratic in u with coefficients being polynomials in v:
[math] u^2(3v) + u(3v^2 - 24) -24v[/math] has the roots [math] \displaystyle \frac{-3v^2 + 24 \pm \sqrt{9v^4 + 576 - 144v^2 + 288v^2} }{6v} = \frac{-3v^2 + 24 \pm \sqrt{(3v^2 + 24)^2} }{6v} = \frac{-3v^2 + 24 \pm (3v^2 + 24) }{6v}
= -v,\ 8/v[/math].

So [math] u^2(3v) + u(3v^2 - 24) -24v = (u + v)(uv - 8)k [/math]. The value of k can be found to be equal to 3 by equating the coefficients of u^2 on both sides. In this case, the discriminant happened to be a perfect square so the solution was clean but that need not always be the case.

Fellas, I'm wicked perplexed.

I just made myself a glass of RumUp, or 7Rum. Whatever you prefer. I'm not a Nazi about it. But it's a mixture of rum and 7up and it's awfully heavy on the rum. However, I'm noticing a distinct separation of liquids in the glass. about 2/5 of the way up the glass from the bottom there is this line where I can see a separation of the solution.

What gives? Isn't rum just sugary ethyl alcohol, which is completely soluble in water? Or is it only soluble in certain concentrations. Bully me if you will for being a daytime alcoholic ( I work graveyard shift at a menial minimum-wage job six days a week so I feel almost perfectly justified drinking at 9:50 AM PST ), but don't bully me too much about being ignorant in such topics as the one I'm asking about. I failed out of the first semester of high school chemistry because I was busy getting high and driving girls who would never fuck me around in my used V6 car (which was apparently impressive at the time for a 17 year old).

Enlighten me, if you deign it worth doing so, kind /sci/ciopaths.

>pic mostly unrelated

I have what is supposed to be a fairly straightforward exercise in my calculus book, I assume. (This isn't homework, I'm just a neet trying to learn calculus.)

So the problem is to find the value of h that maximizes the angle ß (beta in case the ascii breaks in the post.)
a and b are known, theta and beta unknown. (See pic related)

So I tried to write beta as a function of h so that I could maximize it, but I got an expression in terms of arctan:
theta = arctan(a/h)
beta + theta = arctan( (b+a)/h)

beta = arctan( (b+a)/h) - arctan(a/h)

I guess technically, I could differentiate that, but it looks pretty messy. Furthermore, the book hasn't shown me how to differentiate inverse trig functions yet, so I expect that I'm supposed to find a method that doesn't require taking derivatives of arctan.

I feel like there must be a basic geometric or trigonometric fact that makes the solution elegant, but I can't figure it out. Can you solve this anon?

Proof by definition
limit (1/x) = 1, as x approaches 1

>>9960492
Maximize tan(beta) instead of beta.

I've been making some huge-ass compilatory folders about science stuff, and I'm having some trouble categorizing stuff

I'm interested in software/manufacture methodologies, But I really don't know under what branch of knowledge to place that under

It feels more like tools to other sciences. But even if it were to be that, under which one?

>>9952775
starting CS this year. have a choice between taking my calc 1&2 as infinitesimal calc 1&2 for math majors and discrete mathematics which the math majors take instead of equivalent CS courses

should i increase my workload? no reason for me to do so other than deeper understanding would help me in the future somehow. the alternative would be to take easy CS courses and work on projects in the free time i get

>>9960477
Need to know the proof, density, and saturation of both liquids. But yeah it shouldn't separate

>>9960754
Sorry for wasting your time. I drank all the proof away about 3 glasses ago. But now I know what the purpose of hookers is for. I used to think that my hand would do just fine. But now I'm too drunk to jerk off to completion. If only I had some 3rd world slut to finish me off then I could go to bed and stop drinking.

I understand now. Thank you /sci/.

>>9960526
Thank you for the tip.
I found out that this is actually a version of a well-known problem - https://en.wikipedia.org/wiki/Regiomontanus%27_angle_maximization_problem

>>9958695
Yes. The identical parents would make them full siblings.

>>9958919
I think it grew over the edge. When water evaporates the salt should be left in-solution.

If you want perfect crystals you need a seed crystal, a glass WITHOUT ANY MICROSCOPIC NICKS (like by using a common spoon in the glass) and a place without disturbance. A cool place would give a bonus.

>listen to the podcast
>''So yeah, instead of a great book, we feel like DF is more like a real cheap book. But it's actually a library with ten thousands of really cheap books
>And that's what we are trying to give people''
Wow, what a cool phrase, wonder what the interviewer will say
>Literal 5 seconds silence
>''Can you hear me? I think my connection's keep droping''

What the fuck dude

>>9961144
ah, wrong thread, my bad

Astronomy student here, looking to get a telescope for local viewing for fun. Problem is I don't really know what to look for when getting one. I don't really know a range to budget, but just throw out some tips and recommendations for a beginners telescope.

Also,
>Refractor v. Reflector v. Cassegrain
From what I've seen via youtube, I've been leaning towards a Cassegrain, but please let me know how you feel about the various other designs also.

Also, as I assume light pollution will play a role into what I can see, and what'll be worth getting, the light pollution where I live is ~21 (a little over 6.2x10^-4 cd/m^2 according to lightpollutionmap (dot) info

>>9959600
Different guy here.
>Would it help if the order the sites are tied together is fixed?
Gut feeling says yes.
>Or if I wanted the maximum area (or the minimum convex area)?
This should be doable too.
In case a > b > c > d we'd have 4! permutations of the order at max, not considering identical permutations because the ends are tied. The mirrored permutations are basically the same, so they have to go too. Hmm.

>abcd abdc acbd acdb adbc adcb bacd badc bcad bcda bdac bdca cabd cadb cbad cbda cdab cdba dabc dacb dbac dbca dcab dcba
>abcd abdc acbd acdb adbc adcb (without mirror/rotation-twins)

Though not being a kind of rectangle would lock it into place. Wouldn't it?

https://en.wikipedia.org/wiki/Quadrilateral#Bimedians
https://en.wikipedia.org/wiki/Varignon%27s_theorem
>If the quadrilateral is convex or concave (that is, not self-intersecting), then the area of the Varignon parallelogram is half the area of the quadrilateral.

So the maximum area would be the case where the height of the Varignon parallelogram is the biggest. Since we know the distance between neighboring midpoints there are triangles on the corners with three known sides. If the lengths of all three sides of any triangle are known the three angles can be calculated. (This is probably overly complicated to get the area.)

Without the side-permutations the max area is pretty much clear (only a parallelogram can be distorted when the side lengths are fixed).

>>9959757
Definitely*

>>9960803
Alcoholic solutions may contain several distinct liquid phases dependent on solutes, temperature, and pressure [1297] with greater segregation at higher pressures [2769] and, in the case of glycerol, at lower temperatures [2770]. In contrast, simulations indicate that water molecules form long chains in very cold ethanolic solutions with lower segregation [3087].

>>9952775
CScum here.

Learning math & physics at 26 because I just realized that if you want to do cool shit with programming you need to know some deeper sciences?

Is this a valid answer?

How might I go about proving this? Can't seem to find a good starting point - tips/tricks/hints appreciated

>>9952775
What about if all matter in the universe is expanding relative to empty space as time moves forward. That way as objects get bigger the distance between them gets smaller ,but since we as the observer are expanding at the same rate we perceive it as objects getting closer, aka gravity. Just a thought I had at work, I'm not that well versed in physics.

>>9961585
No. There are a couple holes in this as stated that I would deduct marks for if I was grading it.
First off if the entire crux of your argument is the comparison test, you should actually _do_ the comparison instead of just claiming an >= bn with no argument as to why. This is maybe a 1 point nitpick.

The bigger problem is that your claim that an >= bn implies an is unbounded is false without more conditions. For example, the bounded sequence 0,0,0... is strictly greater than the unbounded sequence -1,-2,-3...

>>9962042

What is the source on this problem? It looks like a Putnam problem?

>>9962042
If you integrate x over those ranges, you get 4. And the expression is always <= x (the denominator is always >= 1).

>>9962110
Was I on the right track at least?

what are the two bottom boxes asking for exactly?

>>9962373
I am baffled.
How are you presumable studying functions if you have no prior knowledge of algebra

>>9962383
fuck off mate. This question was thrown in with partial derivatives and I thought that I was supposed to do the same here. I got the answer. I also tried to delete my post after posting but it didnt for some reason

>>9962233
Sure. The idea is fine, you just need to patch it up a bit by writing some more details.

>>9962080
But... We observe just about everything getting further away, so...

How to pursue a career in reseach when graduating from engi with a 2.8 GPA ?

Is there any simple methods to understanding what sorts of equations make these sorts of graphs in 3 space?

>>9953137

PDEs is basically all of those courses rolled up into one, so PDEs.

> If x = 0, attribute values to y and z:
> y^2/9 - z^2/16 = 1
How the fuck do I solve this?

>>9962865
> y^2/9 - z^2/16 = 1
=> (y/3)^2-(z/4)^2 = 1
Which is a hyperbola with a 3:4 aspect ratio.
> If x = 0, attribute values to y and z
Where does x come into this?

>>9962594
Straight lines have the form a*x+b*y=c. Evenly-spaced values of c will produce evenly spaced lines. Unevenly-spaced values of c will produce unevenly spaced lines.

Circles centred on the origin have the form x^2+y^2=r^2 (alternatively, divide through by r for (x/r)^2+(y/r)^2=1). Evenly-spaced values of r will produce evenly spaced circles. Unevenly-spaced values of r will produce unevenly spaced circles.

Ellipses centred on the origin have the form (x/a)^2+(y/b)^2=1 (they're just distorted circles, where the width and height are 2a and 2b).

A hyperbola has the form (x/a)^2-(y/b)^2=1. Put u=a/b => b=a/u to get (x/a)^2-(y/(a/u))^2=1 => (x/a)^2-u^2(y/a)^2=1. Multiply by a^2 => x^2-u^2*y^2=a^2. Different values of a give different hyperbolas; a=0 gives x^2-u^2*y^2=0 => x^2=u^2*y^2 => x^2/y^2 = u^2 => x/y=±u, which is a pair of straight lines intersecting at the origin.

Is getting a degree in CS (is called Computing Engineering here) worth it or it is a meme?

>>9963066
Computer Science and Computer Engineering are not the same thing.
CS is more flexible than a CE degree, but there is a rather large demand for CE type jobs. This might change in the future since there are plenty who are jumping on the CE bandwagon

>>9959315
The wikipedia article does a fine job of describing the answer to your question. I can't improve upon it, so here it is

>In band structure theory, used in solid state physics to analyze the energy levels in a solid, the Fermi level can be considered to be a hypothetical energy level of an electron, such that at thermodynamic equilibrium this energy level would have a 50% probability of being occupied at any given time. The position of the Fermi level with the relation to the band energy levels is a crucial factor in determining electrical properties. The Fermi level does not necessarily correspond to an actual energy level (in an insulator the Fermi level lies in the band gap), nor does it require the existence of a band structure. Nonetheless, the Fermi level is a precisely defined thermodynamic quantity, and differences in Fermi level can be measured simply with a voltmeter.

>>9952775
Do electrons really have a negative change or is it just a word used to show that they are opposite relative to protons?

>>9963081
Okay, thanks.

Which are the recommended books about linear algebra?

>>9963092
https://4chan-science.wikia.com/wiki/Mathematics#Linear_Algebra

>>9963105
Oh shit sorry, I checked the guide on the sticky but I forgot about the wikia.

>>9962594
it is relatively simple to get the equations by just plotting them in an xy plane and looking at the relations you get by the definitions. more care is needed if you want them in standard form however.

For example, the definition of an ellipse is as the locus of points whose distance from two foci is constant, d.

now plot in the xy plane some random ellipse, and to make it easier for you, put the foci at (f,0) and (-f,0), so that the ellipse's major axis lies on the x=0 line.

At any point in the ellipse, draw two lines from the foci to the point. Now you want to use pythagoras twice to calculate the distance from this random point to each foci.

The distance from the negative foci is sqrt(y^2+(x+f)^2) and from the positive is sqrt(y^2 + (x-f)^2), and it is easy to check this (notice that the squaring operation makes this very much easier!).

now their sum has to be d. Hence you get that the equation of the ellipse with foci (f,0), (-f,0) is defined by [eqn]\sqrt{y^2+(x+f)^2}+\sqrt{y^2+(x-f)^2}=d[/eqn]
Since the foci are fixed, then concentric ellipses will be defined by the same equation with differing d, so in a way, d is the parameter that creates new concentric ellipses

>>9963085
it's arbitrary up to sign, but the two species of charge are of opposite sign

Yo, could we build a series of dams accross the bering strait to control the flow of the Pacific into the Atlantic?
a) stopping Ivan and gook submarines
b) saving the Arctic ice caps
c) allowing us to influence global temperatures

>>9963162
51 mile long dam, maybe 50 meters tall... I think we'd need Ivan's cooperation for that, possibly among others. Not that he can get through there most of the year, hence Crimea.

Not sure about how much one could tweak global temperatures that way - possible - though the real game changer is going to be the cascades around Denmark.

>>9952775
Is there a form of math that makes Pi rational?I don't think this works but i'm thinking of something like a postional numeral system of "base pi", but i'm not sure if that would even technically make it rational.

I don't have a stem degree so i figured I'd post here and see if anyone smart has an answer

>>9963269
No because it still isn't the ratio of two integers.

So let's say I have a 2D parametric curve in terms of t, then make a function of arc length and relate it to the change in angle, so I have a map from arc length to derivative of angle. What would this be called? Is this a legitimate technique? I did this a while ago so I could get a robot to follow a path using just distance traveled and heading data as feedback and I just want to know how to formalize it.

>>9963297
that's actually kind of aggrivating, there's nothing at all you can do to "rationalize" an irrational number like Pi? not even with a positional numeral system? (also do you have any lectures or something about "it still isn't the ratio of two integers"? i'd be actually very thankful.

>>9963393
>that's actually kind of aggrivating, there's nothing at all you can do to "rationalize" an irrational number like Pi?
Define a new set of integers which include two integers whose ratio is pi.

>>9963368
https://en.wikipedia.org/wiki/Tangential_angle

>>9954401
You can do the same with rational numbers though

>>9963421
why not 1Pi and 2Pi etc?

sorry not the most mathematically inclined here, why exactly can't 1pi-10pi just be considered integers?

>>9963368
is that not just a particular instance of a Legendre transformation?

>>9963456
what do you think an integer is exactly?

>>9963462
a whole number that's positive right? I mean don't get me wrong, i know i'm probably not right in this line of thinking, otherwise it would probably be Popsci/math. I just want to be shown why exactly i'm wrong. why can't 1pi-10pi be integers in their own number system?

Please keep in mind, i want to be proven wrong, I just don't see why with my own education

>>9954897
>>>/pol/

are quantum mechanics real?

>>9963547
how can they be if our eyes aren't real?

>>9963547
lol nah

Having a tough time coming up with a proof and example for what should be a fairly simplex complex integration problem.

I have to prove for a piecewise simple smooth curve thats not necessarily closed that:
[math]\int_{c} zdz=0 \Rightarrow \int_{c} z^3dz=0[/math]

and find a curve st
[math]\int_{c} zdz=1[/math] and [math]\int_{c} z^3dz=0[/math]

>>9963651
I should mention I got stuck trying this: with a,b endpoint and startpoint we have:
a^2/2-b^2/2=0 and a^4/4-b^4/4=0 but (a^2/2-b^2/2)^2=0 doesnt seem to get you anywhere.

So apparently excess sugar consumption doesn't directly cause diabetes? I feel like that's bullshit. Wouldn't a person who drinks 5 cans of coke per day have higher insulin resistance to someone who didn't?

What is the dimensionality of span(0)?

>>9954859
Bump too senpai

>>9952775
>>9953336
Yes, there are roughly twice as many integers as there are even integers
Yes,for each prime integer there is at least more than one other non prime integer. More specifically, every even integer excluding 2 is non-prime by definition and the only way for there to be as many primes as even integers is for all odd integers to be prime, which is not the case
Yes, every integer is the result of an infinite amount of rational number's ceiling and floor function. Moreover, there exists an infinite amount of p and q integers for which p/q = Z
Yes, every rational number is real, but not all real numbers are rational
For each rational number, there exists an infinite amount of irrational numbers.

I always feel like I'm being trolled when I read this shit off /sci/

>>9963909
Actually since for each rational number r there are infinitely many integers p,q with p/q = r, this proves that there must be more integers than rationals.

>>9963913
for each p there are infinite q in N\{0}, and for each q there are infinite p in N that make a rational number
since all integers are rational numbers but not all rational numbers are integers, there exists infinite p and q that make integers, and there exists infinite p and q that make non-integers. so for each integer N there exist infinite r not in Z for which floor(r) = N or ceiling(r) = N

>>9963659
a^4 - b^4 = (a^2 - b^2)(a^2 + b^2). What's the problem?

>>9962080
A problem with this is that it doesn't account for things accelerating due to gravity if everything is expanding at a constant rate

>>9963269
>>9963484
You could make up a new set of numbers containing 1pi-10pi etc. but they wouldn't have the same properties as integers.

One property of integers is that they have an identity element for multiplication (which is 1, because x*1 = x), so unless you're redefining what multiplication and addition mean, 1 needs to be in your new number system.
Because the integers are closed under addition (integer + integer = another integer), you'd need pi+1 and 1+1 and all the other integers in there, plus any multiple of pi plus any integer, eg 3*pi-9.

At this point, this new set doesn't look very much like the integers at all.
If I wanted to find a number in this set between 0.42 and 0.43, say, I could found one by noticing that 3*pi-9 is between them and in the set. You can hopefully see that you could use a similar method to find a number in this set between any two other numbers, which is definitely not something we can do with the integers. Overall, there's no real benefit to this over just saying things are multiples of pi like we already do.

As an aside,
>a whole number that's positive right?
they can also be negative or zero, all whole numbers are integers (natural numbers are the ones that can only be positive).

>>9963897
>What is the dimensionality of span(0)?
What have you tried?

>>9963914
>N\{0}
What did he/she mean by this?

>>9963929
Oh thanks Im dumb. Any idea about the second part?

>>9964046
Actually nevermind. Endpoint is 1 startpoint is i.

>>9963987
She meant to say [math] \mathbb{Z}^+[/math]

>>9963981
I first thought that basis is {0} and dim=1, but if we define a sum of all elements in an empty set as 0, then basis is {} and dim=0 as it is usually defined.

>>9963968
Thanks that answers my question pretty well lol

how can i estimate a rate of dessication??
say I place a glass of water on a pile of salt and seal the two in a plastic bag
How much water will be absorbed by the salt over how long a timeframe, assuming STP and 100ml/100g
any relevent equations i should look for?

>>9954905
This is correct

It is like no one in this thread has done Analysis before

>>9963269
Pi is not rational because it is not the ratio of two integers. That is literally the definition of rational. Creating some new concept of rationalness is not going to change anything about the fact that pi cannot be written as a rational number. However, it is well known that any real can be approximated arbitrarily well by sequences of rational numbers. The best approximations (in terms of how close the fraction is to pi with the amount of digits of the integers) are called convergents of continued fractions. look it up

Dudes I need advice.
The Bailey–Borwein–Plouffe formula allows you to calculate the nth digit of pi in base 16.

The nth digit of pi in base 16 is 4/(8n+1) - 2/(8n+4) - 1/(8n+5) - 1/(8n+6)

So clearly, if we take the limit of this expression as n tends to infinity, we'll get the last digit of pi.

Then comes the tricky part:

Calculating the limit of this expression isn't that easy. I had to resort to using Wolfram|Alpha, which isn't real math, but I couldn't find any other way. Apparently, the limit is 0. I don't know how they came to that result, and that's really the only thing preventing me from publishing this discovery.

So there you have it. The last digit of pi is 0, but I don't know why...

WHAT IS TORQUE!?!?!??!?

>>9954594
because the atmosphere has a mass, so its affected by gravity, the rest is just friction

>>9964472
Nothing much, what’s torque with you?

1. No since they have the same (aleph0) cardinality
2. No since they have the same (aleph0) cardinality
3. No since they have the same (aleph0) cardinality
4. Yes since 2^aleph0 > aleph0
5. There are more irrational numbers since 2^aleph0 > aleph0

What is the German word used in the math world which means something like "to be able to work on a problem for long periods of time at a desk"?

>>9964532
lost

>>9964532
I know it but I can't speak it and it sucks.

>>9964444
>The nth digit of pi in base 16 is 4/(8n+1) - 2/(8n+4) - 1/(8n+5) - 1/(8n+6)
nope the BBP formula can be used to find the nth hex digit of pi but not in the pretty form, you have to manipulate it into a rather dirty formula as follows
[eqn] 16 \cdot \textrm{frac} \left ( 4\Sigma_1-2 \Sigma_4 - \Sigma_5 - \Sigma_6 \right ) \\
\Sigma_j = \sum^{n}_{k=0}{\frac{16^{n-k} ~\textrm{mod}~(8k+j)}{8k+j}} + \sum^{\infty}_{k=n+1}{\frac{16^{n-k}}{8k+j}} \\

\textrm{frac}(x) = \left\{\begin{matrix}
x-\left \lfloor x \right \rfloor & \quad x\geq 0 \\
x+ \left \lceil x \right \rceil & \quad x< 0
\end{matrix}\right. [/eqn]

>So clearly, if we take the limit of this expression as n tends to infinity, we'll get the last digit of pi.
I would not say that this is clear at all, a last digit doesn't even make any sense for a number with a non terminating decimal expansion such as pi, for a number such as 1.0000... we can say that if there was a last digit, then it certainly must be 0, but what of [math] \frac{10}{99} [/math] = 0.1010101... how could we possibly attribute a last digit to that? the very concept of a last digit implies that there is a greatest integer which is easily shown to be false

Uhhhh what the FUCK is a projection. Like where does a projection vector live and why does it help you find solutions I do not understand.

>>9965087
The projection of a vector v on a subspace W is a vector v' in W with the property that v - v' is orthogonal to every vector in W

>>9965087
a projection of a vector v onto a vector w is basically telling you how "w" does "v" have.