/sci/ - Science & Math

>>10634836
>Does stacking several corpses in a single crematorium increase the rate at which corpses are being incinerated?
Why don't you try it and find out?

>>10634909
I found a nice paper but it later turned out that the results were faked for a profit

>>10629355
>muh black hole

Why is it that if any boolean function over n inputs could be computed using a circuit of size polynomial in n, that P = NP?

This is in my lecturer's notes, but I don't understand how taking the fourier transform of the constant c, gives c \hat y. I get the first two terms. However, shouldn't the fourier transform of c be 0? If you plug that in as f(x) in the fourier transform formula I'm pretty sure that's what you get.

>>10635430
he probably meant to write cy, not c. otherwise this problem is much easier.

Can someone explain how complex numbers are 2d to me. I get the nongraphing part of it, but I want to see how this looks in graph. For example the following simple equations.
[eqn]\sqrt{4}×\sqrt{4}=\neg{4}[/eqn]
[eqn](\sqrt{4})^2={4}[/eqn]

Does [math]det(A) = det(B)[/math] imply [math]det(A + C) = det(B + C)[/math]?

>>10635498
Nope. Set A=C=
(1 0)
|0 0|
B=
(0 0)
|0 1|
>>10635492
Because when we add a root of -1 we can write every complex number as a combination of a real number and a real number times the root.

why the FUCK do people drink so much soda and juice and not water?
the majority of sodas taste like fucking shit and juice is less refreshing than water
my mom is literally fucking dying and she continues to drink about 2 litres of coke per day and when I ask her why she doesnt drink water she says "why should she"
what the fuck is wrong with these people? do they have different taste buds than me?

how much time should i spend self studying per week? or should i focus more on a certain number of lessons instead of hours?
plan to self study optics by hecht, some laser textbook, and french this summer and need a good schedule

>>10635526
>Because when we add a root of -1 we can write every complex number as a combination of a real number and a real number times the root.
I get that. But how does it look in a graph?

>>10636198
We put the real number that's alone as the horizontal axis, and the real number multiplying the root of one on the imaginary axis.
>>10636159
How the fuck should I know how long you should study? If you feel like you're not making sufficient progress, study more. If you feel like you're making too much, study less.

>>10636204
*vertical axis, not imaginary.

>>10635981
>do they have different taste buds than me?
babies finally realizing people are different from him

Is there an online blackboard or any similar software that can be used as an online blackboard? I want to teach my friend some math through the internet, and such a tool would vastly help me in this endeavor.

Bump.
>>10636691
https://awwapp.com/

[eqn]a_np^n=-a_{n-1}p^{n-1}q-\dots-a_1pq^{n-1}-a_0q^n[/eqn]
Why is [math]p[/math] multiple of the left-hand side and [math]q[/math] of the right-hand side?

>>10637848
Sorry, why the left-hand side is an integer multiple of [math]p[/math] and right-hand side is an integer multiple of [math]q[/math]?

>>10637848
>>10637855
someone?

>>10634898
So let's say I know some NET after-tax salaries of my country... I have a set of them.

A = 2726 = top 8% of earners.
B = 1957 = top 16% of earners.
C = 1286 = top 54% of earners.

How would I figure out something like D =? = top 25% of earners.

>Second question:
It happens that I know the median value for all incomes but out of fear of it being wrong as it comes from another source I put it in the question 2

>which starts here: Given you know the exact value of the median number 50% - how do you determine then let's say 33.33% value?

If I had the basic math vocabulary I would be able to google this, but it's painfully hard to find out what I actually mean... I hope a human understands me and helps me out.

>I desperately need a book to familiarized with math terms and commonly asked questions or problems.

>>10638151
>>10637855
>>10637848
because that's what polynomials are. I don't think I understand your question. the pattern is
[eqn]\sum_{i=0}^na_ip^iq^{n-i}=0[/eqn]

>>10637848
>>10637855

because that's what polynomials are. I don't think I understand your question. the pattern is [math]\sum_{i=0}^na_ip^iq^{n-i}=0[/math]

>>10634898
Can someone explain the Legendre Transformation simply to me and how it relates to the Hamiltonian? I’m just lost. I don’t see how we get the same information from the Lagrangian

>>10638184
>>10638191
why is my tex not working? that's my stupid question

>>10638195
i see it working just fine, do you just see an issue with your own posts or is it not working in the whole thread?

>>10638316
wtf? all the tex in this thread is working except for the two posts I made. you can see them?

>>10638322
yes it's working normally, it's something on your end, are you on desktop? with an extension?

Could somebody point me to a formal proof of the concept that if we have a tree with [math]\ge 2[/math] vertices and the degree of the first vertex is [math]n[/math] and the degree of the second vertex is [math]m[/math], the tree has [math]\ge n + m - 2[/math] leaves? It's easy to see why it has to be true when looking at graphical representation like the picture related and using the conditions that a tree has to be a connected graph and cannot contain cycles. However, I feel like my current approach is too simplistic and would like to see a more thought out version. I tried Googling, but didn't really find anything relevant.

Is every hyperplane an affine hull?
Is every affine hull a hyperplane?

>>10638357
The number of leaves attached to the first vertex is n-1, the number attached to the second is larger or equal to m-1.
The result immediately follows.

>>10638401
you meant to respond to >>10638337

>>10638357
affine hulls are defined with respect to a set S
any hyperplane can be the affine hull of a certain S in a euclidean space, sure
not necessarily, an affine hull can be any affine set in the euclidean space [math] \mathbb{R^n}[/math], it's not restricted to just hyperplanes. it can be a singleton or a line or in general have any dimension other than n-1

>>10638184
Ok, I'll rephrase it. What does it mean for something to be multiplicative of something? Please explain using that equality I provided.

>>10635981
water tastes good only when ice-cold.
cold tap isn't cold enough, you need to cool it in the refrigerator for a few hours, or add ice cubes so that the glass has more ice than water.

>>10638337
What do you mean by first and second vertex?
In your picture, what is the first vertex and what is the second vertex?

>>10638195
doesn't work with me either,
protip: always add a space before backslash
[eqn] \sum_{i=0}^na_ip^iq^{n-i}=0[/eqn]

>>10638470
>not necessarily, an affine hull can be any affine set in the euclidean space Rn
>\mathbb{R^n}, it's not restricted to just hyperplanes. it can be a singleton or a line or in general have any dimension other than n-1
that's only when the vectors in set S are linearly dependent, right? what if we add the restriction that they are linearly independent?

>>10638495
do you not keep a pitcher of water in the fridge?

>>10638625
not really, affine hulls aren't necessarily linear, they are affine (which means linear + a translation, so for example a line or a plane in the space that don't go through the origin)
in [math] \mathbb{R^{3}}[/math], a set S formed by the two linearly dependent vectors (0,0,1) and (1,0,0) will just have the affine hull formed by the line that goes through both points, and it's still not a hyperplane
at the same time, if you have the set S defined by (0,0,1), (0,0,2) and (1,0,0), S isn't linearly dependent, but its affine hull is a plane (the xz-plane) in [math] \mathbb{R^{3}} [/math] (which is obviously a hyperplane in that space), and it is even linear

>>10638337
The number of leaf nodes is the total number of nodes minus the number of non-leaf nodes (this is just rearranging total=leaf+non_leaf).

The total number of nodes is the sum of the degrees of all of the nodes plus one (the root node doesn't have a parent so it isn't counted in the sum of degrees). The sum of degrees is just the number of edges.

> a tree has to be a connected graph and cannot contain cycles.
Which means that the number of edges is one less than the number of nodes. Every node which isn't the root has exactly one parent, every edge connects a node to its parent. So there's a one-to-one correspondence between edges and non-root nodes, and exactly one root node.

>>10638657
so that's interesting. if all 3 vectors were linearly independent, you'd still only have a plane. if all 3 were linearly dependent you'd have only a line. it seems like the 3rd vector, the one which may either be linearly independent, or linearly dependent, isn't actually doing anything (we get a plane either way). how does this relationship generalize into higher dimensions?

>>10638699
Two linearly-independent vectors give you a line, three give you a plane, four a volume.

Because it's affine rather than linear, you "lose" one of the vectors to define the translation. Each vector defines a point. 3 points give you a triangle. If it's not degenerate, then the triangle lies in a specific plane. If the three points are colinear, the triangle is degenerate and you have a line rather than a plane.

If it was linear rather than affine, you get an extra point (the origin) thrown in for free, so you'd need one less vector.

>>10638699
when we talk about linarity (linear spaces, linear maps, linear dependency), it is always assumed that the origin is part of the set we are working with. a plane or a line is linear if it contains the origin, if a map is linear then f(0)=0 (so (0,0) is a point defined by it), and so on.
linear dependency is basically the same. grab two linearly dependent vectors, and we usually say that they are multiples of one another by a scalar factor. but what this actually means is that we are comparing THREE vectors, the two vectors you are starting with and the origin. a line is usually defined by two points, but if by adding a third one we still get a single line then that's where the linear dependency comes from. it's because the origin and the first vector already form a single line, so the second one being a multiple of the first one just means it's in the same line, and therefore it's superfluous

for affine objects, we no longer get to consider the origin implicitly. so two points define a single line (as it should be normally), and even if they are multiples by a scalar factor, the fact that the origin is not considered means that there's no problem, there's no "superfluous" vector. when you have a single point in space, it's not enough to define a line, since there are infinitely many lines that go through it.

something you can do if this causes confusion is consider one of your vectors as a new "origin", as a frame of reference. so if you have one additional vector (even if it's a "multiple" with respect to 0), it will still only define a single line. now, if your third vector is still in the same line, now you have a superfluous vector, and then the same phenomenon as linear dependency happens. if the third vector isn't in that line then you get two "affinely" dependant vectors with respect to your new frame of reference, so that defines a plane like how it would if you had two linearly independent vectors and the origin

I want to know why the fuck the -6 changes to positive +12. This is te most retarded question in this thread for sure.

>>10638743
thanks that makes sense

>>10638748
what is the context?
what does that colon mean?

>>10638699
>how does this relationship generalize into higher dimensions?
the last paragraph in >>10638743 should give you an idea, the third point that you think isn't doing anything may actually be seen as the new frame of reference, or as a substitute for the origin. by considering that, you can analyse the dependency of the other remaining vectors with respect to that new frame of reference, which should tell you the dimension of the space you are going to obtain by finding it's affine hull

as a sort of loose equivalence for the sake of clearness, you can think of the affine hull as the linear subspace generated by every but one of the vectors in S, if the origin was the last remaining vector in S instead of 0

>>10638770
This is the full exercise

>>10638748
the - before [math] \frac{x-6}{3} [/math] affects both the x and the -6, not just the x

>>10638776
thanks anon

>>10638748
>>10638773
oh I see, I got confused by that r, but I guess that isn't part of the exercise

[math] \frac{x}{2} - \frac{x-6}{3} + 8 = \frac{3x}{6} - \frac{2x-12}{6} + 8 = \frac{x+12}{6} + 8 [/math]

Anyone know a resource i can routinely use to learn the purpose of different ingredients in a buffer sol’n?
E.g. sm buffer has Tris, MgSO4, NaCl, and gelatin
If i google i understand that tris is for buffering, gelatin is for stabilizing phage, but NaCl and MgSO4 are not explained. Is there a reason im just expected to know, why these are commonly in buffer solutions?

My prof like to quiz minutae like that so i figured it’d be easier to learn this stuff if i understand it instead of memorizing

The function f(x)= 2x^2 + 4e^5x has an inverse function f^-1(x). Find the slope of the normal line to the graph of the inverse function at x=f(0).

I've gotten every other problem on the review but this is killing me for some reason.

>>10638815
-20

Should I get a graphical calculator or Maple is a way better use of the budget?

I could porbably get by without understanding this, but can someone explain how water being both an acid and a base works?
I understand the H3O+/H2O and H2O/HO- part of it, but physically how do these molecules coexist, does water just cycle like so:
(H3O+) + (OH-) -> 2H2O
H2O -> (H+) + (HO-)
(H+) + H2O -> (H3O+)
then again the cycle starts
(H3O+) + (OH-) -> 2H2O
??

How do I rewrite the function

f(x) = {0, x <= 0; x, x>0}

in a single function?

>>10639111
f(x) = max(0,x)

>>10639111
>>10639118
or f(x) = x + abs(x)

>>10639111
or f(x) = (x + abs(x))/2

>>10639005
Yes, just that. Both reactions (separation into base/acid and recombination) in equilibrium.

>>10639118
>>10639127
Oh, thank you.

>>10639127
>rewriting a piecewise function using another piecewise function

>>10639164
ok how about this:
f(x) = (x + sqrt(x^2))/2

>>10634898
Stupid question: if I have a metal, with melting point of 1300°C, in a fire of ~600°C, would it eventually melt?

guess I'll shoot my shot even though it's hardly relevant here:
anyone know of any databases for raw magnetic resonance spectroscopy data? I can't find anything and I'd like to fuck around with a dataset in matlab

The forcing term is making me shit my pants. I don't know what to do when my seperated equations aren't in sturm-louville form

>>10639128
ty

Can somebody tell me what a power engineer does exactly? Like do they build generators or do something else?

I'm going back to math after not having done it in any real capacity for over 15 years. How long will it take for me to get up to calculus if I devote like an hour or two a day doing math?

>>10639867
What's the last math you did? What do you remember?

Are math professors experts at deciphering first order logic. If I showed a theorem with several nesting of different quantifiers and predicates, would they find some intuition just by looking at it.

>>10639871
Probably remember only algebra and algebra 2 stuff. The last math I took was some bullshit college algebra in 2003(?).

>>10639177
sqrt(x^2) is just a convoluted way of writing abs(x).

For the degradation of the antibiotic clindamycin, which is held at pH 4.0 in an
aqueous solution, kinetic measurements show that at 343 K the reaction is firstorder
with a rate constant equal to 2.49 x s-]. Over the temperature range
320 K to 360 K, the activation energy was found to be 123.3 kJ mol-l. Calculate
the rate constant at 295 K. Since the degradation reaction is first-order, it turns
out that the time taken for 1% decomposition turns out to be close to 0.0llk~
and this time is independent of the initial concentration of the antibiotic. Hence,
is it possible to conclude that if the compound were to be stored at 295 K, it
would remain safe for use at the end of an economically acceptable shelf-life?


How do i do the last part if not given the activation energy for that time?

>>10639901
no
dont be an ass and decipher it yourself

>>10634836
Depends on the corpse.
Until the corpses start blocking the cremation process of the other corpses, it'll just go faster.

I'm planning on taking Calculus 2 over the summer but the catch is that my college decided to use the new calculus 2 class which is essentially the entirety of Calculus 2 + Three Dimensional Coordinate Systems, Vectors, Dot Product, Cross Product, Lines and Planes in Space, Cylinders and Quadric Surfaces, Functions of Several Variables, Limits and Continuity in Higher Dimensions, Partial Derivatives, and The Chain Rule.
Is it possible to do all of this in SEVEN weeks and get an A?

Why is math not considered to be a science?

I'm referencing this:
https://math.stackexchange.com/questions/566475/what-is-int-01-fracx7-1-logx-mathrm-dx/566481

Why are people just jamming lnx into the denominator here as if it's equivalent to 1/logx? No one says anything about it, and they're not substituting anything. Also, none of these explanations make any sense to me really.

>>10640984
log(x) and ln(x) are the same thing

>>10640991
How is it the same, the bases are different

Serious question, assuming that I hardcore 9am-5pm and then 8pm-12am study for 3 months, can I plausibly clear calc 2 and calc 3? I'm planning to be ahead of my calc classes over the summer so that I can focus on other classes, is this plausible or am i just being retarded and should just focus on calc 2 only and not calc 3

>>10640957
I'm sure some people could discuss about that for hours, so I'll try to make it brief. Science is considered as the studies of the phenomena and laws that govern nature, the universe, and so on. Basically, we want to describe and understand as accurately as possible the things that are present in our universe.
Math doesn't do that, math is basically an extension of logic, albeit and very rich one. It turns out its tools are very useful as a language to describe these natural phenomena science is concerned with, but pure math doesn't actively try to describe or understand nature, it's just developed independently of what happens in the actual world. Axioms, for example, are not natural laws, they are the framework we decided make the most sense for our goal of pushing our work as far as possible without falling in logical contradictions. In math we get to create and define the tools we need to make progress, while in other sciences we can only work with what we can observe and test with the scientific method.

In the end the line between both is kinda blurry, but this is the basic gist of it.

>>10640995
No I think they both have base [math] e [/math]?
If the log has a different base, such as 10, it should really be specified as [math] \log_{10}x [/math]

>>10641012
The natural log has base e, and logx, without being specified, is always to the base 10.

>>10641009
makes sense, thanks

>>10641023
>logx, without being specified, is always to the base 10.
no, not really

https://math.stackexchange.com/questions/293783/when-log-is-written-without-a-base-is-the-equation-normally-referring-to-log-ba

>>10641026
What sort of retard thought it was a good idea to have different conventions for log bases throughout the disciplines. Every other time I've taken anything it has always been base ten.
Thanks mate, that was driving me crazy.

Can someone explain Leibniz Rule to a brainlet?

>>10641073
Write it down and take the integrals, it will make sense instantly

>>10641097
Oh I was thinking of other thing, nevermind. With that said, it's due to the fact that sum is commutative. Replace the integral with an infinitesimal sum. It's just the statement that the derivative of the sum is the sum of derivatives

>>10641128

i could/should have posted this here

>>10641142
What are you even asking? Is it ok to think about yourself when you masturbate?

>>10641103
Oh okay, cool.
I do understand the last part, but I will have to learn how to do it from YouTube or something similar. Thanks anon!

>>10641073
Look at the Taylor expansion. A function can be written as
[math]f(x+h) = f(x) + f'(x)h + \tfrac{f''(x)}{2}h^2 + \dots[/math]
where the dots stand for higher order terms (i.e. terms involving higher powers of h). Conversely if you obtain an expression for your function like
[math]f(x+h) = f(x) + Ah + \dots[/math]
then it must be true that [math]A = f'(x)[/math].
So you just write
[math]
f(x+h) = f(x) + f'(x)h + \dots [/math]
[math]g(x+h) = g(x) + g'(x)h + \dots [/math]
and multiply both sides together, you get
[math](fg)(x+h) = f(x)g(x) + [f(x)g'(x) + g(x)f'(x)]h + \dots[/math]
where the dots again stand for higher powers of h. So it must be true that [math](fg)'(x) = f(x)g'(x) + g(x)f'(x).[/math]

>>10641180
i'm looking for perspective so i don't take it for granted

>>10641288
It should be obvious that you're really fucking lucky.

Let x be a real number such that x^2 and x^3 are both integers. Any hint on showing x must be an integer as well?

>be me
>math/CS double major, just finished first year
>had fantastic GPA in first semester but barely pulled through in second due to rushing a fraternity plus getting sick numerous times
>all my routines, schedules, positive habits were thrown down the shitter, ending year with 3.4
>C in computer systems course (basically a senior class at my uni, no less)

How fucked am I for study abroad/grad school apps?

Electric field is different for each dielectric, right?
Because Capacitance = Q/(Ed) = (eA/D)
where e is the electric permittivity.

is water wet?

>>10642127
define wet

>>10642127
is fire on fire?

>>10642127
yes

i feel like i'm becoming stupid, how can i start retaining what i learn?
i read books, watch lectures but nothing sticks
finding good courses on memrise/quizlet/anki seems impossible, there are so many mistakes and i hate it when it tells me i'm wrong when it's not my fault
how do you guys learn?

>>10642659
>how do you guys learn?
By application. Use new skills early and often, that'll help.

>>10634898
Theoretical question, if you were to build a steel (or any durable strong material) sphere with a cavity in the middle that was filled with water completely (no air in the cavity), and proceed to heat up the sphere so that the water would boil in the middle, once the water would start boiling would the sphere explode? would the pressure build up and explode the sphere? thanks

Can someone explain the differences between diffusion and dispersion in fluid dynamic to me, this stupid ESL?

at what point is one finished learning algebra?

Can someone link me to a braindead guide to FIRST and FOLLOW sets, and ideally an LL(1) transition table construction?
I have no fucking clue how FOLLOWs are meant to work as I get all of the examples partially wrong.

Does this residuals plot show heteroscedasticity? It looks a bit like it but maybe it looks too little like it. (the slope of the linear model is negative btw)

How do I find the state of the art of a subject?

>>10643226
looks like it

>>10643053
There is literally no end to algebra

>>10643249
Yeah maybe. It's mostly just 2 of them that gives it that appearance though. There seems to be very little to read to help when you're not sure if it's really heteroscedasticity or not, I can only find things explaining what it is.

how bad of an idea is to wash your hands with urine? assuming you're drinking a lot of water

>>10643314
Not bad. It will just smell, but urine is pretty sterille.

>>10641961
Use the boundary conditions for normal and tangential components between the layers. Notice the spherical symmetry; can there be a tangential component to E? How do the normal components relate?

>Thomas’ Calculus: Early Transcendentals
or
>James Stewart's Calculus: Early Transcendentals
For self-studying over the summer hardcore?

>>10643547
bumping this

>>10643564
oh shit, you need advice on textbook suggestion too?

>>10643576
yes sir I do

>>10643752
I just went on amazon, apparently the 7th edition of Stewart (latest is 8th), is extremely cheap for used in good edition, I just went fuck thomas and went with that since the editions doesn't really matter and the cheapest for Thomas is still more expensive than the 'close to new' for Stewart. I also bought a Physics textbook that is a edition lower than the latest one for extremely cheap as well. Bro, you can just buy both if you're really stuck since the used for both in good condition are both less than a single new one. Good luck!

Can we define a variable that is free as the negation of being bound and vice versa
So any variable must either be bound or free but not both?

I fucking hate chemistry
how the shit are you supposed to approach balancing a chemical equation without resorting to linear algebra

>>10634898
Whats a cool genetic algorithm project I could code for my AI class' project?

>>10644114
There are rules of thumb for it, I don't remember them now but if you do certain elements first it gets easier, try to google it or look in a book

Im thinking of an integer between 1 and 1000. Guess what integer i am thinking of. Every guess you make i will either tell you my number is higher or lower than what you guessed.

My question is on average how many guesses will it take to correctly guess my integer? Also how will that change from 1-10000 etc? What is best approach too.

>>10644114
LCD, get the products on the left, reactants on the right always start with the worst chemical on the left and then work your way down the hiearchy of bullshit until you have to come back and fix your mess, check LCD again, leave the monoatomic and diatomic molecules on their own, remember what kind of reaction it is for context, stop being retarded

if I work out but dont have access to protein supplement or big meals (I'm quite poor) will I experience no muscle growth at all or will it just be a lot slower?

>>10644629
beans

>>10644629
>>>/fit/

Slower. Don't eat sugar, cookies, bread.

Can someone please assist with some group theory. I have no idea what the fuck they're asking me to do. I get that Dn is symmetries of n-gons and that (p^iψ^j)^-1 is itself but I don't know how to show any of it. The part b makes sense also but don't know how to show. bleh.

>>10644313
Well, how much time you got?

Find the perfect shitpost. Genomes are Markov chains. Fitness function is the amount of (You)s.

Good Luck!

What are some ways to test if engineering is a career path for me? I don't have any intro to engineering classes at my college so I'm unable to see if I like this shit without committing to a degree I don't know if I wiill like.

I'm probably retarded but I don't know where else to ask.
/dpt/ perhaps?
Either way.
I'm trying to write a formula that spreads the required amount to return to neutral over the next 7 entries.
So in this neutral is 1500, and the first 2 entries in total were 700 over.
So I want the next 7 entries to be 1400, but I can't wrap my fucking head around how to write this.
I currently just have

=1500-((SUM($H3:H$4)-COUNT($H3:H$4)*1500)/7)

But this calculates it every time, so it won't ever return to neutral.
Is this an excel question or is this a maths question?
Am I retarded?

So I am hoping some statistician or someone good at math can help me here. The NBA draft just happened tonight and I managed to figure out most of the mathematical processes and stuff they didn't show in the video in this post.

>>>/sp/92774895

Where my question comes from is this post

>>>/sp/92774953

>The combination was 4, 7, 12, 13. That's combination #754 (in numerical order). The Pelicans had combinations 741-800. The bulls had combinations 421-545.

What formula would you need to use to get the numerical order of this particular combination?

In case you don't know how it works, the link explaining everything is at https://www.nba.com/nba-draft-lottery-explainer

>>10644903

Unless you are naturally gifted, most engineering majors are difficult. They take a large amount of rigor and work to get understand to pass classes in later years. I would not really advise going into engineering at your college if they can't prepare you with engineering 101 classes. Even easier ones like environmental engineering can be difficult. I would really either ask yourself if you can imagine you can tolerate getting through the classes and doing a job in the field from 9-5 and not wanting to quit and kill yourself after a good amount of time would be the signal that you want to do it. Which was enough motivation for me to get my EE degree.

>>10644944
I cant be bothered actually working it out but I imagine they just enumerated the combinations like so: 1:=(1,2,3,4), 2:(1,2,3,5), and so on, and just from inspection it looks about right that (4,7,12,13) would land around 3/4 of the way through.

>>10644659
You should be able to work out question a. from the rules you given: [math]\rho^n = e[/math] (what is the inverse of [math]\rho^k[/math], when [math]1\leq k<n[/math]?), [math]\psi^2 = e[/math] and [math]\psi \rho \psi^{-1} = \rho^{-1}[/math] (what happens if you multiply by [math]\rho[/math] by the right on both sides?). These "rules" are simply ways to express the behavior of a group as synthetically as possible (read: https://en.wikipedia.org/wiki/Presentation_of_a_group ).
Generally, if [math]G[/math] is a group and [math]a,b\in G[/math]: [math](ab)^{-1}=b^{-1}a^{-1}[/math] — this can be verified by multiplying on both sides. A expression for [math](\rho^i \psi^j)(\rho^k \psi^l)[/math] should be easy to deduce using the third "rule".
Question b. is just asking you to verify that a triangle is a 3-gon and a square, a 4-gon. Your book has probably already introduced their symmetry groups as examples. This is the kind of exercise that you don't really write out — just read the page where these examples were introduced and maybe verify that the three "rules" work on them.
>>10644905
I'm not getting it with all the finance/accounting jargon. Can't you just copypaste 1400 into the next 6 entries, or equivalently write something such as =H3 in all of them?

Can someone explain to me why polynomial division theorem is true?
>Suppose d(x) and p(x) are nonzero polynomials where the degree of p is greater than or equal to the degree of d. There exist two unique polynomials, q(x) and r(x), such that p(x)=d(x)q(x)+r(x), where either r(x) = 0 or the degree of r is strictly less than the degree of d.

>>10644944
>The combination was 4, 7, 12, 13. That's combination #754 (in numerical order).
> What formula would you need to use to get the numerical order of this particular combination?
Lexicographic order, aka phone-book order. E.g.
> import itertools
> c = list(itertools.combinations(range(1,14+1),4))
> print c.index((4, 7, 12, 13))+1
754
As for a formula, you'd count all the combinations prior to the one requested:
[eqn]\sum_{i=1}^a {14-i \choose 3} + \sum_{i=a+1}^b {14-i \choose 2} + \sum_{i=b+1}^c {14-i \choose 1} + \sum_{i=c+1}^d {14-i \choose 0}+1[/eqn]
But note that [math]{a \choose 1} = a[/math] and [math]{a \choose 0} = 1[/math] so those sums can be simplified.

>>10645171
> Can someone explain to me why polynomial division theorem is true?
It's fairly obvious if you actually divide two polynomials. The entire process is deterministic. There are no choices to be made, and you always get a result.

Note that
> either r(x) = 0 or the degree of r is strictly less than the degree of d
is a prerequisite, not a consequence. If you remove that restriction, there are infinitely-many <q,r> pairs which satisfy the equation. You can pick any polynomial q and there will be a corresponding r=p-d*q.

Because deg(r)<deg(d) => deg(r)<deg(d*q) so each coefficient of q is uniquely determined by the coefficients of p and d; all of the terms of r have lower degree than the leading term of d*q at each stage in the division.

anyone have any particularly good youtube vids to recommend for learning basic calculus. Looking to supplement my reading with lectures. I know of 3 blue 1 brown as well as Strang's lectures too. Seems there are a bunch but I'd rather not sift through all of them. I'm a beginner (if that wasn't clear). Thanks in advance.

I am never doing a group assignment again. What are some reasonable excuses I can tell my professors to not have to work with people again on academic tasks? Autism?

>>10645215
thanks, it is obvious i just misunderstood
>is a prerequisite, not a consequence
exactly this

What job in industry is as close as it can get to feel like you're doing pure math?

My book says that using these two expressions for a funcion F:
[math]F=-\frac{Qq-q^2\frac{cos\theta}{2}}{sin\theta}+c(Q,t)[/math]
[math]F=-\frac{Qq-q^2\frac{cos\theta}{2}}{sin\theta}+C(q,t)[/math]
you should get this:
[math]F=-\frac{Qq-(Q^2+q^2)\frac{cos\theta}{2}}{sin\theta}+\alpha(t)[/math]

But how? And why the dependence from Q and q disappear in alpha?

my book says that using these two equations for a funcion F:
[math]F=-\frac{Qq-q^2\frac{cos\theta}{2}}{sin\theta}+c(Q,t)[/math]
[math]F=-\frac{Qq-Q^2\frac{cos\theta}{2}}{sin\theta}+C(q,t)[/math]
you should get:
[math]F=-\frac{Qq-(Q^2+q^2)\frac{cos\theta}{2}}{sin\theta}+\alpha(t)[/math]

but how?

>>10645431
well i don't understand why the fuck my third expression is not working but it's pic related

>>10645217
don’t use lectures if you can help it

>The HVAC unit in an apartment is failing. When inside the apartment, you can hear a repeated "humming" sound - wwwwwwwwwwwwWUB, wwwwwwwwwwwwWUB, wwwwwwwwwwwwWUB; Where the "WUB" denotes an increase in loudness and deepness to the sound. Provide a simple labelled plot to describe this phenomena.


pic related what i came up with, anyone else?

Specifically, why does [math]r\get0[/math]?

Specifically, why does [math]r\geq0[/math]?

>>10645217
Literally just find the solution manual to your textbook and look for the solutions that involve algebraic tricks or that yield somewhat unique graphs. Those are the questions you'll be asked on exams. Most profs won't cover the tricks because, "you should remember it from __insert course from previous year/highschool__". PatrickJMT covers some of these in his videos. He has a lot of examples you can work along with.

Calc is taught so fucking stupid.

Okay here is a question for chemists:
Imagine you have the perfect sealed unbreakable container. In this container is Carbon and hydrogen gas. What happens when you increase the temperature? At which temperatures do which stable molecules form?

>Look into making FOLLOW sets
>If there is a rule B -> aAb where A and B are non-terminals, do whatever
>Look at own example
>A -> BaC where a is a terminal
>None of the rules in the example I have match this form
So according to this every single non-terminal's follow set is the empty set? That seems quite silly.

>>10645179

Oh wow, this makes sense now at least to me. Shame it still is confusing as all hell to everyone else. But at least I understand now somewhat how the numbers drawn get determined.

>>10645263
If by industry you mean not a university or college, then probably some research/problem solving company.

>>10645179
Thanks.
It looks correct to me too.

What is the threshold in a D'Hondt voting system?

Say there are P parties standing and S seats up for grabs. D'Hondt works like this:

>party with most votes gets a seat
>party's vote is divided by n+1, where n is the number of seats they've won
>e.g. if a party originally had 100 votes, they'd have 50 votes after wining one seat, 33 votes after winning 2 seats, 25 votes after winning 3 seats...
>process repeats until all S seats have been awarded

By threshold I mean the minimum vote % required to possibly get at least one seat. E.g. if there were 6 parties standing and one party got 0.1% of the vote, they wouldn't get a seat no matter how the other votes were distributed, they're below the threshold. For any D'Hondt vote there must be some threshold function f(P, S) that gives the minimum vote share necessary to be in contention.

European elections are coming up and I see thresholds talked about a lot casually (oh, that party's at 6%, the threshold in this region is 10-12%, they'll never get in) but I don't know how you'd actually calculate the threshold formally.

What is the 'symmetry' of the unit cell? Is it referring to "Cubic close packed, primitive cubic" etc.

Doing statistical physics course right now. Why do I feel like they are pulling all these derivations out of their ass compared to the other courses?
What are Helmholtz/Gibbs free energy and enthalpy supposed to be compared to just normal energy U?
>>10644529
Keep guessing in between seems the fastest to me. number is 333 then guess 500-lower-250-higher-375-lower-313-etc
maximum number of guesses you need is log(maximum)/log(2) rounded up. Average guesses I dont know other than just brute force calculating it like this if you have matlab https://pastebin.com/8FjRLcA4

>>10646274
1/(S+P-1)
Consider that there's one seat left to allocate; the other parties have vote counts of v1,v2,... and seat counts s1,s2,.... The no-seats party has a vote count of v0.

If all of the parties are tied for the last seat, then
v0 = v1/(s1+1) = v2/(s2+1) = v3/(s3+1) = ...
=> v1=v0(s1+1), v2=v0(s2+1), v3=v0(s3+1), ...
The total number of seats allocated is s1+s2+s3+... = S-1
The total vote count is
v = v0+v1+v2+v3+...
= v0 + v0(s1+1) + v0(s2+1) + v0(s3+1) + ...
= v0(s1+s2+s3+...+P)
=> v0/v = 1/(S+P-1)

>>10646317
look up unit cell before asking a retarded question like this and read more carefully

Day 1 of ODEs.
I'm trying to derive [math] (\frac{dy}{dt} = at) \rightarrow (y = C_1e^{at})[/math].
My attempt:
[math]\frac{dy}{y}=adt[/math]
[math]\int\frac{1}{y}dy = \int adt[/math]
[math]\ln|y| + C_3 = at + C_4[/math]
[math]\ln|y| = at + C_2[/math]
[math]|y| = e^{at + C_2}[/math]
I want to know:
- Where does [math]C_1[/math] come from?
- How does the absolute value resolve? (related to the above, I guess; once I work in [math]C_1[/math] it won't matter because it could be positive or negative
- Why do my notes not have a [math]C_2[/math] in the exponential?

>>10646628
Mods delete this I'm retarded. I forgot about exponent rules. This is what happens when you take two semesters of lab sciences only

>>10646654
mods delete this or anon will be embarrassed by his absent mindedness!

>>10646654
Well, not so fast there. The exponent is only part of the story, getting you from [math]e^{at+C_2}[/math] to [math]e^{C_2}e^{at}[/math]. But that factor is always positive, and on the other side of the equation, you still have an absolute value.

That, and the fact that y=0 is a solution (often), is why you go from [math]|y| = K e^{at}, \ K > 0[/math] to [math]y=Ce^{at}, \ C \in \mathbb{R}[/math].

>>10646620
If don't want to answer my question that's fine but don't spew your autism onto me thanks

>>10647512
hold your horses there buddy

>>10647753
What does that even mean?

>>10647754
>hold your horses
Cool your jets there laddy

>>10647792
Yeah yeah I'll put it on the list, matey. I have to untangle these panties first.

>>10645709
>Maths makes no sense except when people says it does
Stop the presses

So what the hell is a tensor and how do they work?
Decided I would take Physics seriously after all, but whelp, first slide in my entry-level theory lecture (the first part is Maths anyway) and immediately this guy throws a tensor into the mix without explaining what a tensor is. "Oh yeah this is a metric tensor but I'm not gonna tell you anything about it it just exists"

https://en.wikipedia.org/wiki/G%C3%B6tz_von_Berlichingen
what the hell? i thought prosthetics were a sci-fi thing
how does that even work? aren't the nerves permanently cut when a limb is severed?
can you actually get an iron arm
is it possible to have a cool robot arm?

>>10648020
A type [math](n,m)[/math]-tensor over a manifold [math]M[/math] is a section of the vector bundle consisting of [math]n[/math] times the tangent bundle times [math]m[/math] times the cotangent bundle [eqn]\underbrace{TM\otimes\cdots\otimes TM}_{n \text{ times}}\otimes \underbrace{T^*M\otimes\cdots\otimes T^*M}_{m\text{ times}}\to M[/eqn]

So essentially a tensor assigns to every point in your manifold (for example, 3 or 4-space) a collection of tangent vectors and cotangent vectors in a smooth way.

>>10643882
>>10643752
>>10643576
>>10643564
>>10643547
If you're self-studying, I recommend late transcendentals. As for what book, it really depends on what your objective is. If your objective is to prepare for a class (engineering, physics perhaps), then just do Stewart, it's been extremely optimized through its overuse. I'd recommend just downloading it for free on libgen anyways.

If your objective is just to get good at math, then it's way better to start up with a more rigorous introduction. For example, Spivak's Calculus or Apostol's calculus. In fact, there's a /sci/ study group for the former starting on the 20th: https://discord.gg/THs4t6P

>>10643908
You should explain what you mean. Not everyone that has studied that subject would immediately understand what you're talking about. I'm assuming it's linear algebra. And yes, you're right, and that's precisely because the definition of being "free" is that within a selected spanning set of variables, adjoining that variable would not lead to a linear dependence relation, while being bound is precisely the opposite.

>>10643237
asking the leading thinkers of the subject

>>10643053
Depends. If you're a baby, I'd say when you learnt how to solve a quadratic equation. When you're a preteen, I'd say the Sylow theorems for groups and PID implies UFD for rings. When you're a teen, I'd say after applications of fundamental theorem theorem of Galois theory, Krull's Hauptidealsatz, Wedderburn structure theorems, and representations of Lie algebras. After you learn all that, you learn that you're never finished. Because then comes algebraic geometry.

>>10641031
Because nobody but retarded engineers and code monkeys use anything other that based base e.

So event horizons are perfect spheres for nonrotating black holes.

If you have a nonrotating lopsided mass that collapses into a black hole, does the event horizon form as a perfect sphere at the first planck time? Or does it wobble for a very short time before asymptotically approaching perfect sphere-ness?

Why does the middle finger have a negative connotation?

Is a line a boneless hyperplane?

So if vaccines cause autism, does that mean non-autism is a virus?

Suppose I have a given product and from past tests I've found out that between 1 and 3 of it are defective in each batch of 100.

I've tested through 50 of a batch, none of them was deffective. What function best describes the chance that the next one is going to be deffective as the total amount tested gets closer to 100?

why am I suddenly retarded

I was doing very well in college, getting good grades
now everything is a struggle, I get tripped up on the easiest of problems, I forget the most basic of properties when I most need them, and whenever I study it feels like water and oil, the knowledge just slips right out
Classes that by all means should be an easy A are now a struggle

it's absolutely terrifying and I don't know what to do about it

>>10650158
you are experiencing late onset mental illness probably depression or schizophrenia

If I want to be a statistician would it make sense to get a CS BS and then a Statistics MS?
Or would it be better to get some other undergraduate degree?

room temperature IQ reporting in;

say I have 3 EV loads with availability and battery states, 2 independent energy supplies and both a cost to import and export from the grid.

What algorithm would you use for scheduling?

>>10649774
Batches are a red herring. Previous tests give you a probability of any given item being defective. The probability of the next item tested being defective is independent of how many previous items in the current batch were defective.

How does gravity work inside the radius of a sphere? For example at point halfway the radius of the earth.

I've been trying to find a solution for a Jackson E&M problem for over an hour now. It seems so absurd that a book that has been so frequently used over the last however many years doesn't seem to have a readily available set of the full solutions anywhere online that I can find. I've found sites that have some of the solutions but nowhere near all of them. It's ridiculous that I can't even find a mention of this particular problem through all kinds of google searching.

What is the point in learning how to solve problems with the Smith chart nowadays if software-based solutions are so easy to find and use ?

>>10651059
If you could freely float through the volume of the earth at a radius r from the center, the gravity from the earth outside of that radius r cancels out. It essentially works like Gauss's law, but for gravity. So, the effect of gravity would be the same as if you were on a new planet with radius r but the same density of the earth (you'll probably want to make the assumption that the earth has a uniform density for a homework problem).

>>10651067
it's all fun and games until you can't get the software to work right

>>10651156
lol boomer

>>10651167
it's like trying to use a CAS to do integration or something and it spits out some fuckass weird function rather than anything remotely manageable, sometimes it's just easier to do by hand

I need a topic for an essay about a recent (~10 years) development in physics.
The audience is full of brainlets/biology students, so it should be an easy topic like a new measuring technique.
Any ideas?

>>10651182
just use wolframalpha.com or integral-calculator.com to do integration, boomer

>>10651070
>>10651182
Thanks for the answer, I guess it is the same reason I prefer to use a calculator rather than my phone.
>>10651167
>>10651282
wtf

>>10651268
blue LEDS 2016 nobel prize i believe

>>10648559
Way back they were already able to make a robotic arm move through the net by reading a monkey brain through electrodes, by now something like you want should be possible

>>10649602
People associate it with an erect dick

>>10640995
ln(x) is physicist/engineer notation. Matematicians seldom consider irl measurements, so there's no need to them for a special notation for the logarithm in basis 10. So log is used to denote logarithm in basis e without ambiguity.

>>10652721
ln is mathematician tier. It means logarithme népérien (like John Neper)

log is an engineering/physicist notation because they care more about log10 and log2

>>10638171

My net would be : A + B

Now let's say that I use net taxes to calculate what a NET person earns in taxes.

Let's say that I calculate what the NET person saves into one year, and the net person spends on the year.

I calculate what the NET person's saving rate would be if I have:

A Net A - A - A = D

I would calculate the net person's income with :

A = A + D (D x A)

Now the net person's net income is : A = A + D (D x A)


That's the simple math. The answer can seem so hard after I get it right a few times.

>>10645460
WUBBA LUBBA DUB DUBBBBB
I'M HVAC RICCCCKKKKK

>>10653068
You have that backwards. ln() is only used in contexts where it's actually necessary to state that base e is being used, i.e. where there's at least a possibility of some other base being assumed. That doesn't include mathematics, where a "logarithm" is assumed to be a natural (base-e) logarithm unless explicitly stated otherwise.

ln() is mainly for engineering where base-10 logs are common, although it has some origins in the use of (base-10) log tables for arithmetic before calculators were commonplace. I've also seen it used in CS, where "log" with no subscript is often used where the base is irrelevant (e.g. big-O notation or ratios of logs), and occasionally used for base-2 logs, but base-10 logs always have a subscript.

FWIW, almost[*] every programming language I've encountered (which is a couple of dozen by this point) uses "log" for the natural logarithm and "log10" for base-10 (if that function is even provided). [*] BASIC uses LN() for natural logs and LOG() for base-10.

Probably very trivial but I cannot seem to derive that [math]\frac{1}{h}\int_{-\infty}^{\infty}K(\frac{x-y}{h})f(y)dy = \int_{-\infty}^{\infty}K(u)f(x+hu)du[/math].

When I substitute [math]u = \frac{x-y}{h}[/math] with [math]du = - \frac{1}{h} dy [/math] I obtain [math]\frac{1}{h}\int_{-\infty}^{\infty}K(\frac{x-y}{h})f(y)dy = -\int_{-\infty}^{\infty}K(u)f(x-hu)du[/math]. Can someone please shed some light on whats going wrong?

>>10653952
How sure are you that what you are trying to derive is actually true? What happens in the specific instance where h=1 and x=0?

Also, in the derivation you did, you have a sign error, because you apparently failed to account for how the change of variables affects the limits of interation. As a check, if K and f where both positive-valued functions, the two sides of your equation (that you did derive) would have opposite sign.

>>10653976
>Also, in the derivation you did, you have a sign error, because you apparently failed to account for how the change of variables affects the limits of interation. As a check, if K and f where both positive-valued functions, the two sides of your equation (that you did derive) would have opposite sign.
You're absolutely right, the sign should be positive. I forgot that the kernel [math]K(\cdot)[/math] is assumed to be symmetric, so [math]\frac{x-y}{h} = \frac{y-x}{h}[/math] which leads to the required formula.

>>10653976
>>10653976
>Also, in the derivation you did, you have a sign error, because you apparently failed to account for how the change of variables affects the limits of interation. As a check, if K and f where both positive-valued functions, the two sides of your equation (that you did derive) would have opposite sign.
You're absolutely right, the sign should be positive. I forgot that the kernel [math]K(\cdot)[/math] is assumed to be symmetric, so [math]K(\frac{x-y}{h}) = K(\frac{y-x}{h})[/math]. Thank you though.

Can someone please explain how to solve this ?

A man running on a horizontal road at 8km/h finds the rain falling vertically He increases his speed to 12 km/h and finds that the drop makes angle 30 with the vertical.
Find the speed and direction of rain

>>10654641
The tangent of the angle with the vertical is the ratio of the horizontal component (relative to the runner) to the vertical component.

From the first case, clearly the horizontal component (relative to the ground) is 8km/h in the same direction as the runner. The second case tells you that tan(30°)=(12-8)/v => v=4/tan(30°) = 4√3 = 6.93 km/h.

Overall, the speed is √(8^2+(4√3)^2) = √(64+48) = √112 = 4√7 = 10.58 km/h, and the angle is atan(8/(4√3)) = 49.1°.

Scientifically speaking, if a women is 4 weeks pregnant, is that a baby in her belly?
If so, is it murder to have it aborted?

>>10651067
To verify the software, I guess.
Straightline bode plots created by hand can give you more intuition and insight on your circuit as apposed to an accurate bode plot created through simulation/software

I'm not sure of linguistics belongs here, but I can't think of a better place on this site to dump this question, so here it goes.

What makes one language have a higher resistance to noisy environments compared to other languages (such as crowded rooms, echoy environments, or the speaker being constantly interrupted)? Any examples of languages with such resistance? What features would such a high resistance language have?

I've read a small research article that suggested that Swedish is better at handling noise than English, but it didn't explain why, so that got me curious.

>>10654759
Thank you anon you explained it way better in a few lines than pic related

I was just introduced to complex numbers and I'm asked to simplify [math]1/(1+i)[/math]. Now the problem is that I'm thought to multiply numerator and denominator with conjugate of denominator but in this case I get [math]1-1[/math] in the denominator which is unacceptable. Is this a trick question? This can't be simplified, right?

>>10654973
No one knows when life begins m8. No on even really knows what a good definition of life is.
It's a life at the point of conception imo.
Catholics get it.

What the hell is the importance of green epoxidation of a chalcones? I was trying to look this up, and understand the reaction process it goes through, but i can't find anything regarding what its actually used FOR and WHY

Is this correct? Can I say e*dE/dT = dMu/dT?

If x=y+z and y<0.7, z<0.7 is it completely correct to say that x<1.4?

>>10657416
I'd say yes. Due to the fact that neither y nor z can't have a value of 0.7 nor greater. So if y and z have their maximum allowed value, then x would be less than 2 times 0.7 (i.e. 1.4). That's the best I can describe it. I'm sure that there's some theorem that you can quote, but I wouldn't know.

>>10657416
y < 0.7 means there's some positive y1 so that y + y1 = 0.7 which means y = 0.7 - y1
z < 0.7 means z1 etc
x = y + z = 0.7 - y1 + 0.7 - z1 = 1.4 - (y1 + z1)
y1 is positive and z1 is positive so y1 + z1 is positive
1.4 minus that positive number has to be less than 1.4
Pretty much yes you were right and I'm a retard for writing this post

>>10653848
Yeah it might be best to avoid `log` in multidisciplinary works. In chemistry I used `ln` for natural growth, `lg` for pH etc., and `lb` for half-life.

Which mathematical functions are used to model chemistry titration curves?

Is there any material that is at the same time: hard, tough and transparent?

>>10634836
>How could I find about this, other than incinerating corpses myself
Simulation.
>Maybe if you have 2 it will take 3 hours
I doubt about that. The more mass you have, the more fuel+oxidizer you'll need. And the mass you are burning will get in the way of the reaction, so it will become impurity that will lower the temperature of the reaction thus making it take longer.

>>10629369
Multiplexing

>>10630048
>electric field of a charged particle in uniform motion
[eqn]\vec{E} = -\frac{q \hat{r}}{4\pi\epsilon_0 |r|^3}[/eqn]
>Also, since any changes in the field propagate as a wave at the speed of light, doesn't that mean the particle is radiating some energy even though it's not accelerating?
No, but I don't understand your question. If it's not accelerating there's no change in the field.

>>10634774
This is trivial but either your equation or your answer is wrong.
[eqn]\frac{y_0}{2} = y_0 \sin\left(2\pi \left(\frac{1}{6}-\frac{8}{\lambda}\right)\right)\\
\arcsin\left(\frac{1}{2}\right) = 2\pi\left(\frac{1}{6}-\frac{8}{\lambda}\right)\\
\lambda = 48
[/eqn]
Which is half your answer.

>>10657975
>electric field of a charged particle in uniform motion
Correction
[eqn]\vec{E} = -\frac{q \vec{r}}{4\pi\epsilon_0 |r|^3}[/eqn]

>>10650624
Optimization theory. Minimize for cost.

is it possible to find

[math]\lim\limits_{n\to \infty}{(1 + \frac{1}{n})^{2n}}[/math]

without using L'Hôpital's rule? know the limit is [math]\infty[/math] but can't find any solution that doesn't use L'Hôpital's rule

>>10658182

\lim _{n\to \infty }\left(1+\frac{1}{n}\right)^{2n}

\left[\lim _{n\to \infty \:}\left(1+\frac{1}{n}\right)^n\right]^2

e^2

How do I find

\lim _{x\to 0}\frac{ln\left(1+x\right)}{x}

without using L'Hôpital's rule?

>>10658182

[math]\lim _{n\to \infty }\left(1+\frac{1}{n}\right)^{2n}[/math]

[math]\left[\lim _{n\to \infty \:}\left(1+\frac{1}{n}\right)^n\right]^2 = e^2[/math]

How do I find

[math]\lim _{x\to 0}\frac{ln\left(1+x\right)}{x}[/math]

without using L'Hôpital's rule?

>>10658246
>>10658236
I fucked up, I actually meant

[math]\lim\limits_{n\to \infty}{(1 + \frac{1}{n})^{n^2}}[/math]

sorry

>>10658182
[math]\lim _{n\to \infty }\left(1+\frac{1}{n}\right)^{2n}[/math]
[math]\left[\lim _{n\to \infty \:}\left(1+\frac{1}{n}\right)^n\right]^2=e^2[/math]


How do I find
[math]\lim _{x\to 0}\frac{ln\left(1+x\right)}{x}[/math]
without using L'Hôpital's rule?

>>10658259
wtf is happening here?

>>10658259
dude use the TeX preview tool. regardless you're trying to answer the wrong question, I actually meant >>10658258

>>10658258
>>10658273

[math]\lim _{x\to \infty }\left(1+\frac{1}{x}\right)^{x^2}[/math]

[math]\lim _{x\to \infty }e^{x\cdot \:ln\left(1+\frac{1}{x}\right)^x}[/math]

[math]e^{\infty \:\cdot 1}=\infty[/math]

>>10658258
>>10658273

[math]\lim _{x\to \infty }\left(1+\frac{1}{x}\right)^{x^2}\\

\lim _{x\to \infty }e^{x\cdot \:ln\left(1+\frac{1}{x}\right)^x}\\

e^{\infty \:\cdot 1}=\infty[/math]

>>10658298
thank you! god I am retarded

Let's say I get a lecture that's 200 slides long and doesn't have any real learning goals highlighted. How the fuck am I mean to take notes or study it? It's literally just a bunch of disjointed information and anecdotes being spewed at me.

Is it possible for a technically illiterate person upload something to the internet without leaving a trace that could direct authorities to himself?
It's for a book I'm writing.

>>10634898
i'm trying to convince myself that

[math] f(x) \operatorname d\!x = \operatorname d (\displaystyle \int f(x) \operatorname d\!x )[/math]

does this hold always? what does it follow from. it's used in a thermodynamics equation derivation

>>10658698
nevermind it's trivial

I have Calculus I exam in like an hour and half
It's not really a question, I just wanted to anchor somewhere to come back and tell how it went
I'll be back in about 4 hours

>>10658708
I'm back
it was a tragedy to say the least
[math]3x + 9 ln \left ( 2 \left ( \frac{x-2}{x-1} \right ) \right )[/math]
the study of this function is the only thing I couldn't complete. I got as far as finding [math]Dom(f(x)) = (-\infty,1) \bigcup (2,\infty)[/math] and (0,0) as the axis intersection for both x and y, didn't have time to progress past that
this sucked big time. What's the easy way out as far as sign determination for such a function goes?

Can you do KVL from the V1 (left) to the -Vee (center)? Voltage drop on this side of the Q1 is Vbe, but that's not important, current source is what's fucking me over.

Should be (Ib is base current for Q1, not important either): V1=Ib*R1 - Vbe - ???? - Vee?! Or is this not allowed at all, KVL through the current source? What do I do for that branch if it's not allowed?

Got a conceptual question to ask. Why is a conservative force defined as the negative of the gradient of the potential?
[eqn]\mathbf{F}=-\nabla V[/eqn]
Why is the negative sign there and what difference does it make?

>>10659428
Also, a bit more advance, but probably still a stupid question. Is this allowed when it comes to BJT? Can do KVL through a terminal of BJT like this? Starting from V1, through R1, then Vbe, jump over to Vce and go all the wayto Vout?

>>10659443
There's a simple proof for that, it involves taking the partial derivative of it and then working a little bit on it. I'll upload it if O find it

>>10659450
I was thinking more about why the negative sign is there. I can't find the physical reasoning for it.

I am not sure if it is a stupid question or not, but I won't start a thread yet. And I am a noob.
I am learning how to use neural networks, and I wanted to build one around a problem I thought was simple: a model that, given a distance in metres and a mass in kg, outputs the gravitational acceleration in m/s^2. So basically an approximator of a well known function (G * M / r^2). It is sort of useless but seemed more interesting than making a logic gate or something (which I already did), plus this way I learned about regression (most courses/tutorials out there focus on classification problems).
So I made a CSV with about 6000 examples of the problem. 3 columns (distance, mass, acceleration)
First thing I read everywhere is that normalisation/standardisation is a must for the inputs, so I do so. I use the MinMax from scikit. I write a small network in Keras:
Input (size 2) > 12 "neurons" > relu > 8 neurons > relu > 1 output (linear)

Reading tutorials about that house pricing dataset, I use the mean squared error loss function with the Adam optimizer, but I get very bad results. So I switch to the mean absolute percentage function, which at first seems to be better. But it is not.
After 2000 epochs using a batch size of 16, I can get the loss to about 20. The loss of the validation set is higher, tho, and does not decrease after 1000 epochs.

When it comes to recreational stuff, that loss would seem acceptable to me, specially if I am not running it for a gorillion epochs. The problem is that when I try to run predictions on new values, the results are very random. It is extremely bad at getting realistic values and I suspect the few times it does it is by chance (since when I change parameters and get the loss lower, it does not get more "approximate", but instead the predictions vary wildly from the last training)
I feel like I am doing many things wrong. For a start, I am not convinced by the normalisation thing.

>>10659443
the negative sign has to exist somewhere. one could define potential differently (ie, with an extra negative sign) and it would all cancel out.

I highly encourage you to work out familiar problems (two body gravitational problem, maybe) without the negative sign and see what the results are.

>>10659475
(follow)
Why would I normalise data that is arbitrary? (mass and distance)
What happens when I try to predict something out of the range of the training dataset? Doesn't it break?

>>10659428
Q2's base is tied to ground, so if Q1 and Q2 are conducting then both emitters are at -Vbe and Q1's base is also at ground. The voltage across the current source is just the difference between -V_be and -V_EE.

KVL isn't going to be of much use here. The behaviour is entirely dependent upon your transistor model. If V_be is constant and I_c = β*I_b, then the voltage gain is just β*R_c1/R_1. I_EE and R_c2 set the bias, V_EE is irrelevant.

If I_b is a function of V_be, then it gets more complex.

>>10659475
The outputs of a neural network are effectively boolean values. Neural networks are pattern classifiers. Each output indicates whether or not an input vector matches some pattern. The only reason why each neuron's weighted sum is subject to a sigmoid rather than a step is because you can't back-propagate through a step.

>>10659506
Thank you for taking the time to write all of that for me. This particular problem is not the one that I need to solve, it's just a first network I found on google images while searching for current sources and BJT's in the same network, to ask about KVL. But you did answer my question I think, current source is there to set the bias and I should not use KVL.

While I have you here, I must ask one more question which I cannot find on google for the life of me. Can I do KVL "around" a transistor like BJT and MOSFET? Especially MOSFET, if I calculate for example Vsd and Vsg in a p-type mosfet, is it valid to say Vdg=Vsg-Vsd? I think I read somewhere (Could be Sedra/Smith) that this is true only in saturation, but I can't seem to find it again anywhere.

>>10659526
> Can I do KVL "around" a transistor like BJT and MOSFET?
You can do it around any loop. But in order for the system to be soluble, you need as many equations as you have unknowns. For two-terminal devices, there's a linear relationship between voltage and current, so if one is known then so is the other (i.e. adding such devices doesn't change the number of knowns or unknowns). For three-terminal devices, you need a model which relates one parameter to another (e.g. BJTs are modelled as current-controlled current sources, FETs typically as voltage-controlled current sources).

> if I calculate for example Vsd and Vsg in a p-type mosfet, is it valid to say Vdg=Vsg-Vsd?
Yes. That's always true (for anything); Vgs=Vg-Vs, etc. Each differential voltage is just the difference between the potentials at the two terminals.

>>10659665
You saved my ass man, I love you.

I want to draw a bunch of random samples from a multivariate Gaussian distribution with known mean and covariance. Is there a way to judge if I've drawn enough samples to essentially cover the whole distribution in some sense?

If I remember correctly, Descartes' Rule of Signs says that the function
[eqn]f(x)=x^2-4x+13[/eqn] should have 1 positive REAL zero, but it has only two complex zeroes: [math]x_1=2+3i,x_2=2-3i[/math]. What's the catch?

Anybody else feel like the more you learn about science and philosophy the less common ground you have with normies?
Am I not Feynman enough?
I can barely communicate with them anymore.

>>10659931
Dude, ever since I took the /begenuinelykindtoeveryoneimeet/ pill I literally cant relate with most people anymore.

>>10659933
It just keeps getting worse and worse.

>>10659701
Dude you're taking samples out of a probability distribution, the number of values that fall around x is is N * p(x) * dx where N is the number of samples.

If you want say around 3 per point you make sure the value above is always larger or equal to three for example

>>10659982
Alternatively you can play around with the variance until it's close to the theoretical maybe. Try a few different approaches and pick one that looks good

I've been noticing a lot of schizo posts on /sci/ lately. What's going on?

>>10634898
I really like the smell of bourbon biscuits, how do I extract the smell out of them into an air freshener?

How come we can hear noise better at night compared to in the day?

>>10660588
Polarity

>>10634898
Can someone confirm the nformation in the attatched picture

>>10660593
It's wrong.

So does this mean 2(nCn+1)+(nCn+1)^2 = 0?
I don't get it

>>10660935
Nevermind I'm dumb

How can I do science on a small budget at home?

Hello /sci/. Can you help me with >>>/wsr/668754?

I've sent an email to a professor, he replied and now I have to reply back, something I've never done. I know how to write the first email, but how do you proceed from there? Am I supposed to repeat the opening of the first email ("Dear Professor X" [slighlty different in my native language]) at every reply I send? Do I also have to repeat the final greetings "Best regards" at every email? It feels silly to furnish an email with all that when you just have to set up a time or say yes/no to a question

>>10661294
I'm so glad I live in a culture where we don't get hung up on this kind of thing. If I had to think of something other than 'Hi' and then 'Thanks' or 'Cheers' I'd never get any emails sent.

I got one email that was closed with 'Kind regards' once. I don't even know what that's supposed to mean.

>>10661294
it depends on the professor. some dont care at all, some are insulted when you don't give their full honorific

keep giving the full dear professor, signed, anon until you notice that they are just replying without that thing. then relax your style.

What goes wrong here?

>>10661780
Been a while since I've done surface integrals. Isn't the constant of 2 in front of the double integral unnecessary? I don't see where it comes from.

>>10661812
It comes from the symmetry of z. The answer is supposed to be 8pi/15. Interestingly enough if I had one less factor of r in my integral it would come out to that.

>>10661780
The jacobian is what's wrong, probably.

How can I prove that 1+1=2?

>>10661815
Oh yeah duh. I would try this
>>10661818
probably need to factor the z into the coordinate transformation

>>10661818
>>10661846
Yes, that was it. The Jacobian is not just r, as it is with a standard switch to polar coordinates, instead it's a bit more awful, but it gives the correct answer.

I might as well ask, what's the relationship between the Jacobian for change of variables, and the norm of the cross product of a parametrization when finding the "surface element"? So for example, when doing a change of variables to polar coordinates we find the Jacobian [math]\frac{\partial(x,y)}{\partial(r,\theta)}[/math], but when finding the surface element we instead look at
[math]
\Big|\frac{\partial \gamma}{\partial u}\times \frac{\partial \gamma}{\partial v}\Big|
[/math].

>>10661822
what have you tried?

>>10661822
Don't worry about it. Just assume that is the definition of 1 and 2.

>>10661822
Use induction and then don’t bother with it till you know why that might not be enough

>>10660573
>schizo

>>10661822
From the definition of +

>>10634898
How do the anticommutation relations of fermionic operators ensure antisymmetry of fermionic states? I mean, it makes intuitive sense, but I'm not sure how it works mathematically. How do you write out the permutation operator in terms of the annihilation/creation operators?

Also, while I'm at it, is the "occupation basis" of the fermionic Fock space just a notational shorthand? Should I really just think of every [math]| f_0 f_1 \ldots \rangle[/math] as a Slater determinant? And how the fuck do you write out a Slater determinant in ket notation (i.e. without writing states as "wavefunctions"). Or is that why we use the occupation notation in the first place?

>>10648631
That's a tensor field though. Tensors in general need not be defined over a manifold at all (or rather, you don't need a manifold structure to talk about tensors).
>>10648020
A tensor is just a multilinear map that takes elements of a vector space and its dual and spits out a real number. In math speak, that says: a type [math](r,s)[/math] tensor [math]T[/math] over a vector space [math]V[/math] is a multilinear map
[eqn]T : \underbrace{V^* \times \cdots \times V^*}_{r \text{ times}} \times \underbrace{V \times \cdots \times V}_{s \text{ times}} \to
\mathbb{R}. [/eqn] In physics speak, we often represent tensors by the values they take, given a choice of basis for [math]V[/math]. Often you'll see tensors with "contravariant" and "covariant" indices, and this is precisely the representation I'm speaking of. In particular, given an orthonormal basis [math] \{ e_i \} \subset V [/math] and its "canonical cobasis" [math] \{ f^j \} \subset V^* [/math] (i.e. such that [math] f^j(e_i) = \delta^j_i [/math]), then the "physicist's tensor" is the symbol
[eqn] T_{i_1 \ldots i_s}^{j_1 \ldots j_r} := T \left( f^{j_1}, \ldots, f^{j_r}, e_{i_1}, \ldots, e_{i_s} \right) [/eqn], where the notation assumes that the choice of basis is known/obvious. Note that this is indeed a generalization of matrices (i.e. linear operators), which are type [math](1,1)[/math] tensors (you need a "column vector" and a "row vector" (which is dual to the "column vector") to obtain the real-valued matrix elements, which can be stored in an array in the familiar matrix representation).

>>10634898
Let A,B be ideals. How do I prove that the variety V(A \cap B) = V(A) \cup V(B)?

>>10662903
>that's a tensor field
>tensors need not be defined over a manifold at all
>goes on to define a tensor field over a manifold

>>10661866
Looked at some of my old notes to try and answer this. The cross product (evaluated at some point) is the normal vector for the surface at that point. This is needed in computation of the surface area, for example
[math] \gamma: U \subset \mathbb{R}^2 \rightarrow \mathbb{R}^3 [/math]
[math] A = \int_{U} \left| \frac{\partial \gamma}{\partial u} \times \frac{\partial \gamma}{\partial v} \right| dA [/math].
However I don't think this is related to the Jacobian. The Jacobian is needed when doing a coordinate transformation (change of variables) to evaluate an integral. For example you might find that computing the area of some surface is easier if you change to polar coordinates: then you would need the Jacobian of your change of variables in the above integral. So you would deal with both the parametrization of the surface (and its normal vector) and the Jacobian of the coordinate transformation.
Also, in 1D integrals you need the derivative of your substitution when you want to integrate something by substituting your variable for something else. The Jacobian is basically the same thing in multiple dimensions.

You have a continuous function y = f(x). You need to find the smallest x where f(x) > threshold t.
My initial thought was to just sample the function a bunch of times until you find the value.
But i'm sure there's some clever math way to do this. Is there?

>>10664192
Find all zeroes of f(x)-x and sort them?

>>10664206
Is there like a quick method/algorithm for this? I need it to be instant and not iterative.

>>10662843
> How do the anticommutation relations of fermionic operators ensure antisymmetry of fermionic states?

[math]
c_i^{\dagger} c_j^{\dagger} | \psi \rangle = | i, j, \psi \rangle

c_j^{\dagger} c_i^{\dagger} | \psi \rangle = | j, i, \psi \rangle

Sum both equations

( c_i^{\dagger} c_j^{\dagger} + c_j^{\dagger} c_i^{\dagger} ) | \psi \rangle = | i, j, \psi \rangle + | j, i, \psi \rangle

However the anticommutator defines \{ c_i^{\dagger}, c_j^{\dagger} \} = c_i^{\dagger} c_j^{\dagger} + c_j^{\dagger} c_i^{\dagger} = 0

Hence | i, j, \psi \rangle = - | j, i, \psi \rangle which is antisymmetry condition of fermions.

You could do the same with the annihilation operators and get the same result.
[/math]

>>10662843
> How do the anticommutation relations of fermionic operators ensure antisymmetry of fermionic states?

[math]c_i^{\dagger} c_j^{\dagger} | \psi \rangle = | i, j, \psi \rangle[/math]

[math]c_j^{\dagger} c_i^{\dagger} | \psi \rangle = | j, i, \psi \rangle[/math]

Sum both equations

[math]( c_i^{\dagger} c_j^{\dagger} + c_j^{\dagger} c_i^{\dagger} ) | \psi \rangle = | i, j, \psi \rangle + | j, i, \psi \rangle[/math]

However the anticommutator defines [math]\{ c_i^{\dagger}, c_j^{\dagger} \} = c_i^{\dagger} c_j^{\dagger} + c_j^{\dagger} c_i^{\dagger} = 0[/math]

Hence [math]| i, j, \psi \rangle = - | j, i, \psi \rangle[/math] which is antisymmetry condition of fermions.

You could do the same with the annihilation operators and get the same result.

>>10664211
>I need it to be instant and not iterative.
Good luck lol

>>10664211
Nope. There's no constructive way of getting all the zeroes of any continuous function, and it's been proved.
And continuous functions can be very pathological.

>>10664192
>You need to find the smallest x where f(x) > threshold t.
if your function is continuous then that is guaranteed to not exist

>>10664248
Well that's disappointing. I just need the first zero, not all of them.
Can you show me the proof or tell me what to google to find it?

>>10664250
Oh i should have mentioned smallest positive x.

>>10664262
Uncountable number of continuous functions lad.

>>10664271
Well yeah, i mean, what? I have a specific one function that i need the zero for, not all functions in the universe.

>>10664192
I'm not sure why everyone else is beating around the bush on this, but from what I can tell it should be as simple setting f(x)-t=0, which shouldn't be mathematically intensive unless it's very complicated. You can just add a single value of your resolution (or the smallest interval you care about) to get the smallest non-zero relevant x. What I mean by that is if you're measuring something in meters, even though your function might be continuous, you probably don't give a fuck about nanometer variation, so just decide where that lowest resolution is.

a part of the hamiltonian operating on the hydrogen wavefunction is
[math]\frac{2}{r}\frac{\partial }{\partial r}{e}^{-r/a_{0}}[/math]
as I understand it it should be like deriving [math]\frac{2}{r}{e}^{-r/a_{0}}[/math] using the product rule, but the given answer is just the deriviation of e, leaving 2/r as is. What's going on here?

Retarded undergrad engineer here
Going to be tuning a PID controller using the Ultimate Cycle method. Do I need to do the tuning at the desired steady state value or will the gains be the same if I tuned it at a lower steady state?
I have some concerns about the safety of exceeding the desired value.

>>10663359
Not once did I ever mention a manifold in my construction though. This is all through the vector space structure.

>>10664217
I see, thanks.

Are people born with schizophrenia or can it be developed?
If I have two uncles who are schizophrenic am I at any risk of having it? I'm concerned, I've always spoken with myself, a LOT, but I deem that normal. I've also always been distrustful of others but lately I've been behaving that way towards my parents as well. People have been telling me that I'm acting strangely.
I do not think I have/developing schizophrenia but I am worried.
Is there any info you guys can give me on this stuff?

>>10664796
You're using the vector bundle structure of [math]\mathbb R[/math] implicitly

>>10664812
fuck off schizo

>>10664872
Please man I'm being serious.

>>10664812
You're not schizophrenic, you're just an asshole

>>10664885
Then don't ask on 4chan.

>>10664515
The differential operator does not act on anything left of it, only on exp(...)

I want to know how to find a function f, such that it will map like shown.
I thought the way to do this would be exponentials, but I'm having a lot of trouble trying to work out how to get the actual function.
f:[0,100] -> [a,c] with f(50)=b (b in [a,c]) and function is "even" (has continuous derivatives)

>>10665746
f(x)=b ist a function with all the properties you desire.

>>10664192
Just Google bisection.

>the smallest x where f(x) > threshold t.
You mean >=.

>>10664211
>I need it to be instant and not iterative.
And I need a gf to loose my virginity to.

>>10665928
f(0) = a
f(50) = b
f(100) = c
where a,b,c are not in a line
and f is strictly increasing I should also add
anyways I worked it out by solving for
f = ae^(bx)+d

>>10665947
>he didnt use the logistic function

>>10664812
>Are people born with schizophrenia or can it be developed?
They are born with it,if you read the medical literature all books say that the symptoms start manifesting themselves at the age of 21 for some reason.
Peer pressure can give you a mental breakdown with is a developed condition.
You should probably visit a doctor.

if i want to start undergrad research with a professor in the fall, should i ask him now or a few weeks before the semester begins?

>>10660998
A bit of paper and a pencil is extremely cheap, textbooks are on libgen.
That's pretty much all you need.

>>10666012
It shouldn't hurt to ask now, I see no harm in talking to him early and if I were a professor it would nice to to know of such things a bit earlier.

>>10635146
Unironically
>https://www.youtube.com/watch?v=TfAKsZOWBVg
>https://www.youtube.com/watch?v=nSVrNaXSx4k
>https://www.youtube.com/watch?v=CJlMoLkfhI8
>https://www.youtube.com/watch?v=XkqmuUg_yFs
>https://www.youtube.com/watch?v=AeSt2KNUdXY
>https://www.youtube.com/watch?v=r5dPasQtbY8
>https://www.youtube.com/watch?v=t4LadFEJArM
>https://www.youtube.com/watch?v=2aM6kKSf4R0