/sci/ - Science & Math

Is the fear of death more biological or psychological? I would argue more psychological, your lower brain doesn't actually know what death is, it just evolved to keep your organs running and avoid pain. Everything else is up to your conscious, decision-making brain.

>>9680852
How do I make a unit vector that passes through a given point (q, f(q))

I have parameteically made a line and know the slope s(q) . I want the vector to have a magnitude of 1 yet when I divide by its magnitude (the square root of each component squared, I don’t see the vector )

I’m not doing this for jistbcircles but instead any curve

How much wood could a woodchuck chuck if a woodchuck could chuck wood?

>>9680916
are you sure you are writing the vector right? Should be [math]\frac{1}{\sqrt{q^2+f(q)^2}}(q,f(q))[/math]

>>9680929
That’s a vector passing through the point I think but it doesn’t satisfy he condition of being perpendicular to the red line

>>9680953
well, maybe if you worded your problem, then it could be easier for me to answer?

your question just asked "how do i make a unit vector that passes through (q,f(q)" you retard

Can someone explain me the passage in pic related please

>>9680961
Oh you’re right, I’m sorry.

The question still stands... how do I make a perpendicular unit vector that passes through (q,f(q)) given I know the equation of the perpendicular line?

The perpendicular line is the unclicled function in the screenshot

>>9680966
It's just splitting the sum into even and odd denominators.

>>9680972
still not clear what you want. the unit vector is irrelevant of where it starts. if you have a desired unit vector (a,b), then you can define a line that passes through your point (q,f(q)) as the line L: (q,f(q))+r(a,b) where r is a real number. If your unit vector is a variable depending on q, then you instead define a curve.

>>9680992
It makes sense but if two sums are equal doesn't it mean that their "content" (sorry idk the proper word) should be equal too? In this case it's not true

>>9681025
Consider 1 + 1 = 2 + 0

>>9681025
no, look up riemann series theorem

>>9680993
Hmm, maybe I’m over complicating things or over simplyfying

I want a unit normal vector that is perpendicular to the tangent line of a given curve.

Given a curve (the black curve in the image) I can find the tangent line (in red) by just finding the slope/derivative and evaluating at some point, q, let’s call this slope f’(q) = M . To make the tangent line I can say that this lines formula is given by y = f(q) + M(x-q). And again that’s the red line

I know that any line perpendicular to the red one will have a slope of -1/M = S

Parametically one such perpendicular line will be (t, S*t) for all t. I can make this the normal unit vector by dividing by the magnitude which is sqrt(S^2 + 1)

However I want to see this unit normal vector to start at the point (x , f(q) ) but I can’t seem to do it properly

>>9681045
Nvm, I got it

God I’m a brianlet

What the fuck does a triple integral in [math]\mathbb{R}^3[/math] even mean? Is it finding a hypervolume? I'm confused conceptually, yet double integrals are crystal clear in my mind.

>>9681057

>>9681060
Volume (M) of a closed surface is given by [eqn]\iiint_M 1\cdot \mathrm d V[/eqn]

>>9681039
But 1+1 is actually equal to 2+0

>>9681040
Right, i forgot about that. It's one of the things that makes me think that math is bullshit

>>9681077
Yes, I understand this so far, but what if you're integrating your dV underneath a curve [math]f(x, y, z)[/math]?

>>9681086
notice that to represent a function of three variables f(x,y,z), you need 3 axes, one for x, y and z, and one for f. So yes, in fact, you are finding the volume of a hypersurface

>>9681089
4 axes*

>>9681082
things are weird at infinity man

It's probably dumb but what exactly is going on here?


[math] \frac{\partial V }{\partial q_{k}}=\frac{\partial V}{\partial x} \frac{\partial x}{\partial q_{k} } + \frac{\partial V}{\partial y} \frac{\partial y}{\partial q_{k} }
\\ \\
x = x(q_{1},...,q_{k})
\\ \\
y = y(q_{1},...,q_{k})
\\ \\
V=V(x;y)
[/math]

Is it considering that you can write:
[math]q_{k}=q_{k}(x,y)[/math]

I'm not sure that's legal, or how it would make sense

>>9681171
its just chain rule.

>>9681025
Most operations on limits (and yes, that's a limit in the pic) are only defined if the limit exists and is finite (which is not the case in your pic).

do birds breath

>>9681177
yea of course what was i thinking

>>9681177
But why are there two terms afterwards?

>>9681204
Yes.
In fact, incredible fast birbs breath in incredible high speed ~512b/pm

>>9681246
thnx nigga thats cool

>>9681253

>>9681246
>512b/pm
nigga it's either bpm or b/m

>>9681253
>>9681375
sorry I mean to say 512 beats/per minute for heartbeat during flight but you can compare the breath frequency against human

>>9680852
How do I prove the reimman hypothesis? I’m having a little trouble with it

~ thanks

>>9681384
by inspection

>>9681384
>>9681387
RH already disproven
On The Riemann Zeta Function
http://vixra.org/abs/1703.0073

wouldn't global warming be stopped if we killed everything that ate phytoplankton and just let them develop an excess of oxygen?

>>9681428
no because it's the GHGs that are the problem

>>9680860
At what point does biology become psychology? At what point does animal turn into man?

It's also funny to note how, the fear of /death/ itself doesn't compare to the fear of a poor life. Dying at 40 after becoming a billionaire and having a good family? Damn, that sucks. Dying at 80 and never living up to your potential? Fucking terrifying.

>>9680860
this completely ignores the argument that some living things don't feel pain but still try to avoid death and i do believe some things do actually not feel pain so how would they know to avoid things if not for a fear of death. i would attach that webm of the wasp getting its face eaten by a preying mantis or whatever it was but i don't have it

>>9681271
that's a fricking cool webm. what was destin doing

For this, do I just expand it out and show that any matrix A can be represented by a lin comb of the others unless ai = 0?

So I guess some Russian spy was poisoned the other day but he survived. I decided to read up articles about why he was targeted and what poison was possibly used, but I couldn't find much info on the latter. One thing that struck me about the articles is that many are headlined with "Poison was delivered in liquid form."

I was wondering, why is that such a big deal? Wouldn't the poison obviously be in liquid form? This question may seem a little too /pol/itical I guess, but I'm more interested in the chemistry side of the story.

http://abcnews.go.com/International/wireStory/uk-nerve-agent-poisoned-spy-liquid-form-54522705

http://www.bbc.com/news/uk-43798068

>>9682505
>British officials say the Skripals were poisoned with a military-grade nerve agent that was smeared on a door handle at Sergei Skripal's house.

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

>Dispersed in an ultra-fine powder instead of a gas or a vapor, they have unique qualities.

im guessing that this nerve agent isnt normally utilized as a liquid, nor in such a method (i imagined the victim had his food poisoned prior to reading your article)

>>9680852
What does finding the limit when a number approaches infinity or 0 even fucking mean?

where did the 71 come from?

>>9682385
What is your definition of linearly independent?

>>9682582
>where did the 71 come from?
By expanding out the square and subtracting 3

>SI base unit for length is the meter and not the kilometer
>SI base unit for time is the second and not the kilosecond
>SI base unit for mass is the kilogram

why

>>9682615
why do you think it should be?

>>9682616
I don't think anything in particular. It just really bothers me that that particular SI base is prefixed for no reason that I can discern.

>>9682620
simply practicality. no other reason.

>>9682630
That's a really shitty reason to use a non-base unit as a base unit. And the fact that it's a fucking lump of metal that changes weight over time is yet another problem.

It's retarded.

>>9682601
here is whole context

>>9682670
suppose some [math]a_i \neq 0[/math] and find the contradiction

>>9682685
So [math] a_1A_1 + a_2A_2 +....+a_kA_k = 0 [/math]

Then we assume [math] a_i != 0 [\math], then subtract [math] a_1A_1[\math] from both sides and get [math] -(a_1A_1) = a_2A_2 + ... + a_kA_k[\math]

Then divide by [math]a_1[\math] since we are assuming some a is not zero, and get a linear combination for [math]A_1[\math] which is a contradiction if the set is linearly independent.

Is this correct?

>>9682696
sorry I butchered the latex badly, still new to it

>>9682696
>>9682698
>>9682685

Then we assume [math] a_i != 0 [/math], then subtract [math] a_1A_1[/math] from both sides and get [math] -(a_1A_1) = a_2A_2 + ... + a_kA_k[/math]

Then divide by [math]a_1[/math] since we are assuming some a is not zero, and get a linear combination for [math]A_1[/math] which is a contradiction if the set is linearly independent.

Ok hopefully I fixed it

Explain Graham's Number to me like I'm a complete retard.

>>9682709
>Explain Graham's Number to me like I'm a complete retard.
https://simple.wikipedia.org/wiki/Graham%27s_number

>>9682726
I literally forgot that Simple Wikipedia exists.

Homework on countability

Do there exist five countably infinite disjoint subset A,B,C,D,E of the integers such that [math]A\cupB\cupC\cupD\cupE = Z[/math]

I'm pretty sure this is true because in my textbook there is a theorem saying Every infinite subset of a denumerable set is denumerable. But how can I show that the union of the sets = Z?

>>9682766
>Do there exist five countably infinite disjoint subset A,B,C,D,E of the integers such that A\cupB\cupC\cupD\cupE=Z
Yes, A={...-5,0,5,...}, B={...-4,1,6...}, C={...,-3,2,7...}, etc.

>I'm pretty sure this is true because in my textbook there is a theorem saying Every infinite subset of a denumerable set is denumerable.
This doesn't imply what you're trying to show.

>But how can I show that the union of the sets = Z?
Which sets?

>>9682771
The union of A,B,C,D, and E. Sorry i fucked up the latex.

>>9682726
>>9682736
>Graham's number is a very, very big natural number

Weeb here, I was watching a certain series and thought to myself:
Would a limb made out of artificial organic materials be able to be controlled by your mind?
I know that sounds confusing so let me explore the question:
We already know that prostethics can be controlled by either your mind or nerve endings, look at the multi million dollar DARPA program, but that was done using polymers and metals, I'm asking if it's possible to do the same thing with artificial organic muscle and tendons, we've already begun printing organs, surely in a couple years we could do the same with muscles.
Complete brainlet so I could have just spewn out some dumb shit but oh well.

does flushing a spider down the toilet = spider kill? i do not know how the plumbing works. can it escape? do i need to guard it in the toilet bowl for a while to make sure it drowns?

>>9682558
well, you want to find out how the function behaves near a certain number like 0, so you ?probe' your function by taking values very near to 0 to see how it goes. For infinity, you're looking at how your function behaves for very large values. Usually, a function may become very large or very small, or become a fixed value, or oscillate forever, so you wanna see what happens again.

>>9680852
A serious question, why doesn't this work (in theory)?
>Take a stick of a solid material that doesn't compress
>one human at each end has access to it
>human 1 pushes it
>human 2 sees that because the stick is coming towards him
Now:
>Said stick is 1 light year long
>human 1 pushes it, human 2 sees it 1 second later because it's just a moving stick
>instantaneous information transfer????

If this doesn't work because the stick rather compresses than move instantaneously (to be proven). New situation:
>long stick is inside a long tube that's closed on one end
>human 1 pushes stick, at his end it moves immediately
>the "compression wave" takes a while though to reach the other end
>as soon as human 1 is finished with pushing, he puts a cap on his end of the tube
Now there is a stick in the tube that is actually longer than the tube itself.
How is this possible?

pic related

If light is affected by gravity, does that mean that static electric fields are also affected by gravity?

>>9682505
Poison can be in powder form too.

>>9680852
Switching major from CS to Physics yay/nay?

I don't have to much experience in physics but I like math and things that are actual concepts. This is what I strongly dislike about CS it's like do X in the given framework not so much concepts.
I do not care about career pay at all.

Pic not related

Can you recommend a good book (or books) about mathematical logic, that covers everything from propositional calculus to Peano's arithmetic and Godel's theorems?
I'm starting to think that the course of lectures I was given was full of meme Soviet terminology nobody really uses outside of my university.

>>9683141
1.there is no such thing as an incompressible solid

2. elastic deformation

I was given a good explanation of why x/0 != inf: Plot it and it approaches both +inf and -inf depending on direction, meaning a limit is not defined.

But:

1) What about abs(x/0)? This only approaches +inf so its limit would seem to be defined
2) Why can't we handle this the same way we handle square roots, and just say that x/0 = +/-inf?

I realise that a lot of things become very inconvenient if division by zero is defined, but it doesn't feel very right to just say "x/0 can't be done because it would break other things". Why can't the other things be wrong?

Given the function f(x,y), discuss the decidability of the problem of whether the decimal expansion of pi contains a sequence of h > x digits repeated y times, in which case f returns 1, and 0 otherwise. I think it's undecidable but I don't know how to show why.

>>9683393
infinity is not a number

How does [eqn]\sum_{m=1}^\infty \sum_{j=1}^\infty j^{2k-1}q^{ mj}[/eqn] become [eqn]\sum_{n=1}^\infty \sigma_{2k-1}(n) q^{n}[/eqn] where [math]\sigma _{2k-1}(n)=\sum _{0<d|n} d^{sk-1}[/math] and [math]q=e^{2\pi i x}[/math]. My book says by setting [math]mj=n[/math] and that's it.

>>9683393
The problem is your treating infinity as a number. Don't. It's just a shortcut, one you need to use with caution. Expressions like [math] \frac{1}{\infty} = 0 [/math] don't actually define a new operation, they merely reflect the properties of the limit.
Treating infinity as a number breaks arithmetic. It's bad for mathematics when something breaks.

> 1) What about abs(x/0)? This only approaches +inf so its limit would seem to be defined
Yes, [math] \lim_{t \to 0}{\frac{|x|}{|t|}} = +\infty [/math].

> 2) Why can't we handle this the same way we handle square roots, and just say that x/0 = +/-inf?
First of all, there's only one "square root" of [math] x [/math]. It is by definition the positive solution of [math] x = y^2 [/math] . Secondly, both [math] \sqrt{x} [/math] and [math] -\sqrt{x} [/math] are correct solutions of the aforementioned equation irrespective of [math] x [/math]. In the case of diving something by zero it depends on the function you use to approach that zero. This kind of uncertainty would defeat the purpose on introducing this notation.

>>9683457
Thanks anon, this was helpful.

Brainlet here.
Since alpha radiation consists of two protons and neutrons, would it be possible to turn it into helium by ionizing the radiation?

>>9683457
>Treating infinity as a number breaks arithmetic.
How so?
https://en.wikipedia.org/wiki/Extended_real_number_line

>>9683457
>It is by definition the positive solution of x=y2 .
You want "non-negative solution" here.

>>9683597
[math] 0 \cdot \infty = ? [/math]

>>9683599
Mistakes like that don't matter as long as they are obvious. You didn't have to point that out, it's a post on 4chan, not a scientific article.

>>9683609
>0⋅∞=?
see https://en.wikipedia.org/wiki/Extended_real_number_line#Arithmetic_operations

>>9683622
Has undefined expressions = broken.

>>9683625
So should we not use zero either since 1/0 is an undefined expression?

If I get an associate's degree in IT and then 5 years or so later decide to get a Bachelor's too, would it only be 2 years? Or would it still be the full 4 years?

>>9683628
Zero not having a reciprocal is fine, the definition of a field is met. Stuff like [math] \infty - \infty [/math] being undefined makes it impossible to even call R extended a group under addition.
I never understood the importance of formally extending R. As long as you know what you're talking about, you don't need to develop a new kind of algebraic system just to explain why
[math] \int_{0}^{\infty} \frac{dx}{1 + x^2} = \text{arctg} \left( \infty \right) - \text{arctg} 0 = \frac{\pi}{2} [/math]

>>9683655
>Zero not having a reciprocal is fine, the definition of a field is met.
So? As you said, "Has undefined expressions = broken.". If you want to define 0*infinity, then you can just extend the algebraic structure, and the definition of a wheel is met.

Does earth move under helicopter or person when they gain altitude, that is there any drift gained from earths rotation.
I know that we earth wont move 1000miles/h under object that ascends, but shouldnt there be some drift.
My reasoning is that object on surface has same tangential speed as earth, v=1000miles//h, and when it ascends it needs to cover more distance to stay in same location relative to earths surface since now it moves in larger radius.
For example if we have object, at equator, that is 10 miles from surface and it has same tangential velocity as when it was on earths surface it should drift 62 miles every day.

Is this wrong? Is angular velocity instead of tangential velocity conserved in this system.

>>9683260
How could you create a static electric field around a black hole? The particle causing the field would inevitably move because of gravity.

>>9683666
....
Nah, fuck it. Let's say you're right and I'll get back to my homework.

>>9683523
Ionizing means removing electrons from around the nucleus. An alpha particle is a helium nucleus without any electrons around it. So no, you cannot ionize something which cannot be ionized.

>>9683669
By Newton's third law, when you jump on earth, the earth will move a distance too, where your momentums are equal. By Newton's law of gravitation, when you are in the air, both you and the earth will move closer to each other, such that momentum is equal.

It is negligible, but it does exist theoretically.

>>9683649
bump

>>9683696
t. Retard

Ionization is the process of removing or adding electrons around the nucleus

>>9683409
Enumerate the digits, check for the sequence. If it's true, you'll find such a sequence eventually. If it's false, you'll be checking forever. Decidability requires that both affirmative and negative answers can be given in finite time.

>>9683703
I know that earth moves closer to me. What im asking is the ground move under my feet when im in air. Do i land in the same spot after jumping. My intuition would say yes, but if i look at conservation of momentum ie tangential velocity i get a small drift.

>>9683260
no, you can have charged black hole. Interaction between charged particles is mediated by virtual particles that dont obey "standard" laws of physics.

>>9683685
you can have charged black holes. that have their own electric fields.

>>9683649
bumpp

Why am I seeing a rise of Climate Change deniers? Is it linked to Trump or is it a rising movement?

Also what basis do they use for their denial? Are there questionable practises in some major papers or is it like the anti-vax movement where one paper has suggested that climate change is fake and people have bandwagoned on that?

>>9683905
https://www.edx.org/course/making-sense-climate-science-denial-uqx-denial101x-6

>>9683905
It's a community thing. If they "reject" climate change, they create a place for themselves in said community, and so they can just follow the herd on who to vote for, what car to drive, who to marry, what to eat, etc. instead of thinking for themselves.
More of a sociology than sci question, but that's the basic idea.

>>9683938
It's a community thing. If they "accept" climate change, they create a place for themselves in said community, and so they can just follow the herd on who to vote for, what car to drive, who to marry, what to eat, etc. instead of thinking for themselves.

kys

>>9683938
I have noticed its mainly people leaning to the right I see sharing stuff on social media. So its just identity politics?

But back to the initial point, what do they do to dispute the evidence in papers? Surely they must have some argument against it.

>>9683905
these are the people who shill climate change:
https://www.youtube.com/watch?v=VtJFb_P2j48

>>9683948
http://www.drroyspencer.com/2012/02/ten-years-after-the-warming/

>>9683941
If you wanna argue that, you'd have a harder time but yes the reverse works too.

>>9683980
http://www.drroyspencer.com/my-global-warming-skepticism-for-dummies/

>>9683948
In my experience, they nitpick data/conclusions for specifics (perfectly reasonable), then because the specifics are more complex and build into the "simple" answer instead of the simple answer being the only answer regardless of complexity, like a is the answer, but it's actually c+b=a but just b!=a and just c!=a, the they jump that a must be a false answer.
False understanding leads to false conclusions.

>>9684008
almost no one doubts that humans have at least some impact on the climate, but it's pretty bold to claim that humans are the dominant factor

If [math] \sum f_{n} [/math] converges uniformly, then [math]\forall[/math] [math]\epsilon > 0 [/math], there exists [math]N\in\mathbb{N}[/math] such that [math]|f_{n}(x)|<\epsilon[/math] for all [math]n\geq N[/math], and [math]\forall[/math] [math]x\in A[/math]

is this a correct definition to use for determining uniform convergence of a series of functions? apparently it's a special case of the Cauchy criteria.

>>9684021
what you wrote is the uniform converge towards the zero function

how about an analogy, take the stock market, the companies and the markets are real, but how can anyone know exactly what a company's stock is worth and where the markets are heading, some companies have valuations that are obviously ridiculous, there's a lot of psychology and politics built in, same with man-made climate change

I'm a chemist who recently got to work in a surface physics department and I'd like to get familiar with optics and Maxwell's equations so I can get a deeper understanding of surface plasmon resonance spectroscopy. Are there any comprehensive books on those matters for people who are okay at physics but never studied it in depth? We're talking about "wtf light is an electromagnetic wave" tier.
>TD;DR recommend me some good books on optics and Maxwell's equations that are fairly easy to understand

studying electromagnetism
what the fuck does this prof want? whats d for?

>>9684285
a vector

>>9684285
find the electromagnetic field for each sphere individually then add them together

>>9684353
how do you supoose i add two spheres? do i need to convert them back to cartesian first?

>>9684408
if the field is a vector, then it should be quite easy to add to vectors i'd say

>>9683649
never mind, just found out the answer

>>9684410
except a spherical vector radiates outwards from the origin? i can only have 1 point of origin but i have 2 different center of origin

>>9684417
physics is symmetric upon translation. That is, if you place a sphere in some point in space, it should be the same as if it were in another. So if you have that the sphere radiates a field [math]\vec{F}=f(\vec{r})\cdot \vec{r}[/math], where [math]f[/math] is a scalar function, then upon moving it to the new "centre of origin" which is a distance [math]\vec d[/math] away, then the new force is going to be [math]f(\vec{r}-\vec d)\cdot (\vec{r}-\vec d)[/math]

can someone please give me a linear map [math] f\colon\mathbf{R}^2\longrightarrow\mathbf{R}^3 [/math] with [math] \ker f\neq\{0\} [/math]
im trying to visualise/build some intuition about the rank-nullity theorem. i can only think of linear maps with ker f={0}, which isnt that interesting

>>9684432
[math](x,y)\mapsto (x,x,y)[/math]

>>9684432
just take any 3x2 matrix where at least one column contains only zeros

>>9684424
>F⃗=f(r⃗)⋅r⃗
>\vec{F}=f(\vec{r})\cdot \vec{r},
why do you need to dot this it with the r vector again if the f is a function of vector r already?

>>9681060
Let [math]f:M\rightarrow N[/math] be a diffeomorphism between [math]n[/math]-dimensional manifolds [math]M,N[/math], and let [math]\nu_N \in \Omega^n(N)[/math] be the volume form on [math]N[/math]. On forms, [math]f[/math] pulls back to an isomorphism [math]f^*: \Omega^k(N) \rightarrow \Omega^k(M), 1\leq k \leq n[/math] such that the induced volume form [math]f^*(\nu_N)[/math] satisfies [eqn]\int_M f^*(\nu_N) = \int_N \nu_N.[/eqn] Now if [math]M[/math] admits a trivial cover, [math]\Omega^n(M)[/math] is spanned by [math]dV = dx^1\dots dx^n[/math] as a 1-dimensional [math]C^\infty(M)[/math]-module, and hence there exists a smooth function [math]\phi_f:M \rightarrow N[/math] such that [math]f^*(\nu_N) = \phi_f dV[/math], which leads to [eqn]\int_N\nu_N = \int_M f^*(\nu_N) = \int_M \phi_f dV.[/eqn] Hence if [math]N \hookrightarrow M[/math] is an embedding, then [math]\int_M \phi_f dV[/math] is the volume of [math]N[/math] in [math]M[/math] with respect to the volume form [math]\nu_N[/math].
>>9681171
Consider the case [math]k = 1, q_1 \equiv t [/math], and let [math]\gamma:\mathbb{R} \rightarrow M[/math] be a curve on [math]M[/math]. Your function [math]V[/math] is then the evaluation of an associated function [math]V:M \rightarrow N[/math] along the curve [math]\gamma[/math]. The vector at [math]\gamma(t) = x\in M[/math] tangent to [math]\gamma[/math] at time [math]t\in\mathbb{R}[/math] is given by the vector field [math]v_\gamma = \frac{d \gamma_\mu}{dt} \partial^\mu \in T_* M[/math] which satisfies [eqn]\frac{dx}{dt} = \frac{d\gamma_\mu}{dt} \partial^\mu x \equiv v_\gamma(x).[/eqn] On vector fields, [math]V[/math] pushes forward to a map [math]V_* :T_* M\rightarrow T_*N[/math] with the property that the tangent vector on [math]N[/math] along the curve [math]V \circ \gamma[/math] is given by the vector field [math]V_*(v_{\gamma})(x) = v_\gamma(V(x)) = \frac{d\gamma_\mu}{dt}\partial^\mu V.[/math]

>>9684443
i said it was a scalar function, i was just making it clear that it was a multiplication, but i guess it looks awfully close to a dot product

>>9684432
also, note that kerf = 0 is equivalent to the map not being injective, so its pretty easy to come up with both

I know /sci/ isn't for homework but I'm fucked right now. I can not for the life of me figure out compounding interest for future values. I'm being asked
What is the future value of a $10,000 university tuition fund if the nominal rate of interest is 12 percent compounded monthly for five years?
And when I try
10000(1+ r/m) ^ m x n OR
10000 (1 + 0.004166666) ^ 12 x 5
I get 12833. The only problem is I'm given 5 answers and none of which are less than 16000

>>9683260
Indeed. Let [math]M[/math] be a Riemannian 4-manifold with a metric [math]g[/math], then the Yang-Mills action for the EM field is [eqn]\mathcal{A} = \frac{1}{4\pi^2}\int_M F^2 = \frac{1}{4\pi^2}\int_{\mathbb{R}^4}dV\sqrt{\operatorname{det}(-g)}F^2[/eqn] where [math]F =dA \in \Omega^2(M) \otimes \mathbb{R}[/math] is the [math]U(1)[/math] field strength. By a conformal expansion [math]g_{\mu\nu} \sim I + \epsilon_{\mu\nu}\partial^{\mu}\partial^\nu[/math] in the metric, a coupling between gravitons [math]\epsilon[/math] and photons [math]A[/math] is possible.
>>9684432
Take a local section of the the Hopf fibration [math]S^3 \rightarrow S^2[/math].

>>9684478
nigga da fuck do those formulas mean. Have you tried 10000*(1.12)^5

>>9684478
>>9684496
Nevermind, I'm just an idiot. I was using the 5 years as interest instead of 12

>>9684435
maybe i have brain damage but isnt the kernel of that 0?
>>9684438
>>9684456
thanks anon
>>9684487
t-thanks

Going to study Computer Science and Informatics soon.
Any good recommended books to read?

>>9684505
how is the kernel of >>9684435 0? Check out my other post >>9684456 and think how. Do you know what the kernel is?

The kernel of a linear map is the set of elements that get mapped to 0. The map [math](x,y)\mapsto (x,x,y)[/math] can only be the zero map if [math]x\mapsto 0[/math] AND [math]y\mapsto 0[/math]. But that means that both [math]x,y[/math] are precisely zero.

Maybe you are confusing it with surjectivity (although out of the scope of your course, you're confusing it with the cokernel!). In which case, clearly there are no surjective linear maps R^2->R^3 by rank-nullity

>>9684514
>The kernel of a linear map is the set of elements that get mapped to 0. The map (x,y)↦(x,x,y) can only be the zero map if x↦0 AND y↦0. But that means that both x,y are precisely zero.
But he/she asked for a linear map with non-zero kernel

>>9682607
I dun get it :-(

>>9684523
>I dun get it :-(
Are you not able to expand ((x-2)/5)^2?

>>9684520
Oh right, well thats a stupid question then

>>9684432
the map [math](x,y)\mapsto (0,0,0)[/math] has full kernel (that is, ker = R^2)

the map [math](x,y)\mapsto (x,0,0)[/math] has kernel R^1

the map [math](x,y)\mapsto (x-y,x+y,x)[/math] has kernel? exercise

>>9684523
you need a common denominator for that 3 so you have to turn it into [math] \frac{25}{25} \cdot 3 = \frac{75}{25} [/math]

>>9684525
Since the value of x is unknown, nope sorry i don't get it

>>9684540
Do you know how to expand ((10-2)/5)^2?

How easy/hard is it to make nuclear weapons out of power plants?

>>9684544
Yes but why 10, where did it come from

>>9684551
>Yes but why 10, where did it come from
The 10 doesn't matter, you expand ((x-2)/5)^2 the same way as ((10-2)/5)^2.

>>9684540
it doesn't ask you to find x m8

[math] (\frac{x-2}{5})^2 = \frac{x-2}{5} \cdot \frac{x-2}{5} [/math]
[math] \frac{x-2}{5} \cdot \frac{x-2}{5} = \frac{(x-2) \cdot (x-2)}{5 \cdot 5} [/math]
[math] \frac{(x-2) \cdot (x-2)}{5 \cdot 5} = \frac{ x^2 -2x -2x + 4}{25} [/math]

>>9680860
Νοt as "fear", but as resentment to death as it being "not life". Every living creature just wants to keep on living. Thus creates offsprings to "fool" death.

Any of you lads ever study, do an assignment or take a test drunk?
>get drunk for online psych test
>87
>turn in lab report drunk
>81
>show up buzzed for lecture test
>76
>review test material sober then assess self when drunk to simulate test day feeling

how the fuck do i do this shit

>>9682615
>burger base unit for length is the inch, foot, yard and/or mile and not the meter
>burger base unit for time is the second and not the sleepytime
>burger base unit for mass is the pound of fatass

why

>>9682615
>burger base unit for length is the inch, foot, yard and/or mile and not the meter
>burger base unit for time is the second and not the microwave time
>burger base unit for mass is the pound of fatass

why

>>9684632
clearly there are two possible subrepresentations

So I'm in a Real Analysis course and the professor started throwing Flux and Work and Curl and Divergence at us and I'm not really sure what any of them actually mean because I've never seen them before. Are these useful mathematical objects or are they just physics things he is using as examples for calculations?

how do i do this? I dont think i can use Gauss Law right? like sure the Q_enc is zero, but its not exactly symmetrical to begin with right?

>Present values
>Future values
>Compounding interest
>Nominal interest
>Effective interest
>Multiple cash flows
>Annuities
>Perpeutities
>Bonds
How the fuck am I meant to remember all of this and the formulas

>>9684951
Just get a financial calculator for 30 bucks my dude.
Ba 2 plus

>>9684414
this guy isn't me, very funny ha ha

but srsly can someone answer my question>>9683649
>>9684414

>>9684847
Did you read the hint? Find the electric field due to the whole sphere and then subtract the electric field due to the carved out cavity.

>>9685021
How does that help me remember the formulas?

>>9685027
Just study them or better yet just do all types of problems over and over until it’s second nature..unless you literally are going to Ben regurgitating them for your exam

Why is college so difficult? Does everyone struggle or am I just a moron?

how do i understand curl in vector calculus? i know what it means sorta but dont know how to understand the formulas

>>9684801
im retarded and have no clue

>>9685047
having autism helps
>>9685083
who cares about understanding calculus, just memorize problem solving strategies

I take in some amount of a gas at temperature T. I use an amount of energy E to raise it to 2T, then put it through a Carnot process before venting it at T again, for a Carnot efficiency of 50%. Does this mean the process recovers E energy, .5E, or some other amount?

>>9685113
pls halp

Just started my Intro to Proofs class and was wondering, if I decide to use logical identities to prove a set equality like in pic related, is it correct to argue in step 9 that all my other steps are reversible such that I don't need to do a separate proof starting from the right side to the left side?

Before doing it this way, I was used to first showing that if an arbitrary element x is in the left side then it is in the right side and then doing a separate proof for the opposite case (from right to left).

I would appreciate any feedback since I just started with LaTeX, so if there is anything wrong with the style I am using to present my proof or a mistake.

>>9684219
pls respond

>>9680852
Does anyone have a recommendation for a free introductory calculus based physics textbook? I tried google but the only non-sketchy thing I could find was really verbose.

I'm trying to find the area enclosed by 2 polar curves r = 2+sin(th) and r = 3sin(th), which only intersect at pi/2. So what do I use for the other boundary in order to integrate A? Should I just use 0 to 2pi instead?

Help an idiot out.
Does this result in 0=0 or x=0?

>>9685552
>Does this result in 0=0 or x=0?
What have you tried?

>>9685552
Both give x = -(8/52)
I don't get your problem with this.

>>9685558
But shouldn't the pair eliminate each other if you're kind of supposed to add them together?

>>9680852
>Gracchus brothers
>hating Plebians

>>9685568
>But shouldn't the pair eliminate each other if you're kind of supposed to add them together?
What for?
You have only one variable, you'd pair something that has 2 or more:

ax+bx+c = 0
y = kx+m

>>9685568
Yes, if you add them together, they'll eliminate and you'll be left with x=0

>>9685591
no he wouldnt, he would end up with 0=0 because -52x and 52x will self-destroy, no X left not adivision

>>9685590
Fair point, I hadn't thought of this.

>>9685552
0=0 but that's pointless, 0=0 is obvious

>>9684509
http://4chan-science.wikia.com/wiki/Computer_Science_and_Engineering

>>9685423
http://4chan-science.wikia.com/wiki/Obtaining_textbooks
http://4chan-science.wikia.com/wiki/Physics_Textbook_Recommendations#High_School

Why am I good at (okay at) mathematics but bad at programming? What am I missing?

>>9685870
Not good at structured, algorithmic thinking?

Suppose [math]f[/math] and [math]g[/math] are functions on [math][0,1][/math] such that [math]f[/math] is Riemann integrable and [math]g(x)=f(x)[/math] except possibly at [math]x=1[/math]. To prove: [math]g[/math] is Riemann integrable and [math]\int_{0}^{1}g = \int_{0}^{1}f[/math]

Certainly, [math]g[/math] is Riemann integrable on [math][0,1)[/math], which equal value to [math]f[/math]. How do I go about the remaining bit?

>>9686050
could it be that since [math]f[/math] is bounded, thus [math]g[/math] is bounded on the appropriate portion, and so for all but a finite number of potential points the integral will remain unchanged?

How do I prove that a function doesn't have an anti-derivative? I asked my proff, and he gave vague details but he couldn't quite remember much of it.

>>9686078
there are some theorems on the behavior of derivatives.. e.g. a derivative cannot have jump discontinuities or something like that.

>>9686096
no, no, I mean for functions like [math]f(x) = e^{x^{2}}[/math]

>>9686050
this heavily depends on what machinery you can use. the true answer is: the functions coincide except for a set of measure zero and that's why they have the same integral. but you can prove this directly from the definition, without knowing what a measure zero set is.

>>9686099
this function DOES have an anti-derivative, it's just that it cannot be expressed using elementary functions. this is a completely different question.

>>9686105
Sorry, that is what I meant. An anti-derivative in terms of elementary functions.

>>9686110
prolly something to do with taylor series representations

>>9686113
I know that [eqn]F(x) = \sum_{n=0}^{\infty}\frac{x^{2n+1}}{(2n+1)n!}[/eqn] is a suitable anti derivative. The question is why it can't be represented using elementary functions. Sorry if I misinterpreted you.

>>9685183
>is it correct to argue in step 9 that all my other steps are reversible such that I don't need to do a separate proof starting from the right side to the left side?
i don't know if i understand what youre asking.
in step 9 it is enough to show that step 9 is true if and only if step 8 is -- you don't need to mention any other steps because they are all reversible (on account of them being definitions and equalities).

(also i am presuming the term reversible means [math] \longleftrightarrow [/math])


as for latex, it looks fine to me. personally, in proving something like that, i'd use the following form
[math] \begin{align} x\in A\cap(B\cup C) \longleftrightarrow\ &x\in A\wedge x\in(B\cup C)\\ \longleftrightarrow \ &x\in A\wedge (x\in B\vee x\in C )\\ &\vdots \end{align} [/math]
but since youre taking a proofs class i imagine your style is more suitable

>>9686110
well I know next to nothing about this. but the question whether a function has an elementary anti-derivative (or more generally whether a given function has can be expressed using only elementary functions) is HIGHLY non-trivial, I can tell you that much. I think you're keywords are differential algebra, risch algorithm, liouville's theorem.

>>9686139
*your, fuck me

>>9686139
thank you, i will search for these terms and see what I can find out.

my psychology 101 professor lectured us today about how chemical imbalance explanations of depression and other mental illnesses are actually bullshit and are pushed by the pharmaceutical industry. it reminded me of when i went to a small christian middle school and my 7th grade science teacher taught us that evolution and climate change are false. except i don't know shit about psychology whereas everyone would agree that science teacher was insane. is it the same type of quackery, or does my psychology professor speaking the truth?

>>9686181
University of Toronto?

>>9686208
sadly no, if i had the chance to piss in peterson's coffee i would've done it long ago.

>>9686118

neat question. liouville's theorem is still beyond me, but since ERF is analytic but doesn't diverge, oscillate, go to zero or some constant, or have a finite taylor series, i can see why it might be hard to define using a finite composition of elementary functions.

>>9686118

something doesn't square here. wikipedia says that ERF is entire, but the liouville theorem in my book says that bounded entire functions are constant. what gives?

>Recently diagnosed with autism
>Got a letter just now asking me to take part in a research study for some uni students PhD
>"A single blind, randomised controlled trial of anodal transcranial direct-current stimulation against cathodal and sham stimulation in Adults with High-Functioning Autism"

Basically it's researching working memory and using electrodes placed on your scalp to do it, it would be 2 hours in total.
I am a /sci/ pleb and am just wondering if this is worth the 25 pound Amazon voucher it promises as compensation. It says side effects are highly unlikely but maybe you guys have some redpills on this, I don't know.

>>9686317
> 25 pound Amazon voucher
dead meat worth more but that's just my opinion

>>9686317

i don't think i'd let anyone stick something in my brain

>>9686118
>>9686139

seconding this. i'd like to see an outline of how the proof goes. why is ERF non-elementary when other sigmoid-shaped functions with the same limits are?

is this the correct translation of pic related?

[eqn]
\forall g \in C^1([x_0, x_1]) : \left( \forall h \in \left\{ f \in C^1([x_0,x_1]) : f(x_0) = f(x_1) = 0 \right\} : \int_{x_0}^{x_1} g(x)h(x)\ \text{d}x = 0\right) \implies g = 0
[/eqn]

>>9685870
>What am I missing

Experience. Force yourself to work through a data structures and algorithms book and eventually it will click. You'll look back and wonder why the fuck you were so retarded.

>>9685870
One explanation is that you're not actually good at math.

I feel like a brainlet but can someone explain what is going on here?

>>9686901
https://en.wikipedia.org/wiki/Product_rule

>>9686660
The phrasing is dogshit, it should say FOR x_0<x<x_1 or in ]x_0,x_1[. It's also bullshit, h(x)=0 satisfies that for any g(x).

>>9686906
ah okay so

[latex] \frac{d(v_i v_i)}{dt}=\frac{d(v_i )}{dt}+\frac{d(v_i )}{dt}=2\frac{d(v_i )}{dt} \rarrow \frac{1}{2}\frac{d(v_i v_i)}{dt}=v_i\frac{d(v_i }{dt}[\latex]

how do i solve questions like pic related in general?
i got [math] m_{\alpha}(X)=X^2+2X-2 [/math] by factorising, but i'm not sure if it's right

>>9686915
[math] \frac{d(v_i v_i)}{dt}=\frac{d(v_i )}{dt}+\frac{d(v_i )}{dt}=2\frac{d(v_i )}{dt} \rarrow \frac{1}{2}\frac{d(v_i v_i)}{dt}=v_i\frac{d(v_i }{dt} [\math]

>>9686918
[math] \frac{d(v_i v_i)}{dt}=\frac{d(v_i )}{dt}+\frac{d(v_i )}{dt}=2\frac{d(v_i )}{dt} \rightarrow \frac{1}{2}\frac{d(v_i v_i)}{dt}=v_i\frac{d(v_i }{dt} [/math]

>>9686913
>The phrasing is dogshit, it should say FOR x_0<x<x_1 or in ]x_0,x_1[.
Why?

>It's also bullshit, h(x)=0 satisfies that for any g(x).
What's your point?

>>9686913
>]x_0,x_1[.

Fucking kill yourself faggot. Use () like good heteros.

>>9686920
whats the code to write in tex? also I just realised I didn't write it properly but now I get it thanks

>>9680852
Is the Cayley/Hamilton theorem good for any particular purpose? Why do I want to put an endomorphism into a polynomial?

>>9686922
That the conclusion of the lemma is false. And the phrasing is bad because the word "in" means something is in something else. x_0<x<x_1 is comparing numbers, nothing is in anything. The condition holds for x less than x_1 and more than x_0.

>>9686925
you just put the slash the wrong way around in the maths tag. it's [/math] not [\math]

>>9686928
>That the conclusion of the lemma is false.
How so?

>And the phrasing is bad because the word "in" means something is in something else. x_0<x<x_1 is comparing numbers, nothing is in anything.
x_0 < x < x_1 means x is in (x_0,x_1), what's the issue?

>>9686932
Let h(x)=0, then g(x) can be any continuous function and the integral will still be 0. It won't have to be 0 on the interval.
And no x_0<x<x_1 means x is less than x_1 and more than x_0, x\in]x_0,x_1[ means that x is in the open interval from x_0 to x_1. They may be equivalent statements depending on the situation but they don't mean the same thing.

>>9686953
>Let h(x)=0, then g(x) can be any continuous function and the integral will still be 0. It won't have to be 0 on the interval.
The lemma says "where h(x) is an arbitrary function in the same interval with h(x_0)=h(x_1)=0", the zero function is not the only function on that interval with h(x_0)=h(x_1)=0.

>And no x_0<x<x_1 means x is less than x_1 and more than x_0, x\in]x_0,x_1[ means that x is in the open interval from x_0 to x_1. They may be equivalent statements depending on the situation but they don't mean the same thing.
But you just showed they mean the same thing.

>>9686966
If h(x) is arbitrary then it certainly can be 0, in that case g(x) is not forced to be 0 refuting the lemma...

>>9686966
And "x_0<x<x_1" is not an interval, it's an inequality, or a couple of inequalities.

>>9686982
Oh, he means for all h(x), again, shit phrasing.

>>9686982
>If h(x) is arbitrary then it certainly can be 0, in that case g(x) is not forced to be 0 refuting the lemma...
It can be zero, and it can be other functions too, so I don't know why you interpret "arbitrary" as "only the zero function". The lemma is not refuted

>>9687001
>>9686989
Is English not your first language?

>>9686989
>And "x_0<x<x_1" is not an interval, it's an inequality, or a couple of inequalities.
Those two inequalities define an interval, and an interval defines two inequalities. How could they mean different things?

>>9687005
He/she probably isn't a native English speaker, I don't think any "English as first language" country uses the notation ]x_0,x_1[ as in >>9686913

>>9680852
Isn’t increasing your iq just bullshit? I heard somewhere you can increase your iq to a maximum of 30 percent

What's the IRL equivalent of this? Trying to to implement FILO on an analogue circuit board, and some distilled summary might help a lot

>>9687290
If you're dedicating more than two neurons to this for any given amount of time then you're already too far gone for a 30% boost to be of any use.

>>9687290
you can study IQ tests, which makes them invalid but who cares, you can larp as the smartest man in the world

>>9683752
Do the electric fields from charged black holes diminish according to the inverse square law?

>>9686928
>That the conclusion of the lemma is false
That's the fundamental lemma of variational calculus you fucking retard. Do you not understand the distinction between [math]\exists[/math] and [math]\forall[/math]?

Can someone just confirm for me real quick. Is entropy simply where the universe spreads out so much that there is too much 'space' in between atoms, so they dissipate their energy instead of transferring it?

>>9686660
The phrasing is *really bad*, firstly you are looking for C not C^1, there is a substantial difference there, secondly the picture doesn't mention the space from which h is, but you imply that it is C^1.
Aside from that it looks good.

>>9686660
>>9686913
>>9686928
>>9686922
it's obvious the lemma meant that h is ANY arbitrary function, that is, if for all continuous functions h satisfying the condition, then g =0

>>9686925
if you can 4chanX (maybe in the original 4chan too idk) if you press alt+m or alt+e you get the tex brackets done for you, also there's a preview tex button in the reply box in both

>>9687817
never mind, just found out

>>9682582
You view the three whole as 75 twentyfifths
+4/25 and 3=75/25

(75-4)/25 = 71/25

What's the largest 8 digital number you can express in hex notation?

Can someone explain how the Borsuk Ulam Theorem proof involving temperature and pressure can be purely mathematical? Like, just as a thought experiment what if instead of earth, we have a video game world where each part is some dramatically different environment?

>>9688020
The theorem is purely mathematical by nature, the physical application is an interpretation that provides a contextualizing example on how to use the theorem in the "real world".
In a fantasy world where temperature and pressure follow videogame-logic, you can code whatever you like. You can simulate a planet using ones and zeroes and program any laws of physics that you want, but if it doesn't obey the conclusions of the Borsuk-Ulam theorem then you know that your simulated planet isn't a mathematical n-sphere.

>>9688018
What is the largest 8 digit number you can express in the decimal system?

>>9688068
I don't get that though. I mean what if we have a sphere and let's say there are 8 quadrants and we have Ice world opposite fire world and jungle world opposite mountain world and water world opposite space world and candy world opposite electric world. Why is there some pair of points with the same ANYTHING by virtue of this being some particular shape, namely an n-sphere?

>>9688020
To clarify >>9688068
>your simulated planet isn't a mathematical n-sphere
means that your fantasy laws of physics don't match up with the "real" laws of physics that make planets look like Euclidean spheres (i.e. having the correct metric).

>>9688081
oh, so it has to do with physics? I was under the impression somehow this was supposed to be a purely mathematical abstraction. Sorry. Pic related, me.

>>9688077
Sorry, didn't see your response the first time round.
>Why is there some pair of points with the same ANYTHING by virtue of this being some particular shape, namely an n-sphere?
Borsak-Ulam requires the vector field to be a continuous function, and "real" physics tells us that temperature and pressure vary continuously.
This means that points which are only a small distance apart (this ties in to the Euclidean metric that I mentioned earlier) will have ANYTHING values (e.g. ANYTHING = temperature, pressure...) that differ only by a small amount.
In videogame logic you're free to either simulate worlds with non-Euclidean geometry, or to implement physical ANYTHINGs that don't vary continuously. Either would cause the hypothesis of Borsak-Ulam to fail, and the conclusion of the theorem would not apply in such a world.

>>9685183
Yes, if you are trying to show A <=> B, then it is enough to show that A <=> C1 <=> C2 <=> ... <=> Cn <=> B
(where "<=>" denotes equivalence)

If you use one implication in the chain, then the reverse does not need to be true, and you have to make a separate proof for the other direction (e.g. if your proof looks like this: A <=> C1 => C2 <=> B, then you only proof that A => B)

Proof that [math]\forall n,m\in\mathbb{N}

\int_0^1\!t^{m}\log^{n}(t)dt=(-1)^n\frac{n!}{(m+1)^{n+1}}[/math] I have no clue how to tackle this problem, can anyone give me a hint? Tried to substitute but I am only making it harder. Partial integration gives me also just shit.

>>9688186
Surely you've tried mathematical induction?
Let m be a fixed but arbitrary natural number, then induct over n?

>>9688186
>>9688194
I'd suggest induction too, but differently.

If P(n,m) equivalent to the statement holding for that n and m, then prove:
1 P(0, 0)
2a P(n,m) => P(n+1, m)
2b P(n,m) => P(n, m+1)

You can do these three steps in any order

>>9688194
Ok, I've done it with induction. Damn, my pavlovian Reflex on natural numbers is getting weak lately

>>9688077
> ANYTHING by virtue of this being some particular shape, namely an n-sphere?
That isn't the only requirement. The other is that the function is continuous, i.e. the temperature/pressure/whatever cannot instantaneously jump from a low value to a high value or vice versa.

To see why this is, consider the case of temperature around a circle (e.g. the equator). Pick two antipodes (opposite points) on the circle. If the temperature is the same at both points, the theorem is trivially proven. Otherwise, name the highest point A and the lowest B. Now consider the graphs of temperature as a function of angle a) as you move clockwise from A to B and b) as you move clockwise from B to A. a) starts high and ends low, b) starts low and ends high. Now overlay these two graphs (which are 180-degree regions of a function, 180 degrees out of phase). If the function is continuous, the lines must cross at some point (possibly multiple points). Any such crossing corresponds to a pair of antipodes where the function is equal.

To see why this is true for N dimensions, consider the 2D case (the surface of a sphere in 3D). Pick two antipodal points, draw any continuous path between those two points and add its reflection in the origin to give a closed path where for every point on the path, its antipode is also on the path. You've now reduced it to the 1D case, and the same reasoning applies here: the graphs for two halves of the path must cross.

This is also true for anything with similar topology to an N-sphere. If the concept of an "antipode" exists and you can construct a closed path which is its own reflection, any function which is continuous on that path must have the same value at some pair of antipodes.

its been 8 years since i studied linear algebra at school, and now i need to know trig. what should i read to go from "wha is pythagoras again?" to knowing how to find the closest point along a vector to a given point, and how long will it take me if i have nothing else to do with my time but study math?

what did they mean by [math]1_{[0, x]}(|T|)[/math]?

>>9688492
Is the Image of |T| a subset of the domain of the indicator function?

>>9688530
it's not, that's my problem exactly
T: H -> H is an operator on Hilbert space
|T| is also H -> H

Will adding ethanol to a sugar water solution cause it to precipitate?

>>9688579
Have you looked for the definition of the indicator function, maybe they some definition for that case.
But this just seems ill defined.

This is for a semiconductors class. Does anyone know what type of device this structure defines?

>>9688633

touchscreen

Hijacking /sci/'s [math]\LaTeX[/math] facilities for >>>/wsr/47425

>Find a generating function in closed form for the sequence {1,2,3,4,1,2,3,4,1,2,3,4,…}
You're looking for a closed form for the function
[eqn]F(z) := 1z^1 + 2z^2 + 3z^3 + 4z^4 + 1z^5 + 2z^6 + 3z^7 + 4z^8 + 1z^9 + \ldots[/eqn]
which you can get by starting with the basic geometric series
[eqn]u(z) := 1z^0 + 1z^1 + 1z^2 + 1z^3 + \ldots = \frac{1}{1-z}[/eqn]
and "modulating the frequency"
[eqn] u(z^4) = 1z^0 + 1z^4 + 1z^8 + 1z^{12} + \ldots[/eqn]
and then using the phase-shifting rules
[eqn] z^nu(z^4) = 1z^{0+n} + 1z^{4+n} + 1z^{8+n} + \ldots[/eqn]
for each of n=1,2,3,4, along with the "amplitude modulating" rules
[eqn]nz^nu(z^4) = nz^{0+n} + nz^{4+n} + nz^{8+n} + \ldots[/eqn]
which, when written out in full, gives you the four disjoint components whose sum is the function you want:
[eqn] F(z) = \sum_{n=1}^4 \frac{ nz^n }{ 1-z^4 }.[/eqn]
(Alternatively, instead of multiplying the amplitude by n, you could have superposed n copies of [math]z^nu(z^4)[/math] together, which works out to the same thing.)

I don't think there's space left to address the combinatorics questions, so I'll just say that:
>they're asking you to count derangements
>the usual method of doing this uses recursion as described in
https://en.wikipedia.org/wiki/Derangement#Counting_derangements
>there's definitely a link between these questions and the generating function question, though I'm not quite sure how to describe it

>>9688763
Errata: Cross-link should be >>>/wsr/494725.

>A company of four hobbits and three men enter are exiting a tavern, the tavern owner makes a mistake in returning the company their cloaks. While he is able to distinguish the two sizes of the cloaks (each hobbit gets a hobbit sized cloak, each man gets a man sized cloak), no party member has his own cloak. Given these conditions, how many ways could the tavern owner have returned a cloak to each party member.
Since the hobbit-cloaks and man-cloaks aren't getting mixed up with each other, the two systems are independent (i.e. non-interacting) and so
(No. of ways to return cloaks) = (No. of ways to return hobbit-cloaks) * (No. of ways to return man-cloaks) = 4-subfactorial * 3-subfactorial.

>How many ways can you assign 4 caretakers, each of whom takes care of 2 lighthouses for a year (for a total of 8 lighthouses) and then assign each caretaker two beacons in the following year such that none of them tend the same two lighthouses both years?
The problem is to find n_2(4) where n_L(C) = no. of ways to reallocate CL lighthouses evenly amongst C caretakers satisfying the given conditions.
We can tackle this by counting the total number of ways to allocate lighthouses unconditionally (it's the multifactorial [math]\frac{(CL)!}{(L!)^C}[/math]) and then subtracting the cases where some number [math]D \in \{1, 2, ..., C\}[/math] of caretakers [math]are[/math] assigned the same set of lighthouses, since [math]that[/math] can be recursed over. By definition the lighthouses assigned to these D caretakers are fixed, while the remaining [math]C-D[/math] get different lighthouses, so we have
[eqn] n_L(C) = \frac{(CL)! }{ (L!)^C } - \sum_{D=1}^C 1^D \cdot n_L(C-D)[/eqn]
a recurrence relation for [math]n_L(C)[/math] with initial condition [math]n_L(1) = 0[/math]. So you can either substitute L=2 and work the answer out, or get the closed form of [math]n_L[/math] before substituting (again, essentially the same thing).

I do not understand this "special case" that my textbook states only occurs in 3 dimensional force systems. I have noone else to ask so I am here.

It states that skew forces (nonconcurrent nonparallel forces) cannot be reduced into one single force or one signle couple but a combination of the two. Makes no sense for me. Is this not also possible in 2 dimensions?

pic not too related

What is N! times M!?

>>9689915
[math] \left( \prod_{k=1}^a k \right)^2 \cdot \prod_{j=a+1}^A j [/math]

where
a = min(N,M)
A = max(N,M)

>>9680852

Hey, is it wrong to use the molar ratios of net ionic equations?
I'm trying to decide which molar ratio I should use for a heat question. In the prelab, we wrote out a net ionic equation for reacting HCl and NaOH as:

[eqn] H_3O^+ + OH^- -> 2H_2O [/eqn]

The molecular formula is: [eqn] HCl + NaOH -> NaCl + H_2O [/eqn]

Again, is it wrong to use the molar ratio of the former, net ionic equation?
thanks

>>9682287
>this completely ignores the argument that some living things don't feel pain but still try to avoid death and i do believe some things do actually not feel pain so how would they know to avoid things if not for a fear of death. i would attach that webm of the wasp getting its face eaten by a preying mantis or whatever it was but i don't have it

that's because some members of the species behave in a way that makes it harder for them to die while some other members engage in ways that make it easier for them to die. Over time the second group dies and you're left with the first so to us it looks like they're actively avoiding death, but they're just following their pre-programmed behavior which happens to be death-avoiding. Pain is just one such mechanism that evolved to make us avoid being dead because organisms that can't feel pain tended to die and not pass on their genes compared to those who could.

If I have an invertible matrix of the form [math]\Phi \in\mathbb{R}^{2n\times2n}, \Phi= \begin{bmatrix}
X & -Y \\
Y & X
\end{bmatrix} [/math]
With [math]X,Y\in \mathbb{R}^{n\times n} [/math] Can I conclude that the individual blocks [math]X,Y[/math] are invertible? Or is there any formula for the determinant?

>>9688625
PLEASE RESPOND

>>9690125
>Can I conclude that the individual blocks X,Y are invertible?
No, the 2*2 identity matrix is a trivial counterexample with |Y|=0.
>Or is there any formula for the determinant?
Yes, look up the Schur complement.

>>9690342
For that it seems [math]X[/math] must be invertible at least, does that follow?

>>9690380
>For that it seems X must be invertible at least, does that follow?
No, consider [math] \begin{pmatrix} 0 & -1 \\ -1 & 0\end{pmatrix}[/math].

>>9690390
Shit, well thanks bro. I Just have this weird question that has as a hint to relate de determinant of [math]\Phi[/math] and the "complex determinant of [math]X+iY[/math]". I don't really understands what it means, and I only have the [math]\Phi[/math] is invertible so I don't know how to relate the determinants nor what it means by the complex determinant of the other matrix.

>>9690406
Well, I never took complex analysis so I can only offer limited help there, though I would (gently!) suggest that in the future you watch out for the trap (outlined in the OP link) of asking for help on the step rather than the goal:
>http://www.catb.org/~esr/faqs/smart-questions.html#goal
That said, I'm not completely ignorant, so I'd guess that what you're trying to do is to prove necessity or sufficiency of the Cauchy-Riemann equations in characterizing the conformality of some process or system? One of the reformulations of those equations is that the real and imaginary components can be collected into a partitioned matrix that can be interpreted as a Jacobian for said process/system, giving meaning to the notion of complex differentiation.

https://en.wikipedia.org/wiki/Cauchy%E2%80%93Riemann_equations#Preservation_of_complex_structure

*Errata: Matrix in >>9690390 should have 1 in the lower-left corner, instead of -1.

I understand that it is possible to find the global minima of a 2 variable function over some domain by using calculus to find the local minima, and find the minima along the boundaries of the domain and choosing the smallest of all of these.

However, the function I'm interested in is rather nasty so I'd rather not go through the process of taking the derivatives and proving that no local minima exist in the domain.

I know from graphing it that the global minima exists along one of the boundaries and I was able to find what it is my just minimizing along that boundary.

Is there some easier way to prove that it's the global minima?

>>9690085
so you introduced a group that was biologically programmed to avoid death to avoid my death argument?

>>9690472
Without seeing the function in detail (and why you're calling it "nasty" -- is the expression complex, is the domain arbitrary pieced together, etc.) all I can suggest is that you'd probably need some kind of superharmonic condition or some variant of Green's theorem to ensure that the interior local minima don't overshoot the boundary minima.

>>9680852
give me resources that I can use (can be books or websites) to study math from a high school level all the way to multivariable calculus including linear algebra?

thanks

>>9690480
Thanks. I'm not sure if I can get a condition like that here though.

The expressions is $f(a, b, c) = (a + 2b\sqrt(1 + \frac{b}{c}))^2 (4b - 1 + 2c - c^2)$
I want to find the global minima given fixed a, on the triangle $b \in (0, 0.25)$ and $c \in (0, 0.5-b)$.

I'm pretty sure the actual minima exists for $b = \frac{1 - C}{6}, c = 0$ in which case my expression just simplifies to $-(\frac{1}{3} + \frac{2*a}{3})^3$, but the square root makes the derivative root finding kind of annoying so I want to avert that somehow.

>>9690492
well, that was embarassing

>>9690480
Thanks. I'm not sure if I can get a condition like that here though.

The expressions is [math]f(a, b, c) = (a + 2b\sqrt(1 + \frac{b}{c}))^2 (4b - 1 + 2c - c^2)[\math]
I want to find the global minima given fixed a, on the triangle [math]b \in (0, 0.25)[\math] and [math]c \in (0, 0.5-b) [\math]

I'm pretty sure the actual minima exists for [math]b = \frac{1 - C}{6}, c = 0 [\math] in which case my expression just simplifies to [math]-(\frac{1}{3} + \frac{2*a}{3})^3 [\math], but the square root makes the derivative root finding kind of annoying so I want to avert that somehow.

>>9690480
bah

Thanks. I'm not sure if I can get a condition like that here though.

The expressions is [math]f(a, b, c) = (a + 2b\sqrt(1 + \frac{b}{c}))^2 (4b - 1 + 2c - c^2)[/math]
I want to find the global minima given fixed a, on the triangle [math]b \in (0, 0.25)[/math] and [math]c \in (0, 0.5-b) [/math]

I'm pretty sure the actual minima exists for [math]b = \frac{1 - C}{6}, c = 0 [/math] in which case my expression just simplifies to [math]-(\frac{1}{3} + \frac{2*a}{3})^3 [/math], but the square root makes the derivative root finding kind of annoying so I want to avert that somehow.

What's the best way to gain experience or build a resume if my major is applied mathematics/stats.

Should I program statistical models that are useful to industry, or offer to help optimize the small businesses of my family via entry/exit surveys? (I'm a freshman so I can't get an internship)

My relatives have a small English school in Japan, and I've thought about having them give an entry test, exit test, entry survey, and exit survey to decide what actions result in the greatest increase of fluency.

>>9690554
your best bet would be to either go into data science and get a microsoft accredited certificate in data science, a masters in data science or better yet stats, or a masters in engineering of sorts.

>>9690503
Yeah, that looks like it could get nasty. The sqrt(1+b/c) term suggests that you might want to rewrite (b,c) in polar form -- ideally such that the resulting expression, when interpreted as a complex number, is meromorphic(?) -- though if you just want to verify the conjecture that the local minima don't matter, you could try the second derivative test, hoping that the Hessian matrix wrt. (b,c) is negative semidefinite (and this may be where the ability to interpret f as a complex function is most helpful).

Help a brainlet out, how do I simplify this?
1/x^2 / (1+1/x^2)^(3/2)

>>9690560
I actually hadn't considered trying that substitution or looking at the second derivative (mostly because the sqrt term makes things nasty, and because I suspect that there are local minima outside the domain). I guess I'll give those a go, thanks.

Most of what I've been trying is to see if I can get any sort of inequalities that would make it ok only to prove for a = 0, since that expression is a much nicer regular polynomial.

>>9690570
Start by bringing both x^2 up to the numerator by making them x^(-2). Multiply/ expand out and simllify. Im on my phone and drunk in bed. Would do it bro i swear

>>9680852
>tfw most of these "stupid questions" are actually too smart for me to understand

>>9690558
Should I change my major? I like mathematically optimizing existing processes in industry.
I'm trying to decide between mathematics, applied mathematics, or stats. I could do CS but I don't really want to get too heavy into it, I like data science more.
I go to the University of Manitoba so I'm not exactly in a target school, that's why I'm trying to build a resume.

>>9690594
most are low to mid range undergrad m8

>>9690570
dividing is multiplying by a reciprocal

multiply 1/x^2 by (x^2/1+1)^(3/2)

>>9690597
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHHHHHHHHHHHHHHHHHHHHHHH!

>>9690570
>>9690570
Comes out to x^(-2)/(2x^(-2))^3/2 which becomes
1/(2^(3/2)*x^-1)

Which is x/2^(3/2)

Dont quote me tho hammered n tired and doing in my head

>>9690596
Stats is a subset of its own and that's worth pursuing. A lot of jobs in data science are actually basic bitch data analytics jobs. The pay is quite high but can be expected to fall as more people catch on. The actual data science, the models and machine learning, are done by the guys with PhDs and Master degrees in Stats, computer science and data science.

Applied maths seems like its pretty unmarketable unless you do a Masters in Engineering hence my suggestion before.

I don't see a math degree by itself being very useful.

Okay so you have a number of options.

If you wish to finish your degree:

1. Do a Masters in Engineering so that you have some real-world marketable skills
2. Do a Masters in Data Analytics/Science. Although I would advise against it. Since you can get away with self-learning it and getting the aforementioned Microsoft credential. Also your Stats background is useful. In fact I have heard a Masters in Stats is preferred over a Masters in Data Science. Since it's just an intersection of programming, some computer science concepts with statistics.

If you wish to change your degree:

1. Do computer science. Computer science is all about algorithms and optimizing them. Get a bachelors in computer science. You might get a few credits.

2. Do an engineering degree in mechanical, electrical or computer engineering. Research it and find a discipline that's employable and that you like.

>>9690604
>implying

>>9690603
>>9690605
I still dun git it. How do I get to this?

>>9690604
AAAAAAAAAHHHHH JUST BLOW MY BRAINS OUT

>>9690594
knowledge isn't the same as intelligence
if pajeet can learn, so can you

>>9690627
r-right

>>9690632
>algebralets

>>9690632
d-don't need to rub it in

>>9690632
>>9690627
>>9690638
Ok so if you have a division problem, say (1/5)/(20/1)
you do (1/5)/(20), right?
so really this is the same as (1/5)x(1/20) which is 1x1 over 5x20
or 1/100

So try this with a variable. (5/x^2)/((x+9)/20)
This is (5x(x+9))/((x^2)(20))= (5x^2+45x)/(20x^2)
cannot simplify past this point.

Just remember that division is multiplying by the reciprocal.

>>9690570
>>9690632
>>9690669
The answer is (1+x^3)/(x^2)
I can show you why if you want.
If I'm wrong someone correct me.

>>9690630
Thanks anon, your casual racism has inspired me

>>9690613
So you're saying I should drop stats for comp sci, and do the masters in stats?
Thanks for the help, I might do that.

How the fuck do I find a partial sum at n for this? I swear the professor is just trolling at this point.

>>9684951
Fucking grind anon
No other way

>>9690759
you can just calculate it can't you

>>9690762
that's what I'm saying, there is no way to find a partial sum, it IS the partial sum. You just do the sum at infinity for (-2/3)^k + sum at infinity for (-2/3)^k 1/(2^k). You get 1 - 0.4 = 0.6.

>>9690769
>You just do the sum at infinity for (-2/3)^k + sum at infinity for 1/(2^k).
fixed

>>9690759
It's a sum of two absolutely convergent geometric series, so you can split it up into
[eqn]\left( \sum_{k=1}^N ( -0.666...7 )^k \right) + \left( \sum_{k=1}^N (0.5)^ k \right)[/eqn]
where I have used the uglier decimal notation to emphasize the absolute convergence.

Then just get the partial sums for each subexpression and put them back together using commutativity of addition.

>>9690481

>>9690773
thanks anon

How do I handle group assignments where several members are non-communicative? They sit there in utter silence when the group meets, and will respond with single word answers when addressed. Even in online group chats they won't say anything, even when directly addressed. The fuck's their problem? I feel like they're either going to produce substandard work (which will be held against the rest of the group), or other members will have to do their shit for them (there's an oral component so we're fucked there either way). This doesn't seem to be simple introversion.

What am I suppose to do here? how does the fact that the Sylow subgroups are Abelian help?

>>9690858
Either they're socially inept or they don't know the material. Either way, you'll need to step up and force them to do their part, or do their part and let them and the Prof know they aren't pulling their weight. Just don't let them drag you down.

>>9690603
but that's wrong, if you want to replace division by multiplication in a fraction it would be:

[math]
\frac{1}{x^2} * \frac{1}{ 1+(1/x^2))^(3/2)}
[/math]

>>9690878
What have you tried?

>>9689885
please help I just want to know why forces and couples cant be reduced in 2D (according to my textbook)

>>9691456
can't not be reduced*

>>9691456
never heard of that shit, you must be interpreting it wrong. Any two vectors clearly will add to a third, single vector

>>9691510
yes I think I messed up the definition of a couple. thank you for making me think.

new question then. is pic related a couple, couple-force system or just a force system?

>>9691601
ask in new /sqt/

New
>>9692414
>>9692414
>>9692414