/sqt/ - Stupid Questions Thread

[Anonymous No.9466071]

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

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

Previous thread: >>9450832

[Anonymous No.9466080]

Reposted:
>What are the prereqs for me to learn how to do Regression?

Where's a good place I can learn about this in full anons.

[Anonymous No.9466083]

How do I show linear independence of polynomial vectors?
e.g. if I have
[math]$(a-5, a^2 - 5a, a^3 - 5a^2)$[/math]
I *know* they're linearly independent because they have different degrees, but I'm not sure where that proof comes from?

[Anonymous No.9466106]

>>9466083
Read the definition of linearly independent vectors.
Proof that it applies here.

[Anonymous No.9466111]

>>9466080
Depends in what context you want to use it, statistics, calculus or linear algebra.

[Anonymous No.9466127]

>>9466106
I know that linear independence means no vector in the set can be made from a linear combination of the others, and that the only scalars [math]a_1 .. a_m[/math] that make [math]a_1v_1 + ... + a_mv_m = 0[/math] is all 0, but I don't know how to show that for polynomials

[Anonymous No.9466128]

>>9466127
[math]c_{1}(a-5) + c_{2}(a^{2}-5a)+c_{3}(a^{3}-5a^{2})=0[/math]
I think

[Anonymous No.9466132]

What additional latex packages do you guys have installed?

[Anonymous No.9466142]

>>9466128
So just the standard proof applies? I don't have to do any stupid bullshit because they're polynomials?

[Anonymous No.9466164]

Train travels at 60km/h subject gets in train at point A and get outs at point B, how much distance train traveled?

[Anonymous No.9466165]

There's this question i'm having a brainlet moment in: let [math]B=k[x][/math] with [math]k[/math] a field. A [math]k[/math]-automorphism of [math]B[/math] is a ring automorphism that is the identity on [math]k[/math]. Describe the group of [math]k[/math]-automorphisms of [math]B[/math].

Isn't this literally just the trivial group?? Since there is only one "extra" element that can be sent anywhere, then the automorphism is entirely defined by where [math]x[/math] is sent. But it cannot be sent to an element of [math]k[/math], otherwise it's not an isomorphism, and it cannot be sent to a different power of [math]x[/math] since then again it's not an isomorphism.

?????

[Anonymous No.9466230]

>>9466111
W-which one do I need for data science anon? I thought statistics.

[Anonymous No.9466367]

>>9466142
Yes. No, 1, x, x^2 and x^3 are linearly independent by definition.

[Anonymous No.9466373]

>>9466083
Assume not
then there are x, y, z with at least one of them not 0 such that:
x(a−5)+y(a^2−5a)+z(a^3−5a^2) = 0
Factor by term.
z(a^3) = 0 a^3 so z must be 0
(y - 5z)a^2 = 0 a^2
ya^2 = 0 a^2 so y must be 0
x(−5) = 0 so x must be 0
Thus x=y=z=0

CONTRADICTION!!!!!!11one QED

[Anonymous No.9466384]

>>9466230
Statistics and linear algebra are both relevant to what I assume you mean with "data science". At the essence it's all the same thing, but if you're studying it for an exam you'll have soon, it matters. Do you use random variables in data science? If not, it's probably Least Squares Approximation you're after.

[Anonymous No.9466388]

>>9466083
looks like someone needs to watch some wildberger

https://www.youtube.com/watch?v=KhxiBgNfPBg&index=20&list=PL01A21B9E302D50C1

[Anonymous No.9466402]

>>9466373
>CONTRADICTION!!!!!!11one QED
kek.
That actually clears a lot up. I bumbled my way into a theory of linear alg class without taking intro, so I'm trying to figure all this stuff out with generic variables and no concrete examples. It's twisting my brain a bit.

>>9466388
Gunna watch all of this tonight, thank you.

[Anonymous No.9466445]

>>9466384
no exam, it's all self study

[Anonymous No.9466476]

Yeah I have a stupid question; I'm an extremely stupid person who'd like to get back into basic learning and help my overall function. Im noticing Im getting worse in critical thinking, memory, and everything else. I passed High School I wasn't smart and was never in any of the higher-tier classes.

Are there any sites to help stupid people like myself get better at mostly everything?

[Anonymous No.9466536]

>>9466476
>>>/pol/catalog

[Anonymous No.9466548]

At what in learning algebra does topology become useful? I see topological concepts come up occasionally when I look at more advanced material but I don't usually see it tied in on book lists.

[Anonymous No.9466634]

>>9466373
>>9466402

I would be careful about using this. All he did was use the linear independence of 1,x,x^2, etc. They are not "linearly independent by definition", as someone else said. It's possible your professor doesn't care. If he does, you actually do have to do more work.

To show that the first m terms 1,x,..x^m are linearly independent, suppose there is some set of coefficients a_{n} such that \sum_{n}^{m} a_{n} x^{n} = 0 for all x in the domain. Since a polynomial of degree m has at most m solutions (this is a basic result from algebra; you could also invoke the fundamental theorem of algebra if you are unfamiliar with that), those coefficients actually can't exist in the first place. Hence, monomials of differing degree are linearly independent.

[Anonymous No.9466668]

frictionless Inclined plane that is 40 degree angle.
a ball has a initial velocity of 4 m/s.
how far does it go up?

i'm not sure how to approach this 100%.
i know that the motion in x, is:
fx = force applied - mgsin40

can i have some help

[Anonymous No.9466697]

>>9466668
Just use conservation of energy. The ball has initial kinetic energy of 8*m joules (m is mass in kg). When it reaches its max slope is has 0 joules of kinetic energy so it must have 8*m joules of gravitational potential energy.

8*m = m*g*h
h = 8/g

h gives you the vertical distance so use this to find total distance.


The alternative (harder) way to solve this is to take the portion of gravity that's parallel to the slope (f = g*sin(40)) and plug that into:

x = x0 + v0*t + .5*a*t^2

[Anonymous No.9466734]

>>9466548
Topology isn't used much in pure algebra. I mean adic topologies are pretty important, but not much else.

[Anonymous No.9466744]

>>9466634
You can probably take that for granted as the professor has almost certainly used them as an example vector space with {1,x,x^2,...,x^n} as a basis.

If you need to prove it, you could also invoke DEs and say they are the solutions to [math]d^{n+1}y/dx^{n+1} = 0[/math] and therefor linearly independent.
Or if you're really anal(yst), invoke the Wronskian.

[Anonymous No.9466754]

>>9466548
Normed space : it's a metric space
Banach space : it's a complete metric space
Hilbert space : it's a complete metric space with the metric defined as an inner product

The stuff is more useful for infinite dimensional vector spaces (aka function spaces) which you learn in functional analysis. Linear Algebra just provides the foundation for it.

[Anonymous No.9466755]

>>9466476
Khan Academy.

[Anonymous No.9466758]

>>9466071
old thread >>9451520

[Anonymous No.9466781]

>>9466165
>Isn't this literally just the trivial group??
No.

>But it cannot be sent to an element of k, otherwise it's not an isomorphism, and it cannot be sent to a different power of x since then again it's not an isomorphism.
There are other options.

[Anonymous No.9466784]

>>9466755
This is a memelist.

[Anonymous No.9466789]

>>9466548
>At what in learning algebra does topology become useful?
Never.

[Anonymous No.9466798]

are the people in this thread right about studying
>>9466628
it seems that studying is only for retards

[Anonymous No.9466818]

What do people do when they don't have a university near their parent's place? I assume most would move into some squalid shared accomodation near their chosen university and work a part time job. Do any medical students do this? I kind of want to but I really doubt I'd be able to work a job and not fail all my exams, plus shared accommodation sounds like a whole other nightmare.

[Anonymous No.9466930]

>>9466071
>In one hour, the minute hand of a clock moves in a a full circle and the hour hand moves 1/12th of a circle
So does this mean that in 45 minutes, the hour hand moves 1/45th of a circle? or would it be 1/45th of 1/12th of a circle?

[Anonymous No.9466933]

>>9466930
It move 45/60ths of 1/12th of a circle, i.e., 3/4 * 1/12 = 3/48.

[Anonymous No.9466935]

>>9466818
I live with my mom and commute to university every day. It's about an hour and 20 minutes away.

[Anonymous No.9466938]

>>9466933
thanks for helping a brainlet out anon

[Anonymous No.9466961]

How many distinct derivative notations are there and what are they called?

Derivative notation fucks me up from a conceptual standpoint, what do I google to learn in order to be able to keep them distinct in my mind and understand stuff?

[Anonymous No.9466967]

>>9466935
We have no public transport to the nearest good uni, and driving would actually more expensive and time consuming than paying rent at the actual place.

[Anonymous No.9467272]

>>9466961
It's just symbols. There's no differencce.
https://en.wikipedia.org/wiki/Notation_for_differentiation

You are probably not understanding something essential if notation confuses you.

[Anonymous No.9467310]

>>9467272
Aye bruh do you know how to make lean? I recently started listening to Lil Wayne and I want to sip some of that sizzurp even know what I'm saying bruh

[Anonymous No.9467396]

how the FUCK do I get better at programming? I'm in EE, and I feel like I'm gonna choke to death thanks to this data structures/algorithm class this term. It doesn't help that I have another class in the next term on microprocessor systems.

[Anonymous No.9467409]

>>9466935
>>9466818
>>9466967
>tfw you have a 4 hour commute
>tfw you have 2,5 more years of this shit

[Anonymous No.9467630]

on a scale from 2 to 4, which calc are eigenvalues and eigen vectors from?

[Anonymous No.9467636]

>>9467630
>on a scale from 2 to 4, which calc are eigenvalues and eigen vectors from?
None. They're from linear algebra.

[Anonymous No.9467651]

>>9467636
Thanks. I finished math like 2 years ago and haven't used beyond calc 2 in more than a year and a half.
My professor pulled out eigenvalues and eigenvectors during a lecture long derivation and just assumed we would remember something we haven't seen/used in years.

[Anonymous No.9467664]

>>9467630
you use them in differential equations (calc 4?)

[Anonymous No.9467725]

>>9467396
SICP

[Anonymous No.9467741]

>>9466818
I get free money to finish my studies and more free money for living in a rented apartment.
People in USA take student loan I guess.

[Anonymous No.9467790]

Anyone help me figure out how to solve this? I saw that diagram they posted and figure I should solve it using [MATH](theta) =
s/r[/MATH] so multiply [MATH] 2(pi)[/MATH] * 93 million, right?

[Anonymous No.9467827]

What purpose do the curly brackets around the summation index serve in the pic ?

[Anonymous No.9467866]

>>9466071
To all those who are at least familiar with matlab, is there a better way to write the vector in pic related?
[math]\vec{b} = [sin(k)\ cos(k)\ 0\ 1] \[\math]
for k = 1, 2, 3, 4

And I want a way to have the variable b_vec have all the b's for k = 1:4 without needing to type out "b_fn(x)" each time. Hope my question made sense
(Not sure if my latex will be fucked up or not but here goes nothing)

[Anonymous No.9467873]

>>9467866
Gosh dang forgot my picture

[Anonymous No.9467899]

Is equipotence still an equivalence relation in its negation? That is, 'not equipotent (to)'.

[Anonymous No.9467906]

I am having trouble understanding how to find this electric field. Is dV = drdz? and would sigma = (p*2*pi*l)/(r^2+(z+L)^2)^(3/2) where the limits of integration are from 0 to R and 0 to L+z?

[Anonymous No.9467909]

>>9467899
>Is equipotence still an equivalence relation in its negation?
Probably not reflexive

[Anonymous No.9467913]

>>9467909
Yes, I just seen that. Thanks.

[Anonymous No.9467917]

>>9467909
It is a strict order though, yes?

[Anonymous No.9467941]

I'm an amateur blacksmith, carpenter, and welder
What degree path will get me out of this factory and behind a desk doing the things that I can at least pretend to enjoy, I'm leaning toward material science, but it feels to vague of a program
What even is the actual goal of adding a degree to your resume do you want it to be super specific for one high paying position or is a generic "x engineering program" good enough to move you behind a desk?

[Anonymous No.9467992]

I need help with this:
Determine a and b so that (2x+13)/(x-1)(x+2) = a/(x-1)+ b/(x+2)

[Anonymous No.9467998]

>>9467992
What have you tried?

[Anonymous No.9468008]

>>9467998
I've been looking at the algebraic rules for division but I can'tfind any I can input there.

[Anonymous No.9468023]

>>9467992
>>9468008
isn't this just partial fraction decomposition?

[Anonymous No.9468026]

>>9468008
Multiply both sides by something so that you're not dealing with any quotients

[Anonymous No.9468060]

I have a set of 5 slots. each slot will display a letter A,C,T, or G So the possible permutations number 4^5. What is the probability of a random set of 5 find a match in a random string of 1000 where each character can be A,C,T, or G?

[Anonymous No.9468069]

[math]\frac{a}{x-1}+ \frac{b}{x+2}=\frac{a(x+2)+b(x-1)}{(x-1)(x+2)}=\frac{(a+b)x+(2a-b)}{(x-1)(x+2)}[/math].
Now the problem becomes determine a and b so that [math]\frac{2x+13}{(x-1)(x+2)}=\frac{(a+b)x+(2a-b)}{(x-1)(x+2)}[/math]

[Anonymous No.9468077]

>>9468026
>>9468023
Thankyou!

[Anonymous No.9468092]

If Card(A)<Card(B) and Card(B) [math]\leq[/math] Card(C) how do I prove Card(A) < Card(C) ?

I know that Card(A) < Card(B) [math]\iff[/math] Card(A)[math]\leq[/math]Card(B) and Card(A)[math]\neq[/math]Card(B). So from what I have here I can deduce there exists two injections, [math]f: A\to B[/math], [math]g: B\to C[/math] which a defined injective composition, [math]g \circ f: A\to C [/math], which gives me the Card(A)[math]\leq[/math]Card(C) , but I'm struggling on how to show Card(A)[math]\neq[/math]Card(C), seeing as I'm just given that Card(A)[math]\neq[/math]Card(B).

What am I overlooking?

[Anonymous No.9468121]

>>9468092
Since Card(A)=/=Card(B), by transitivity of equality, Card(A)=/=Card(C). If it were, we would have Card(A)=Card(C) and:
1. Card(B)=Card(C) implies Card(A)=Card(B), which is impossible;
2. Card(B)=/=Card(C) implies Card(B)<Card(A) which is also impossible

[Anonymous No.9468125]

>>9468121
Fuck, it's so simple. How could this happen to me...thanks.

[Anonymous No.9468126]

>>9468092
if card(A) = card(C) then there's a bijection h from C to A, which would make hg an injection from B to A, which would imply card(B)<card(A), a contradiction to the assumption.

[Anonymous No.9468127]

>>9468092
[math] f [/math] is not surjective.

[Anonymous No.9468143]

Got a PhD interview that's mostly medicinal chemistry and my knowledge base is mostly biochemistry.

How fucked am I? I feel out of my depth just looking at these papers, and shitting six bricks thinking about the questions they're going to ask me.

[Anonymous No.9468257]

what is the order of operations for calculating the discriminant?

b^2-4ac
(-3)^2 - 4 * (1) * (-3)
this is where I get stuck.
do I multiply -3 by -4, or do I multiply it by 4 and then subtract the result from 9?

[Anonymous No.9468271]

>>9468257
The order of operations is always the same, regardless of what you're doing.
(-3)^2 - 4 * (1) * (-3) = 9 + 12 = 21

[Anonymous No.9468335]

>>9468257
If you want to remove any chance of you messing it up just write it like [math]\sqrt{(b)^{2} - (4ac)}[/math]. But what >>9468271 said is true too

[Anonymous No.9468345]

>>9466071
First, thx for this thread

I want to do a multiple factor optimization:

x1 +x2 +x3 +x4 +x5 +x6 = 1

(w1*x1) +(w1*x2) +(w3*x3) +(w4*x4) +(w5*x5) +(w6*x6) ≤ W

Maximize:(i1*x1) +(i1*x2) +(i3*x3) +(i4*x4) +(i5*x5) +(i6*x6)

I'm aware that it is possible to do this with the excel solver, but I would like a general formula because i'm using it in Vensim (system dynamic).

[Anonymous No.9468503]

What the hell is 1d incremental smoothing and how do you do it on a 2d array?

[Anonymous No.9468560]

>>9466071
what do you guys think of this brainlets??
>>>/pol/158346712

[Anonymous No.9468568]

>>9468560
meant for
>>>/pol/158344934

[Anonymous No.9468590]

>>9467827
It means "all configurations labeled by [math]l,{\bf k}, \sigma[/math]".

[Anonymous No.9468683]

Why is the dual basis defined in terms of the Kronecker delta?

[Anonymous No.9468723]

>>9467866
>>9467873
Problem is that b_fn throws the vector straight into sin and cos, so you get a matrix looking like this:
[math]\begin{bmatrix}s_1&s_2&s_3&s_4\\c_1&c_2&c_3&c_4\\0\\1\end{bmatrix}[/math]
This is obviously not rectangular. Just set
b_fn = @(k) [sin(k);cos(k);0*k;1*k];
after which b_fn(1:4) works.

[Anonymous No.9468726]

>>9468723
Oops, that last part in b_fn should be ones(size(k)).

[Anonymous No.9468748]

>>9468683
>Why is the dual basis defined in terms of the Kronecker delta?
It's concise, what would you prefer?

[Anonymous No.9468764]

>>9468060
Interesting question, here's one approach I found
http://answers.google.com/answers/threadview/id/508010.html
This involves a lot of computation, so you'll want to find symmetries in the 4^5 set that have the same matrix structure. Not sure if there are more than the 4! letter permutations, but that's something at least.

[Anonymous No.9468790]

For this table, I understand the 30,45, and 60, but i'm hazy on the 0 and 90 degree rows. For 0, what are they using? Neither triangle has an angle == to 0, so how did they get the values to plug in for Sin/Cos/Tan there? For 90, which triangle did they use? And relative to 0, which is considered "Opposite"? For example, Sin 90 here is listed as "1". How? On the 45-45-90 triangle, wouldn't that be 1/sqrt(2)? Its bad to leave a sqrt in the denominator, so I guess then we'd have 1sqrt(2)/2, which still doesn't explain the 1.

So I look at the 30/60/90 triangle. I'm not 100% sure which is "Opposite" so I see 2 possibilities then. Sqrt(3)/2 or 1/2. Still not a 1. Where did the 1 come from?

[Anonymous No.9468799]

>>9468764
Here's one method from google
http://answers.google.com/answers/threadview/id/508010.html
It shows how to compute the probability if the 5-slot sequence is known. Then you essentially have to do the computation for all 4^5 sequences. Note that the matrices can also be represented as regular automata, which may help in constructing them.
To compute it faster, you have to find symmetries in the set of 5-slot sequences that have the same matrix structure, as described in the link. They also have isomorphic regular automata representations. The symmetries should include at least relabeling the letters that appear in the 5-sequence. If there is at least one of each 4 letters, then there are 4!=24 relabelings, which might be good enough for feasible computation.

[Anonymous No.9468803]

>>9468799
Meant to quote >>9468060

[Anonymous No.9468812]

>>9468723
Thanks!!! That helped a lot!

Still not sure why my math tags weren't working. Here's another shot:
[math] y = mx + b[/math]
(Oh okay. I accidentally used the wrong backslash)

> For 0, what are they using? Neither triangle has an angle == to 0
Sine, Cosine, and Tangent are defined in terms of a triangle with a hypotenuse of length 1. In the case where there's a zero-angled elevation, you don't have a triangle, just a horizontal line with length 1. The horizontal length of this line is 1 (cos 0 == 1) and the vertical length of this line is 0 (sin 0 == 0)

>For 90, which triangle did they use? And relative to 0, which is considered "Opposite"?
Unless otherwise stated, all these angles are relative to the x-axis, with a counter-clockwise rotation.
Have you gone over what's called the *unit circle*? It's a very useful tool to consider the different signs of the trigonometric functions (see pic related and this video: https://www.khanacademy.org/math/algebra2/trig-functions/unit-circle-definition-of-trig-functions-alg2/v/unit-circle-definition-of-trig-functions-1))

>On the 45-45-90 triangle, wouldn't that be 1/sqrt(2)? Its bad to leave a sqrt in the denominator, so I guess then we'd have 1sqrt(2)/2, which still doesn't explain the 1.
Because 1 is a multiplicative identity, [math] 1 \cdot x = x[/math] and in this case, [math] x = \frac{\sqrt{2}}{2} [/math]

When you consider "Opposite" sides, it's always the side not touching the angle.

Hope this helped, and good luck with trigonometry! It's an important building block for a lot of future math, so make sure you get all the help you need!

>Just had to fill like seven captchas
Fuck you google

[Anonymous No.9468817]

>>9468812
God damn it, meant to reply to you
>>9468790

In this post:
>>9468812

[Anonymous No.9468844]

Wait so does this mean no photographs or images exist of an actual atom and we know they exist purely out of evidence? What the fuck

[Anonymous No.9468847]

>>9468844
How would you take a photograph of an atom?

[Anonymous No.9468858]

>>9468847
I guess photograph was a bad term to use but I figures you could map a physical atom into an image somehow

[Anonymous No.9468935]

>>9468858
>physical atom
Atoms are mental constructs, they are physical insofar as imaginary concepts (electric currents in your brain) are physical.

[Anonymous No.9468950]

>>9468935
Even for physics that makes it sound a little too philosophical, I mean if the rules have been proven so much what's not to say they could be physically real?

>inb4 maths m-muh proofs

[Anonymous No.9468995]

>>9468950
>Even for physics that makes it sound a little too philosophical
Physics (much like mathematics) can be seen as a branch of philosophy, so that shouldn't be too surprising.
>what's not to say they could be physically real
Current knowledge basically outright denies this. They could be physically real only if our current understanding is somehow deeply flawed.

[Anonymous No.9469009]

>>9468995
That's fascinating they cant be physically real basically. I'm currently reading Richard Feynman's lectures online since it's free, will he get to that or will I have to wait to be able to afford that young and freedman book?

[Anonymous No.9469056]

Starting points/links on the possibility (or impossibility) of self-gravitating structures that aren't spheroid? I'm coming up short when I try searching.

[Anonymous No.9469125]

Are there any certifications or exams I can take to prove I can do maths? Say I learn how to do maths very well outside of school and want to prove it to potential employers.

[Anonymous No.9469160]

>>9469125
>prove it to potential employers
I highly doubt you can "do maths very well".

[Anonymous No.9469268]

>>9469160
I can do it well enough. My degree just happens to be in something unrelated. No need to be hostile.

[Anonymous No.9469271]

>>9467941
Some sort of Mech engineering job maybe?

[Anonymous No.9469275]

>>9469125
Gre math maybe

[Anonymous No.9469377]

>>9467396
Data Structures and Algorithms by Aho, Ullman, and Hopcroft

[Anonymous No.9469387]

>>>/k/36630954

guys k needs your help big time

[Anonymous No.9469394]

>>9467866
>>9467873
b_k = @(k) [sin(k); cos(k); zeros(size (k)); ones(size (k))]
b_(1:4)=
0.84147 0.90930 0.14112 -0.75680
0.54030 -0.41615 -0.98999 -0.65364
0.00000 0.00000 0.00000 0.00000
1.00000 1.00000 1.00000 1.00000

[Anonymous No.9469401]

>>9468844
Read textbooks and not popsci plz

[Anonymous No.9469422]

>>9468683
It's like a characteristic function for the point subsets, much like the atoms of the dual Boolean algebra

[Anonymous No.9469429]

>>9468844

What are you even trying to say here? Babbys first exposure to quantum mechanics?

[Anonymous No.9469437]

>>9469268
>I can do it well enough.
For example?

[Anonymous No.9469453]

>>9469437
I'm a disgusting computer programmer so I took the usual math classes. I'm going to attempt to learn more though and go for a second degree in maybe stats

[Anonymous No.9469476]

>>9466755
>carroll and ostlie
>1500 pages of GR and black holes
>easy
what a meme

[Anonymous No.9469483]

>>9466798
>believing 200 IQ LARPers
kek

[Anonymous No.9469489]

>>9466961
like this? Or are you asking for >>9467272

[Anonymous No.9469494]

>>9466164
60kms

[Anonymous No.9469498]

>>9467651
We use them in modelling all the time

>Pain

[Anonymous No.9469500]

>>9466164
is this bait
>>9469494
why

[Anonymous No.9469516]

Alright, not math exactly, more of an economy question, but what is up with the multiplier effect?

What does 1/mps mean? And why is tax mpc/mps?

[Anonymous No.9469517]

>>9466071
Could a small lump of lead embedded under a scalp cause cancer?

[Anonymous No.9469526]

from chapter 1 of sakurai's modern QM book:

let x' and x'' be eigenvectors and let A be an operator. ( I dont know how to put this in latex)

we now look at <x'|A|x''>, where <| and |> are bras and kets. let A = x^2

<x'|x^2|x''> = (<x'|) * (x''^2|x''>) = x'^2*dirac delta(x'-x'')

why has the x''^2 become x'^2 ?

[Anonymous No.9469528]

>>9469526
Theres a delta function, so the whole thing is only nonzero if x' = x''. It doesnt matter which one it is

[Anonymous No.9469535]

>>9469526
>I dont know how to put this in latex

learn nigga

[Anonymous No.9469536]

>>9469528

okay glad to know it wasn't anything beyond that. thanks

[Anonymous No.9469591]

How does language start and grow? Id assume it started by associating sounds with objects but how does the vocabulary advance into more abstract concepts? I feel like a retard here but i cant think of a solid model for it.
Im more interested in how they start and develop rather than how they get accepted by various groups.

[Anonymous No.9469623]

>>9469476
Are you confusing the book for something else? He didn't recommend MTW

[Anonymous No.9469647]

How come the speed of light can be used to relate mass and energy?

[Anonymous No.9469787]

How do I prove given two vector spaces, U, V, and [math]U\subseteq V[/math] that dim(V)=dim(U) implies V=U? If dim(V) = n, then the basis for V is at most n vectors large. So any vector in V can be written [math]\vec{x} = a_{1}\vec{v}_{1}+\dots +a_{n}\vec{v}_{n}[/math], which is unique. Similarly since dim(V)=n, dim(U)=n, and any vector in U can be written [math]\vec{y} = a_{1}\vec{u}_{1}+\dots +a_{n}\vec{u}_{n}[/math], is unique. [math]\vec{y}\in U[/math] so it has to be in V as well. QED?

[Anonymous No.9469789]

>>9469787
>If dim(V) = n
Are you assuming V is finite dimensional?

[Anonymous No.9469793]

>>9469789
Yes.

[Anonymous No.9469799]

>>9469793
>then the basis for V is at most n vectors large
This is garbage, you should say "any basis" and "contains exactly n vectors".

>So any vector in V can be written x⃗ =a1v⃗ 1+⋯+anv⃗ n, which is unique. Similarly since dim(V)=n, dim(U)=n, and any vector in U can be written y⃗ =a1u⃗ 1+⋯+anu⃗ n, is unique.
You haven't actually done anything here.

>y⃗ ∈U so it has to be in V as well.
You already knew this by assumption.

>QED?
No, you haven't shown V is contained in U.

[Anonymous No.9469808]

>>9469647
Because we have the formula [math] E^2 = m^2 c^4 + p^2 c^2 [/math] which in the particle's restframe reduces to [math] E=mc^2 [/math]
Since c is a constant the only variables are energy and mass. Special relativity is probably the most written about physics subject in popscience so it should be very easy to find an article that explains why c is constant if that's what you want.

[Anonymous No.9469810]

How would you go about figuring the angle from this when you don't know the value of X?

[Anonymous No.9469847]

>>9469810
draw a right triangle, see if the relationships suggest anything to you

[Anonymous No.9469866]

>>9469808
>pop"science"

[Anonymous No.9469933]

>>9469810
I did a thing. Haven’t done trig in a while though.

[Anonymous No.9469966]

I'm looking through some old chem notes from undergrad. I can mostly make sense of my notes but there's one table in a margin I can't figure out.
3.5 Q 4H
1.3 S 6H
1.1 T 6H
I'm pretty sure it is comparing double and single bonds but I can't for the life of me remember what Q S and T stand for. If it matters at all the previous section was looking at different organic functional grpups involving oxygen (alcohols, ketones, esters etc...).

[Anonymous No.9469996]

>>9469810
tan x = sqrt(1/2)

[Anonymous No.9470027]

What does it mean to raise a number to fractional exponent?

Say 6^2 = 36; here we added 6, six times.

But when we raise 6^(1/2), what does it mean? Did we add 6 1/2 times?

[Anonymous No.9470051]

>>9470027
>But when we raise 6^(1/2), what does it mean?
Square root of 6.

[Anonymous No.9470056]

>>9470027
It's 6 to the exponent of the top number then to the root of the bottom number. So 6 ^2/3 is the cube root of 6^2

[Anonymous No.9470057]

if a molecule doesnt have a chiral centre does that mean it can't be an enantiomer?

[Anonymous No.9470064]

>>9470056
>>9470051

Okay, how do we evaluate 6^(0.1)?

[Anonymous No.9470068]

How do i solve for B?

[Anonymous No.9470071]

How do you clear yourself of brain fog?

I was stuck in brain fog for over a month and only just got over it today and got some serious work done, how can I avoid or treat this faster when it happens next time?

All that time wasted.

[Anonymous No.9470116]

>>9470068
first: does a solution exist? it might not, because there are more rows in the left matrix, than there are columns. You can determine if a solution exists by attempting to compute the matrix B.
forget about the bottom row on the left hand matrix. Now, you have a matrix with 2 rows and 2 columns, which is easy to invert. Its determinant is non-zero, so you can invert that matrix, and multiply it by the matrix on the right hand side (with the bottom row removed, of course). Once you have a candidate for the top two rows of B, verify that the math for the bottom row checks out. If it does, then B exists, if its inconsistent, then B does not exist. (fyi, B does exist).

[Anonymous No.9470125]

>>9469933
Cool, I like it.

[Anonymous No.9470128]

>>9470116
nxm = nxa * axm
3x4 = 3x2 * 2*4

Really not that hard to determine a solution for B.

[Anonymous No.9470129]

>>9470071
Avoid masturbation. Even a couple times a week will send you to your own world for a while.

[Anonymous No.9470131]

>>9470064
Rewrite as a fraction.

[Anonymous No.9470143]

>>9470129
Does sex count anon?

[Anonymous No.9470161]

>>9470143
Fuck knows, mate.

[Anonymous No.9470299]

>>9468683
Kronecker delta is just notation.
All you are doing is defining functionals that are the "same" as the original basis.
I.e. given a basis e1, e2, ... , en you define
φ1 to be the functional such that φ(e1)=1 and for the rest of the elements of the basis φ(ei)=0.
φ2 to be the functional such that φ(e2)=1 and for the rest of the elements of the basis φ(ei)=0.
etc.

[Anonymous No.9470554]

Suppose a differentiable real-function f is such that [math]|f(x)|=C[/math] and there exists a point [math]x_0[/math] where [math]f(x_0)=C[/math].
Does [math]f(x)=C[/math] and how do i prove it?

i have literally no idea where to start

[Anonymous No.9470585]

>>9470554
>i have literally no idea where to start
Think about what |f(x)|=C means

[Anonymous No.9470588]

>>9470554
Let X be the domain of f, and C its image

f: X -> C, -C
Define it it as follows: for x0, f is C, and for all other x belonging to X, f is -C

[Anonymous No.9470589]

what is the geometric shape called where as on a möbius strip, the point furthest away is also the point on the other side of the surface, but where this is valid for all possible directions you can take from a point so that it's closed (or compact?)?

I'm trying to read about manifolds, Riemann surfaces, n-spheres, hypershit and whatnot on wikipedia and can't wrap my head around this kind of terminology and notation so if anyone has any recommended literature on the subject that would be helpful as well.

[Anonymous No.9470598]

>>9470554
is this right, or is there a simpler way?
WLOG assume C>0. For each point [math]x_i[/math] either [math]f(x_i)=C[/math] or [math]f(x_i)=-C[/math]. Suppose there is a point [math]x_i[/math] such that [math]f(x_i)=-C[/math], otherwise there is nothing to prove. Then [math]-C=f(x_i)<0<f(x_0)=C[/math]. By the IVT there is a point such that [math]f(\lambda)=0[/math], but [math]|f(\lambda)|=0[/math]; a contradiction.

[Anonymous No.9470604]

>>9470598
meant for
>>9470585
>>9470588

[Anonymous No.9470612]

>>9470598
>WLOG assume C>0
What is preveting it from being zero?


C = abs. value of a number. The absolute value of a real number is nonnegative (either positive or zero)

[Anonymous No.9470617]

Hoe do I stop myself from playing Monster HUnter World so I can study?

[Anonymous No.9470626]

>>9470612
but then |f(λ)|=0 wouldn't bring about a contradiction
plus the zero case isn't hard to deal with separately since |f(x)|=0 means f(x)=0 or f(x)="-0"=0

[Anonymous No.9470632]

>>9470554
a differentiable function is continuous and a continuous function is locally constant. therefore it depends on the domain: if the function is defined on a connected domain (i.e. the whole real line) then local constant implies constant. otherwise it's only constant on a connected component (i.e. if f is defined on the union of (0,1) and (2,3), it is may be possible that f(x) = C on (0,1) and f(x) = -C on (2,3) - this function is still differentiable and satisfies the hypothesis)

[Anonymous No.9470637]

>>9470632
>continuous function is locally constant
this is nonsense of course. I meant something like "continuous function with values in a discrete set ( {-C,C} in our case) is necessarily locally constant"

[Anonymous No.9470654]

>>9470626
The point is you are losing generality, even if you just seek contradiction and only for C>1 you get it, you cannot legitimately claim WLOG as a least a case is lost.

[Anonymous No.9470838]

>>9470027
it's the side length of a square whose area is 6.

[Anonymous No.9470985]

Why the hell do people say you can't treat a derivative like a fraction? The analysis definition of a derivative is a sequence of fractions. Can mathematicians seriously not just pretend they are choosing some term far enough into the sequence that that fraction basically is equal to the derivative (I mean, choose epsilon equal to 10^(-10^(10^10)), no one cares!)? They know such a term exists, surely they can exercise that knowledge and make things easier on people beginning to learn calculus.

You can prove so much this way in a way that is laughably trivial. Product rule, chain rule, quotient rule, etc. You can introduce partial derivatives in a more understandable way. Just why?

[Anonymous No.9470999]

>>9470985
>You can prove
no, you can't.

[Anonymous No.9471017]

>>9469799
how should I have proceeded

[Anonymous No.9471089]

>>9470985
>Why the hell do people say you can't treat a derivative like a fraction?
but I don't

[Anonymous No.9471093]

>>9471017
>how should I have proceeded
Show every v in V is also in U.

[Anonymous No.9471095]

>>9470985
Helps with differential equations a lot

[Anonymous No.9471100]

>>9470999

You can prove the result for a sequence of fractions and take the limit like you always would. Now, it may require some padding and wouldn't work in pathological cases, but the point is that in a lot of early college education, the point of calculus isn't to teach analysis. It's to teach an intuitive understanding of calculus. What people do now amounts of relaxing rigor in all the wrong places and only being rigorous where its inappropriate.

[Anonymous No.9471113]

>>9470064
To compute a^b with a>0, b real numbers:
Approximate a and b to rationals p/q=a and u/v=b, with p, q, u, v integers.

Use the general algorithm to approximate a 'v' root of positive real number a=p/q. Multiply the result by itself 'u' times.

[Anonymous No.9471116]

>>9470985
It's difficult to prove that you can treat them like fractions, whereas the limit definition is quite nice and intuitive.
See https://en.wikipedia.org/wiki/Hyperreal_number#From_Leibniz_to_Robinson

[Anonymous No.9471131]

>>9471116

I'm totally in agreement that the standard approaches of teaching analysis are fine. I think it's done quite well. My point, though, is about teaching introductory calculus.

In intro calculus, all proofs are done in a hand wavy way as it is (does a Calc 1 student even know what a limit really is?). You could do the fraction proofs in a hand-wavy way as well. I don't think there would be any harm in it. When students get to real analysis, the only difference they'd make is considering sequences of what they considered before.

[Anonymous No.9471147]

This is a prelab for an iodine clock reaction we are doing, (iodide and persulfate variant) and this question stumped me. I think it is poorly worded, but I can't quite understand what they are asking. A stock solution would have a constant concentration, but the samples used for each trial are in separate volumes, so the ratio of moles is not the same in each trial as far as I know. The first trial uses a 1:1 volume ratio of iodide and persulfate, the second a 2:1, the third a 4:1, etc. Why use a volume ratio instead of mole ratio in this case?

[Anonymous No.9471172]

>>9471093
Can the basis in U be extended to a basis of V? Then any vector in U can be expressed as a vector in V?

[Anonymous No.9471181]

What are some basic algebraic laws that you always come across in Calculus that end up being absolutely necessary to complete the problem? I always find myself struggling to simplify certain integrals and derivatives since I'm just not very good at algebra

[Anonymous No.9471206]

>>9471181
trig identities
partial fractions
rules of logarithms/exponents
top three off the top of my head, but really you need everything

[Anonymous No.9471212]

>>9471206
If I did poorly in precalc, do I have a chance at getting an A in Calc 2? I work my ass off in the class and I'm already struggling solely because I can't fucking simplify the integrals I get from surface area and center of mass

[Anonymous No.9471215]

>>9471147
The script is familiar but it's arranged in a way I do not recognize. Like a chinese man decide to write using english for the first time.

[Anonymous No.9471226]

>>9471212
Students only do bad in calculus because of bad algebra, in my experience. Post an example of an integral, we could work through it

[Anonymous No.9471228]

>>9471206
Also, is it important that I go through all of the integration techniques first? my calc class began with applications and is moving into techniques after for some reason.

[Anonymous No.9471234]

>>9471228
Yes. Only backwards shit unis do application first.

[Anonymous No.9471237]

>>9471212
I mean, how poorly are we talking?
It could be you just didn't learn it properly in the first place, and since it's pretty fundamental there are a variety of different style education resources to relearn.

[Anonymous No.9471251]

>>9471237
I mean, I suppose someone with a poor background in precalc could do well, but the one who has mastered precalc material will have a much easier time, since they'll be able to see how to reduce problems into simplier problems, and be much more dexterous and confident in complex maniplulation of expressions.

[Anonymous No.9471256]

>>9471237
So, I'll start this problem. Find the derivative f(x) and get the most confused when squaring it to place it in the arc length equation in order integrate. this is a surface area of revolution problem. being rotated among the x-axis

[Anonymous No.9471262]

>>9471237
>>9471226
http://tutorial.math.lamar.edu/Classes/CalcII/SurfaceArea.aspx

also, example 2 from this site. The algebra is very confusing for me,

[Anonymous No.9471271]

Please help me with my entire assignment, pic related it's my assignment.

[Anonymous No.9471309]

Should I pursue a career in electrical engineering? Recently I'm starting to help my dad build a dealership and think it might be better to get a business because I wouldn't have to invest about 6 years in time and cash into a hard degree while I have this opportunity. If I'm being honest I'm more interested in making cash and think that starting this business would be a good income.

I'm just worried that a business degree is'n as useful as a engineering degree.

[Anonymous No.9471314]

>>9471309
You could do a minor in business and a major in EE, I'm currently doing a minor in business alongside my ME major.

[Anonymous No.9471319]

>>9471262
that's because they work through the entire problem every single step at a time, except for that one part where he skips 3 steps all at once (at the very beginning from (dy/dx)^2)

all he's doing here is trying to find a way to pull terms out of the sqrt term, since that almost always makes the math easier

also his -2/3 looks like a 2/3 but with a longer division line, due to the font rendering, which could contribute to some of your confusion

so when you have something like [math]\displaystyle \sqrt{\frac {4x+2} {3x^{\frac {2} {7} }} }[/math] you can rewrite that as [math]\displaystyle \frac { \sqrt{4x+2} } {3x^{\frac {1} {7} }} [/math], which is what i mean by pulling out a term from the root

the only way to _know_ what steps to take is by practicing
>but how can i practice if i don't know it
struggle until you figure it out for one, then struggle on another, and repeat about 20 times

[Anonymous No.9471327]

HOW THE FUCK AM I SUPPOSED TO PLOT A CURRENT-VOLTAGE GRAPH FOR A DIODE?

[Anonymous No.9471331]

>>9470064
There are two questions.
1) What do we mean by fractional exponents?
2) How do we compute them, if we want the answer to some arbitrary accuracy?

The first is relatively easy. We interpret fractional (and real) exponents so that the properties of exponents already established are consistent, which is to say, [math](x^a)^b = x^{a \cdot b}[/math] and [math] x^a \cdot x^b = x^{a+b}[/math].

The second is a matter of some taste. If you only want rational exponents, you can use your favorite root-finding algorithm on a polynomial you construct which has this as a root. For arbitrary real exponents it's not going to be trivial to perform by hand, but you could leverage logarithms and exponentials to manage alright, if you understand how errors in approximation come from these functions, and how they propagate.

[Anonymous No.9471348]

>>9471314
Not a bad idea, how difficult is that? I'm a brainlet when it comes to science and math but have been going steady in both.

Is a business degree easier? I just want to choose the one that'll Pay better

[Anonymous No.9471356]

>>9471131
>In intro calculus, all proofs are done in a hand wavy way as it is (does a Calc 1 student even know what a limit really is?).
man how far education has fallen. I took calc in high school (class of '94) and we absolutely drilled the FUCK out of limits and proved everything about them, including the derivative, and riemann sums, including the usual limit and the norm limit, etc. We even proved the fundamental theorem of calculus.

Do kids really not learn about limits for calc1 anymore? How are they ever supposed to understand multivariable calculus or complex analysis without understanding limits?

[Anonymous No.9471359]

>>9471348
To do the minor I had to extend my ME degree from four years to five years. I wouldn't say it's any more difficult, I'd actually say it's easier because the business courses are much easier than the engineering courses.

[Anonymous No.9471360]

>>9471212
>If I did poorly in precalc, do I have a chance at getting an A in Calc 2?
Personal experience: I went from almost failing the first quarter of precalc in 11th grade to an average of 98 in calculus in 12th grade. It's definitely possible. But the work I had to put in to dig myself out of the hole my previous 10 years of "learning" put me in was enormous.

[Anonymous No.9471364]

>>9471359
>>9471359
But don't you have to take all the engineering courses either way? Or are they just more evenly distributed?

[Anonymous No.9471372]

>>9471364
Yes I still have to take all the engineering courses, but they're spread out over five years instead of four years. The gaps are then filled in with business courses.

[Anonymous No.9471375]

>>9471356
Usually professors give that talk about "you're supposed to learn more on your own time and read the book or meet with me during office hours", which while of course is important doesn't really help when it's usually first years trying to adjust to a new life and environment so they spend most of their time not spiraling into depression and not dropping out instead of doing the professor's job they're being paid for.

[Anonymous No.9471402]

>>9471375
they do this a lot more for freshman classes than later classes
they still do it junior/senior year but they aren't half as bad

>>9471356
yes, students still learn limits, but not all schools are the same
first time i've ever heard of someone in calc 1 who hasn't done limits

[Anonymous No.9471413]

>>9471319
do you recommend any problem sets?

thanks a lot anon.

[Anonymous No.9471419]

>>9471356
Limits are only really useful for just analyzing behaviors of functions at 0 or infinity as far as I'm concerned.

[Anonymous No.9471443]

>>9471413
if your main problem is even understanding that you could pull terms out from radicals, then i'd recommend making your own problems here http://www.math-aids.com/Algebra/Algebra_2/Radical_Functions/

if your main problem is just knowing what steps to take, just do problems from your calc textbook
if you don't have a textbook i'd recommend getting one
here's tan's calculus, which had some good problems
http://libgen.io/get.php?md5=48BA2C698F083C85F8073B034E4709F1&key=L3RBWYJUTHL4ORLU

[Anonymous No.9471445]

2sqrt(2)/2 = 1/sqrt(2)
Why?
Doesn't the 2 cancel with the top and bottom so you get sqrt2?

[Anonymous No.9471467]

>>9471445
2sqrt(2)/2 =/= 1/sqrt(2)
1.414=/=(1.414)^(-1)

[Anonymous No.9471497]

>>9471445
sqrt(2)/2=1/sqrt(2)
2sqrt(2)/2=sqrt(2)

[Anonymous No.9471539]

when exactly do we learn shit about products (i.e. [math]\prod[/math])?
in calc 2 we learn summations but when do we learn about products?

[Anonymous No.9471549]

>>9471539
Typically in analysis. An infinite product [math]\displaystyle \product_{n=1}^{\infty} b_{n} = b_{1}b_{2}b_{3}\dots[/math] is said to converge if the sequence, [math](p_{n})[/math] of partial products, defined by [math]p_{n}=b_{1}\cdot b_{2} \dots \cdot b_{n}[/math] converges. There are a few nice equivalnces with series that come in handy when dealing with them. A couple in particular are [math]\product (1+a_{n})[/math] converges if and only if [math]\sum a_{n}[/math] converges; and [math]\prod a_{n}[/math] converges if and only if [math]\sum \ln(a_{n})[/math] converges.

[Anonymous No.9471551]

>>9471549
>>9471539
uhgg..
[math]\displaystyle \prod_{n=1}^{\infty} b_{n} = b_{1}b_{2}b_{3}\dots[/math] *
[math]\prod (1+a_{n})[/math] converges if and only if [math]\sum a_{n}[/math] converges*

[Anonymous No.9471552]

what's the most painful way of killing myself on the spot when i fail the orgchem pre-lab in 5 hours because I am a FUCKING RETARD who doesn't understand chemistry despite this being a course from 2015 that I'm retaking in the current year

[Anonymous No.9471555]

>>9471552
get to the nearest bathroom and drown yourself in a dirty toilet

[Anonymous No.9471557]

>>9471552
Drink any chemical compound that lies in your eyesight, then try a backflip from the lab table.

[Anonymous No.9471581]

>>9471552
Don't because you're going to do great

[Anonymous No.9471588]

Let [math][v_{1}],[v_{2}],[v_{3}]\in P(V)[/math] be non-colinear, [math]P(V)[/math] is of dimension greater than or equal to 2. I wish to prove that there is a unique projective plane in [math]P(V)[/math] containing these points.

WLOG let [math][v_{1}],[v_{2}],[v_{3}]\in P(V)[/math] be distinct. Then define [math]w = \{ v_{1}, v_{2}, v_{3} \} [/math] a spanning set of a vector space [math]W[/math] (possible since distinct). This is dimension 3, and since [math]v_{1},v_{2},v_{3}\in W[/math], [math][v_{1}],[v_{2}],[v_{3}]\in P(W)[/math] has dimension 2, which is indeed a plane.

Uniqueness is simple to show I believe, but my biggest question is about the approach here. Is this the proper way to start this out? I then would have to show this holds for all dim >=2 , yes?

[Anonymous No.9471589]

Ive got a question that cant be answered by either my friends or me (none of us is stemfag), here it goes:

We suppose there are two types of flow patterns, laminar and turbulent. If thats the case, are those patterns an absolute state, or are they susceptible of some kind of intensity measure? That is to say: can a flow pattern be *more turbulent* than other?

[Anonymous No.9471590]

>>9471581
I'm sitting with the questions right now
they want me to draw the products for a reaction where a curly arrow from an amine group goes to the boron in triphenylborane and I have no clue what to do
i've been sitting with this for an hour
I want to die

[Anonymous No.9471594]

>>9471552
At least be trendy anon.

Read about time management and spaced repetition for memory and other study tricks. If your methodology for school sucks try something else.

[Anonymous No.9471614]

>>9471590
I am familiar with those words individually but not in that sequence.

[Anonymous No.9471634]

Is the Earth having a north and south pole an arbitrary distinction? By which I mean, let's say we viewed maps "sideways," with Asia being at the top of the map and the Americas at the bottom. Would we then say we have West and East poles?

[Anonymous No.9471654]

Does anyone else get physical pain in their head when attempting to visualize a 4-D space?

[Anonymous No.9471660]

Is there a website that I can input equations into and it'll spit out the 4chan [math] text so I can easily post equations to this site?
Also, does the [math] work on other boards?

[Anonymous No.9471677]

>>9471660
have you even tried google there's plenty of latex preview places

or you could just install latex

[Anonymous No.9471697]

Can anyone help me solve this difference equation initial value problem?

[math] x_n = 3x_n-1 [/math]
[math] x_0 = 1 [/math]

I've done some examples and watched youtube videos usually involving something like a [math] dy/dx [/math] on the left hand side, but in this problem there are just sub scripted values of x and I dont really know where to start.

Do I integrate the RHS?

[Anonymous No.9471705]

[math] x_n = 3x_(n-1) [/math]

fuck i messed up the latex formatting, the subscriped part below 3x on the RHS is supposed to be (n-1)

[math] x_0 = 1 [/math]

[Anonymous No.9471706]

>>9471697
i hope you meant [math]x_n = 3x_{n-1}[/math]
if so, x_n = 3^n

either way they wanted you to do like dx/dn

[Anonymous No.9471712]

>>9471706
like finding the derivative of both sides? I was getting confused when it came to finding the derivative of a subscripted number

[Anonymous No.9471730]

>>9471697
https://youtu.be/3LJ-R9Lp_iQ

[Anonymous No.9471735]

>>9471712
honestly i'm not even sure what you're trying to do, since initial value problems are usually like y'=4y, y(0)=1

can you show me exactly what video or problem sheet is asking for this?

[Anonymous No.9471757]

>>9471735
I'll type the exact problem and question:

Solve the difference equation initial value problems. If the problem is nonegative, find the 'big O" order of the solution and compare it to the 'Big O" order in the notes

1)

[math] x_n = 3x_{n-1} [/math]
[math] x_0 = 1 [/math]

[Anonymous No.9471768]

>>9471757
what the fuck

what class is this?

if this is from a textbook, what unit is this?

[Anonymous No.9471773]

>>9471757
Difference equations are the discrete-time analogue of differential equations (which operate in continuous-time). The theory of difference equations has some similarities and symmetries with that of differential equations but for the most part they are distinct areas.

There are systematic ways of solving difference eqs just as there are for solving differential eqs with many books written on the subject.

Google "how to solve first-order difference equations" for a start.

[Anonymous No.9472268]

>>9466071
Alright, this one's a doozy, so sorry in advance.

I want to make a sort of "compact" way of doing vector operations. For example, if we have a vector,
[math] S = [1, 2, 3, 2, 1] [/math]
and a set of weights, [math] W = [1, 2, 3, 4, 5] [/math]
with W representing a "score" and each entry in S representing how many people gave that "score" (so two people gave a score of 4, 1 a score of 5 and so on)

To take the average, it'd simply be the weighted sum of S and W (the dot product) divided by the number of people that rated a show (sum S), giving us the expression

[math] avg = \frac{S^T W}{sum(S)} [/math]

This is the part where I'm stuck: Finding the variance/std-dev.
Variance is the "Mean distance squared from the average", so below are the steps I'm performing:
[math]
t = (S .* W) - (S .* avg)
[/math]
to find the distance from the average (and a .* b represents an element-wise multiplication)
[math]
t_2 = sum( t.^2)
[/math]
and this should give us variance = [math] \sqrt{t_2}[/math] ,but for some reason I'm getting the wrong answer when I use my method and Matlab's way (after writing out the "compact vector as [math] [1, 2, 2, 3, 3, 3, 4, 4, 5] [/math] and using `var(vec)`)

[Anonymous No.9472271]

>>9472268
Sorry,
[math]
t_2 = sum(t.^2) / (sum(S) - 1)
[/math]
and variance = [math] t_2 [/math] and std_dev = [math] \sqrt{t_2} [/math]

[Anonymous No.9472273]

>>9466071
I'm a math major, but I've always sucked at Euclidean geometry. I couldn't even solve the advanced section of a 9th grade textbook back in school, and it's been two years since I tried improving my situation.
Is it going to be a problem?

[Anonymous No.9472282]

>>9472273
>I'm a math major
In this case you should know that Euclidean geometry has basically nothing to do with math.

[Anonymous No.9472296]

>>9472271
Okay figured it out:

I was essentially taking the wrong dot product. The expression for variance was in pic related:

[Anonymous No.9472298]

>>9472282
Well, as I understand, Euclidean geometry is equivalent to analytical geometry in [math]R^3[/math] vector space, and you can use the theorems provable in Euclidean geometry while solving the problems in analytical geometry.

[Anonymous No.9472309]

>>9472298
>analytical geometry in R3
"geometry" with coordinates has basically nothing to do with math.

[Anonymous No.9472316]

>>9472309
Am I being trolled?
What do you think "math" even is, calculus?

[Anonymous No.9472320]

>>9472316
He does this in every thread.

[Anonymous No.9472321]

>>9472316
"calculus" and anything even remotely related to it can't be called "math" in any meaningful sense.

[Anonymous No.9472348]

19 y/o depressed ex polydrug addict brainlet here
I dropped out of a liberal arts course at university because of the above
my mind is starved of any thought or understanding
I want out of this miserable existence
where do I start?

not really feeling suicide desu

[Anonymous No.9472387]

>>9472348
Maybe you should try >>>/adv/, they're usually pretty helpful.

[Anonymous No.9472391]

>>9472348
>brainlet
>my mind is starved of any thought or understanding
No need to explicitly state this, it was clear when you said "liberal arts course"

[Anonymous No.9472583]

>>9470057
No, some compounds without stereogenic centers are chiral, like (+) and (-) BINAP

[Anonymous No.9472635]

>>9466071
Is time actually passing at a constant rate or are we only experiencing it as such due to our physiology?

[Anonymous No.9472652]

How to take notes quickly?
I write down what I've read but this takes a lot of time.

[Anonymous No.9472674]

>>9472652
Put things in your own words, use diagrams/flowcharts, etc.

[Anonymous No.9472721]

Proof: 0x = 0 for any cardinal x.

Let card(A) = x. by definition, 0x = card([math]\emptyset \times A[/math] = card([math]\emptyset[/math]) = 0

qed?

[Anonymous No.9472724]

>>9472721
fucked up the brackets, but you know what I mean

[Anonymous No.9472885]

Does anyone know how reaction time varies by ethnicity? Possibly the variation is negligible though. I don't think I can ask this anywhere else without being murdered.

[Anonymous No.9472893]

>>9472321
FINITIST GET THE FUCK OFF THIS BOARD I'M SERIOUSLY GETTING SICK OF THIS SHIT

[Anonymous No.9472933]

>>9472893
>FINITIST
Where did I imply I was a finitist?

[Anonymous No.9472998]

Can somebody give me a 5sentence explanation of box plots or am I going to have to search for a pajeet youtube video.

[Anonymous No.9473304]

in a solution to a DE, suppose you have a constant plus some number C+n. Can you just write this as one constant K?
for instance in pic related, could that not be written [math]y(x) = 1 -\sqrt{K + 2 x^2 + 2 x}[/math]

[Anonymous No.9473401]

>>9472721
yes

[Anonymous No.9473402]

>>9473304
>Can you just write this as one constant K?
Of course.

[Anonymous No.9473418]

Homework assignment I have no clue (but didn't really think over it for more than 2 Minutes and it is a bonus anyway):
[math]M \in Mat(n,n, \R)[/math] with [math]M^2 = -Id \textsubscript{n}.[/math]
Show that [math]n[/math] is even.
Sadly nothing like Eigenvectors and -values are allowed, not even determinant.

[Anonymous No.9473430]

Utter brainlet from humanities here. Is the chain rule wrong in this pic?

[Anonymous No.9473440]

>>9473430
Yes. The correct rule is that d/dx f(g(x)) = (d/dx f)(g(x)) * d/dx g(x). Or, in notation that you may be more familiar with, if h(x) = f(g(x)), then h'(x) = f'(g(x)) * g'(x).

[Anonymous No.9473468]

>>9473440
Thanks.

[Anonymous No.9473474]

>>9470589
https://en.wikipedia.org/wiki/Klein_bottle

[Anonymous No.9473574]

Is there a way to formally prove that a Turing machine computes a certain function? I've been given a machine that maps x to x + 2 and I'm not sure how I'd go about formally proving this besides appealing to 'well, it's obvious'.

[Anonymous No.9473674]

>>9473574
Just leave it as an exercise for the reader :^)

[Anonymous No.9473683]

>>9473574
Let x be stored little-endian
start start: tape head is on lsb
state 1: move tape head++
state 2: a<-read tape
state 3{a=0,1}: write a xor 1
state 4{a=0,1}: if a==0 goto complete state, else move tape head++
state 5{a=0,1}: b<-read tape
state 6{a=0,1; b=0,1}: write a xor b, set a=a and b, goto state 4{a}
complete state: number on the tape is x+2

Since this implements a ripple carry adder, the result is correct. Since # states are finite and #symbols are finite, this is a single tape Turing machine.
QED

[Anonymous No.9473690]

>>9473574
Yes, but it's a pain in the dick. You need to prove something like:

For a Turing machine state Z consisting of (tape contents, head location, finite state), let step(Z) be the state after executing one TM step. Let step((A, B, halt)) = (A, B, halt), for convenience.
Let I(X) be the combination of (tape contents, head location) "encoding" the input number X, specified as <tedious crap here>. Let O(X) be the output state, likewise.
You then prove:

For a Turing machine configuration Z = (I(X), initial state), there is a number N, such that step^N((I(X), initial state)) = (O(X + 2), halt.

To prove this, you will need to do something like:
Define a set S of convenient representations of all possible intermediate states your machine should go through in your computation, for any input parameter. Perhaps this is something like (represented number, head position relative to represented number, program phase = {walk-to-end, add 1, add another 1, halt}). This set contains only the states your Turing machine should reach in normal computation from a valid input tape, not unreachable states.
Define F(s) for s in S to be the state Z that the machine should be in, for a given semantic state s.
Define a partial order << such that s << t if and only if F(s) = step^N(F(t)) for some N. Prove that this is a well-founded relation.
Define a function R(s) for s in S describing the desired output of the Turing machine, when resuming from s. In your example, this is a natural number.
Then prove the following proposition:
For all Turing machine states F(s) for some s, there is an N such that step^N(F(s)) = (O(R(s)), halt).
Substituting F(s) = (I(X), initial state) yields your desired result.

To prove this generalization, use induction on s, based on your << partial order. That is to say, in proving this generalization for F(s), you can assume by induction that it holds for step(F(s)), for step(F(s)) << F(s).

All of this is horrible, but it can be done. Godspeed.

[Anonymous No.9473691]

>>9473574
If existence, see >>9473683
If a given turning machine does something, no. See https://en.wikipedia.org/wiki/Rice%27s_theorem

[Anonymous No.9473842]

Ok so I'm currently getting into nootropics and wondering how I can improve in terms of actually getting accurate data here is an example page I plan to add benchmarks and measurements at the start and end of peak onset, it's currently all just a single person I'm testing them on (myself) and I read about the drugs before taking them so I'm worried about the placebo effect, how can I improve? also how would I accurately measure if my baseline has improved I was thinking work out the average baseline for the last four days then compare it to the baseline of the first day?

[Anonymous No.9473849]

I'm taking intro to chemistry and I don't fucking understand significant numbers at all. At first I just thought it was any number that isn't a zero after the decimal, but that isn't the case either. Can someone explain it to me like I'm 5?

[Anonymous No.9473869]

If I know a component of something weighs, say, 45 lbs, and I know that's only 54% of the total object, how do I find the weight of the total object?

[Anonymous No.9473884]

>>9473869
54/100 * X = 45

[Anonymous No.9473906]

Sorry, only marginally related but I figured that if anyone would know it'd be you guys. I tried this free IQ test https://stanfordbinettest.com to see if taking a real one would be worth the effort, and it seems I only managed to answer 27 questions. Now, considering I only scored 27% I assumed it'd rate me as a complete brainlet, but it says I am in the 16th percentile. Personally I am wondering whether that is on the retarded end of the scale or if I am actually above average intelligence. I am an ESL so I've had some trouble with the language questions.

Anyone have experience with IQ tests by the way? Don't need it for a job or anything, but everyone in my family thinks I am retarded and I certainly don't want to prove them right which is why I am gauging the risk.

[Anonymous No.9473914]

Question!
Given a vector x, how do you categorize all matrices A, such that Ax=[1,0,0,..,0]^T ?

[Anonymous No.9473923]

>>9473914
What do you mean by categorize? The first row of A has dot product with x equal to 1, and the rest of the rows give dot products of 0 (so each of those row vectors are orthogonal to x).

[Anonymous No.9473930]

>>9473906
just took a quick glance and let me assure you this test is bullshit that has nothing to do with your IQ
don't obsess over it, if your IQ is 3 digit then you are suitable for everything humanity has to offer
you cannot choose your IQ or do anything to change it, therefore you should never feel inferior to others

[Anonymous No.9473937]

>>9473923
Oh, I see that's pretty fucking simple. Thanks for helping brainlets like me. :)
What do I mean by categorize? Well, let's say that your answer is enough. Ie Row Matrices of the form [[a1][a2]..[an]] where <a1,x>=1 and the rest <ai,x>0.

[Anonymous No.9473962]

>>9473930
I'm really not feeling inferior to anyone. I just think it's an interesting bit of information to have about yourself and, if it's a good value, possibly something to show to an employer or boast about. I am a student and despite struggling with a lot of the tasks I manage with diligent work and proper learning methods so I am not worried about my intelligence in terms of what is possible for me to do. I am also learning a 4th language besides getting my degree which probably isn't something unambitious so that's really not the issue.
As for the question you posted, that's just some basic multiplication isn't it? Is that a bad way to gauge intelligence? Saw some tests that were more language focused and some that just wanted to me to find patterns. I have yet to take a real test, which I will probably do before graduating. You say I can't do anything to change my IQ, but is that really true? I have read that by learning new things and actively keeping your mind engaged, solving problems and challenging yourself you can actually become smarter.
As for test taking, especially in the language problems, it seems I can just score higher just by consuming literature. One question was
>Rearrange "Any time" to another word with 7 letters
and the answer was amenity, a word I have never even heard before. I assume the same would be true if I took the test in my native language. Math (especially simple operations like this) is also something you can train, the same is probably true for pattern finding. All in all it seems to me you could score quite high, no matter your intelligence, if you really trained yourself for IQ tests.

[Anonymous No.9473992]

>>9471589
No answers? :(

[Anonymous No.9474073]

>>9473849
Any zeros after the decimal (at the end of the number) and any non zero numbers are significant.
Zeros in front of nonzero numbers but not in between other nonzero numbers (sandwich zeros) are not significant

0.0030500 has five
3.050 has four
305.0 also has four
0.0040008 has five

[Anonymous No.9474083]

>>9473849
To add to what >>9474073 says, it's basically how much precision is involved in a number.

If you ask a manufacturer to make a 5 inch tool (1 significant digit), you're going to get a less precise size than if you ask for a 5.000 inch tool (4 significant digits).

[Anonymous No.9474091]

>>9473849

I have a stick that bout a meter long. I measure something that's 3 meters long. It's 3.m ±less than a meter. So it has a 1 sig fig since the first digit is the size of the error.

I have a meter stick that marks off centimeters. I measure something that's exactly 3 meters long to the centimeter. It's 3.00m ±less than a centimeter mark. So the error is the cm place and there are 3 digits from the start of the number to the cm place so it has 3 sig figs.

sig figs are the length in base ten of the ratio of the number and it's error. sig figs = ~log_10(measured number / error) +1.

If you add a number a±1m and another b±1cm, the big error of ±1m dominate the tiny error ±1cm so you get a+b ±1m. So you round to the biggest sig fig place when adding numbers.

If you multiply numbers, you have a±error = a(1±10^1-a's sig figs) and b±error = b(1±10^1-b's sig figs), so a*b(1±10^1-a's sig figs)(1±10^1-b's sig figs) = a*b(1 ± 10^1-a's sig figs ± 10^1-b's sig figs ± 10^2-b's sig figs-a's sig figs). Here which ever number has the smallest sig figs dominates so round to that one.

[Anonymous No.9474101]

>>9473914
The first column is x^T/<x,x> + any orthogonal vector^T
The other columns are orthogonal vectors^T

[Anonymous No.9474115]

Hey /sci/, community college bro here studying calculus 1. The class is five credits, we meet for 70 minutes every day and I find myself working on the class for 3 hours a day AT LEAST. I ask you the following...
>Am I spending too much time on the class, indicating that I'm dumb as fuck?
>Can you give me or direct me to some advice on how to better absorb these new math concepts better? Our text seems to greatly over complicate things.
Thanks /sci/.

[Anonymous No.9474121]

>>9474115
Check the sticky.
As long as it's not taking you forever because you're doing the wrong steps, I wouldn't worry about it.

[Anonymous No.9474156]

>>9474115
>short
https://www.amazon.com/Calculus-Made-Easy-Silvanus-Thompson/dp/0312185480/
https://www.amazon.com/Manga-Guide-Calculus-Hiroyuki-Kojima/dp/1593271948/

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

[Anonymous No.9474160]

>>9474156
>>9474121
Thank you senpai anons.

[Anonymous No.9474292]

It's been a while since I've dealt with these, how are they deriving this?

[Anonymous No.9474298]

>>9474292
>how are they deriving this?
What step are you confused by?

[Anonymous No.9474300]

>>9474298
I have no clue why c is being divided by r in the sum

[Anonymous No.9474302]

What should I do if I realize I hate my major but it's too late too change due to excessive credit hours? Should I keep going and hate my life?

[Anonymous No.9474314]

>>9474300
>I have no clue why c is being divided by r in the sum
You use the formula for the sum of a geometric series, and then the r comes out after you simplify.

>>9474302
>too late too change due to excessive credit hours
What do you mean?

[Anonymous No.9474317]

>>9474302
What do you want to do and what is your current major? If they are somewhat similar you could possibly apply for grad school in a new field and just make up a few credits while in it. Employers will only care about the most recent education gained

[Anonymous No.9474326]

>>9474314
If I change, I would have at least six excess credit hours...

[Anonymous No.9474351]

>>9474317
Computer Science and I would rather switch to Computer Engineering

[Anonymous No.9474362]

>>9466071
The center of a black hole is a singularity and the universe came from a singularity. Is it possible we're just the result of an exploding black hole from a larger universe?

[Anonymous No.9474439]

>>9474351
If you are up for it I think doing a masters in compE would be worth it if switching majors is not possible. If you have time left then maybe even try to take advantage of compE research opportunities as it will make you look better for admissions. A masters as an engineer is always a plus anyways

[Anonymous No.9474450]

>>9473418
haha, seems like no brainlet here has a clue, either.
well nvm I got an idea which seems pretty reasonable to get a solution with.

[Anonymous No.9474454]

If I earn a PhD at the best university in a country, should I be able to get a job in that country even as a foreigner? Asking as US citizen looking at grad programs in Switzerland, Germany, and the UK as options

[Anonymous No.9474462]

>>9474302
>>9474351
Try to switch anyway. Talk to a Dean.

[Anonymous No.9474466]

>>9474326
>If I change, I would have at least six excess credit hours...

Meaning what? When I graduated, I had 240 credit hours when I only need 120 to graduate.

[Anonymous No.9474479]

>>9474292
[Principle*(1 + interest) - payment ]*(1 + interest) - payment = 0

in general for n payments

(((....((Principle*(1 + interest) - payment )*(1 + interest) - payment) ... ))) - payment = 0
factor out
Principle*(1 + interest)^n - payment*(1 + interest)^n-1 - payment*(1 + interest)^n-2 .... -payment*(1 + interest)^0 = 0

[eqn] Principle = \frac{payment}{(1 + interest)^n} \sum_{i=0}^{i=n} (1 + interest)^i = payment \sum_{i=0}^{i=n} \frac{1}{(1 + interest)^i}[/eqn]

[Anonymous No.9474549]

can someone give me a 2 sentence explanation on how differential equations works. I get what it finds but not sure how it DOES it.

[Anonymous No.9474554]

>>9474549

You don't know the function y(t) but know something about the function. Like it equals it slope.

Take a physics course

[Anonymous No.9474810]

Does someone have the kindle (epub/pdf) version of chen's " introduction to plasma physics and controlled fusion " ? All I could find online is poor quality scans of the older versions (<2010) ?

[Anonymous No.9474827]

Any hints? I tried cylindrical and spherical coordinates in the domain, but I can't even begin to solve the integral itself

[Anonymous No.9474853]

>>9474073
>>9474083
>>9474091
Thanks lads, I appreciate it.

[Anonymous No.9474860]

>>9474827
The domain is the fucking horn of Gabriel. Use cylindrical ffs.

2π∫dr r*ln(r) (∫dx x [x from 0 to 1/r]) [r from 1 to e^2] = π∫dr r*ln(r) * 1/r^2 [r from 1 to e^2] = π∫dr ln(r) * 1/r [r from 1 to e^2] = π∫ u du = π/2 u^2 = π/2(ln(r)^2) | [r=e^2 - r=1 ] = 2π

[Anonymous No.9474867]

>>9474860
I've never seen that particular case, thanks. What I don't understand is why we are given problems in exams we've never gone through in lectures

[Anonymous No.9474882]

>>9474827
Dude you have the term y^2 + z^2 all over the place. They are literally telling you what to do man.

x=x
y=rcos(o)
z=rsin(o)

[Anonymous No.9474919]

Brainlet here.
How Mathematica deals with trigonometric functions using angles in degrees and decimal numbers (for inverse trigonometric functions)?

[Anonymous No.9474938]

>>9473849
https://en.wikipedia.org/wiki/Significant_figures#Concise_rules

[Anonymous No.9475083]

>>9474919
protip, pi/3=1.0472

[Anonymous No.9475097]

If dinosaurs were alive for however million years, why didn't they invent shit like computers, cars, planes, rockets, sex dolls and interstellar travel?

[Anonymous No.9475186]

>>9475097
Dino's no smart

[Anonymous No.9475290]

>>9475083
LOL

[Anonymous No.9475295]

>>9475290
what

[Anonymous No.9476095]

>>9474810
Took me less than a minute to find
Try using libgen.io next time, it's a pretty useful website:
http://libgen.io/book/index.php?md5=D5179C6954DA29CC155A412E26F9E6B3
(Didn't actually download this, but I'm assuming it's of a reasonable quality)

[Anonymous No.9476450]

>>9474919
It's likely that Mathematica converts numeric literals to rationals rather than floats. Pi will be kept as a symbolic constant. Trig functions will convert angles to fractions of a circle, and be evaluated exactly where appropriate. If an angle is a rational multiple of pi, then it's sine/cosine/etc are algebraic (morever, constructible if the denominator is a power of two).

[Anonymous No.9477213]

>>9468844
>images exist of an actual atom
https://i.imgur.com/1SMvE7C.jpg

[Anonymous No.9477215]

Just finished my last exam and I'm bored. On my phone so slow, but ask away.

[Anonymous No.9477216]

>>9466071
So I've been wondering about annihilation when matter and antimatter meets, and how it's described as a huge release of energy with gamma radiation. I tried to search for visualizations of it but only came across dramatic "documentaries" and pictures of what looked like nuclear explosions. My question is: what would the power of a singular annihilation be?

I'm not a very scientific person, but I do like to do my homework (not literally) before going to talk or write about something, and my assumption is a reasonable amount of antimatter particles colliding with matter particles could create something destructive, but is it the amount of particles that determine the amount of energy let off, or is it the particles in question?