/sqt/ - Stupid Questions Thread

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.

?????

W-which one do I need for data science user? I thought statistics.

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

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

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.

looks like someone needs to watch some wildberger

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

>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.

Gunna watch all of this tonight, thank you.

no exam, it's all self study

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?

...

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.

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.

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

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

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

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.

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.

Khan Academy.

old thread

>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.

This is a memelist.

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

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

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.

>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?

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

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

thanks for helping a brainlet out user

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?

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.

It's just symbols. There's no differencce.
en.wikipedia.org/wiki/Notation_for_differentiation

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

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

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.

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

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

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

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.

you use them in differential equations (calc 4?)

SICP

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.

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

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)

Gosh dang forgot my picture

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

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?

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

Yes, I just seen that. Thanks.

It is a strict order though, yes?

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?

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

What have you tried?

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

isn't this just partial fraction decomposition?

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

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?

[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]

Thankyou!

If Card(A)

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)

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

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)

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

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.

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?

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

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

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).

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

what do you guys think of this brainlets??

meant for

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

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

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.

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

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

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?

Here's one method from google
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.

Meant to quote

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: 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

God damn it, meant to reply to you
In this post:

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

How would you take a photograph of an atom?

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

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

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

>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.

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?

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.

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.

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