SQT

kernel is {1,5,25} so image is size 30/3=10

Ok, thanks. I've googled it, it's one of applications of the first isomorphism theorem. The thing is, that textbook I'm reading assumes I don't know about kernel and group quotients(and hence about the theorem). I'm not fully satisfied with this solution as I don't know anything about quotients(familiar with kernel tho)
Could anyone guide me to another way to conclude that order of solution divides 10?

They say it right there, it's the current best action, what's not to get? I understand this just fine and it seems like pseudo-math or light philosophy to me. Pretty lame.

Agreed, what a shitty read. Philosophical probability with no sense of how a distribution is derived is an absolute waste. Figuring out how to say
>Well you can do this with this information
>And if you have more information you can do that
>Well the value of the new information is (2)-(1)
Is much harder than figuring out what the hell kind of information you are to find and what will result (!!!) as well as how likely each of those things are.

Let [math]{\bf A},{\bf B}[/math] be Subrings of a Ring [math]{\bf R}[/math] where
[eqn]{\bf R} / {\bf A} \not \cong {\bf R} / {\bf B}[/eqn]
does that imply [math]{\bf A} \not \cong {\bf B}[/math]?

yes because A isom B implies R/A isom R/B

You know how in scifi they'll be there on a spaceship and something bad happens and they're like

>Hull integrity at 75% and holding

What metric would this be? 75% of what?

Why does solvability of the Galois group of the splitting field of f(x) imply that the roots of f(x) are algebraic?

Think about the definition of algebraic

is that a covariant derivative of a coordinate function? I thought you could only take covariant derivatives of tensor fields, and coordinate functions aren't tensor fields I think.

If photons can have phase velocities greater than c, can't we slow them down so their group velocities are less than c and then extract info from them?

That's where I fucked up, I saw a superscript and blindly thought "hur dur (1,0) tensor field".

But the coordinate functions are literally just functions of our other (arbitrary) coordinates. Aka use the regular Laplacian wrt the unbarred coordinates and it worked out

Oh, so they do not specify what the actual action is, just that it exists and its value is the result?

What is it called, when the parameter is not actually used in the expression, if that has a name?

z = y*1.015 + 1/100 (0.1 x + 3000) + x + 500;
x + y = 10000

maximize z

lagrange multipliers, friend

>
Wish I knew what that was (what class covers it?), but I solved it and think that y = 10000, x = 0.

this isn't for homework either, it's maximizing a bank interest rate on two accounts

It's a calc 3 concept. Given a function f(x,y) subject to the constraint g(x,y) = constant,

gradf(x,y) = λgradg(x,y)

Gived you the extrema

Wow, I never learned that in Calc 3... Although it looks familiar

I have zero experience in chemistry but want to get my head around it for biology.

Why the hell is glucose in pic related C6 H12 O6? I don't understand why C is 6 or where the carbons actually are, nor do I get why H is 12. What do the dotted and straight lines mean?

Have you heard of Reimannian normal coordinates? If so, das it mane. Choose a local frame where [math]\partial_i X^{j} = delta_{ij} [/math] (Normal Coords). Then argue why the result is tensorial, then you done.

>y = 10000, x = 0
I don't think so. I didn't solve it, but immediately y = 9999 and x = 1 gives larger z

Each vertex is a carbon. The compound is presented in the plane of the viewing surface with the dashed lines representing a functional group at an angle away from you, while the dashed lines represent a functional group at an angle toward you. If the hydrogen atoms are bonded to carbon, they are usually not drawn--they are just implied. Each carbon will have four things bonded to it, if it you see less than four things coming out of a vertex, there are implied hydrogen atoms (however many it takes to add up to four).

For example, the carbon directly beneath the OH group on the top of that picture would have two hydrogen atoms bonded to it, etc. etc.

Sorry, the dashed are angled away, the bolded wedges are angled toward you. Typo.

If you're looking parallel to the positive x axis, the angle is arcsin(3/2).

How does that relate to the contractions on the connection coefficients vanishing?

Statistics
I have a sample of 4 randomly generated numbers, [0.0023, 0.0605, 0.0661, 0.0364]
I pick the largest value (0.0661) this is my guess.
Now, I want to know how confident I am in that guess, relative to the other numbers... Is there a way to do this?
You could, just arbitrary say you require a difference of greater than 0.1 between the highest and second highest value.
(0.0661 - 0.0.605 = 0.0056 implying failure, in this case)
However, I want a more... uh, statistical way to do this, not just somehow deciding 0.1 or something as a magical number.
I'm a statistics brainlet, please assume very basic knowledge

Your guess of what? If you're trying to estimate the mean of whatever this random number generator produces, you could just take the mean of your four numbers and run a t test

Not trying to estimate the mean.
I have 4 signals (vectors) and I transmit one of these 4. After travelling - or, in my simulation, adding noise - the signal arrives. On the receiving end, then, I received a signal (noisy) and want to know which of the 4 it is. So I take the dot product of the received with each individual signal possible. I get 0.0023, 0.0605, 0.0661, 0.0364. The receiving end knows all possible signals.
The highest value of the inner product is going to then be my guess of what signal was actually sent. So my guess here would be 0.0661, which is signal C
However, since noise is added randomly to the sent signal, sometimes the noise overpowers the sent signal and the highest value of the inner product is a different signal, so I would guess wrong.
Is there a way, given my distribution of 4 numbers/signals, that I can define exactly how confident I am in my choice?

Veeky Forums, when is it appropriate to use the therefore symbol?

here

That's totally not my work btw. Just in case you guys think I think 5 times 1 is 25.

Hah, I imagine you'd have to be pret-ty tired indeed to make that mistake. Mm hm.

Given u-shaped pipe with a pressure difference delta p at both ends.
How can I show dp/dphi = delta p/pi?

Prove me that a map [math]\pi_m^n:\mathbb{Z}/n\mathbb{Z} \rightarrow \mathbb{Z}/m\mathbb{Z}[/math] defined as [math]\pi_m^n([a]_n) = [a]_m[/math] preserves multiplication if [math]m | n[/math]. [math]\mathbb{Z}/n\mathbb{Z}[/math] is an additive group modulo n

I'm told that electron microscopes are better than light microscopes because electrons have more energy and thus shorter wavelength than light, so smaller details can be detected using electrons. Going further, particles with more energy, such as protons, would detect even smaller details (suppose vacuum and stuff).

However, I would think that the radius of a particle also increases with mass. A larger particle is obviously worse at detecting smaller details.

There seems to be a discrepancy when comparing the expected behaviour as waves and particles. Have I misunderstood some basic fact? In the end, would more massive particles make for better or worse microscopes?

in rough work

Same user that was using a test battery to study a few weeks ago.
Came upon this problem
For set A that belongs to R; and f:A→R a function so that exist the following:
m=min{f(x)/x∈ A};
Sα(f)={x∈ A/f(x)≤α}; with α∈R
If λ

Probably "supremum"

is the following function a bijection? (provide proof):
f(a,b) = (2^a)*(2b+1)
f is from (N+, N+) to N+
it's surely surjective, but I'm not completely sure it's injective. Any thoughts?

it's injective because every number has a unique factorization.
(2^a)(2b+1) = (2^x)(2y+1) implies that 2^a = 2^x which implies that b = y

They leave it up to you to decide what the result is when you are given some information and you decide what the best action to make a result happen, you choose the action that maximizes the value of the result. The new information you do the same thing except now you have a potentially greater value since you can incorporate more information to make a better decision for more value in the result. The value of the information is then the difference of your new result and the former result.
I don't know what you mean the parameter a is not used in the expression, it's clearly there but it's inside the function "You decide what the result is when you put this action a in"

thanks man! actually already solved it by now using the same idea.

ugh meant to comment to

[math] m \mid n \implies n=mq [/math]

Now let [math] z = xy [/math]
[math] \pi(x) \pi(y) = (kn + x_*)(cn + y_*) = (kqm + x_*)(cqm + y_*) = um + x_* y_* = um + z_* = z_* \mod m [/math]

Where u is simply the bunch of stuff that is going to be multiplied by m if you actually expand the parenthesis completely.

On the other hand, [math] \pi(z) = \pi(z_*) = z_* \mod m [/math] so the classes coincide.

If correlation does not mean causation, how do I show that plants need water to survive?

What was the name of the function that went f(x)=(ax+b)/(cx+d) ? Trying to study some stuff and I remember it looking like two sorta-hyperboles that were mirrored.

>how do I show that plants need water to survive?

By describing the internal mechanism of the water use of plants, which has already been done so you are 500 years late to this party.

Stop giving water to the plant

Except that if I do nothing more than describing it, it's unproven.

That's for correlation.

Same user, what do double parenthesis mean? Not multiple ones for hierarchy, but something like
[[3n/n+1]][[2n-2/n]][[n/n+1]]

> f(x)=(ax+b)/(cx+d) ?
That's just an affine transformation of f(x)=1/x.

Specifically, put
x=((bc-ad)u-cd)/c^2
y=v+a/c

and you have v=1/u

Thanks there.
Thanks, it's so obvious after it being pointed out.

dude that's literally just binomial theorem

>I don't know what you mean the parameter a is not used in the expression, it's clearly there
but the parameter is alpha, not a ?

I am not just being dumb, these authors clearly forgot a normalizing factor right?

[math] P(h|data) = \frac{P(h,data)}{P(data)} = \frac{P(data|h)}{P(data)}P(h) = \alpha P(data|h)P(h) [/math]

arctan

Why do people just assume things like ghosts and werewolves don't exist even though we don't really have any evidence that they don't? I mean with all the stories of them existing surely not all of them can be false?

That's not how evidence works fampai. There's no evidence for it so we don't believe it.

And it's perfectly possible for people to make shit up: there are tons of stories in various cultures about all kinds of crazy shit and we've never found a shred of evidence for 99.99999% of it.

Not to mention that werewolves and shit are biologically impossible by the very way biology works. Ghosts you could maybe argue for.

when working with bayesian statistics a lot of people just ignore the constants and calculate them at the end, since its cleaner and easier than calculating the constant each step. usually abusing notation by using the same variable for both, or an equals sign when it fact it should be a proportional too sign.

the thing is they included the constant in earlier chapters, so it looked a bit off when they did it like this.

How do I into LaTeX?

Just learn as you go with it. Write and when you don't know how to do something Google it and move on.

Make sure you use arctan2(y,x) instead of arctan(y/x) which is commonly implemented. Otherwise you run the risk of the point (2,3) being confused with the point (-2,-3) since they both have the same value of arctan(y/x) even though they are at different angles relative to you.

en.wikipedia.org/wiki/Atan2

I got a fairly simple question anons. I'm working on a physics problem where we shoot a ball from a catapult. In the first part of the problem we are supposed to find the max height that the ball reaches in the air.
We already know the starting speed is Vo=32 m/s, we know that g =9.81 m/s^2, we also know that the catapult is l θ = 52◦, so we are able to use a formula that looks something like this : 2gy=V^2-Vo^2 => y=(-Vo^2)/(2g)

Here is the simple question. When do you multiply the velocity with sin and when do you multiply with cos? I can't really grasp the concept of this somehow.

real analysis in a month. how to prepare?

Read up on basic proof methods and logic if you haven't already, make sure everything from elementary calculus is easy and intuitively obvious.

Maybe read up on limits (ε-δ, clearly), constructions and properties of the reals, and metric spaces.

do you have a good recommendation for an introduction to metric spaces?

are the steps (in reverse) really this simple?
Assuming invertibility and all that.

[math] w^* = (X^\top X)^{-1} X^\top y[/math]
[math]\dots[/math]
[math] (X^\top X)w^* = IX^\top y[/math]
[math] (X^\top)^{-1} (X^\top X)w^* = (X^\top)^{-1} X^\top y[/math]
[math] IXw^* = Iy[/math]
[math] Xw^* = y[/math]

[math](X^T)^{-1} [/math] exists iff the equation
[eqn]X w = y [/eqn]
has a unique solution [math]w^*[/math] obviously this solution will minimize the squared error since it will be 0.

p-please respond !

so using that is pretty much what they did to go from Xw to w expressed in terms of X and Y, nothing elaborate?

If M is a module over a ring R, then R doesn't need to be commutative for M to also be a module over [math] \mathrm{End_R(M)} [/math] (the ring of R-linear endomorphisms on M) right? I'm asking because Lang defines R to be commutative for some reason.

I'm trying to create a formula that ranks certain weapons used in a game in tournaments, based on how often they're used in each time and how often they win.

The formula I got was
50(W^2) / (AM)
W = how often the weapon wins a match
A = how many times a weapon appears on a team
M = total matches recorded

My problem is that this formula ranks weapons that only appear infrequently but win more often, more highly than ubiquitous weapons. A weapon that was used in every single match would have a winrate of 50%, but would be lower tier than a more rare weapon with a better winrate. How do I adjust this formula to account for this?

how'd you derive that formula

If you take the direction of gravity as your vertical axis, multiplying by sine is equivalent to pulling out the vertical component of velocity. Cosine takes out the horizontal component.

So if you're dealing with a force (or force component) which is vertical, like gravity, the acceleration will only affect the vertical direction i.e. you use sine.

If you're dealing with horizontal motion, you use the cosine.

This is, again, assuming you chose gravity as the vertical direction and the one perpendicular to it as horizontal

I've only read Shilov's Elementary Real and Complex Analysis because Dover is cheap, can't speak for any other texts.

It's a Soviet kind of book and thus the proofs are obscenely concise, requiring the reader to produce most of the details.

I created it just by thinking about the results I wanted to get, with a lot of trial and error. Now that I've got some data I realized it's not working the way I wanted. The 50 is just for aesthetics, as I liked the output to range somewhere from 0 to 25 on average. The goal was to create output that could tell if weapons were successful due to widespread use or great win ratios. I would want widespread use to rank higher.

Makes sense when you put it like that. Thanks user.

can you provide some samples for us to experiment with

Here is my current data.

I'm worried weapons like weapon 4 will become the highest ranked due to performing outstandingly well in a small number of matches, even though they may not be used that often, when using the current formula.

Give us more of your handwriting and FUCKING ROTATE YOUR PICTURES!!!!!!

>differential equations is the most useless and boring class I've ever taken
>nearly every physical law is a differential equation
>useless
ok

how do you define a "small number of matches". could you just make another formula which compensates the rank?

The problem with the current formula is if you look at what it does to weapons that are exceedingly common in usage. For example, let's say we had a weapon that is used in every single match, on both teams. That weapon would by definition have a use rate that's equal to the number of matches, and a win rate equal to half the number of matches. With the current formula, that would output a rank of 12.5. Essentially the formula would be saying that a weapon that's used less often, but that has a better win rate, will be more valuable than a weapon that's used in every single game. It's not very representative of what you would expect when looking at tournament results. I'm not sure what I could do differently with this formula to get the results I'd like.

Oops, I mean it would have a use rate equal to DOUBLE the number of matches, because its being used twice per match on both teams, and a win rate equal to the number of matches. That would actually give a ranking of 25, which is pretty good.

However, it would still be possible to get a ranking that's even higher than that, by having less use but more wins. A weapon that was used only half the time, but won every single match, would have double the ranking of the weapon used every time. That doesn't sound right to me, no?

Sup guys following the guide in pic related. I'm halfway through keisler's calculus. I'm wondering if its ok to start a linear algebra text before moving onto book of proof. Reason being I'm starting physics at uni in a months time and will be doing linear algebra in semester 1

okay, so im obviously handicapped...
given two 2D axis aligned rectangles A and B, how do i find the matrix that will transform A into B?

i dont understand how they say this

I know nothing of physics/chemistry, I have a question: why does soda fizz up when you pour it too quickly?

Draw lines from (0,0) to the two points given. You get a triangle and a quarter circle.

I can accept that high x1, low x2 vs low x1, high x2 separates the examples into two regions.

But why are say high x1 low x2 points for which [math] -4.9 + 1.7x_1 - x_2 > 0 [/math] ? I do not see how the expression for any [math]x1[/math] or [math]x2[/math] places it either above or below the line.

I do see that points for which the expression is 0 are on the line, though, just now how greater than or less than occurs.

i'm confused how that's a quarter circle

from the picture it looks more like 1/6th or 1/8th