/sqt/ - Stupid Questions Thread - No Spergs Allowed Edition

For the rare polisci people who dare to post here

Say a future environment that proceeds ours by two centuries is filled with extremism and each nation's political faction is more linear, say North Korea levels of fanaticism for that particular government.

Would it be possible for these people to be so intensive in their rules, that they completely tide over after the 'bubble bursts' to their opposite?
For example, communism becoming so extreme it becomes feudalism.
Or syndicalism becoming so warped it becomes anarcho-capitalist?

Shit, crazy story man. Hope your health is good now. What's your end goal? You want to work in public research with just an undergrad? That's pretty hard. You're doing pure or applied math research?

How do I get a hand of trigonometry?
I'm currently in third year and somehow I still don't have a solid background in it. Any recommendations and tips?

It's so counter-intuitive to me somehow

Which parts specifically?

Basics. I know about unit-circle, sin/cos/tan and so on but I just memorize the shit. I can't derive it from scratch out of logic. It's really annoying.

Basically I would love to learn it properly from scratch. Maybe someone will hand out some gud ressources or whatever they have. I would be eternally thankful

If I have an electrically powered propulsion system that produces 4N/kW, what equation would I use to figure out the power-to-weight ratio I would need from a power source to produce the necessary thrust needed to accelerate it (the engine) at 9.8m/s^2? Assume all other components are weightless.

I know this is simple algebra, but I just can't mentally arrange the terms in the right order no matter how hard I try.

Accelerate the power source rather, not the engine.

hey Veeky Forums

I recently did a year of computer science
don't get me wrong it's my favourite hobby but holy shit they teach fuck all in it and everyone complains "waa waa waa algorithms waa waa waa" -- and my university is known for being quite theoretical so it's not like we're doing boring intro to java shit only -- but we get a good balance imo, but they should also push students a bit harder.
So I'm going to transfer into pure maths instead, and self teach computer science on the side, maybe pick some mathsy units from the faculty because that stuff is pretty interesting,

anyway enough of my life story / blog. I find group theory really interesting and that kind of stuff, is there any recommended readings for learning about abstract algebra and whatnot.

Sorry for the dumb post I'm not a regular on Veeky Forums, used to go on /g/ a lot but then I quit lol..

It's the guy on the left because he has the same haircut as me.

no need to make this so personal, your post comes off as awkward

but it also comes off as honest and open, so here's some suggestions. Artin's Algebra is a classic book, but might be a bit dated. Dummit and Foote's Algebra is a very common undergrad book. My favorite is Rotman's "A first course ...". Any should do it for you, check out all three, read a bit, and pick one without much thought into it. Then read and do the exercises.

Khan academy is where I learned and should still be good: khanacademy.org/math/trigonometry

I'm a second year CE student and I really love the subject, but I just can't read textbooks.
I just get exhausted after a few pages, is there something wrong with me? How do I sit down and just read a chapter in an algorithms or math book?

Read whatever you feel comfortable with. Not need to read a whole chapter in one sit. Read a little think about what you understood and go back to it later. How do you eat an elephant ?

Why are no spergs allowed here?

In probability, "X and Y are independent" actually means "X and Y are independent when no other variable is observed".

"X and Y are cond. independent given Z" means "X and Y are independent when only Z is observed, and nothing else".

Is this correct? I was always confused by the names that made me think independence is more general.

No, independence is a property of the joint distribution.
It's a super strong property that almost never holds for nontrivial applications; basically the statistician's equivalent of the ideal gas or frictionless spherical cow.

1.5 years out from my last surgery with no signs. Fingers crossed, man haha

My end goal was to get a job as a quant on Wall street. So, ideally I get to do some research in mathematical finance, then continue in a PhD.

Since you're the only one replying (thanks for that by the way), let me ask you this: do you think somewhat irrelevant research is better than the little experience I have? I know 2-3 professors from my last 2 years who would definitely take me on to research with them, but they're in unrelated fields like math bio, and computer science.

Political science is not science.

Is it possible to go from an Engineering undergrad to a Physics grad?

Im in a specialist aerospace program atm, so I have some background on Orbital Mechanics and Astrodynamics. Will that help at all?

No. You need to learn serious math.

Are there any alternatives to "An Introduction to Modern Astrophysics" by Carroll and Ostile? Or does anybody have a good copy of it?

I can find a djvu on libgen, but it's pretty unusable.

I think that's something else called "mutually independent", not just "independent"

"Mutually independent" is nothing more than independence for > 2 random variables.

Formally, X1,...,Xn being mutually independent is defined to be the same as the following: "if you take any two distinct random variables, they will be independent".

So when n=2 it's the same as independence.

>if you take any two distinct random variables, they will be independent".
That's pairwise independent, which is a weaker condition.

>A student that has studied CC should be able to do a problem like 243 - 87 in his or her head easily like 243 - 87 = 243 - 100 = 143 + 13 = 143 + 10 + 3 = 156.

Can someone kindly tell me the point of making the problem this long, even following this logic? I see what's being done here is using round numbers to make things simple, right? Given that instruction I would do something like (250-90) + (-7+3).

I'm not an opponent or proponent of CC, I just want to know what it is.

You can convert djvu to pdf easily online if thats your problem?

Fug, you're right.
It's been too long since I've actually had to use this (unrealistic) shit.

Right, here's the actual definition then:

>Let S = {X1,...,Xn} be a set of random variables. Then these variables are mutually independent if and only if, for every subset S' of S containing at least two elements, the elements of S' are mutually independent.

(Pairwise independence replaces "at least two" with "exactly two".)

This definition of mutual independence eventually reduces to the case where S' consists of exactly 2 random variables, in which case it falls back to the usual definition of independence.

It's basically continuation-passing-style but for calculations.

The trade-off for breaking the problem into many, many steps is that each step is simple and you can do calculations of arbitrary length (e.g. 10-digit subtractions) in your head, where the method you propose becomes impractical due to limitations on short-term human memory.

would an example of pairwise independent but not mutual be
[X,Y,X+Y] ?

I don't think X and X+Y are pairwise independent in general (though they could be for specific choices of X and Y).
The typical example for 'pairwise but not mutually independent' is to (independently) flip two fair coins, and from there define the following events:

A = First coin is heads
B = Second coin is heads
C = First and second coin land the same way (i.e., either both heads or both tails)

Then A,B,C are pairwise but not mutually independent.

en.wikipedia.org/wiki/Line–line_intersection#Using_homogeneous_coordinates

what is this??? what are a1,b1,c1 and a2,b2,c2???????????????????????????

and is it exactly equivalent to this:

en.wikipedia.org/wiki/Line–line_intersection#Given_two_points_on_each_line

If a function is continuous in a closed interval from a to b, why doesn't it imply it's differentiable in both a and b?

I mean a better question would be: FORMALLY speaking, is an interval [a,b] considered differentiable in [a,b] only when you have both left and right derivative for each endpoint?

Nah, the problem is that almost every other page is like 10 times larger than the other pages, so I have to constantly zoom in and out and pan around to read it. Don't know if it's possible to fix the sizes of pages in either djvus or pdfs, haven't really looked into it.

Is the explanation for bellman-ford only requiring v-1 iterations because the correctness is kinda spreading out like a bfs search?

I get the part that the max amount of edges without a cycle is v-1.

What's combinatorics?

The study of finite sets.

> If I have an electrically powered propulsion system that produces 4N/kW, what equation would I use to figure out the power-to-weight ratio I would need from a power source to produce the necessary thrust needed to accelerate it (the engine) at 9.8m/s^2?
Power depends upon speed: P=F.v. For vectors, it's the dot product; applying a force in the direction the object is moving adds energy to the object, applying a force in the opposite direction removes energy, applying a perpendicular force changes the direction but not the speed (e.g. circular orbit).

For a stationary object, applying a force doesn't require any power.

Thus, the efficiency of a thruster increases with speed. This is also why the EM drive, which is claimed to produce constant thrust for constant power and no mass, violates conservation of energy: above a certain speed, the rate of change of kinetic energy would exceed the input power.

How many hours do you usually invest in your 3 credits math course/class like Calc I-III?

what is the highest math that engineers will generally take in university?

mine stops at differential eqns and vector calc and i'm wondering if others are the mostly the same

Fourier theory

>tfw proof makes sense

Yeah seems pretty standard to me. Curriculum at my school has Calc I-III, differential equations, discrete math, linear algebra, and statistics

exactly the same here
after differential equations im done Math courses

I am starting the coursera Introduction to GR. Why is the 4-velocity squared = 1? He set c=1. How can I expand the equation and come to this result?

Polisci isn't a science, it's a liberal arts.

Self-studying with stewart's calc text and I'm new to calc, should I just follow the chapters in sequential order or should I skip to certain sections first?

take 1/x for example, it's continuous in (a,b) but it's not differentiable in x=0

>(a,b)
(0,1)

Is a distended spring slightly more massive than a spring at rest?

people seem unwilling to give a plain yes/no answer but it seems like a no

physics.stackexchange.com/questions/212082/does-the-rest-mass-energy-include-the-potential-energy-of-the-particle

...

>people seem unwilling to give a plain yes/no answer
Which means my question is using "lies told to children" concepts.
Thanks.

i think the take-away from this is that newtonian physics isn't completely accurate (but accurate enough for a lot of calculations), and in newtonian physics you regard mass and energy as separate things, and e=mc^2 doesn't apply to the newtonian concept of potential energy

linear algebra over [math]\mathbb{F}_1[/math]

Can you get an engineering job with no internship?

There seem to be two competing philosophies when it comes to reading a textbook:
1. You ought to read the book from front to back to gain a thorough exposure to the material. OR
2. Textbooks aren't meant to be read front to back, so you should instead focus on finding and learning about specific concepts in the book.

Here's a good method that is pretty much a compromise between these two modes of thought:
A. First, get a general overview of the subject, by, for example, reading the Wikipedia article, so that you have a vague idea of what you're getting into, and what some of the concepts are that you will be learning about.
B. Do a "superficial reading" of the textbook. That is, read the preface and table of contents, then skip around and read anything that catches your eye. You're basically skimming around and familiarizing yourself a bit further with the concepts and the structure of the book.
C. Read through the book. Do not get stuck on any details for too long. If you kinda think you get the gist of something but you aren't fully confident yet, just move on. Make sure you are doing/attempting most of the exercises.
D. After you finished the book, go back to those parts that you didn't fully understand, and seriously make the effort to understand every detail.
(Source: math.stackexchange.com/questions/279079/how-to-read-a-book-in-mathematics/279125#279125)

The basic concept behind this method can be applied to many things. The idea is that, instead of working through something linearly (fully understanding one concept before moving onto the next concept), you are starting with a vague conception of all of the things you will learn and then sharpening that conception by filling in the details.

Jesus Christ, son
r = 1
pythagorean theroem: side^2 + otherside^2 = r^2
fuck man

>1. How many liters of gasoline or diesel do you get from refining/processing 1 barrel of crude oil?
quora.com/How-many-liters-of-petrol-are-produced-from-one-barrel-of-crude-oil
>2. What was the reason for the drop in oil prizes in 2008?
From wikipedia:
"On July 15, 2008, a bubble-bursting sell-off began after remarks by President Bush the previous day that the ban on oil drilling would be lifted."

>"On July 15, 2008, a bubble-bursting sell-off began after remarks by President Bush the previous day that the ban on oil drilling would be lifted."
was it a sell-off of oil futures (or something) on the stock markets, or a sell-off of physical oil? or both i guess?

How valid are IQ tests as a measurement of intelligence?

this is a very nice question

Closed interval, not open
1/x is not continuous for [0,1]

Thanks user that actually makes perfect sense. Working through it linearly seems too robotic and bullheaded so I will try that.

Are there any places on earth where there is no electro magnetic field?

Let's suppose I have a network. It's cyclic and undirected and every node n has an unknown value (ranging from possibly 0-x, realistically spoken from 0-100 max). If you add all values up, that would be the population I am actually interested in.

I want to take a sample of that population. Now that the size and the distribution of the values over these nodes is unknown (and possibly not random!) this seems impossible.

Now I am introducing a second stage of the sampling process. AFTER the first stage (after some nodes have been selected) I am able to find out the values of those nodes and take a second sample of those.

My question is, if I ran a random walk on said graph to take a simple random sample of nodes, then take the values of said nodes, take each element out and randomly select another sample of these, would that be considered an actual random sample of the described population (the sum of all node values)?

For example the graph could have these 10 nodes with corresponding values: A:0, B:52, C:21, D:15, E:41, F:2, G:4, H:6, I:12, J:2.
Of course I wouldn't know these values yet, but the population would have a (also unknown) size N of 155.

In sampling stage 1 I'd use a random walk algorithm and get for example C E F and A.
Now I'd look up the values and get a sample size of 21+41+2+0= 64.
In samling stage 2 I'd roll a 64sided dice a certain number of times and get my desired sample.

Would this be considered actual random? Would it create bias in some way?

Wouldn't there have to be? Seems like an application of the Hairy Ball Theorem, but maybe there is a nuance to electromagnetic fields I don't understand

Does that mean that there is a place on earth where no light can go to or go through?

So your sample is the numbers you get in step 2?

Well, it's always going to be random. Are you asking if you're more likely to see certain numbers in the sample?

Continuous functions don't have to be differentiable anywhere.

I'm a physics major going to EE grad school to study optics.

Would learning real analysis be useful for me? I'm reading baby rudin, 3 chapters in, this stuff seems really very intuitive practical stuff formalized with an autistic amount of rigor.

Does anyone have good resources to master the Jordan Normal Form and git gud intuition on the subject?

What makes the least upper bound property so important?

Can someone define what a tensor is for me?

I probably worded it pretty badly. I am just gonna jump straight to what I want to do now.

The nodes are houses on a city map, connected by streets, ways etc. There are different amounts of people living in the houses, I want a simple random sample of the city population.

Now I am asking if the described process would generate that. A simple random sample is a sample, where every object of the population has the same probability of getting into the sample (and where that probability is greater than 0).

I think this would do the trick, but I am really not sure. That's all I am asking.

Please help a brainlet like me.

A (p,q) tensor on a vector space V is a multilinear map from p copies of V and q copies of V* to the underlying field.

A tensor field is a pointwise assignment of tensors on the tangent spaces of a manifold.

Let [math]P[/math] be the plane that the line [math]L[/math] is to be perpendicular to. Let a point on the line be [math](x_L, y_L, z_L)[/math] and a point on the plane be [math](x_P, y_P, z_P)[/math]. What you are aiming for is defining such an [math]L[/math] so that the dot product between two vectors [math]\mathbf{x}_P \in P[/math] and [math]\mathbf{x}_L \in L[/math] such that [math]\mathbf{x}_P \cdotp \mathbf{x}_L = 0.[/math] Using this, are you able to solve your conundrum?

I was thinking about that exactly, but in a different more brainlet manner. Thank you!

I gotchu covered nigga, a tensor transforms basically like this

[math]\sum_{\alpha}\frac{\partial\phi}{\partial x^{\alpha}}\frac{\partial x^\alpha}{\partial\bar{x}^{\beta}}=\bar{\partial}_{\beta}\phi [/math]

basically just the chain rule

What is the difference between astrophysics and cosmology? also what do nuclear physicists do?

May be more of a Veeky Forums topic, but:

A posted here a couple days ago about killing time in a community college to soak up that dank free fafsa knowledge before jumping into debt and I came across an interesting thought.

I'm coincidentally about 2-3 potential terms away from completing a "certificate of Computer Information Systems" with an option of a focus on network administration..

What would you recommend I do? Stay and burn through fafsa for a little longer to potentially get a comfy job while at uni, or just transfer outta there and not worry about some phony certificate?

think of it as the most generic thing to respect the distributive law. so you have to mathematical objects (rings, vector spaces) A and B then A*B (A tensor B) has elements
a*b
which respect the distributive law
(a1+a2)*(b1+b2)=a1*b1 + a1*b2 + a2*b1 + a2*b2

ie it's the most generic way to define a product of elements from A and B. instead of calling it a distributive law you can also think of multiplication being a linear map in both arguments (multilinear)

>then A*B (A tensor B) has elements
>a*b
correction: thats a pure tensor, but the tensor product A*B has all FINITE SUMS of pure tensors.

If A and B are vectorspaces then dim(A*B)=dim(A)*dim(B)

(dimensions multiply)

If x is an arbitrary real number, prove that there is exactly one integer n which satisfies
x

well you're looking for n, so S should probably be a set of integers. and you know n>=x so it makes sense to let S be the set of all integers >=x. Every set of integers which is bounded from below has an infimum. now try to show that the infimum does what you want.

Calc III

Doable in three weeks? y/n?

Got it, you're the bomb. Working with integers rather than reals did the trick. I was making the wrong inequality.

Unironically yes if you remember your previous calc techniques . You can probably get up to line integrals.

tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx

Unless I'm misunderstanding, you'll end up in the same amount of debt either way. Better to do it more quickly so you can get on the job market more quickly and have more time to earn money. Even if there are classes you want to take, why not just do it at real college, where they'll probably be better?

How do I do this?