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

Is it possible to get post-baccalaureate research experience in mathematics?

I participated in research my freshman, and sophomore years. I was diagnosed with a brain tumor my junior year. Afterwards, I never got back into research because I was just trying to get my degree, and get back to a decent state of health again.

Now, I want to apply to graduate school, but
1. My grades post-tumor diagnosis are mediocre as fuck. 3.1 GPA I think. Probably 3.5-3.6 from before it.
2. I haven't been involved in research for 3 years, and I want to go into a field unrelated to that research.

This should probably go in /adv/, but they're basically no help.

I just e-mailed a prof. at a large university local to me, and the plan is basically to ask him to take me on as a research assistant either with, or without pay, gain some relevant experience, and then re-evaluate what my options are.

not my fault this autist doesn't know how to define a function

>>8556977
Kek'd. I gave you a perfectly suitable example back in my OP >>8554916

>>8557018
yes, i said it works right here >>8554950

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why is ncbi giving me thymine instead of uracil for mrna transcripts

>>8556977
>>8557018
>>8557041

sage

Can you guys recommend me a physics classical mechanics' book but with calculus applications?

I'm trying to learn calculus application into mechanics but it's really hard doing it without a book

If you could, any book that explains linear algebra application into mechanics would be also greatly appreciated

>>8557565
because it's cDNA sequences, equivalent.

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1. How many liters of gasoline or diesel do you get from refining/processing 1 barrel of crude oil?

2. What was the reason for the drop in oil prizes in 2008?

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?

>>8556742
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?

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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

>>8557862
Which parts specifically?

>>8557864
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.

>>8557901

Accelerate the power source rather, not the engine.

hey /sci/

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 /sci/, 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.

>>8557907
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.

>>8557878
Khan academy is where I learned and should still be good: https://www.khanacademy.org/math/trigonometry

>>8556735
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?

>>8558061
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 ?

>>8556735
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.

>>8558105
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.

>>8557839

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.

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>>8557828
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?

>>8558732
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.

>>8558259
I think that's something else called "mutually independent", not just "independent"

>>8559903
"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.

>>8559910
>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.

>>8558990
You can convert djvu to pdf easily online if thats your problem?

>>8559920
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.

>>8559930
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.

>>8559920
>>8560008
would an example of pairwise independent but not mutual be
[X,Y,X+Y] ?

>>8560043
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.

https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection#Using_homogeneous_coordinates

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

>>8560085
and is it exactly equivalent to this:

https://en.wikipedia.org/wiki/Line%E2%80%93line_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?

>>8560120
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?

>>8559979
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?

>>8560230
The study of finite sets.

>>8557901
> 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

>>8560437
Fourier theory

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>tfw proof makes sense

>>8560437
Yeah seems pretty standard to me. Curriculum at my school has Calc I-III, differential equations, discrete math, linear algebra, and statistics

>>8560437
>>8560451
exactly the same here
after differential equations im done Math courses

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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?

>>8557828
Polisci isn't a science, it's a liberal arts.
>>>/lit/

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?

>>8560120
take 1/x for example, it's continuous in (a,b) but it's not differentiable in x=0

>>8561347
>(a,b)
(0,1)

>>8556735
Is a distended spring slightly more massive than a spring at rest?

>>8561432
people seem unwilling to give a plain yes/no answer but it seems like a no

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

>>8557828
>>>/pol/

>>8561460
>people seem unwilling to give a plain yes/no answer
Which means my question is using "lies told to children" concepts.
Thanks.

>>8561469
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

>>8560230
linear algebra over [math]\mathbb{F}_1[/math]

Can you get an engineering job with no internship?

>>8561119
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: http://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.

>>8557878
Jesus Christ, son
r = 1
pythagorean theroem: side^2 + otherside^2 = r^2
fuck man

>>8557668
>1. How many liters of gasoline or diesel do you get from refining/processing 1 barrel of crude oil?
https://www.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."

>>8561815
>"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?

>>8561851
this is a very nice question

>>8561347
>>8561352
Closed interval, not open
1/x is not continuous for [0,1]

>>8561717
Thanks anon 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?

>>8562011
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

>>8562059
Does that mean that there is a place on earth where no light can go to or go through?

>>8562050
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?

>>8560120
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?

>>8562098
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.

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Please help a brainlet like me.

>>8562291
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.

>>8562444
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?

>>8562455
I was thinking about that exactly, but in a different more brainlet manner. Thank you!

>>8562291

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

>>8556735
What is the difference between astrophysics and cosmology? also what do nuclear physicists do?

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May be more of a /biz/ 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?

>>8562291
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)

>>8562540
>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 <= n < x+1.

I was thinking of creating a set S where x=inf(S) but then I just lose it from then on. to prove there is one integer I would go about by contradiction assuming there exists m such that m != n and then showing the contradiction m=n. I have a map of where to go but not how to get there.

>>8562885
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.

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Calc III

Doable in three weeks? y/n?

>>8562898
Got it, you're the bomb. Working with integers rather than reals did the trick. I was making the wrong inequality.

>>8562915
Unironically yes if you remember your previous calc techniques . You can probably get up to line integrals.

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

>>8562538
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?

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How do I do this?

>>8563055
Read your textbook, it's in there.

Mathematicians, really important question. I want to apply a really unorthodox method to a weird problem but I don't know shit about number theory yet and I need to know:

Say that I have a space of 10 things and those 10 things are made of 3 asterisks and 7 O's, how many possible ways are there to reorder these asterisks and O's and what is an algorithm I can use to generate all these permutations.

Example:
***OOOOOOO

But then I could permute to:

**O*OOOOOO

etc.

I know there is a solution for this because I once read about it and it had to do with factorials but I don't remember. And if you remember then please give me the generalized version for an space of N spots, and X asterisks and Y O's. And most importantly, a proven algorithm that will generate all the permutations.

If someone knows what I'm talking about then thank you so fucking much.

i'm trying to figure out the how bright the daytime sky (modeled as light coming from all directions in a hemisphere) is relative to the brightness of the direct sunlight

the guy in the comments here says +4.8 mag for the daytime sky
http://voices.nationalgeographic.com/2011/07/10/how-bright-is-the-daytime-sky/

this page says the sun has -26.8 mag, and it also give the formula for the ratio of flux as 100^((m-n)/5)
https://web.njit.edu/~gary/321/Lecture1.html

the sun takes up 1.08*10^-5 of the area of the sky
http://www.mersenneforum.org/showthread.php?t=11612

putting all of this together as 1.08*10^-5*100^((4.8+26.8)/5) = ~4.7 million

that the sun would look 4.7 million times brighter than the sky seems unreasonable to me. wouldn't this mean that a shadow would look pitch black if it weren't for indirect light (besides the indirect light coming from the sky)? or are the calculations incorrect?

>>8563079
https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)

>>8563079
https://en.wikipedia.org/wiki/Combination
For that particular problem, it'd be 10 choose 3 which is 10!/((10-3)!3!) = 120.

>>8563085
47 million, not 4.7 million

2.5 million with a sky of 1.6 mag

>>8563091
>>8563093

Thank you both, great help. What about algorithms to generate these permutations?

What I want to prove is that given a space of N things, no matter how you permute the things, the space still has a certain property. So an algorithm strongly based on logic that will allow such a proof would be helpful.

Will a book about combinatorics have something like this? If so then what would you recommend? I'm not afraid of digging deeper into a book but I really need to the book to not only include theorems but also algorithms.

>>8563055
s^3-15s^2+54s = 0
s(s-6)(s-9)=0

y=A+Be^6x+Ce^9x
A+B+C=2
6B+9C=6
36B+81C=3

A = 7/18, B = 17/6, C = -11/9

>>8563099
Combinatorics is good to know for algorithms and cs in general. If you haven't done any discrete math, start with a basic intro undergraduate text (I've heard concrete mathematics is good).

If you want to describe the problem and what you've done more specifically, I can let you know if your idea is valid.

>>8563099
>proof by brute force

Nigger, step away from the computer.

>>8563103
I've done discrete math, I study mathematics actually. I just haven't touched this topic before.

Sorry for being selfish but I don't want to potentially spill the beans on what could be a proof for something very important. If you need to know then it is about:

>>8563105
It is a proof by brute force because it has to do with prime gaps. Prime gaps are essentially random but given that today we have nice formulas to approximate the prime counting function maybe I could prove a theorem of prime numbers by showing that no matter how you permute those prime numbers, they still have a certain property.

It is obviously dumb but more direct tools are futile because the moment you want to talk about the nth prime you have no idea how far the previous prime and the next prime are. It is impossible.

>>8563118
It sounds like combinatorics, but it's hard to tell without more info. All I can say for certain is that what you described makes it easy to calculate how many possible permutations there are, but not really any properties of those permutations. If you're trying to easily check every case with brute force it might be doable depending on how big the specific numbers are.

>>8563126
>but not really any properties of those permutations.

Yeah, that is why I'm looking for algorithms based on pure mathematical logic, not just some python implementation which is what I've been able to find.

Also, I'm not trying to find everything through brute force. I want logic. Let me give you an example.

Suppose you have N bars and N-1 stars.

Logically, you can deduce that no matter which permutation you land on, there will always be two consecutive bars.

Why? Because there are too many! So you would need magic to arrange the bars in such a way that there are none immediately next to each other.

That is essentially what I am trying to do. Hope that there are "too many" prime numbers before any arbitraty Nth prime number such that no matter how you permute them, a certain property holds. A property which is very similar to "two primes next to each other" but a little bit more complex. Fortunately, through some computations I've done it does look like there are indeed too many primes, even when I go into the millions.

I guess I will have to design this "logical" algorithm myself.

>>8563133
>Suppose you have N bars and N-1 stars.
>Logically, you can deduce that no matter which permutation you land on, there will always be two consecutive bars.

Oh, obviously assume that N is really big. Obviously for small N then there are counter examples but if your N=99999999999 then there is no way.

>>8563133
>Suppose you have N bars and N-1 stars.
>>8563134

Fuck, second ammendment.

Assume N bars and 1 star.

And N is really big.

Fuck.

>>8563079
I think this might work.
Consider the set S of numbers 1 to 10 (each number stands for a position).
The 7 O's need to go to 7 positions, and once you've done that, the *s positions are determined automatically.
So you just need to generate all combinations of 7 numbers from S.
To do that you could look into:
http://stackoverflow.com/questions/127704/algorithm-to-return-all-combinations-of-k-elements-from-n

>>8563141
Oh, that's pretty clever. Nice one.

>>8563085
this makes more sense

https://en.wikipedia.org/wiki/Lux
>10,000–25,000 Full daylight (not direct sun)[3]
>32,000–100,000 Direct sunlight

still curious how the calculations could get so wrong

Why multiplying polynomial by integer doesn't change roots? It doesn't make sense.

>>8563243
Let f be a polynomial, and c an arbitary non-zero integer. If c*f(x)=0, then f(x)=0. If f(x)=0, then c*f(x)=0.

Was arguing with a moon hoaxer nut.

He thinks the little white specks you see in videos of space walks are air bubbles, and they're filming it all in a special pool on ground.

My question is, what exactly are the specks? I'd guess they could be bits of frozen ice from the air lock. Chips of paint. Or little bits of rocket exhaust from the little maneuvering thrusters.

>>8563243
x=1
2x=2
x=1

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What is a phasor?

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Can't do part A.

Don't really know what to do, rationalising the denominator (ignore that Z is complex) takes me nowhere.

Help?

>>8563564
try turning the page around so you can read it properly

>>8563564
cmon brainlet, you just move the denominator to the other side and then move all the z's to one side and everything else to the other side

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>>8563568
4 u

>>8563543
In Electrical Engineering, it's just a complex vector that describes how much power is being sucked up by magnetic fields.

Can somebody hold my hand through this?
>Derive the metric of a rotating reference frame with angular velocity w.
I tried applying cylindrical coordinates [math] x = r \space cos( \theta + \omega t) , y = r \space sin( \theta + \omega t), z = z, t = t [/math]. Then, deriving the new metric tensor by the formula [math] g_{ij}(x) {\partial x^i \over \partial y^k} {\partial x^j \over \partial y^l} dy^j dy^l [/math] by calculating the jacobians with Maxima, multiplying by its transpose and by the flat space metric (-1,1,1,1) then the differential vectors to get to the desired ds^2. The result was quite a complicated one.

By comparison, this link http://physics.stackexchange.com/questions/53769/metric-coefficients-in-rotating-coordinates gives a much simpler one ( [math] ds^2 = ({r'}^2 \omega^2 - 1) \, {dt'}^2 + {dr'}^2 + {r'}^2 \, {d\phi}' + {dz'}^2 [/math] ) and it is probably the one I am looking for, but I have no idea how to get there. They derive some partial derivatives operators that I've no idea how, and I don't know where they should act. What are those operators and where should I apply them?

Is observation enough to conclude that F in F=ma necessarily have the direction of a? Is there some theory that explains why a mass m moves in the direction of a with a force F when a with said direction is acting on it? This is very elementary but it is interesting.

>>8563543
a vector in the complex space.

A+Bi

>>8563767
I'm sorry, I am having trouble understanding what you meant. I'll write what I understood of each question and you say if I got you wrong.
>Is observation enough to conclude that F in F=ma necessarily have the direction of a?
>Is it obvious that F and a always have the same direction in the equation F=ma?
Yes, since 'm' is a positive scalar, and 'a' is a vector, F must have the same direction as a.
>Is there some theory that explains why a mass m moves in the direction of a with a force F when a with said direction is acting on it?
m doesn't always move in the direction of F. An example is a rotating movement in which F is parallel to the movement of m (m's velocity). This field of study is called mechanics.

>>8563767
a is a scalar, not a vector.

the acceleration could be in any direction or constantly changing in the case of angular velocity.

>>8563795
That is basically what I was asking yes. It's difficult to frame the question fully because I'm not sure whether the question is actually viable or complete nonsense. Sorry about that.

For a moment forget about m. And consider only the direction of F and "a". Is the only thing that says F and "a" are in the same direction Vector Theory or is there some fundemental interaction on a subatomic level that makes it so that F and a is always in the same direction?

Like why doesnt F have a direction that isnt the direction of "a". I know it doesnt, but why doesnt it?

This assumes classical Newtonian physics and that the question isnt complete garbo which is completely likely, like how many ice cubes do you need to experience love, for example. That question has al the words in all the right places but doesnt have an answer that makes sense.

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>>8563570
I hope you got the answer in the time it took for you to get one soon me.

>>8563807
Acceleration is a vector.

>>8563820
not in my opinion. it's pointless semantics anyway.
the point being in the real world acceleration doesn't explicitly have a direction. only in static analysis.

Why isn't 1/x uniformly continuous? If 0 not included, and if you have delta defined for the biggest epsilon (say around ]0, 0,1[) that will work for any (x,y) given on the right of that point

>>8562011
there may be some places with 0 NET magnetic field

>>8563847
Wow you're retarded.

How do chemical bonds in solutions/alloys work?

>>8563899
Where are those? Do they occur in the lab or naturally?

>>8563888
>>8564000
CHECKING IN EPIC BREAD

>>8563765
It's me again. I am loosing all hope here. I calculated ds^2 again this time by squaring every term instead of trying to calculate the metric tensor. The answer the computer spat out was
[math]\left(\omega^2 \,r^2-1\right) \,dt^2+dr^2 +\omega\,r^2\,dt\,d\theta+r^2\,d\theta^2 +dz^2[/math]
Which is a little more similar but I can't be sure it's correct.

>>8563888
I'll give you a hint: the value of [math]\delta[/math] needs to only depend on the value of [math]\epsilon[/math], not on the value of [math]x[/math] or [math]y.[/math]

>>8563888
I dont understand your notation. 1/x is uniformly continuous on [x,infinity] if x>0 this is not hard to check. On (0,infinity] however for any delta with x - y < delta you can find small x and y such that 1/x - 1/y > epsilon for any epsilon. Intuitively you can choose numbers like 10^-14 and 10^-28, these numbers are no more that 10^-14 apart from each other but the difference of their reciperocals is tremendous.

>>8563765
dude, just take derivatives of the vector (x,y,z,t) with respect to the coordinates r,theta,z,t. Then compute the norm squared of each of the derivative vectors (i.e dot with itself USING THE CORRECT SIGNATURE FOR TIME). If you need something to look up, this is called the 'pullback metric' under the map that you have.

>>8564000
It would be very rare to occur naturally, but not impossible. Maybe areas with magnetic mineral deposits?

As for artificial environments:
-There is no field inside a faraday cage
-You could induce a magnetic field equal in magnitude and opp in direction to the pre-existing filed

>>8563847
The only way you could justify your claim that acceleration doesn't have a direction is if you consider direction to only have meaning in an absolute reference frame and posit that there is no absolute reference frame. Let me put it another way, position, regardless of what reference rame it is specified with respect to, is a vector in 3 space of the form
[math]
<a_1, a_2, a_3>
[/math]
where each of those elements are the scalar projections of the position vector into 3 basis vectors. When applying the differentiation operator, which is, in this case, an operation which acts on first-order smooth vectors in R3 and maps to 0th order smooth vectors in R3. It's clear from this fact that when applying the differentiation operator twice, it maps from second-order smooth vectors to 0th order smooth, and these vectors DO have a well defined direction, regardless of what your opinion is.

>>8563807
>the acceleration could be in any direction
so it's a vector, not a scalar

>>8564140
Okay, I did that and every component came out alright except time.
[math]x_i =\left[ t , r\,\cos \left(\theta+\omega\,t\right) , r\,\sin
\left(\theta+\omega\,t\right) , z \right] [/math], then [math]\frac{dx_i}{dt} = \left[ 1 , -\omega\,r\,\sin \left(\theta+\omega\,t\right) ,
\omega\,r\,\cos \left(\theta+\omega\,t\right) , 0 \right] [/math] which when dotted with itself produces [math]\omega^2\,r^2+1[/math]. But it's supposed to be [math]\omega^2\,r^2-1[/math]. No amount of sign changing in the derivative vector is going to fix it since it's going to be squared, changing nothing. I can't also just change the sign of the result as it would become [math]-\omega^2\,r^2-1[/math].

What am I missing?

>>8564121
>>8564129
Maybe I didn't express myself well
The formal definition is:

for any eps>0 there exists delta>0 so that for |x - y|<=delta we have |f(x) - f(y)|<=eps

So what really confuses me here is what role plays the definition of our domain: if we have f(x)=1/x for interval, say, [1/100, +inf[ or [1/100, 1] I think it's safe to say it is uniformly continuous, because you can find delta for any epsilon, but for a ]0, 1] that's not true, why (theoretically speaking)?

>>8564290
I mean of course I understand the implication that for whatever delta we can find x,y such that |f(x)-f(y)|>epsilon, I guess I just want confirmation that's all about that, the function tending to +inf for limx->0

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Statistics - What's the common name for this theorem (pic related)? All that I'm finding online is 'univariate density transformation theorem' although most of those articles are written by foreigners, and my memory is telling me that there's a much simpler name for it in English.

>>8564290
Recall the definition for a function to be uniformly continuous. The definition says that [math]\forall \epsilon > 0 : \exists \delta > 0 : \forall (x,y) \in D_f,[/math] we have that [math]|x - y| < \delta \Rightarrow |f(x) - f(y)| < \epsilon.[/math] In our case, let's take [math]D_f = (0,1).[/math]. Suppose [math]f(x) = \frac{1}{x}[/math] were uniformly continuous. Then it would follow the above definition [math]\forall \epsilon > 0.[/math] We pick [math]\epsilon = 1.[/math] Then [math]\exists \delta > 0[/math] such that [math]\forall x,y\in (0,1)[/math] with [math]|x-y|<\delta, \; \left|\frac{1}{x}-\frac{1}{y}\right| < 1.[/math] We now pick [math]x \in (0,1)[/math] with [math]x < \delta,[/math] and we let [math]y = \frac{x}{2}.[/math] First and foremost, [math]x \in (0,1)[/math] gives that [math]y = \frac{x}{2} \in (0,1).[/math] Then [math]|x-y| = \left|x - \frac{x}{2}\right| = \frac{x}{2} < \frac{\delta}{2} < \delta,[/math] and [math]\left|\frac{1}{x}-\frac{1}{y}\right|_{y=\frac{1}{x}} = \left|-\frac{1}{x}\right| = \frac{1}{x}[/math]. Because [math]x < 1,[/math] we have [math]\frac{1}{x} > 1,[/math] and so we have arrived at a contradiction. Hence, the function is NOT uniformly continuous on the interval [math](0,1).[/math]

>>8564310
Ignore that [math]|_{y=\frac{1}{x}}[/math] part, that's supposed to say [math]|_{y=\frac{x}{2}}[/math], I have no idea how that happened. I guess if you write a large post, the probability that a mistake will occur rises by the law of large numbers or something, idk.

>>8556735
Anyone know of online resources where I can search for the half life of a drug/compound? I'm gonna be using nootropic drugs pretty soon and I'm not trying to rek myself. Thanks /sci/.

>>8564316
Go to the reference section of your campus library, there should be thicc volumes full of data like that

>>8564321
Gnarly. Just wanted some direction, thanks homie

>>8564310
But you proved that there exists an y for which |1/x - 1/y| > 1 for D=(0,1), you can use x=8/10 and y=6/10 and you'll have a value below epsilon=1

To prove the function isn't uniformly continuous you'd have to prove that

there exists epsilon such that for any delta there exists x,y of (0,1) so that |x-y|<delta implies |f(x)-f(y)|<epsilon

>>8564342
Ok, now that I reread it it actually does prove the last point, sorry
but that holds true only for (0 , right?

>>8564199
I am now convinced that the result I got here >>8564107 is actually the correct one and this link http://physics.stackexchange.com/questions/53769/metric-coefficients-in-rotating-coordinates was actually wrong.

>>8556735
When solving for radical equations, I am supposed to balance the index of the radicals on both sides of the equation.

However, how do I go about doing that / what do I have to change to the radical to do so?

>>8564359
I thought about it for a while, and the point where the proof falls apart for the case of the interval [math](\xi,1),[/math] where [math]\xi \in (0,1),[/math] is when we assume that [math]y = \frac{x}{2} \in (\xi,1).[/math] Let's show that [math]\forall \xi \in (0,1) : \exists x \in (\xi, 1) : \frac{x}{2} \notin (\xi, 1).[/math] Thinking about this geometrically on the number line, we are to show that measuring the distance between [math]\frac{x}{2}[/math] and [math]x[/math] doesn't change if we take a detour and first measure the distance between [math]\frac{x}{2}[/math] and [math]\xi[/math] and then measure the distance between [math]\xi[/math] and [math]x[/math] and then add the results together, i.e. [math]\left|\frac{x}{2}-\xi\right| + |\xi - x| = \left|\frac{x}{2}-x\right| = \frac{x}{2}.[/math] Manipulating the above, we get two cases.

CASE 1. [math]\xi \in \left(0,\frac{1}{2}\right).[/math] In this case, simply take [math]x \in (\xi,2\xi].[/math]

CASE 2. [math]\xi \in \left[\frac{1}{2}, 1\right)[/math]. In this case, simply take [math]x \in (\xi,1).[/math]

We have now shown that the proof falls apart at that stage.

Side note: this is the most /diy/ proof I've ever constructed in my life, please excuse its terribleness. I guess I'm proud of making the connection to the number line and thinking about it geometrically, which is the main idea behind the rebuttal, but other than that my algebra was seriously lacking and I had to verify it countless times with Wolfram|Alpha. I think I'm definitely on the money, though.

Is Spivak the right book to continue with my calculus studies? I've finished Stewart. If don't, which book should I get?

I posted a thread about this but relaized it was in the wrong place. I need some answers from anyone who has taken chemistry/biochemistry undergraduate. I have just finished my first semester of my sophomore year of undergraduate. My freshmen year was a mess, I came into college believing I wanted to do psychology, instead I discovered drugs and got involved in a very poor/abusive relationship, my first year I got basically straight C's. Last summer I pulled my shit together and decided that chemistry was my passion, and this semester I was able to pull B's and actually learned the material (never went to class, didn't know about the attendance grade and would have pulled -A's if I did). Unfortunately though, my gpa still sits at 2.3. I realize grades are important to my career but how fucked am I?

The probability of a chi2 test with a chi-sum 3.24 and degrees of freedom 1:

- Wolfram says 0.0438612
- Excel says 0.071861

Why?

>>8564880
Spivak is a good choice for you, as long as you're interested in pure math or preparing to learn analysis.

Besides bookzz and gen lib, where can I search for textbook pdf files?

>Got C's in calc II & III and differential eqs
>Get A's and B's in all my upper course aerospace engineering classes

who /actualpleb/ here ?

Okay. Basics shit. Trigonometry.

I know about...
>unit circle
>interpretation of polar-coordinates in unit-circle
>sin, cos tan, ...
>but I don't get how sin, cos and tan are the respective aspect ratio but at the same time an angle

For example: cos alpha = adja /hypo = 10/2 = 5
Okay. The ratio is 5 of both sides.

But the alpha is an angle, so...calculating the angle of cos 5 would be a angle X.

So what I get. 5 is the ratio of two sides. Alright. It's a number.
But how exactly is the angle we get related with the ratio number?

How does it translate? I don't see the connection between the ratio and the angle

>>8565244
it's the angle between those sides

>ctrl + f
>(you)
>0 results

Could math have all different rules in a different possible world? What level of necessiry does math have?

If i happened to have alot of question about quantum computing, especially about book recommendation and research in the field, shall i post a thread on /sci/ or /g/ ?

>>8565495
both boards are absolute garbage, /g/ is a bunch of underage consumerist kids and linux neckbeards, try /sci/ or both boards i guess but no one will have real expert knowledge of quantum computing, watch out for misinformation

>>8565497
Thx, guess it's worth a try :P

>>8565497
>muh consumerism

commies need to leave

>>8565495
There is(was?) a course on quantum computing on EdX. You may want to check it out.

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This is the kid attempting to learn baba math again.

I'm still attempting to learn radicals, and I've been cruising through the problems in my algebra book, but I've been stuck on this one problem for 1 1/2 hours. Could someone tell me the steps I need to perform?

sqrt(1+x^2) + 1 / sqrt(1+x^2)

I know, it's probably retardedly simple, but I cannot get the solution.

I first thought that I'd just multiply the denominator and numerator on the left side by the denominator on the right side, add it all together, and simplify, but I don't get the solution this way.

I've tried simplifying all of the sqrts to 1+x first, but that hasn't worked either.

>>8565596
>I'm still attempting to learn radicals
If you've already done problems with exponents, just think of radicals as fractional exponents. i.e.:
[eqn]\sqrt{1 + x^2} = (1 + x^2)^{\frac{1}{2}}[/eqn]

>I've tried simplifying all of the sqrts to 1+x first, but that hasn't worked either
That's because [math]\sqrt{1 + x^2} \ne 1 + x[/math], for the same reason that [math](1 + x^2)^2 \ne 1 + x^4[/math]. In general, exponents don't "distribute" like that.

In any case, I don't know what your goal is with this problem. What are you trying to do? What's the problem statement? Are you trying to simplify the expression?

>>8565627
Yes, it asks me to simplify the expression. I'm just attempting to work through this textbook because I'm terrible at math.

Hey /sci/, I'm trying to wrap my head around binomial probabilities.
I was wondering if it is possible to calculate the number of trails (n) when the probability of success (P), the number of successes (x) and the binomial probability (b) are known.
I've never really done anything with factorials.

So for example:
>Suppose a die is tossed 5 times. What is the probability of getting exactly 2 fours?
>P = 0.167 (1/6)
>n = 5
>x = 2
>b = ?
(n! / (x! * (n-x)!)) * P^x * (1-P)^(n-x) = b
(5! / (2! * (5-2)!)) * 0.167^2 * 0.833^(5-2) = 0.1612

>P = 0.167 (1/6)
>x = 2
>b = 0.1612
>n = ?
(n! / (2! * (n-2)!)) * 0.167^2 * 0.833^(n-2) = 0.1612

hellow /sci/ how do i replicate this? does the track have to be smooth and start or is at an angle?

https://webmshare.com/69VNj

>>8565596
sqrt(1+x^2) + 1 / sqrt(1+x^2)
sqrt(1+x^2)^2 / sqrt(1+x^2) + 1 / sqrt(1+x^2)
(sqrt(1+x^2)^2 + 1) / sqrt(1+x^2)
(1+x^2 + 1) / sqrt(1+x^2)
(x^2 + 2) / sqrt(x^2 + 1)

>>8565723
I haven't been in a probability course for 2 years so take this with a grain of salt but it's probably not possible to do what you're trying to do.

The problem is that you end up with some factors of n multiplied by 0.833^n and in almost all situations it's impossible to separate the n without tangling those equations more.

All you can do is get a numerical answer (or find it via trial and error since you know it's an integer greater than 1)

>>8565747
thank you

>>8565723
http://www.wolframalpha.com/input/?i=FindRoot%5B(n!%2F(2!*(n+-+2)!))*0.167%5E2*0.833%5E(n+-+2)+%3D%3D+0.1612,+%7Bn,+2%7D%5D

How does a alpha shape differ from a convex hull?

Is there a way to find out the number of full unit squares that fit inside a sphere of radius r without having to count them one by one?

>>8565868
probably not, these kinds of ad-hoc problems can be extremely hard

>>8565868
If you really meant unit SQUARES inside a SPHERE of radius [math]r,[/math] then the answer is [math]\infty[/math] if [math]r > \sqrt2[/math] and none if [math]0 \le r \le \sqrt2.[/math] If however you mean unit squares inside a CIRCLE of radius [math]r,[/math] I have no idea.

>>8565883
>If you really meant unit SQUARES inside a SPHERE of radius r
are you autistic that's literally what he wrote

>>8565912
The posed problem seemed so trivial, though. It's more interesting if we're considering a circle of radius [math]r,[/math] since then we can't just stack infinitely thin squares in [math]\mathbf{R^3}[/math] and be done with it.

>>8564518
Not one of the guys you were talking to but if you like thinking geometrically think about it like this:

It goes to infinity as x goes to zero so it's derivative increases quickly. This means that the closer x and y are to zero for a fixed [math] \delta [/math] the larger will the difference of their functions be (because the slope becomes larger and larger). No matter what [math] \delta [/math] you choose you can get close enough to zero so that the vertical difference f(x)-f(y) is larger than [math] \epsilon [/math]

What are some good books that can introduce me to some molecular biology lab techniques like immunocytochemistry or FISH?

>>8556735
Good book to learn maxwell's equations and general electromagnetism?

>>8566000
feynman lectures vol. 2

griffiths is ok if you want a more "formal" treatment

>>8561493
i don't get your joke

>>8566010
its not a joke

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>>8566046
>>8566010
i.e. see http://win.ua.ac.be/~lebruyn/LeBruyn2016e.pdf (page 230/page 11 of 52 in the pdf)

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let V be a finite dimensional vector space, than there is a natural isomorphism between V and T_xV, v being mapped to the directional derivative. how do I prove this? it's easy when V is a euclidean space, but the proof involves integration, does it work with a general vector space?

>>8565868
Assuming that you meant cubes rather than squares ...

I'm fairly sure that there isn't a closed-form solution. However, first you can take advantage of rotational symmetries. Each octant is identical, and also has 120-degree symmetry (i.e. permuting X, Y and Z). So you only need to count 1/24th of the squares

Also, there's a closed-form expression for the number of cubes that will fill a right tetrahedron (sum of squares), so you can subtract that out.

Even the most naive approach wouldn't count them individually, but would count 1x1xN blocks; i.e. for all x,y s.t. x,y>=1, x^2+y^2<=r^2, you'd calculate N=floor(sqrt(r^2-x^2-y^2)).

BTW, there's two possible cases: odd diameter (the centre of the sphere is at the centre of a cube) and even diameter (the centre of the sphere is at the corner of a cube). In the odd case, you have to treat the X=0/Y=0/Z=0 planes separately.

>>8565733
[math]\sqrt{1+x^2} \hspace{2mm}+\hspace{2mm}(\frac {1}{\sqrt{1+x^2}}) = \frac{\sqrt{1+x^2}\hspace{2mm}(x^2+2)}{x^2+1}[/math]

That's not right though. This is the solution. I still don't know how to get it.

>>8566218
do what the guy you replied to did

then multiply by sqrt(1+x^2)/sqrt(1+x^2) to get what you have as the solution

>>8566225
oh wow. Now I feel like a complete and total fool. Thanks. I'm guessing it's a math faux pas to leave a radical in the denominator.

>>8566234
>I'm guessing it's a math faux pas to leave a radical in the denominator.
not really

'simplify' doesnt really mean anything specific, you just take it as far as you think seems ok

IMO the one in your solution looks aesthetically worse but if the idea is to always rationalize denominators then go for it

>>8566234
"Simplifying" is just maths speak for "let's make this thing look like something where we can gain more information by looking at the expression at a glance". In this case, I know that if I plug in [math]x=3[/math] I'll get [math]\frac{11\sqrt{10}}{10} \approx \frac{33}{10} = 3.3[/math] without much calculation. However, I wouldn't immediately know that [math]\sqrt{10}+\frac{1}{\sqrt{10}} \approx 3.3,[/math] for instance.

>>8566247
Ah, now that makes much more sense. Thanks for the explanation.

>>8566284
Another thing that should be noted is I use the very, VERY crass approximation of [math]\sqrt{10} \approx 3[/math] there as an example.

How do I find the area of the intersection of the plane z = 1 + 2x and z = x^2 + y^2. I get it to be 2 with substitution but it should seemingly be 2sqrt(5)

>>8565087
Talk to an academic adviser anon, and some professors who are nice guys

Ask for open-ended advice on your situation and tell them your dreams

>>8558732
Talk to professors, don't talk to /sci/

>>8556735
hey sci, is there any scientist, that started it off late? like in their 30s, 40s and accomplished something significant

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Realistically speaking is one month enough time to seriously understand and finish Trigonometry? I signed up for an accelerated online class at my school but I'm having second thoughts. I know a lot of /sci/ like to pretend that they're 100% driven hard workers but anyone with experience in a course like this have any input?

Does anyone know of a good resource I can use to find the average diameter and length of every vein and artery in the human body?

>>8566749
The internet.
http://lmgtfy.com/?q=average+diameter+of+veins+in+human+body
http://lmgtfy.com/?q=length+of+every+vein+in+human+body

A biology textbook.

>>8566805
Google hasn't returned any results I can use.
Are you certain a biology textbook would be specific enough to list the sizes of the veins as opposed to just their names and locations?

>>8566749
the most notable veins and arteries should have this info readily available

for example:
>In the human heart, the pulmonary trunk (pulmonary artery or main pulmonary artery) begins at the base of the right ventricle. It is short and wide—approximately 5 centimetres (2.0 in) in length and 3 centimetres (1.2 in) in diameter. It then branches into two pulmonary arteries (left and right), which deliver deoxygenated blood to the corresponding lung.
https://en.wikipedia.org/wiki/Pulmonary_artery

>>8557656

Pretty much any college level physics textbook is going to include calculus of some type.

Kline's "Calculus: an Intuitive and Physical Approach" has a lot of chapters with physics applications.

For mechanics, Kleppner and Kolenkow is also a good intro physics book (which naturally has calc in it). A really technical book is Corben and Stehle's Classical Mechanics.

Kline and C&S are both Dover Books.

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whats the best circuits 1 class/textbook/online course any of y'all have for me? im trying to get a head start on my class

I am currently doing undergrad in EE with a minor in physics and plan to work after college, but also feel an urge to learn more. I was just wondering if it would be feasible to go back to school after 10-30 years in the work force and get a PhD in physics or EE and pursue academia

>>8566336
You're finding the area of the projection in the Z direction.

Note that sqrt(5) = sqrt(1^2+2^2), i.e. if you project a 1x1 square in the plane z=0 onto the plane z=1+2x, you'll get a 1xsqrt(5) rectangle.

IOW, you're not multiplying by ∂A/∂x.

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>>8556735
I've got a real life physics problem. I have an air conditioner with excess fluid flowing out into a barrel outside. The thing is, the temperature at night falls below zero so the whole thing froze. The shape of the barrel is such that I can't just slide ice out. I have two options on how to unfreeze it, but I want to know which one is the quickest.

One, I bring the barrel inside and let it melt at maybe 21°C ish, or take it outside at day and point the opening at the sun hoping that would be any faster.

The empirical mind in me would test both options, but as I only have one barrel and I need it as soon as possible, I don't really have the luxury of entertaining the child in me.

>>8567134
Forgot to add that the temperature outside is 6°C and the total width of the barrel opening is around 30cm.

>>8567134
>>8567137
I'm not any kind of authority, but my gut says that the heat imparted to the ice by the sunlight would be less than the 15 degree temperature difference between the outside and inside of your house.

You could also boil water and pour it into the barrel to try and speed up the melting.

is OHP still alive? he hasnt posted on mathoverflow in a while

>>8565883
>>8565912
>>8565915
Oh, silly me, I meant to ask about the number of full unit squares that fit inside a circle of radius r. So I guess it's a simpler problem?

>>8567165
Actually it was 6°C when I first took it out at 10am, now it's around 12°C.

This makes me even more curious now though. Dad said it would be better if it were inside. But a friend who's studying physics said that outside might be faster due to IR light, but he also doesn't have a clue whether or not it's significant enough.

>>8557656
John Taylor's "Classical Mechanics" will forever be the best book on that subject. It is easy to read but details every bit of the subject supplemented with examples that work out to beautiful results. Very highly recommend.

is the rational unit circle dense in the real unit circle?

i dont know if this is really easy or really hard, but it has something to do with pythagorean triples

>>8561119
same but this book's shit

>>8566415
yes, the future u

hey, this might be ridiculously stupid but is there anyway to answer this? I'm trying to convert sensitivities between two games with only this information:

if 2.9 = 0.18406

and

2 = 0.127671

and

2.45 = 0.1558655

then what does 1.88 = ?

>>8567263
yes.

https://en.wikipedia.org/wiki/Pythagorean_triple#Rational_points_on_a_unit_circle

basically if you draw a non-horizontal line with rational slope through (0,1), then the other point at which the line intersects the circle is a rational point.

i understand that you can find the integral by the antiderivative of the right-the antiderivative of the left but Y?

>>8567339
plug that shit into a graphing calculator
there's only so many equations types

>>8567340
THANK YOU

I attempt this..

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What happened here? (alpha is >0)

>>8567352
l'hopital's rule

>>8566707
More than enough.

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Can anyone explain to me what the last 2 mean? Is R standard notation for something in particular?

I understand that the first one means AccBalances is an improper subset of the cartesian product of Accounts x R (whatever R means)

Whats really confusing me is the multi directional arrow in the last example. Does that not represent "if and only if". If so, why would you put that between 2 sets, what does that mean?

>>8567357
thought so, had messed up a derivative so excluded that, then wondered if I missed some basic log properties
ty

How would a police officer arrest someone on a billboard catwalk?
No shooting

They cant really go up there, and if they did they couldnt carry you down really.

Can they tase you? Causing you to likely fall and possibly die?

Lets say the perpetrator is mildly belligerent but not more violent than pushing.

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How can I input this in wolfram?

>>8567451
*wolfram alpha

>>8567458
>>8567451
http://www.wolframalpha.com/input/?i=a_%7Bn%2B1%7D%3D1%2F4(a_%7Bn%7D%2Ba_%7Bn%7D%5E2)

>>8567405
the second one looks like it might be 'accbalances is an element of the power set of account x R' (which is equivalent to first one)

no idea what the last arrow means, if and only if doesnt seem to make sense there

>>8567467
Thank you.

>>8567471
Yeah I figured out the second one but I still dont understand what the multidirectional arrow is supposed to mean in this context. It's also annoying because that is the notation used throughout my lecture notes.

Okay, I have this problem here. I'm supposed to calculate the monodromy matrix and Floquet exponents for the two-dimensional system

[math]\frac{dx}{dt} = a(t)Ax(t),[/math]

where [math]a(t)[/math] is a periodic function with period [math]T[/math] and [math]A \in \mathbf{R}^{2 \times 2}[/math] a constant matrix. I'm also supposed to find conditions on the system that imply that all solutions tend to [math]0[/math] or stay bounded as [math]t \rightarrow +\infty.[/math]

The hint I'm given is that I'm supposed to make a change of variable [math]t \mapsto \tau = \int_{t_0}^{t} a(s)ds,[/math] but I have no idea how to fully implement that in my equation. I know that [math]\frac{dx}{dt} = \frac{dx}{d\tau} \frac{d\tau}{dt} = \frac{dx}{d\tau} a(t) = a(t)Ax(t),[/math] but my issue here is I don't know if I should change the variable [math]t[/math] in the RHS to reflect on what's happened in LHS, and also I don't know what the inverse would be. What I can't grasp here is how I'm supposed to go from [math]x(t)[/math] to [math]x(\tau).[/math] Do I just input [math]x(\tau) = x(\tau(t)) = x(a_p(t)-a_p(t_0)),[/math] where [math]\int a(t)dt = a_p(t) + C?[/math] I'm lost.

>>8567508
is it used anywhere else?

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>>8556735
Any help would be welcome
(the problems was translated to english, excuse my mistakes /sci/ )

>>8567639
Define implicitly ( assuming a>0)
[math]y(\tau(t)) = x(t)[/math]
so
[math]y'(\tau(t)) = A\ y(\tau(t))[/math]
which means
[math]y'= A\ y[/math]

>>8567925
Wait, why do we need to assume [math]a(t)>0 \; \forall t \in \mathbb{R}?[/math] (I use [math]\mathbb{R}[/math] here because it's a periodic function, so if it's defined for [math][0,T)[/math] then it surely won't be hard to define it [math]\forall t \in \mathbb{R} = \bigcup_{n \in \mathbb{Z}}[nT, (n+1)T).[/math]) In either case, let's see if I understand this train of thought. The expression to the right says [math]\frac{dy}{dt}(\tau(t)) = Ay(\tau(t)).[/math] As a result, the solution here is [math]e^{\tau A}y(\tau(t_0)) = e^{\tau A}y(a_p(t_0)-a_p(t_0)) = e^{\tau A}y(0).[/math] Is there something I'm misunderstanding when I'm reasoning like this?

>>8567963
If a changes sign, then tau will not be a reparameterization... you can have tau(t0)=tau(t1) with t0 not equal to t1. So tau will not be an invertible function of t.

your reasoning is right
y(tau) = exp( tau A ) y(0)
if a>0, then tau goes to infinity as t does ( because a is periodic is it bounded away from zero) so what happens to y as tau goes to infinity is the same as what happens to x as t goes to infinity.

>>8567984
>If a changes sign, then tau will not be a reparameterization... you can have tau(t0)=tau(t1) with t0 not equal to t1. So tau will not be an invertible function of t.
Okay, so say that we have some [math](t_0, t_1) \in \mathbb{R}^2[/math] such that [math](t_0 \neq t_1) \land (\tau(t_0) = \tau(t_1)).[/math] Why is this dangerous? Because if [math]t_0 \cong t_1 (\mod{T} ),[/math] then that should be perfectly okay since [math]a(t)[/math] is periodic with period [math]T.[/math] Or are we talking about [math](t_0, t_1) \in [0,T)^2[/math] here?

With all of that said, thanks a lot! I appreciate the help.

>>8567992
even if a() is periodic, x() will not necessarily be periodic. it depends on the eigenvalues of A. you need to move back and forth freely from t to tau, so you can move back and forth freely between x(t) and y(tau), so studying y(tau) is equivalent to studying x(t).

happy to help.

>>8568044
Ah! Thank you! I understand this much better now! :D

>>8556735

Is fire a type of electricity ?

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what is x as a function of L,R?

>>8568275
>what is x as a function of L,R?
(R-x)^2 + L^2 = R^2
->
-(sqrt(R^2 - L^2) - R) = x

>>8568279
ty

is there any value for a and b so
a + b = ab ?

>>8568316
a+b=ab
a-ab=-b
a(1-b)=-b
a=-b/(1-b)

let b be anything except 1 and let a = -b/(1-b)

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>>8567875
>problem 3
help guys, I found this
syvum.com/cgi/online/serve.cgi/eng/fluid/fluid204.html
but equation (6), I don't understand

What's the difference between computer science and computer science & engineering?

I'm graduating with a BS in EE next semester. Slightly below average GRE scores (157, 157), OK student (somewhere in the top 15%).

Currently have informal offers to do PhDs in either geophysics or EE (same school as bs). The EE one is funded, prof is young but has good credentials and is cool, have worked with him on some other stuff. GG guy I don't know so well but he seems cool, very smart, does cool research. Have yet to actually apply for gradschool anywhere.

Not sure which to take, or if I should just get a job and reevaluate next year. WW/SQT/D.

When I was on a plane flying from FL to NJ, I noticed that some of the ground is blurry. Is it pollution? Definitely wasn't fog, it was a clear day.

>>8568415
Was the window dirty?

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>>8568449

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>>8567875
>>8568326
;_;

Not trying to be /pol/, but why do I have a harder time relating to and caring about non-whites? Deaths of non-white people make me feel nothing and in every conversation with them I can't help but feel like a human talking to sheep.
Is there something wrong with my brain or am I just racist?

>>8568750
not really /sci/, its pysch so it belongs on /his/ but whatever

are you sure its about them being 'non-white'? or is it because you don't know them/can't relate to them? Empathy does not show itself for every sob story you hear, especially today when you are bombarded with horrifying shit every hour by the news. Empathy is a very selective emotion.

You typically only feel empathy for people you actually care about (friends, family, etc), as well as yourself. If someone isnt necessarily close to you, but they have things in common with you, then you may care about them as well (because you subconsciously see yourself in them).

For example, you probably don't give a shit about inoccent civilians dying in a terrorist attack in Pakistan. You don't speak the language, you know little about the country, you don't know their foods, maybe you have never even met a Pakistani. They are alien to you. Its natural to feel no connection.

But when you hear on the news that inoccent civilians died in a terrorist attack in France, you feel worry and concern. You know France, you know their way of life, you know the language, you know the landmarks, you recognize their western ways. An attack in France may as well have been an attack in your country. It feels a lot closer to you than Pakistan. Thus, you feel an emotional connection.

As for the talking part, it all depends on your exposure. Lets say for example, your only interactions with indian people are with fob mmigrants. They don't speak the language well and you can't communicate your ideas clearly to them. You feel like talking to sheep, because from your perspective you practically are.

This scenario can be extended to different social classes, races, nationalities, etc. If your only intelligent conversations are with white people, then you naturally feel like white people are smarter.

So in short, no, you arent necessarily a racist. It depends on where you are and the people around you.

>>8568750
A more intelligent question to ask would be what racism actually is and if it's as bad as you've been conditioned to believe it is.

>>8568716
try putting some effort in yourself brainlet

you even have the solution, pathetic

Given a convergent power series, there is only one function it converges to, which is the one defined by the interval restricted by the radius of convergence, and a divergent power series never converges to a function, right?

And does the same apply to Taylor series?

>>8569475
taylor series are power series

>>8569481
Sure, but one form is the generalization of the other

I'm going into my 3rd year of a physics major. I seem to be able to do physics problems, but I don't think I really understand the physics. I get the math (or am able to perform calculations at least) but I don't think I really have a physical intuition to look at the world and at nature and see how things work and how they are related and so on and so forth.

How do I remedy this?

So DNAP I (E. coli) is meant to have both 3'-5' and 5'-3' exonuclease activity. Does this mean that when you add it to a double-stranded DNA molecule in the presence of Mg2+ but no dNTPs whatsoever, it will degrade the entire thing from both 5' and 3' ends?

And why is T4 DNA polymerase used instead of Klenow sometimes? For example in sequence and ligation independent cloning (SLIC), T4 DNA polymerase is used to chew back on the DNA in the 3'-5' direction even though Klenow has the same activity. How do they decide which one to use?

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how did they arrive at this?

>>8570353

nvm got it, pardon my brainlet CS brain sempais

>>8570359

sorry guys my brain kannot comprehend this; red pill me on cantor pairing function please, namely the proof to invertibality of the function.

Besides practicing, how do I git gud at Gaussian/Gauss-Jordan Elimination?
Whenever I try to, it would take ages and usually I would do stupid shit like make an entire row 0 but then realize later on that I could have made it all 1s and used that row for subtraction and shit.
Basically, how would a not-retard do Gauss?

Why can we see plasma? I thought photons were generated when electrons change energy levels in an atom. I also thought that in plasma electrons weren't bound to atoms. So if electrons aren't jumping between energy levels in atoms in plasma, how do the photons get emitted?

My friend said the universe is donut shaped, he is studying to be a physician but I don't believe him, can someone tell me if this is true?

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what's the best way to read maths books? my current plan is to read 10 or so pages every second weekday delaying the exercises of that session to the next. i'd then review on sunday doing the questions i couldnt during the week. maybe also review at the end of every couple of chapters.
or should i just plough on everyday and review every so often? any recs

When will science be advanced enough to bring Kurisu Makise to real world?

>>8570736
Not enough evidence to point to it. Last time we measured curvature, it was about 1, meaning flat space.

>>8570780
>what's the best way to read maths books?
It's personal preference. Try a bunch of different ways and see what works for you. I do think that you would be better off, though, without planning things out too much. It's easy to get caught up in the planning and worrying about "efficiency" when you could be actually learning the mathematics. Also, if you're not a very particular kind of person, you'll probably get burnt out by following a strict schedule. And there's not way to predict whether you'll be able to make it through and fully understand any certain set of 10 pages in 2 days.

Also see >>8561717

Is there a book for General Relativity which emphasizes the use of Computer Algebra and/or numerical methods while teaching the basic concepts? I am an engineering student and I really have no interest in expanding all those indices and figuring out what each component looks like. I like to see results and make simulations.

I watched Susskind's lectures online and now I am taking IntroGR in coursera and I feel the knowledge is not very concrete in my mind. All I've seen to this point is "so you have this tensor and it transforms like this and then you multiply by this other tensor and..." but I like exercises and it would take too long for one of these online classes to make a single change of coordinates or even to expand a single of those tensors to show how they would look like, disregard their multiplication with other tensors.

How do I prove that if a rectangle (in R^n), intersects a set and it's complement. Then it must intersect the Frontier (idk if that the traduction, it's also calles the set of limit points I think.)

>>8568334
Someone please? I feel even dumber to ask again.

I am applying to two different universities for CompSci and one has their program simply called Computer science whereas the other is called Computer Science and Engineering. I'm assuming there's a difference because some websites that compare starting salary of degrees have them listed as two separate degrees. The only thing I get when I look it up are comparisons between CS and CE.
So is there a difference or is it just named like that because it's an offset of EE and the other uni is too lazy to add the engineering part?

>>8556735
How the fuck should I find a university specialised in differential geometry (not north america but Germany/EU)?
Bonn is like THE mathe university around, strong in algebra and topology, but not so in graph theory, statistics and diff geometry, as far as I know...

Does anyone a tip for working out questions like this? I have a hard time visualizing shaded areas when it's more complicated than something like p /\ q

>>8571134
What's the question boi?

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sorry

>>8571153
C, use dmorgan

>>8558359
Do math. Its kinda related.

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partially ordered sets hurt my head sometimes

>>8571229
...What? If [math]\{1,2\} = X \subset \mathbb{N},[/math] then the least upper bound of [math]X[/math] is [math]2[/math] because it is the smallest number such that it is greater than or equal to every entry in the set, i.e., [math]\forall x \in X, 2 \ge x.[/math] Similarily, the highest lower bound is [math]1[/math] as it is the highest number such that every number in the set is larger or equal to it, i.e., [math]\forall x \in X, 1 \le x.[/math] Therefore, [math]\forall x \in X, 1 \le x \le 2.[/math]

>>8569475
You've answered your own question, as the guy who replied to you was attempting to indicate.

Given a set with n distinct objects, how many ways are there to partition the set into 2 nonempty subsets, /sci/?

>>8571355
2^(n-1)-1

>>8571389
Why?

>>8571355
We have [math]n[/math] objects we need to consider. For each object, we can make [math]2[/math] choices: either put it in subset [math]1[/math] or subset [math]2.[/math] We don't really have a choice for the first [math]2[/math] objects because one needs to be in subset [math]1[/math] and one needs to be in subset [math]2.[/math] Therefore, we have [math]n-2[/math] remaining objects we DO have a choice in. By the multiplication principle, we obtain the result [math]2^{n-2}.[/math]

>>8571419
wrong

if n = 3 then the partitions are
{1} {2, 3}
{2} {1, 3}
{3} {1,2}

this is not equal to 2^(3-2)=2

>>8571421
Thats because you fucked the formula up. Its not 2^(n-1 -1) (which should have struck you as redundant) but (2^(n-1) ) - 1.

>>8571401
The number of ways you can choose a subset form a set of n elements is 2^n, this counts the full set and the empty set. We subtract those two, then divide the whole thing by 2 to account for how for how we are considering both sides of the partition in our count of the number of sets. In other words each partition is counted twice.

>>8571401
let c_n be the number of ways to partition n elements into 2 non-empty subsets

there are c_{n-1} ways to partition the first n-1 elements into 2 non-empty subsets, and then you can put the nth element into either set (2 choices). and then theres the one other partition where the first n-1 elements are in one set and the nth is in the other, so you have the recurrence relation c_n=2*c_{n-1}+1

by induction we show c_n=2^(n-1)-1:

base case n=1, theres no partitions since one subset must be empty, and we have 2^(1-1)-1=0 as desired

using the recurrence relation
c_n
=2*c_{n-1}+1
=2(2^(n-2)-1)+1
=2(2^(n-2)-1)+1
=2^(n-1)-2+1
=2^(n-1)-1


>>8571449
you wrote the formula 2^(n-2) brainlet, not me, look at your post

Why do I like little boys?

>>8571457
>you wrote the formula 2^(n-2) brainlet, not me, look at your post
[math]2^{n-2}[/math] brainlet here, I got angry at myself when you pointed out to me how wrong I was. I then calmed down and learned by reading >>8571449's answer, who is not me.

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>>8571464
>got angry at myself
> then calmed down

>>8571477
I don't understand, isn't it integral to learn from your mistakes, no matter how embarrassing they are?

>>8571479
skip the 'getting angry' part and go straight to the learning part

also check your formulas for the smallest possible values to see if they even make sense first

>>8571342
you are comparing {1,2} as a subset of the natural numbers

the picture compares the empty set as a subset of {1,2}

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would it be possible to do my bachelors in one uni and then masters in another?
As in, I'd like to major in biology or computer science, minor in biology or computer scienceyt and then complete my masters in a different uni?

Or better yet, would it be possible for me to transfer 1/3, 2/3 years into my bachelor? I imagine I wouldn't be due to the desync of courses.

Also, it's smarter to major in CS/biology instead of majoring in bioinformatics as it limits me less than just having a bioinformatics degree, right?

>>8571481
>skip the 'getting angry' part and go straight to the learning part
Been trying to adhere to this philosophy since summer, but it's only recently that I've achieved partial results.

>>8571342
in fact all that has been proven in this post is that 1 is the smallest element of X, and 2 is the largest element of X, neglecting the empty set completely

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I posted this as an /adv/ thread and someone said rob post it here:

So my girlfriend got one of those DNA test kits as a gift and when she was spitting in the tube, I convinced her to give me a short blowjob to work up more spit. She produced too much and we ended up dumping most of it into the sink, so the container could fit a solution that mixes in when you finally seal it.

Anyway, she's very worried and upset that her sample could be tainted by my DNA, which, in retrospect, could be skin cells or something, but probably not precum considering how short it was. For reference, my girlfriend is Indian, adopted from New Delhi, and I am white, so it think our DNA would be easy to set apart.

If anyone has any reliable answers as to whether her sample will be compromised, I would really appreciate it.

Pic unrelated

why can i cum twice in like 5 minutes?

does the body really start remaking semen that quickly or does the body willfully not ejaculate all that you have stored up?

>>8571604

refractory period

New Thread
>>8571619
New Thread

>>8571621
he said can not can't