/sqt/ - Stupid Question Thread: Milnor Edition

What does it look like to be standing in 3D hyperbolic space? Is it just like normal space, except groups spread out faster as you approach them, and come together quicker as you move away from them?

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>Is Homotopy Type Theory a meme?
Yes.

>What role will it play (if any) in the future of mathematics?
In mathematics, almost none. People like Lurie opposed it from the start.
But it will gather interest in European type computer science and hopefully push related functional languages.

PS: Just this week, one of the HoTT in Agda guys released his PhD thesis
https://www.cs.cmu.edu/~kuenbanh/files/thesis.pdf

>Milnor Edition
I really enjoyed this essay by Thurston
https://arxiv.org/abs/math/9404236

>8794935
Groups?
Anyway, remember that in general relativity, gravitational force is explained by spacetime curvature and that's what shrinking metric distance feels like.
Say you float in empty space far away from any other masses exect a guy 10 meters next to you. Then you both throw away you pants in the same direction, giving you both a parallel impulse in the same direction (exactly negative to where the pants are now moving). You'll move in what seems to be parallel for the longest time, but since you and the guy both have masses, spacetime curves so that the metric distance between you slowly shrinks until you touch each others. That's how gravitational pull is implemented geometrically.
So yes, on the negative curvature plane, you fall or roll towards other things, unless you exert force. Unless you exert force, you'll find you can't stay parallel (at equal distance)

What are the biggest things to read up on going into Calculus 1?

>>8794984
As in, if I see two objects close to each other in the distance, then the gap between them will appear to rapidly expand(relative to how it quickly it would expand in euclidean space) as I approach one object, based on how extreme the negative curvature is.

>>8794991
just open up a calc 1 book and see brainlet

>>8795007
please dude help me out

>>8795005
Well, here will be deformations to what you experience normally, but make yourself clear that the effect as you describe it here is also there is the curvature is zero.
If you see two cities in the far distance of 100km each, their separation as you see them before your eye is 5cm and if you get closer to them, the distance spreads. If you end up between the cities, you observe a maximum distance - the actual Euclidean distance between them.
With other Riemannian manifolds, it's just the same, with a difference you can't gauge locally how far away the cities will end up, unless you know the metric tensor everywhere.

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>>8794984
>I really enjoyed this essay by Thurston
>https://arxiv.org/abs/math/9404236
good read

Anyone here use WordPress on their own server?
I've been using it, but I cannot get LaTeX to work. For example, when I preview
$latex A \subset B$ I don't see it formatted or anything, just as is. Help!

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Sorry for the crappy diagram. I know in set theory epimorphisms are exactly the same as surjection, but I am unsure if this diagram is an example of a surjection.

Are these diagrams an illustration of an epimorphism?

Let this be the category of Set.
Where you have a function,
f: X->Y
g1, g1: Y->Z

Where X is the first set (reading left to right), Y is the middle set and Z is right most set.

The diagram is suppose to represent g1,g2 mapping the same elements from Y to Z.

>>8795195
an epimorphism is a single morphism, your diagram has three of them

>>8795198
How come definitions define it as

f : X → Y that is right-cancellative in the sense that, for all morphisms g1, g2 : Y → Z if it is just a single morphism from f X to Y?

>>8795195
but no f is not an epimorphism in this picture since its not a surjection

in Set, epimorphisms are exactly the surjections

>>8795204
sorry i couldnt copy paste what i wanted.

Why does wikipedia define it as: https://en.wikipedia.org/wiki/Epimorphism

if you are just looking at morphisms between X and Y?

In the wikpedia article it makes me think you would map X to Y and then focus on the morphisms g1, g1 between Y and Z in my diagram

>>8795204
that definition says f is an epimorphism
it doesn't say anything about g1 and g2

the definition just happens to involve a condition with two other morphisms

>>8795209
im confused. what makes f an epimorphism?

In category of Sets how many sets are you looking at?

In my diagram would you just be focused on X and Y and the mappings between them for an epimorphism? Or does Z have to be involved?

>>8795211
f is an epimorphism if it's right cancellative

>In category of Sets how many sets are you looking at?
f is a morphism from one set to another, so two sets

>In my diagram would you just be focused on X and Y and the mappings between them for an epimorphism?
not all the mappings, just f

>Or does Z have to be involved?
not just one Z, you involve every other object Z such that you have maps from Y to Z with f g1 = f g2. f is an epimorphism if for every object Z and every pair of maps g1, g2 with fg1=fg2, you have g1=g2

>>8795216
err g1 f = g2 f

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>>8795228
How do you apply the definition of epimorphism to this diagram?

>>8795244
let g1,g2 be maps from Y to Z such that
g1 f = g2 f

then since f is surjective, for every y in Y there's an x in X with f(x)=y

by the assumption that g1 f = g2 f, we have g1 f (x) = g2 f(x) , which is the same as g1 (y)= g2(y)

since f is surjective this equation is true for every y in Y, so g1=g2, so f is an epimorphism

>>8795253
what confuses me in what you write is you mention Z. There is no Z in this diagram. Where is that coming from? There is only an X and Y. Earlier in the post you said you don't need three sets and then you include a third set in your proof. Can you explain what the fuck is going on? I am self-learning no professor to ask here so thanks for helping

Whats a decent undergraduate research paper writing service?
Google returns like 100x with poorly designed webpages/live chat support and idk if I can trust them to do a biochemistry paper without getting caught on turnitin.

>>8795259
>Where is that coming from?
the definition for f:X -> Y to be an epimorphism says that you need for ANY two morphisms to another object g1,g2 :Y -> Z satisfying g1 f = g2 f, also satisfy g1 = g2

so if you want to show f is an epimorphism it's not enough to pick a specific Z and specific maps g1,g2 like you did in your diagram

the argument i gave did not depend at all on the choice of Z or g1 or g2, it works for any Z and any g1,g2 satisfying g1 f = g2 f

>>8795273
so in order for the definition of epi to be satisfied then f MUST have an arrow from every object in X to every object in Y right?

THEN

g1,g2 :Y -> Z satisfying g1 f = g2 f, also satisfy g1 = g2

must be satisified for ANY Z you choose.

Is all of that right?

>>8795278
>so in order for the definition of epi to be satisfied then f MUST have an arrow from every object in X to every object in Y right?
in Set, epimorphisms are exactly surjections, so for f to be an epimorphism, every element y of Y has to have SOME element x in X with f(x)=y

>>8795278
>g1,g2 :Y -> Z satisfying g1 f = g2 f, also satisfy g1 = g2
>must be satisified for ANY Z you choose.
>Is all of that right?
yes

what do I need to know before I start learning Number Theory?

>>8795295
elementary number theory, nothing

algebraic number theory, some basics about grops and fields

analytic number theory, a strong grasp on calculus

>>8795287
question i have is for Y to Z does mapping of g1, g2 have to be surjective from on Z? In other words for every element z (in Z) Z has to have some element y in Y with f(y)=z?

>>8795299
no, just look at the definition, it says nothing about g1 or g2 being surjective

it just says g1 f = g2 f

>>8795304
ok that makes sense, so really the only thing that is surjective is f that maps X to Y?

>>8795309
yes

>>8795298
is this book a good intro?

https://www.amazon.com/gp/aw/d/0199219869/ref=mp_s_a_1_6?ie=UTF8&qid=1491012386&sr=8-6&pi=SL75_QL70&keywords=number+theory

>>8795314
idk dog read the 20 reviews or just download the book...

>>8795311
ok that makes sense. then what the fuck is the point of g1 and g2 mapping the same element to the same shit from Y to Z then if f is the only thing that is of interest here in terms of surjectivity?

using a bad anaology that is like saying if you turn left then the restaurant is there, then if you go 2 miles up you'll see a gas station. while that might be true the gas station is 2 mles up who gives a fuck when you found the resturant?

similarly, if you know f is surjecive then why does what g1,g2 does from Y to Z matter?

>>8795321
>then what the fuck is the point of g1 and g2 mapping the same element to the same shit from Y to Z then if f is the only thing that is of interest here in terms of surjectivity?
because thats the definition of epimorphism? also this is only in the category of sets, in more general categories there's no notions of elements, and so there's no notion of surjective either

what are you even studying this for?

>similarly, if you know f is surjecive then why does what g1,g2 does from Y to Z matter?
knowing f is surjective let's you prove its an epimorphism

>>8795327
studying it out of interest. want to learn group theory and see how category theory applies to it. additionally want to learn functional programming and want to see how it applies to that as well.

started studying group theory on the side and made more progress with that since i am following a structured approach to studying group theory.

the catgeory theory study is hard to structure like my group theory studies.

kind of have to rely on wikipedia articles

>>8795335
you really dont want to rely on wikipedia articles, just get some standard intro texts like aluffi's chapter 0 or leinster's basic category theory or simmons's 'An introduction to Category Theory'

>>8795335
its also really just game of symbols at this point

in groups if you have group elements a1,a2,b with a1 b = a2 b then since inverses always exist in groups you can multiply on the right a1 b b^(-1) = a2 b b^(-1) to get a1=a2. so here an analogous right-cancellative notion of epimorphism would be boring since everything is right-cancellative

in categories inverses of morphisms don't always exist so you can't play the same game, so having this definition on hand is more useful

>>8795352
>>8795343
ok thanks.

Say you have three sets; X, A, and Y. X is unknown, A is given, and the cardinality of Y is given. Y = { f(x,a) : x ∈ X,a ∈ A }

What I'm interested in learning is how plugging in different values for A, different cardinalities for Y, and different functions for f(x,a) affects the range of possible answers for what the sets X and Y contain. Also, I can't figure out how to type this out in latex.

>>8794772
what is the precedence of the sum (sigma) operator ?

Like unary minus, just the term to the right?

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im a downie retard and i can't do this questions from courant and john.

>>8795556
Since x can only be rational values, the x value cannot go to any other rational value other than 1/2 without first passing through an infinite number of irrational values. For example, to get to .6 from .5, the x value would first half to pass through irrational values like .534324324564267879657565....
you get the idea. Since the function has to be continuous, and has to always be rational, the value is thus always stuck at 1/2.

Did I make sense? Sorry if this is a bad explanation.

>>8795566
i understand it at that level its more actually writing it out and proving it.

>>8795566
>>8795571
for example i tried supposing there was some f(x) which was not a half and tried to show that that would break continuity at x=1/2, but i couldnt figure it out. think i also tried the reverse to .

>>8795579
Assume f is continuous and 1/2 at 1/2 and not 1/2 for some x1. Then look at the interval from x1 to 1/2, and use the intermediate value theorem

>>8795598
thanks, that works. the problem comes before the ivt in the book so i was trying to not use it. w/e though, im satisfied.

Do the unit vectors transform as vectors or pseudovectors?

Show that with the substitution [math]x^{-1/2}y, \; t = \frac{2x^{3/2}}{3}[/math] the differential equation

[math]\frac{d^{2}y}{dx^{2}} + xy = 0, \; x>0[/math]

is equal to

[math]\frac{d^{2}u}{dt^{2}} + \frac{1}{t}\frac{du}{dt} + \frac{t^{2}-1/9}{t^{2}}u = 0, \; t>0[/math]

I am unsure of how to start this substitution, as u is differentiated to t. Should I write x^(-1/2) in terms of t, and consider y = y(x(t))?

[eqn] 2^{\aleph_0} = \aleph_\omega[/eqn]

In ZFC this can be refuted using Konig's theorem, but is there a model of ZF (without the axiom of choice) where it is true?

I'm not at all a metereologist, but i just had this idea to buy a water thermometer, and go to the lake near my house every day and measure the water temperature, and then make a chart showing the development throughout the year, along with the relation between water temperature and air temperature.
I did a 5 second google search and couldn't find a website that already does this. some of them only have values from May to September, but i want to know the values for the entire year.
Anyway, i will almost certainly do this, but i don't plan to swim out into the middle of the lake every day. Does it suffice if i measure the temperature at the shore? or is that too inaccurate?
also, i just realized i would be measuring the surface water temperature, not necessarily the temperature underwater. but i don't care that much about the temperature underwater

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Where can I read Acta Mathematica Sinica online? I can't find it on libgen, my uni only has the English version, etc. Assuming it's not in Chinese...

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Sup /sci/, there is something I don't understand in these 2 circuits

In the left one I thought about applying KCL in that node, and that would give me I = 1 + 2 +3 = 6mA and V = 6V. The answer is actually I = 3mA and V = 3V in the resistor but I have no idea why.

Something similar occurs to the right one, but this time he wants the voltage across the diode, so it gives I = 4mA and V = 1. I really can't see this and why in the left one the higher voltage(3V) prevails and in the right one it's the lower(1V)

Thanks

>>8795013
One thing many people struggle with initially is trigonometry, logarithms, and basic algebra. Be sure your algebra skills are acceptable, work with trig, and know what a logarithms is and you should do fine :)

>>8796919
>I thought about applying KCL in that node and that would give me I = 1 + 2 + 3 = 6 mA

why the fuck would it give you that

also

>Figura
lmao

>>8796919
Is there some additional info about the diodes?

>>8796983
judging by the answer from the answer book he clearly looked at, Vt is zero

>>8794935
Download hyperbolic games

>>8796986
I havent done that shit in a while, but wouldn't it make sense that the non-linearity of the diodes cause the resistance of the 1v and 2v diodes be higher than of the 3v one?

>>8796969
I went full retard on different voltages in the same node, shit is impossible,
>>8796983
The section of the book is about ideal diodes so you should consider it an open circuit or a short circuit.

Btw I figured it out, it's batshit obvious, you can only have the higher voltage in the left and the lower one in the right because otherwise it contradicts the whole shit, it can only work that way.

Thanks for your time anyway.

>>8796990
The only real hyperbolic game is 2D.

if there is an uncertainty in position for each individual particle in my body, is there a (albeit extremely low) chance every single particle in my body simultaneously teleports to the moon, teleporting me to the moon as well?

>>8797075
Not if it would transfer information faster than the speed of light in the process.

what kind of shit does the government inject you with in boot camp? is it even something to be alarmed about, like "this will make you invisible to radar" type shit?

>>8794772
It's not a meme, it's extremely important. However, type theory is still poorly understood so it's probably not the "final" version. People are still actively working on it. It will take some major cultural change and more concrete benefits before most mathematicians adopt it.

>>8794984
>People like Lurie opposed it from the start.

Source? Lurie has admitted to not knowing shit about HoTT, even though he made some angry blog comments about it. (PS: Grothendieck toposes are for noobs.)

>>8795396
It doesn't really have one, just use parentheses to make it clear.

>>8797008
Glad you figured it out. Diode behavior is not always immediately obvious. As a general rule, if there are competing possibilities for a shared cathode node in a set of diodes, it has to be the largest voltage of the possibilities. Conversely, the reverse is true for the anode side (it must be the lowest of the voltage possibilities). But you already know that now.

I like math
I like neuroscience and psychology
I like microbiology
I like applied physics
I have nearly completed minors in all of these.
How the fuck do I choose a major?

I've never struggled with an idea as much as I do with matrix algebra systems.
>It's just highschool math! Haha brainlet.
Don't get me wrong, I understand the process of it just fine. But when I go to write it down I fuck up the whole thing. I write 3 instead of -3. I type one of the countless fractions into the calculator wrong and it fucks everything up.
Am I a brainlet, doing it wrong, or is this normal?
I have until Tuesday to get my shit together.

>>8797716
bookkeeping errors will always be more common in subjects like linear algebra where you have to perform a large amount of computations

some things you can do to help minimize this are
>slow down
>write bigger/clearer
>don't try to skip steps by doing them in your head
obviously you need to balance going slow with actually finishing the exam but most tests will give you enough time to be careful

>>8797743
Thanks anon.

>>8797543
I feel that pain, brother. Love of math, cogsci, physics, comp sci, economics, actuarial/financial mathematics here. Just pick one and do it. Open up a broad second degree and take courses as you please, you don't even need to finish it.

>>8794772
I've had very slight nausea that hasn't made me vomit at all every day for like 4 weeks. Should I be worried that I have some kind of cancer or something?

>>8797756
It's probably just a side effect from the pollution of living in a third world country.

>>8797771
Puerto Rico isn't third world

Should I major in astrophysics?

This is probably dumb but how do I rearrange this equation to solve for x?

[math]309,000 = 0.1 * 2^x[/math]

I got quite lost after trying to xrt 309,000

>>8797988
You divide .1 from both sides, then take the natural log of both sides and use the natural log rule to bring the x down, divide by the natural log of two to get your answer.

Should look like this

X=ln (309,000/0.1)÷ ln (2)

>>8797992
Thanks buddy.

Is there anything significant about the fact that you can solve the equation
[math]a^x=b^x, a\neq b, x\neq 0[/math]
By using complex numbers? Does anything care about finding this "intersection"?

Did ancient namefags of /sci/ actually built a small rocket and shot a squirrel into low orbit in early 2010?

>>8797899
>astrophysics
lots of coding, but since it is applied physics, you can find tenure

>>8796260
>>Anyway, i will almost certainly do this, but i don't plan to swim out into the middle of the lake every day. Does it suffice if i measure the temperature at the shore? or is that too inaccurate?
depends on your goal

>>8795396
>>what is the precedence of the sum (sigma) operator ?
Reminder that it is a frnech who used Sigma for sum

What is it like applying for postdocs after PhD? What are all these ``rumor mill'' things?

Seeing as we dont understand how the universe was created why is it generally accepted that matter and antimatter were created in roughly equal amount and CP violation is needed? Why could the universe just not be created with a large matter dominance seeing as we dont understand it meaning that the small CP violation we see is no problem?

>>8795321
>ok that makes sense. then what the fuck is the point of g1 and g2 mapping the same element to the same shit from Y to Z then if f is the only thing that is of interest here in terms of surjectivity?


for monic f, g1 and g2 are points.
fg1= fg2 => g1 = g2
because points in CT are arrows 1->X, and generalize dpoints are X->Y (meaning any arrow), but all definitions are meant to work with general arrows, not just points 1->X which come from set theory.

g1 and g2 are the points x and y in the domain of f, but now in CT points are general arrows

for epic f:X->Y, g1 and g2: Y->Z are any functions
you want f surjective =>[ g1f=g2f=>g1=g2]
the thing to remember is that functions are defined on the whole of their domain, so here g1 and g2 are defined on the whole of their domain say Y
so if f surjective you have g2=g1

for [ g1f=g2f=>g1=g2]=> f surjective

you want f(X) = Y ie X = f^-1(Y)
but with [ g1f=g2f=>g1=g2], you can choose Z={0,1}
Z={0,1}
g2= cst function 1
now you must find a function g1 st g1f=g2f, so that you get for free g1=g2=cst 1 (1 meaning true)
define g1, for any y in Y, g1[y]=1 iff y in the set f(X), 0 otherwise

now g1f=g2f because you did everything to make it so.


what matters is that, when f is surjective, f reaches the whole of the domain g1 and g2, so you clearly see that if f surjective, g1 (any point point of Y) = g2(any point Y) , then it is natural to have to expect g2=g1. surjectivy means precisely that g1 must be equal to g2

>>8798097
>>Reminder that it is a frnech who used Sigma for sum
for the first time

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>>8795321
also, read set for mathematics to move from set theory to CT

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1. How do we know Na is positively charged and OH is negatively charged? Same situation with 2.

3. Why do we write chemical equations that way instead of other ways? More importantly, how do we know what order to write them in?

Brainlet questions I know but my textbook doesn't really explain this.

[math]\displaystyle\sum_{k=1}^{N}\frac{1}{k}[/math]

Is there a way to find what N would have to be for the sum to reach a certain value?

can someone post the compsci book guide of /sci/

also is there such a thing for pure math?

>>8794772
Let [math]a, b[/math] be two 9-digit numbers made out of all digits from [math]\{1,2,3,4,5,6,7,8,9\}[/math]. Prove that there is no [math]a, b[/math] such [math]a + b = 1000000000 (10^9)[/math]. How do I do that? I have no idea where to start.

>>8798054
Hardly, you need fuckton of power to get to low orbit. It's 160 km high, no amateur rockets made it that high.

>>8798295
Maybe the errorterm of this will help:
[math]\sum_{1}^{s}\frac{1}{x} \approx \ln{x} = \int_{1}^{s}\frac{1}{x}dx[/math]

>>8798284
O is a double electron acceptor.
H is an electron donor.
S is whatever.

>>8798295
I can give you a bound.

recall that [math]\sum_{i=1}^{\infty}{\frac{1}{i}}[/math] diverges because the sum of the second terms is greater or equal to 1/2 and the sum of the next 2 terms is greater then 1/2, the next 4 terms are greater then 1/2 and so on.

So for a bound for N calculate 2v, where v is the value and then take [math]\sum_{i=1}^{2v}{i^2}[/math]

This gives you a (pretty bad) upper bound, which certainly can be improved.

Can somebody recommend a discrete mathematics textbook?
My class was taught using zybooks and my teacher was incompetent, and I plan on going into some cryptology classes later. Would prefer not to be blindsided.

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Can anyone recommend me a good resource for learning optics, please? The simple stuff that's used in computer graphics, for raytracing, simulating light-surface interactions. Reflection, refraction, diffusion, diffraction and absorption. That kind of concepts.

>>8798596
Here are slides and exercises from a computer graphics lecture in 2013 or so.
www116 zippyshare com v/GaTSSqa7/file.html
www65 zippyshare com v/JQzhbnvJ/file.html
possibly useful

>>8798648
thanks a lot! I've skimmed through the slides and they're good so far, they start teaching optics from 0

>>8794984
Could you please elaborate on what does European-type computer science mean?

how do i find out what careers i can get with a specific bio degree?
i'm trying to pick a branch i wanna go into and i thought there would be a database for that sort of thing but i can't find one

Why is it that if I have two parallel wires carrying current and I want to find the magnetic field at a point in the plane of those wires, I add up the magnetic field contribution from each wire at that point.

But if I want to do the same thing with a coaxial cable, I take the net current within the radius?

Why does it not matter that the point outside the coaxial cable is closer to the outer conductor than it is to the inner conductor? (as it would in the parallel wires calculation)

For instance, if the currents in the coaxial cable are equal in magnitude and opposite in direction, the magnetic field outside of the cable is zero, even though you would think the outer conductor is producing a stronger field at that point than the inner conductor due to a shorter distance.

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This is problem 1.5.8 d) from Pitman's Probability book

I have boxes 1, 2, 3 as in the picture. My opponent chooses one of these boxes. They remove a ball from the ball, and I see which color it is. If I see black, I guess box 1 with probability 18/23, 2 with probability 5/23, and 3 with probability 0. If I see white, I guess 1 with probability 0, 2 with probability 11/23, and 3 with probability 12/23.

I need to show that with this strategy, my probability of winning is 9/23 no matter which box my opponent chooses.

The solution manual says
P(guess correctly | black & Box 1) = P(guess 1| black & Box 1)P(black & Box 1| Box 1) + P(guess 1 | white & Box)P(white & Box 1| Box 1) = (18/23) x (1/2) + 0 x (1/2) = 9/23.
And similarly for the other boxes.

I can't make sense of the first part of this equality. Could anyone explain why this is the case?

Are WIldberger's videos on Algebraic Topology and Differential Geometry any good? Will he put his own research into the course or is it just a normal lecture?

Why can I turn my head to the left to about ~150 degrees, but can only turn my head to the right only to ~80 degrees, any more and I feel pain

>>8798869
Go to a doctor.

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>>8798869
please post a photography of yourself turning your head to about 150 degrees

/sci/ help. The unthinkable happened. I'm in a math class that Khan Academy doesn't cover.

Anyone got any good online resources for vector calculus?

>>8798941
http://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx

Also read your textbook, it's probably pretty good.

>>8798949
My tree-hugging school is switching from Stewart to an open-source e-text this term (called Apex Calculus, if you're curious). Instructor flat out told us that she doesn't have much confidence in the text and that we should line up other resources.

Thanks for the link!

>>8798970
You could also read Stewart, go to your university's library, or get a pdf from libgen.io.

>>8797543
Pick your favorite two. Get BS in the more practical one (as far as jobs) and MS in the other.

>>8798873

For what? It doesn't really matter, I just have to turn left if I want to look back to the right side more

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He explained it in the video, but I don't really understand: why does theta go from 0 to pi instead of 0 to 2*pi?

>>8799156
>Above XY-Plane

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Posted this in the last thread, didn't get a whole lot of answers, but I have a BURNING QUESTION

I'm a first year undergrad student, and I've got my mind set on becoming a computer science major BUT I'm interested in mathematics, yet know practically nothing about the field.
The highest level of math I've taken was kind of a dumbed down version of calc1 for econ students, we basically only got up to learning about multivariable functions.
What are some ESSENTIAL READINGS for someone who's trying to get into mathematics?
Any advice going forward?

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It's been a while, /sci/..

I have two applied math phd offers on the table..anyone else torn on decisions and wanna talk?

>>8799271

read
the
fucking
sticky

CH4 (g) + H2O (g) ⇄ CO (g) + 3 H2 (g)

ΔGº = 142.15 kJ
ΔHº = 206.13 kJ
ΔSº = 214.68 J/K

At what temperature will the reaction change the direction in which it is spontaneous under standard pressure conditions?

How do I do this?

Set you have

A={1,2,3}
B={{1}, {1,2}}

Question 1: is 1 a subset od A
Question 2: is {1} a subset of A?
Question 3: is {1,2} a subset of B?
Question 4: is {{1,2}} a subset of B?
Question 5: is {{1}} a subset of A
Question 6: is {1,2,3} a subset of A?

Why is that if I want to calculate the elctric field of a surface I do Surface integral as in not just a doubke integral over a region but as the denisty function integrated over the surface, but when it comes to volumetric charges I only have to perform a triple integral? By this I mean why isn't there a weird "volume integral" that is analogous to the definition of a surface integral?

>>8799476
G = H - TS
Calculate at what T the right hand side, and therefore G, becomes negative.

>>8799624
Yeah, I tried to delete the post. I tried that out and the online input said it was wrong, which prompted me to post... Issue was on the professor's side. Since been fixed. Fml.

>>8799604
Have you tried at all? I'm not going to give you answers but I can let you know if you're right or not.

Remember, A is a subset of B if every element of A is in B.

>>8799698

It confused me. Then I decided to think about it.

My answers:
Question 1: No
Question 2: Yes
Question 3: Yes
Question 4: No
Question 5: No
Question 6: Yes

How did I do?

>>8799604
>>8799604
>Set you have
>
>A={1,2,3}
>B={{1}, {1,2}}
>
>Question 1: is 1 a subset od A
no
>>8799604
>Question 2: is {1} a subset of A?
yes
>>8799604
>Question 3: is {1,2} a subset of B?
yes
>>8799604
>Question 4: is {{1,2}} a subset of B?
no
>>8799604
>Question 5: is {{1}} a subset of A
no
>>8799604
>Question 6: is {1,2,3} a subset of A?
yes

>>8799381
choose the one with the most available supervisor, check where the previous phd students are doing, check how much conferences there are in the uni

>>8799810
Then I understand more than I thought I did. Perfect score. Thank you :-)

Where do I find books full of highschool exercises?
Thanks in advance.

>>8799844
Manhattan Review books for the GRE (5lb book)

>>8799844
https://www.amazon.com/lb-Book-GRE-Practice-Problems/dp/1937707296

What's the greatest known number of consecutive primes? Is there an upper bound?

What is skew and kurtosis supposed to tell me?

I'm working with US census names for a project and I'm supposed to write down the details on what a skew of the name "Zachary" of 1.4 and kurtosis of .5 are supposed to mean in relation to the name's popularity.

But I'm at a loss because I don't even know what skew and kurtosis mean in their base other than they're a measure of symmetry.

>>8799898
Nope

Of the UV radiation from the sun that reaches the earth/us, what percentage is UVA and what percentage is UVB?

In other words, if I'm trying to find a sun lamp or tanning light that mimmicks the natural sunlight as much as possible, what should the percentages be? For example one product claims to provide 75% UVA and 25% UVB, is that roughly the same as natural sunlight?

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Ill suck the anon's dick who helps me with this problem I've been stuck on:

Let M be an n x n labeled directed graph as follows, modeling a potion of Manhattan Island and its one-way street system. The nodes of M are given by pairs of natural (i,j) with i≤n and j≤n. These are edges:

From (i,j) to (i+1,j) (east), whenever j is even and i<n
From (i,j) to (i+1,j) (east), whenever j is even and i<n
From (i,j) to (i−1,j) (west), whenever j is odd and i>0
From (i,j) to (i−1,j) (west), whenever j is odd and i>0
From (i,j) to (i,j+1) (north), whenever i is even and j<n
From (i,j) to (i,j+1) (north), whenever i is even and j<n
From (i,j) to (i,j−1) (south), whenever i is odd and j>0
From (i,j) to (i,j−1) (south), whenever i is odd and j>0

Note that (0,0) is the source node. Find the distance function function D(u,v) for arbitrary nn and for arbitrary nodes u,v assuming that each north-south edge has weight 1 and that each east-west edge has weight 3. For n = 4, find the distance from (1,1) to (3,3) in this new graph. Justify your answer by referring to the behavior of a uniform-cost search starting from (1,1).

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Doesn't pi/2 to the left mean -pi/2 instead of +pi/2?

>>8800286
Nvm I'm retarded

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Is there enough space inside of a human skeleton for a human brain to be shoved into? Not counting the inside of the skull, could you push all of a human brain into the space inside of, for example, the space where marrow resides in the femurs, inside each rib, etc etc?

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Got sent here from /g/prog/

How to I access the colorbar "object" in a matplotlib plot?

Basically I'm using a module which has a function that spits out a well formatted graph with a color bar but I want to change the font size on the tick labels on the color bar without having to rewrite the whole plotting function.

Seems like it should be doable.

This is the plot.

>>8800385
just figured it out, it's in fig.axes[1]

>>8798488
The 1s digits have to add up to 10
The 10s digits in turn must add up to 9
Now the 100s digits must also add up to 9
Same for 1000s, etc
So the total of your sigit values summed must be 8×9 + 10, which is 82. The sum of your current integer sets is 90

>>8799898
What is a consecutive prime? All prime numbers are followed by composite, even numbers except for 2

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>>8794772
What's a quick way to prove primality that I can just drop into a proof?

>>8800418
Like prime twins or any prime k tuple

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I absolutely despise having sticky / greasy fingers and hands. Doesn t matter if from soda or foods or adhesives/residues, it drives me insane. The former is fairly easy to solve with soap and water, but it seems even after several washings, adhesive residues just don t want to budge.

What is the best way to remove adhesives, like from tape or stickers, from your hands? I bought 91% rubbing alcohol but I ve found I m really sensitive to the vapors. Is there any other chemical that will do the trick with out frying my nerve cells from fumes? How about removing it from electronic items like phone, computer or calculator? Please help, I m about to go mad.

For any set A, which may be empty, there is no function [math]f\colon A\to\emptyset[/math] right?

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>>8800695
I think that's true...

>>8800695
If A is empty, there is an "empty function"
[math] f := \left\{ (a,b) \in \emptyset \times \emptyset \right\} [/math]
right?

>>8800741
But isn't { } x { } = { }?

>>8798284
>How do we know Na is positively charged and …
That's in its nature. In the Periodic Table, Na sits in the leftmost column with those elements that gladly lose one electron and thus form a singly positively charged cation. Next column to the right (Mg, Ca, etc.) has elements that would drop two electrons, for instance. On the other hand, Cl is in the rightmost colum and readily accepts one electron to become an singly negativelty charged anion. This rule has exceptions, cf. the concept of valence shell electrons and octet rule.

Now if you are a chemist, the formula "CuSO4" should ring a couple bells: ha! it's sulfate (SO4^2-) of copper (Cu with enough pluses to give a electrically neutral compound, that is 2: Cu++).

And so on.

>that way instead of other ways
Usually, the lexical order (the sequence of symbols) should reflect the spatial arrangement of atoms. So OHNa means O–H–Na which is infuriatingly wrong, but NaOH is correct, and so is technically HONa. Water could be HOH but atom grouping favors H2O (and OH2 is not totally wrong). Finally, on top of that, there are habits : sodium hydroxide is usually written NaOH (sodium then hydroxide, makes sense), and everyone knows water is H2O.

>>8800684
Vinegar should work, if you're looking for a household product. Acetic acid is typically what I've used to remove adhesive from surfaces, and it's worked for me in the past. Vinegar is so mild I'd imagine it'd be safe to use on the hands, but I mean, I'm no expert.

>>8800684
Each adhesive has its preferred solvents. My two favorites are time and elbow grease, as in: wait for the superficial layer of skin to die and scrub it off, or don't wait and just erode it. Else you might try with nail polish remover, but if rubbing alcohol makes you unwell this may too.

>>8800695
The definition of a function permits the domain to be empty (giving you the "empty function"), but not the codomain (unless the domain is also empty).

>>8800747
Yes, that just means f is the empty function.

>>8800774
Ah that's right, a function can be defined as a subset of the Cartesian product of two sets.

>>8800747
I believe it's actually { , }

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What causes this ray pattern in the radar image? Is the radar being blocked by buildings around the weather station or something? Near Morristown, TN right now.

https://weather.com/weather/radar/interactive/l/37814:4:US?layer=radarConus&zoom=8

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>>8800888

>>8800791
>{ , }
that makes no sense.

>>8797187
I also just mean mean blog discussions

I was more excited for HoTT in the past, but it doesn't look like any of the math done in it gets less verbose, looking at the papers, and so I lose hope for anything it would be used for that's not pure logic.
But I'm all for dependent types in general, just not a big fan of the equality musings.

>>8800422
Wilson's Theorem:

A number is prime if and only if (n -1)! mod n = n - 1.

It's computationally slow, as you can see.

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I know the definition of the arbitrary unit vector nHat but what the fuck is S that they dot it with, how on Earth did they find what the Sn matrix is?

I've gotta do basically this but for a Spin-1 particle, but I have no clue how they even did it for for Spin-1/2

Why is it that the left hemisphere of the brain been researched more so than the right side?

For every distinct pair of irrational numbers, does there exist a rational number in between them?

How do I find the limit as x goes to infinity of x^x/(e^x*x!)?

Is
[math]a^x=b^x=c^x[/math]
Ever true when a, b, and c are all different values that aren't 1, and x is not equal to 0? Wolfram seems to think it's never true, but that doesn't feel quite right.

Is it possible boil up an object that has molecules composed of two elements with a high and low boiling point, and harvest the un-vaporized element that has a higher boiling point?

if so can anon give examples of use?

>>8801237
[math] \vec S = (S_x,S_y,S_z) [/math] with [math]S_i = \hbar \sigma_i /2[/math]
sigma_i being the pauli matrices.

>>8801271
Found it on stackexchange
>http://math.stackexchange.com/questions/421580/is-there-a-rational-number-between-any-two-irrationals
(yes there is)
I had something similar in mind to the second answer there.

>>8801294
nvm, I fucked up.

>>8801302
Cheers mate that makes sense

My next question is, how do I find x for
[math]2^x=3^x=4^x=5^x=...[/math]
When [math]x \neq 0[/math]?

>>8801362
it can only be 0, if x =/= 0 then there is no solution.

>>8801362
No solution

>>8801372
>>8801377
When does it stop working? It works up until 2^x=3^x=4^x=5^x=6^x=7^x=8^x on wolfram, but then 2^x=3^x=4^x=5^x=6^x=7^x=8^x=9^x exceeds the standard computation time.

>>8794772

What is the Difference Between Chemistry & Physics?

>>8801419
Chemistry is entirely physics but only of the electron

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>>8794772

asked in diff thread but moved it since this belongs in SQT. apologies.

Are topological spaces just generalizations of loci, i.e. "locus" of anything you want not limited to planar, euclidean, or geometry at all, i.e. up to "conceptual" locus or even a 'locus of relations'?

>>8799613
To find the total charge enclosed by a closed surface you integrate the density wrt the volume bounded by the surface. You can calculate the Electric field in a number of ways by using Gauss's law and the divergence theorem depending on the specific problem.

>>8801293
This limit:

[eqn]\lim_{x\to\infty} \frac{x^x}{e^x x!}[/eqn]

Sorry, forgot to latex.

>>8801477
stirling

Is there a name for a condition wherein a person creates a long-term fantasy in their mind as an escape or a way of coping with a trauma?

>>8801499
"living"

>>8801263
Stroke prevelence for this side? Testing speech /memory malfunctions is easier than testing logic/motor malfunctions?

>>8801506
Said long term fantasy is usually the same thing. Like an imaginary friend.

Is a Physics degree a meme? What's the point in a physics degree when you could just get engineering?

>>8801532
You learn something interesting. - That's something Americans don't seem to get, university shouldn't be job education, it's about being human.

Sure, some might like engineering too. But many tasks an engineer ends up doing, a physicist can learn easily.
Most of the jobs either of those degree holders end up with are largely programming anyway.

>>8801538
So pretty much a person with a physics degree can get a job that an engineer could also apply for?

>>8801532
All degrees are memes. Education is no longer about merit.

>>8801493
Shit, I forgot about Stirling's approximation. Thank you.

>>8794772
Prove that the surfaces are orthogonal where they touch.
z= x^2+y^2
x^2+y^2+2z^2=0
Pls send help

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find the net torque

>>8801712
Nigger why the arrow and what it's written there?

>>8801734
pointing towards that small dot that's supposed to represent the axle.

Here's what the actual question states and asks: The axle in Figure Q21 is half the distance from the center to the rim. What is the net torque about he axle?

I've taken engineering versions of calculus I-III, linear algebra, and differential equations. I want to continue learning math the "real" way. Is this background enough to start learning real analysis, or should I relearn calculus the real way with e.g. Spivak?

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Can someone explain whats wrong with my red answer? I emailed my prof and he said its wrong but I can't see whats wrong with it, specifically he said your proposed solution is wrong, why does y have to be all 0's?

I don't see how its wrong.
We have p 0's, p 1's and p 2's
xyz would look like 0000,...,0 1111,...,1 2222,...,2

such that each section for the 0's 1's and 2's are p long.

since |xy| <= p is a rule, it must be the case that y is all zeros, it cant consist of 1's or 2's because that would make |xy| > p........

I understand the solutions in the book but I don't know why my answer is wrong.

And bonus for anyone who wants to tell me why my green box is wrong...

>Sipsters book pg 97 for proposed sln

thanks..

>>8801499
an hedonist who fails to have the means to have a comfy material life

>>8801773

Real Analysis isn't really "real" Mathematics- this is a misconception from people who didn't go to Grammar school and think quantifiers are esoteric. It is simply Calculus from the perspective of Set Theory which is really just Predicate Logic in disguise. This shouldn't be foreign or impressive to you. If you are consistently getting the correct answer without cheating or mindlessly imitating someone else's problem solving technique, then you are already using Logic. Learning Predicate Logic formally just makes your reasoning explicit by means of a standard notation. Ideally, you should not think of learning Predicate Logic as learning a new way of reasoning, you should think of learning Predicate Logic as new notation for the reasoning you were already using. Since Grammar and Logic are, unfortunately, not taught in public schools, the notation and sometimes even the concepts are mystical to students who are not classically educated, so when they encounter a subject that makes use of the concepts of Predicate Logic and its modern offspring Set Theory, they are intimidated- don't be. You're applying logic to Calculus, that's all.

If you aren't comfortable with Logic, a good exercise to warm up, before you immediately rush to a book on Logic is to do the following: find a textbook on a subject in which you know none of the terminology, and then try to answer questions at the end of each chapter without looking up the definitions. Once you've managed to answer all the questions, good job! Now apply the same thinking to Calculus and you'll be ready for Real Analysis!

>>8801773
>Is this background enough to start learning real analysis, or should I relearn calculus the real way with e.g. Spivak?
"calculus the real way" is just a shitty version of real analysis as far as pure math is concerned. If you have any experience at all with abstraction (and it seems like you do) just start reading analysis.

>>8802129
what the fuck

>>8802139
>what the fuck

Did something I say upset you?

Between "Probability: An Introduction with Statistical Applications" by Kinney and "Statistics for Engineers and Scientists" by Navidi, which is better? Also is the first a lot more basic than the second, because from what I can tell they both cover many of the same things? Thanks.

fuck outta here with this cunt

Is grad school impossible if I have a C average? Non-math classes really tanked my GPA because I'm an idiot.

>>8802033
please respond to this, very curious.

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Im supposed to find Carbons with Chirality from these. Did i do good or did i fuck up?

>>8802503
you did it right, if it is bonded to 4 different things it is a chiral center

>>8802129
>8802129
that's really cool, thank you (not who you were replying to though)

what is 9+11?????????????????????

>>8802506
thank you for checking my answer.

i was thinking on the top one ( lactic acid, if im not wrong) the H3C might also be one but hydrogens are all the same.

>>8802516
np and remember it doesn't matter if the first bond is the same if it's a different chain. Hope that makes sense

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I can't find the bounds for this question.

I'm pretty sure [math]x\in[0,5][/math] but I think I'm getting the other ones wrong.

So if x goes from 0 to 5, then y should go from -1 to 1 right?
[math]y\in[-1,1][/math]

And then z is dependent on the y so it would be
[math]z\in[-1,1-y][/math] wouldn't it? Can anyone tell me what I am doing wrong?

Thanks

>>8802549
Unless it's

[math]x\in[0,5] y\in[-1, sqrt(\frac{x}{5})], z\in[-1, sqrt(\frac{x-5y^2}{5})][/math]? I'll give it a go

>gravity is a "deformation in a field"
>except when it's a wave
>or (possibly) a particle
Modern physics is AIDS.

I am trying to work out how to get to an exact distance with folded paper. Basically that folding paper 42 times will reach the moon meme except I do not want to overshoot it. So instead I want to work out how many piles of paper folded how many times I would need to reach exactly 385,000km, using 0.1mm paper.
I have already used
[math]x=LOG((3.85*10^5)/(1*10^-7))/(LOG(2))[/math]
to find that exactly 41.808 folds would be right.
I then did
[math]x=LOG(((3.85*10^5)-((1*10^-7)*2^41)/(1*10^-7))/(LOG(2))[/math]
To find how many folds would be needed for the next stack, but doing this results in a loop.
Is there some way to change the equation to work better?

Sorry for being dumb

>>8802767
Why would it result in a loop? There's no [math]x[/math] in the right-hand side.

>>8799800
>>8799810
{1,2} is not a subset of B and {{1,2}} is though

>>8794991
A solid background in basic algebra and logic. Once you can wrap your head around the formal logic definition of a limit, then the rest of calc 1 should be relatively easy. It's probably going to be a bit more proof-based than many of your earlier classes.

Calc 2 is much harder, comparatively speaking.

>>8802787
It turns into
[math]x=LOG(((3.85∗10^5)−((1∗10^−7)∗2^{41})−((1∗10^−7)∗2^{41}))/(1∗10^−7))/(LOG(2))[/math]
And repeats similarly.

>>8802794
Shit, that second [math]2^{41}[/math] was supposed to be a [math]2^{40}[/math]

>>8797075
AFAIK, yes, but the "odds" of that happening are way way less than one per lifetime of the universe for the size of the observable universe. In other words, it's so exceptionally rare that it's almost certainly never happened in the current lifetime of the universe - not once across the whole observable universe. It's so incredibly unlikely that it's basically impossible.

>>8798497
Fun factoid: To achieve orbit, only about 10% IIRC of the energy is used to get that high. If you just get that high, to low orbit, then you just fall back down again. Shit sucks. After getting that high, you need to spend rest of the fuel, the 90%, to move really fast laterally, in order to get into orbit.

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>>8802797
BRB teleporting to the future.

>>8800752
I see, thank you.

Should space exploration be our main goal as humans?

>>8797075
No. Particles can't just move anywhere they want, they can only move to a lower energy state. Teleporting to the moon would definitely not be a lower energy state

>>8802856
There is no law that prevents entropy reversing on principle, it's just very unlikely, since there are more ways to reach a disorganized (i.e. low-energy) state than an organized state.

>>8798116
>rumor mill
never heard of something like that. i even googled that and nothing of value came up. are you referring to the huuuuuge gossip mongers most phd students are? because that's what they are. a fucking chatter-box.

>>8802800
so you are basically saying the squirrel fell back down to earth?

any hope of cybernetics/cryonics becoming mature enough to prolong life in our lifetime?

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>>8794772
Medfag needed
Is is possible that I have sleep apnea because i snore like a motherfucker and wake with a sore throat every time (meaning I mouthbreathe)? I don't wake up in the night at all or don't have noticeable midday fatigue and headaches and can go with 5h of sleep. I also have chronic sinusitis. Should I worry about it at all or is it cyberchondria?
pic related, the memebenchmark tests done from 20s to 4 min after waking up.

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Is there a way to efficiently compute the average distance between all pairs of nodes in a graph?

So I'm doing a project in statics where we have to find the forces on a fold up chair. The last part is to find the critical load failure of said chair.
I know that shear and bending moment can cause the chair to break, but when I went to my professor he said that the screws holding the chair together are more likely to break. I don't understand what he means by this or how the forces act on the screw before it breaks.

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What the hell is this symbol for the Molar Mass called? Is this some form of Mu or is it just some custom typeset they use to differentiate it?

>>8803183
it's called M.
like in m.
it's only written in italic so it's not confusing.

I have this recurrence.
[eqn]A_{n+3}=3A_{n+2}-7A_{n+1}+5A_{n}[/eqn]

It's characteristic polynomial is
[eqn]x^3+3x^2+7x-5=0[/eqn]

and the roots are
[math]
\lambda_1=1
\\
\lambda_2=1+2i
\\
\lambda_3=1-2i
\\
[/math]

I need to get the recurrence equation, but I have no idea how to do that.

>>8803243
I figured it might just be that simple. Maybe it was to look unique compared to the 100s of "M"s used as variables in chemistry

>>8803263
>recurrence equation,
like this
https://en.wikipedia.org/wiki/Recurrence_relation#Solving

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>>8800888
>no answer yet

>>8803409
>>8800888
>Echoes from surface targets appear in almost all radar reflectivity images. In the immediate area of the radar, "ground clutter" generally appears within a radius of 20 nm.

"nm" meaning nautical miles


>Source: http://www.srh.noaa.gov/jetstream/doppler/radarfaq.html#projection

>Entropy is increasing
>Net energy sum of the universe is zero

Help me /sci

I have an equation for n-th term of a sequence. I need to find the reccurence relation for the sequence. How should I proceed?

The n-th member equation is [eqn]A_n=3^n+2(2^n)[/eqn]

how to prove that the lebesgue integral can be computed as the antiderivative without going through the riemann integral ?

>>8803508

look for properties satisfying XOR in your property table

is the square root (or any root) of 0 defined?

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Are mathematics worth learning even if you are not going to work in anything related?
Do maths require creativity?

>>8803688
>Do maths require creativity?
Tremendously so. All sciences do.

>>8802033
Bump

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>>8794772
hello cunts. brainlet here, does anyone know how to solve this?
Pls show working out

>>8803732
Are you serious?
There's only one number that's larger than 2.7

>>8803732
Just guessing but it's probably (B)

>>8803763
hey. the answer is actually C but i just dont know how to work it out

>>8803688

maths requires the most creativity of any subject. the reason people think it does not is simply sour grapes. people think less rules make them more creative, when it is the converse that is true.

>>8803732
idk, what if you calculate how much kg are in 1 cm and then substract 3200kg from 4000kg and then calculate how many centimeters you need to reach the result of 4000-3200kg

>>8803763
>Doesn't know what he's doing
>Condescending to others
Woah, nelly

>>8803797
i tried something similar. i tried finding the ratio of height to weight and using it to find height for an 800 kg being, but it doesnt work

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Can someone help me with these 2? Any help on the first one would be especially appreciated

Where does sci find their textbooks?

>>8803860
calculate the residues

>>8803878
google lib gen

>>8794991
Functions, rules of exponents, inequalities, logarithms, trig identities. Try to watch a YouTube video on derivatives, throw in integration while you're at it.

>>8795013
Just understand what instantaneous rate of change means and learn to take the area defined by a curve. Easy peasy japaneasy.

>>8803884

what does calculate the residues even mean? can you please be more specific? I'd really appreciate some help

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Why are real smartfags, especially in hard subjects, not usually excellent in timed essays? In high school and college I noticed that the best scorers in these were consistently just above-average women.

>>8803732
>>8803810
fucking hell it took me a while, but model it as a cube. the large elephant has the same density as the small elephant so [math]\rho=m/h^3=m'/(h')^3[/math] rearranging you get [math]h'=\sqrt[3]{m'/(m/h^3)}[/math] which is 1.7008 substituting the values for their heights and masses

>>8803957
This is wrong. Being good at timed essays is absolutely an indicator of intelligence. My experience is that this is actually a good test of who is really intelligent vs. those who get by in classes with tremendous amounts of memorization

>>8803997
Fact.

>>8802549
Change it to cylindrical coordinates.

Do Americans clap after lectures in uni?

>>8804022
Kek

>>8803997
How? The majority of "good" academic timed essays I've found online aren't particularly insightful; they're just written and organized into the right frame. You'll notice that above a certain point practically all the essays with the same prompt have the same substance.

>>8804040
BTW I'm not talking about essays with prompts that relate directly to the subject of a class but the general and random prompts you'd see in English courses with no previous referencing of past material.

>>8803977
hello what is rhow???

>>8804114
nvm i get it now. thanks a lot

Are averages used as a part of any non-probability formulas?

Was any area of mathematics disconnected from geometry for a significant period of time, then a connection to geometry was made?

>>8803977
>>8803977
>>8804122
hello where did the h^3 come from?

>>8804127
wait nvm its volume. thanks a lot

>>8804125
>Are averages used in any non-stats formulas?
the centre of mass of an object is basically just the average of its distribution, as it is exactly the same as the expectation of a probability distribution.
>Was any area of mathematics disconnected from geometry for a significant period of time, then a connection to geometry was made?
Linear algebra and matrices perhaps? they were originally made to solve systems of linear simultaneous equations but gained a "geometric" representation as linear transformations of the plane

>>8804218
Linear algebra didn't emerge from geometry? That's literally the only useful aspect of it.

>>8802033
Regarding your green box: you have an error in the transformation: [math]a^{2^{n}} \neq a^{2n} = a^{n}a^{n}[/math]

[math]A_3 = \{ a, aa, aaaa, aaaaaaaa, .. \} \neq \{ a, aa, aaaa, aaaaaa, .. \} [/math]

>>8804250
I'm pretty sure it came from trying to solve linear equations, at least matrices anyway. Don't know about vectors.

how can i prove that a taylor series for a function about a point converges to that function? What critera have to be met?

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How does he figure out what to multiply by for a common denominator here?

Normally the formula for adding rational numbers is m/n + r/s = ms + rn/ns, but it doesn't seem to work in this equation.

Why every time I'm about to post on /sqt/ do I find the solution on my own after I've written all the fucking latex?

>>8804348
note that [math]n!=(n-1)!cdot n[/math] and likewise [math](m-n+1)!=(m-n)!(m-n+1)[/math]
Now compare the denominators

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>>8804250
>Linear algebra didn't emerge from geometry? That's literally the only useful aspect of it.
t. brainlet freshman

>>8803678
yes

what do you think it should be?

>>8802495
grad school for what?

>>8803106
can you give some more detail? what information do you have about the graph?

if a < b then abs(a-c) < abs(b -c)


is this true?

sorry i am stoopid

>>8795566
This is somewhat late, but for anyone interested, I thought of a nice proof of this.

Let [math]\{r_n\}[\math] be a monotone decreasing sequence of irrational numbers. The ball around 1/2 of radius [math]r_n[/math] will be both open and closed in the set of rational numbers. By the continuity of f, it follows that the preimage of this ball for any n will be open an closed. The unit interval is connected, and this preimage is non-empty, so it must be the whole interval.

Now, preimages preserve intersection, so
[math]f^{-1}(\{1/2\})=f^{-1}(\bigcap\limits_{n=1}^\infty B_{r_n}(1/2))=\bigcap\limits_{n=1}^\infty f(B_{r_n})= [0,1][/math]

>>8804436
a=0, b=1, c=1

>>8804436
no its not true

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>>8804442
>not just setting b=c

>>8802495
You're fighting an uphill battle, but maybe. I don't understand how electives alone could have dragged down your average that much; if you're expecting to go to grad school you should be pulling straight As in every single major-related course you take.

GPA is not the only thing considered when you apply and if you have very good references or some research experience that might help balance, but a GPA that low is going to get you automatically binned in a lot of departments.

>>8804438
Messed up the tex and can't seem to delete the post. The first paragraph should read as

Let [math]\{r_n\}[/math]be a monotone decreasing sequence of irrational numbers that converge to 0. The ball around 1/2 of radius [math]r_n[/math] will be both open and closed in the set of rational numbers. By the continuity of f, it follows that the preimage of this ball for any n will be open and closed. The unit interval is connected, and this preimage is non-empty, so it must be the whole interval.

>>8804443
>>8804442
>>8804444

thanks brahs
and thank you for not calling me brainlet :^)

>>8804332
You need to check two things.

>The taylor series converges
>the limit of the remainder term is zero as n goes to infinity

Why black people don't have down syndrome?

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If you have a circuit like pic related without the resistor, why would it "short circuit"? Is it because each side of the 120V battery can only hold that much electric potential?

Also, why don't batteries steadily lose voltage as more electrons move to the positive side, deceasing the difference in charge? Shouldn't that decrease the electric potential across the wire?

I am determined to go back to college and complete a BS in math. I have to take trig before I can take calc to continue the program since I already passed precalc, and I haven't taken any schooling since 2014. Looked up some trig problems and had no idea what the fuck I was reading. So as to not get assfucked by classes, I started doing khan academy at work and am working my way back up to trig. Is this a good strategy? Classes start may 8th. Legit started from the top on Khan at Early Math.

>>8804518
Khan academy is a good strategy if you need to learn basic math but you're going to be very behind if you're starting college-level classes in a month.

>>8804453
brainlet

>>8804525
I mean I've taken college level classes before but I just need a good refresher

I know it is an stupid question but what's the difference between arithmetic and algebra? I'm reviewing fundamental operations and its properties in an arithmetic book and all the theorems, demonstrations and proofs are made in the [math]\mathbb{N}[/math] universe. Can I use the same properties in algebra? All I have to do is work in the [math]\mathbb{R}[/math] universe?

>>8797783
Lol u sure m8? I'd double check

What is the norm like in a ring like [math]\mathbb{Z}\left[\frac{1+\sqrt{-7}}{2}\right][/math]?

>>8804653
do you know it has a norm?

>>8804676
well that ring is specifically the ring of integers [math]\mathcal{O}_{-7}=\mathcal{O}_{\mathbb{Q}(\sqrt{-7})}[/math] So I assume it does

>>8804683
>So I assume it does
you probably shouldn't, because not all rings of integers do (O_{-19} isnt euclidean)

the last part of http://mathforum.org/library/drmath/view/62284.html might help though

>>8804676
All rings of integers in number fields have norms. Just multiply the Galois conjugates (at least, this is what number theorists mean by norms and the object he asked about is one number theorists care about).

>>8797992
Wouldn't you use log_2?

>>8797755
Choose in this order: which excites you more, which is in greater demand, which has the most foundational problems you can determine (and aspire to address)

>>8804022
How else would you know that class was over?

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Hello. Why does H+ ions move into the Intermembrane Space when electrons are shuttled across the electron transport chain?

Is it some electric/magnetic field mechanism bullshit?

>>8804494
Without the resistor, the current that flows gets pretty much insanely high, and the thing just overheats.

I'm somewhat certain batteries do lose charge over time, but it's relatively slow so it's negligable when designing a circuit.

>>8794772

Should we not allow multiple negations? Should negation only be allowed to be used once? I was drawing points and labeling them by negation when I realized that with two points, labeling the negations is easy because if you have one point with an odd number of negations, then the other point must have an even number, but even with 3 points, it became too complicated for me to label the points and I didn't want to bother finding a formula. It seemed much easier simply restricting negation one use otherwise you can get really complicated labels which are true.