/sqt/ - Stupid Question Thread: Spec Z[x] Edition

It was very satisfying to realize what Grothendieck meant when he described Spec Z[x] as a magic fan holding together the affine lines over all fields.

>>8812654
Woops sorry buddy, didn't see you had answered. So the thing is that a squarefree number is entirely determined by its set of prime factors (given the number, you take its list of prime factors and conversely, given a finite amount of distinct prime numbers, you get a uniquely determined squarefree number by multiplying them and these are inverse operations).
Through this correspondence, the set of squarefree divisors of n with prime factors among the p_i with i <= j corresponds to the set of subsets of {p_1,...,p_j}, which is how I got [math]\sum_{d^2| n, d \text{ squarefree}} \mu(d) = \sum_{S \subset [\![1,j]\!]} \mu(\prod_{i \in S} p_i)[/math]
The equality [math]\sum_{d^2| n, d \text{ squarefree}} \mu(d) = \sum_{S \subset [\![1,j]\!]} (-1)^{|S|}[/math] then follows from the definition of the Mobius function.
After that, it's all formal: we group the subsets by cardinality (which is formally what you meant by grouping the divisors by their number of prime factors): [math]\sum_{d^2| n, d \text{ squarefree}} \mu(d) = \sum_{i = 0}^j \sum_{S \subset [\![1,j]\!], |S| = i} (-1)^i = \sum_{i=0}^j {j \choose i} (-1)^i[/math] and then we get the conclusion
Let me know if it's still not clear

When a plasma arc slices through a piece of glass, is it doing so with JUST heat, or is there some electrical shit going on too?

File: 1467519275306.gif (1MB, 320x213px) Image search: [Google]

1MB, 320x213px

I understand the thermodynamic argument for Kirchhoff's law of thermal radiation: if a surface could emit like a black body but reflect like a perfect mirror, a perpetual motion device could be constructed using a box painted black on the outside and white on the inside.

But how does an atom on the surface of a reflective object "know" not to emit thermal radiation?

Maybe that's more a problem of not really knowing how radiation works on the atomic level. How does a neutral atom emit electromagnetic waves when it accelerates, anyway? Do its electrons just "jiggle"?

>>8813108
>It was very satisfying to realize what Grothendieck meant when he described Spec Z[x] as a magic fan holding together the affine lines over all fields.
what did he mean by this?

How do I get good at kinetic theory and entropy/second law of thermodynamics?

Assume 10% of cars are blue
What is the probability that more than 20 cars out of a random sample of 150 will be blue.
The answer is apparently 0.0869, but how?

File: nomizi.jpg (108KB, 640x640px) Image search: [Google]

108KB, 640x640px

>>8813783
>The answer is apparently 0.0869

I have a simple and stupid statistics question
Let's say you have a random country, where the most common ethnicity makes up only 40% of the population
The chance of not being born of that ethnicity is 60%, so you are more likely to not be of that ethnicity than otherwise
But it's also the most common ethnicity, so it's more likely than any of the other ones
Which one of these is correct? What am I missing?

>>8813832
>The chance of not being born of that ethnicity is 60%
birth rates vary by ethnicity

>>8813783
You have three numbers; 0.1, 21, and 150. Lets label these a, b, and c, with an output x. x has to approach 1 as a approaches 1, and it also has to approach 1 as c approaches infinity. x has to approach a^c as b approaches c.

File: continuity proof2.png (18KB, 810x86px) Image search: [Google]

18KB, 810x86px

To all the analysts:
How can I express delta as a function of epsilon without including c? I can't seem to figure it out. Any hints?

>>8813839
You're right, but in an idealized model where the birth rate is uniform across ethnicities, the question would still be valid, wouldn't it?

>>8813844
they're both correct, of all the ethnicities you're most likely to be born the most common one but you're still more likely to be born outside of that ethnicity if it's not the majority

it's just that the sum of all the probabilities of minority ethnicities outweights the largest one

>>8813841
doesn't just taking epsilon=delta work?

>>8813849
I guess that does make sense, it just sounded contradictory to me. Thanks for the answer

>>8813783
I have never been to 4chan before and I am not sure if I am replying to this correctly, but regarding the 10% question of cars are blue question, the answer you posted isn't really correct. It's using the normal approximation to a binomial distribution without the continuity correction. Since it seems to have been taken out of an intro stats textbook, I hope these formulas and symbols will make sense: you would use the z-distribution, with x = 20, mu = n*p = 150*0.1 = 15, and sigma = sqrt(n*p*q) = sqrt(150*0.1*.9). Then, use technology or a standard normal table to evaluate the area to the right of 20 (by find the probability z is greater than 1.36). However, since we want the probability that MORE than 20 cars would be blue, and this is really a binomial distribution (a discrete distribution), it would be better to use the continuity correction and find the area to the right of 20.5 (use x=20.5 in the z formula). Ideally, you'd want to use technology to use cumulative binomial distribution from 21 to 150, with p = 0.1 and n = 150. If you are curious, using this "exact" method would give you approximately 0.0721.

>>8813898
http://www.wolframalpha.com/input/?i=1-+(sum+(150+choose+n)+0.1%5En+0.9%5E(150-n)+from+n%3D0+to+20)

Is there a sciency name for a stick?

>>8813852
Yeah it does, cheers for that mate

File: 1468545385545.jpg (170KB, 975x632px) Image search: [Google]

170KB, 975x632px

>>8812892

if a and b are two particles traveling in opposite direction each going the speed of light, how does the distance between them increase?


please fucking answer this it's bugged me for years and I never got a chance to ask my physics professor. My gut tells me it just increases at the speed of light but i'm not sure

>>8813458
Do its electrons just "jiggle"?

correct. kinetic energy from heat causes electrons to jump into higher energy orbitals, say an S to a P orbital. Then the electron releases that energy in the form of a photon as is jumps back down to the original orbital. The energy contained in that photon is equivalent to the difference in energy between the two electron orbitals
as to the rest of your question, what i think you're asking is; when an atom is hit by a photon how is it decided whether to reflect the photon or absorb it as kinetic energy (heat)?

fuck if I know, no idea how mirrors work on a quantum level

>>8813766
I had a hard time with entropy as well. not sure if it'll help but I can tell you what my quantum chem prof told me when I couldn't figure it out.

>People tell you that energy is what drives chemical reactions, but that fucking wrong. Entropy is what drives chemical reactions. There's more energy in a hundred gallons of room temperature sea water than there is in gasoline, but gasoline is useful because it's ordered energy. And this order can be turned into disorder (combustion) with the consequence we can drive the fuck around town

>>8814018
It increases by a rate of 2c, but that isn't a violation of relativity.

What you're probably wondering is how fast one photon appears to be moving from the perspective of the other photon. The answer is that photons don't have a perspective because they are frozen in time.

A better question is what happens when you have two photons traveling towards each other, with you in between them, and you're moving very fast in the same direction as one of them.

>>8814071
>The answer is that photons don't have a perspective because they are frozen in time.

this is hard to understand because the photons obviously still experience time (i.e. being distinct different places at different times).

Can't tell if I believe you or not yet. I'll have to think about that. Relativity is one of those things that can't be taught, it can only be learned.

>>8814083
>being distinct different places at different times
That's only from an outside perspective. A photon experiences its entire lifetime in an instant. This is because moving at relativistic speed slows down your clock, which makes everything around you appear to move faster. Moving at light speed = your clock is frozen and everything that ever happens from that perspective occurs in an instant.

Is there a concept of "realness" in mathematics?

Like prime numbers having properties that have nothing to do with their initial definition is a testimony to their "realness". The exponential function working beyond values outlined in its basic definition(natural numbers) is a testimony to its "realness". And of course, something describing reality is a testimony to its realness.

If (X, *) is a groupoid (or magma if you prefer the term), it is said to be flexible if (xy)x=x(yx) for all x and y, and power-associative if, for every x, the subgroupoid generated by {x} is associative.

Question: Is every flexible groupoid power-associative? My intuition says yes, but I can't seem to get the induction right, and the literature seems to be undecided on the matter.

>>8814135
Sounds like the concept of an extension is what you're looking for.

https://en.wikipedia.org/wiki/Extension#Mathematics

>>8813458
It is all analogies if you dont want to use QM. Buy yeah, jiggling is fair enough.
The microscopic description comes from QM, where the chance for an electron tot be excited from state 1 tot 2 is the same as decaying from 2 to 1. Ie effecient absorbers are efficiënt emmiters. This is a result of the symmetry of the process.

File: ntheory.png (62KB, 943x173px) Image search: [Google]

62KB, 943x173px

Can someone give me a hand with this proof?
[eqn] \sum_{d*e \vert n}^{} \mu(e) \lfloor \frac{x}{d*e} \rfloor = \lfloor x \rfloor [/eqn]

It is the problem in pic related. As you can see, I've slightly rewritten it to make it easier (I hope) to deal with.

The argument I try to put is as follows:
What this sum counts will be pairs of numbers (d,e) such that e is square free and d times e is a divisor of n. Then, if e is not equal to 1, and d is not equal to 1 then each pair (d,e) has an "inverse" pair that will cancel it out, leaving only the pair (1,1) which results in [math] \lfloor x \rfloor [/math]

Case 1: (d,e) where both d and e are square free, and are of opposite parity. (d has an even number of primes, while e has an odd number of primes, or vice versa).

Then the inverse of this pair is simply (e,d) because the mobius function will change sign.

Case 2: (d,e) where both are squarefree but both numbers have the same parity of primes (both have an odd number of primes or an even number of primes).

Then take any prime from e, call it p. Now divide e by p, and multiply d by p. Then the pair
[math] (dp, \frac{e}{p} ) [/math] is an inverse of the original pair.
This is because their product is still d*e but now [math] \frac{e}{p} [/math] has one less prime, which means that the mobius function will change sign.

Case 3: (d,e) where d is not square free.

First, take all the extra primes that d has (the ones that make it not-squarefree) and divide d by them, and multiply e by them. Call this new pair (x,y) which y= e * all the extra primes of d. and x = d / all the extra primes of d.

y may not be squarefree but now shift this pair into (y,x) with x being squarefree guaranteed.

Now, if x has the same parity of primes as e then take one prime from x and give it to y. This way (y,x) is an inverse.

If x has opposite parity to e then leave the pair (y.x) as it is and it will be an inverse.

My question is... is this enough? Or is this argument missing something?

File: 1462633394168.png (17KB, 300x250px) Image search: [Google]

17KB, 300x250px

[math]
\lim_{x\to 1} \frac{x^{1000} - 1}{x-1}
[/math]

>>8814415
1000

>>8814415
Here is the hint:

Do long division with x^1000 - 1 over x - 1
You don't have to do it all, just keep going until you see the pattern.

Then you will be left with a degree 999 polynomial and then you just have to evaluate it at 1.

I need to come up with some silly questions about a big pile of data from a random census. I've already got 7 but I need 3 more; the questions are for a high school IT competition's Excel part, so they should be somewhat challenging to get the correct answers to. Any tips?

>>8813783

0.1^21 * 0,9^129 + 0.1^22 * 0,9^128 + 0.1^23 * 0,9^127 +...

>>8814415
use l'hospital's rule

The inverse of a 1x1 matrix is just the inverse of the element itself, right?
Say the matrix is (10), then the inverse would be 1/10? (assuming 10 is a real number)

>>8814493
yes

File: 1488584239270.jpg (109KB, 500x582px) Image search: [Google]

109KB, 500x582px

f(x) = ax+b , x > 0
sin 2x, x ≤ 0

How do I find the values of a and b for which the function is continuous but not differentiable?

>>8814359
from flexibility, [math]x^3[/math] is well-def, and then [math]x^3x = (xx^2)x = x(x^2x) = xx^3[/math]. so you can prove left association equals right association on any string of [math]x[/math]'s. however, this says nothing about [math]x^2x^2[/math].

commutativity implies flexibility so it would suffice to display a commutative but not power-associative magma. i came up with [math](\mathbb N,{*})[/math] where [math]m*n = mn+1[/math].
[math]1*1 = 2[/math] and [math]1*2 = 3[/math] and so on, but [math]2*2=5\ne4=1*3[/math]. so [math]x=1[/math] is not power-associative in this flexible magma.

>>8814415
Literally just one application of l'Hospital's rule

>>8814505
I think as long as b=0 and a is nonzero this works

File: Untitled.png (40KB, 689x631px) Image search: [Google]

40KB, 689x631px

I need to find what the true anomaly v is given a longitude from the reference direction.
I swear to God I've tried every projection thingy I can but I can't find some way of going from
longitude -> v

>>8812892
I've heard that doing many many problems is the best way to "get gud" at new math areas
So what are some good book with tons of problems (that include solutions)
Are Schaum's considered good?
These are some of the topics I'm interested in for reference

>topology
>proofs
>real analysis
>abstract algebra
>number theory
>any other upperclass math undergraduate topics.

File: 1488414394723.jpg (91KB, 578x800px) Image search: [Google]

91KB, 578x800px

>>8814505
>>8814550
This is from the solution:
"since g(x) = ax+b
and h(x) = sin 2x are continuous functions the only place where f(x) might be discontinuous is where x = 0"

Why though? How do I prove this?

>>8814584
>number theory
d. p. parent - exercises in number theory
ram murty - problems in algebraic number theory
ram murty - problems in analytic number theory
ram murty - problems in the theory of modular forms
gouvea - p-adic numbers: an introduction

http://math.stackexchange.com/questions/185607/problem-books-in-higher-mathematics
might be useful

>>8814584
also http://www.springer.com/series/714?detailsPage=titles

File: 5102Y4WACTL.jpg (33KB, 379x475px) Image search: [Google]

33KB, 379x475px

>>8814584
>>abstract algebra
hungerford has lots of problems and solutions for odds

>>8812892
I have a question for a chemist if there is one around.
I need generalized opinion on the state of polymer advancement and manufacturing.
Are there any compounds that the regular guy should be on a lookout for or we are on the same plateau just like after 1907?

>>8814596
>>8814605
>>8814610
Thanks, I'll check them out.

>>8814659
Polymer/clay nanocomposites are pretty hot.

>>8813747
In the picture, you can see that Spec Z[x] sits over Spec Z in a natural way, and the fiber over each point is the affine line over the corresponding prime field, which in turn hold together affine lines over all extensions of that prime field.

>>8814679
That is pretty cool I will be sure to look into it.

>>8812892
I'm about to graduate with an engineering degree.

Would someone who has been an engineer for a while give me advise on what to expect?

What did you not learn in school that came up in the job, like soft skills?

Would you tell me about any hard lessons you had?

File: 1488258642989.jpg (868KB, 1920x1080px) Image search: [Google]

868KB, 1920x1080px

Can a BS physcist land many of the jobs a math BS can?

Can a pure math BS land the same jobs as a statistics BS can?

I'm looking for the best middle ground between employability at the BS level, while keeping grad school options open for Pure Math or Machine Learning.

Was defining e the first problem that was solved used limits?

What causes you to feel hungry or full? Is it calories, nutrition, weight of food, or something else

I'm trying to do a Calc3 assignment dealing with 1D line densities.
But I'm confused, the grid we've been provided has the coordinates on each box rather than each line, like an excel spreadsheet rather than a cartesian graph.
I'm meant to approximate the arc length between a variety of points, but a lot of these points, if I'm reading this graph correctly, share X/Y coordinates despite clearly having a change in those coordinates.

For example, p0 and p1 clearly have an upward curve, but their coordinates based on this system are (3,3) and (1,3)? Meaning the approximated length is "2"? Am I reading this right or am I missing something?

>>8814947
No,its something called Leptine.
Google the rest.

>>8814917
bernard bolzano was the first to use limits
he used them to solve problems about the real number line

>>8814722
http://4chan-science.wikia.com/wiki/Universal_Material#Professionalism_and_Career_Development

>>8814968
thanks senpai

If there are multiple values that work for x, can x be said to be a set containing those values?

>>8815069
The set S of solutions to an equation is the set of all the numbers x that satisfy the equation if that's what you're asking for.

>>8815106
I was wondering what is x as an entity when you lift it from the equation and perform other operations on it. But what I now think the answer is that the entity is what you get(another equation) when you isolate x on the other side of the =.

File: IMG_20170409_142030.jpg (179KB, 1392x594px) Image search: [Google]

179KB, 1392x594px

>>8814963
What the fuck does this mean

>>8814415
Don't listen to all the idiots >>8814419, >>8814460, >>8814544. You should notice immediately yourself that [eqn]\frac{x^{1000}-1}{x-1}=1+x+x^2+x^3+\cdots+x^{999}[/eqn] Hence the answer is obviously 1000.

Looking to pursue a career in forensics which most likely means a BS in chemistry to start with.
Is it really complicated material or is it more a matter of just putting in the time to study? I'm not dumb but not a genius either and I haven't taken a chemistry course since high school

>>8815235
Are you actually retarded?

To get what you did, you have to do the long division I described. The difference between your statement and my statement is that while you just pulled an answer out of your ass, I explained HOW to reach that answer.

>inb4 he probably already know how to get there
If he knew then he wouldn't be asking.

>>8815241
>Doesn't recognize geometric series

brainlet

>>8815241
Are you actually retarded? To get what I did you multiply both sides by (x-1) and you're immediately done. Or more practically speaking, if you're learning about limits then you're BOUND to have seen the formula for geometric series before and one of the biggest "applied" lessons in mathematics is that you should always recognise the formula when it pops up. Don't be daft.

File: Screen Shot 2017-04-09 at 22.41.34.png (49KB, 1366x260px) Image search: [Google]

49KB, 1366x260px

Can anyone help with pic related? This has got me really stumped for a while now...

>>8815252
>>8815248

>forgetting that if the asker knew any of this he wouldn't have even asked such a simple question. It is clear that he DOESN'T know how to derive that identity and that is why he had to ask

Can someone tell me what topics/books I should read to be able to understand what is in OP's picture. I did mostly analysis and probability theory in undergrad before doing a masters in computer science. Took a class on group theory but feels really long ago.

I'm interested in solid foundations. Thanks

>>8815274
Mind letting me know where that quesion is from

Some book on linear on algebra?

Hopefully I'm not using the wrong terminology here.

How hard is it to show that a problem is NP complete? Has there ever been a case of people trying to find an efficient way to solve a certain type of problem, then somebody showed that it was NP complete, causing most people to give up?

>>8815386
It's a picture from Mumford's Red Book of Schemes. Open the book, and it will tell you what you should know heading in.

In a ring, does existence of inverses imply existence of a unity?

The functions f(x) and g(x) in the table below show Jane's and Mariah's savings respectively, in dollars, after x days. Some values are missing in the table.


x(years) 1 2 3
g(x) = 3x
Jane's savings in dollars 3 9
f(x) = 3x + 3
Mariah's savings in dollars 6 9


Which statement best describes Jane and Mariah's savings in the long run?

>>8815416
Alright. Thanks.

>>8815435
I don't know of anyone whose definition of a ring doesn't include the existence of a unit. Anyways, the notion of inverse doesn't make sense without a notion of unit.

>>8815408
I don't recall it being too hard. We did it in our second course on algorithms. Though the problems were most likely contrived, making it easy to reduce some NP-complete problem to ours.

>>8815438
Literally plug in the values and see what you get

File: rings.png (82KB, 741x657px) Image search: [Google]

82KB, 741x657px

>>8815451
Wot? My book says a ring is 1. An abelian group under addition 2. Associative over multiplication 3. Distributive over multiplication.

e.g. [math]$2\mathbb{Z}$[/math] is a ring with no unity

Is Dummit and Foote good for studying on my own? I'd like book with lots of problems and hopefully solutions to compare.

>>8815465
I don't know about your specific textbook, but nobody actually working in the field would call that a ring.

http://math.mit.edu/~poonen/papers/ring.pdf

>>8815465

>>8815475 is kinda right in the sense that no one uses rings without identities but checking my freshman year notebook, my professor back then did make the distinction between unitary rings and non-unitary rings.

But again, after that intro to algebraic structures, all the rings I've been made to work with have had a unity. It is kinda pointless to study rings without identities because of the most fundamental questions you can ask about a ring is which elements have inverses.

Tackling your original question in >>8815435, there are no inverses without a unit so yeah.

>>8815435
You cannot have (a)(a^-1) = 1 if 1 is not in the ring.

>>8815451
Nobody's _definition_ of a ring should include unit. That's very bad form; there's nothing in the ring axioms that requires a unit, and there are many natural (enough) rings that don't have one.

But there are many situations where the case without unit is either not relevant or not interesting so a lot of places will begin with "we assume all rings in this book/paper/whatever have 1" which is fine.

>>8814415
It's the derivative of [math]x \mapsto x^1000[/math] at 1, ie. 1000. What do they teach you in school ?

>>8815487
Your second point makes me wonder whether we gain anything of interest in knowing a theorem holds on a rng (which likely implies it holds on a ring)

So the equation
[math] z^{n} = 1, \, n \in \mathbb{Z} [/math]
has [math]n[/math] roots. So is it valid/possible to define a unit circle as the roots of [eqn] \lim_{n\to\infty} z^{n} = 1\, \,?[/eqn]
and if not, why not?

>>8815548
kind of. I think what you're getting at is the set of all roots of unity, [math] \{z: z^n=1\text{ for some } n\in N\}[/math]. this doesn't include every point on the unit circle, since for example if you choose any irrational number r, then no integer power of [math] e^{2\pi i r}[/math] will be equal to 1.

>>8815548
Hmm
Solutions are of the form exp(2pi(k/n)). Feels like there are some values we can't reach for any values for k and n. If we substitute irrational instead of k/n

>>8815566
Forgot the i >__<

>>8815566
>>8815570
Noob tex test
[math]\exp\left(2\pi i\frac{k}{n}\right)[/math]

>>8815566
With this change if pi is proven normal?

>>8815561
>>8815566
fair enough, irrationals seem like a good counter example

I'm about to graduate but have difficulties solving putnam problems. Am I a brainlet?

Is
[math]
\sum_{k=1}^{\infty} k - \sum_{k=10}^{\infty} = 1+2+3+4+5+6+7+8+9 = 45
[/math]
correct? Can you just pull out those terms and subtract the other two summations?

>>8815626
Second summation is supposed to be
[math]
\sum_{k=10}^{\infty} k
[/math]

>>8815590
no

>>8815640
Oh dear god what was I thinking

>>8815626
essentially yes, but you have to be careful with your notation. the problem is that the sum [math] \sum_{k=1}^{\infty} k [/math] is not a well-defined real number, so you can't manipulate it as if it were. what is correct is saying

[math]\lim_{n\to\infty}\sum_{k=1}^{n} k-\sum_{k=10}^n k=45 [/math]

Ring question guy here

What are the zero divisors of the ring of 2 x 2 matrices? (an nonzero element a is a zero divisor if there exists a nonzero element b in the ring where ab = 0)

>>8815705
think about what it means for a 2x2 matrix to be invertible, or not invertible

see if you can link this back to your question

>>8815705
>>8815740
To clarify, since we don't have commutativity what do we mean by zero divisor. Do we need ab=ba=0?

>>8815751
Non-commutative rings can have one-sided zero divisors.

File: 7c1928b8f3f4f99c36521d72b7fb0719.png (17KB, 898x162px) Image search: [Google]

17KB, 898x162px

Having trouble with this problem, I could really use some help

>>8815782
Imagine the same problem but replace roational intertia with mass, replace torque with force and consider a linear speed.

Are limits just a way to divide by zero, divide by infinity, and raise numbers to infinite powers without getting yourself into trouble?

>>8815791
Thank you so much

>>8815815
This is an intuition, and it's hard to say it's "wrong", but I wouldn't recommend thinking about limits this way. For one thing, depending on which functions you're using, using limits to "divide by zero" or "raise numbers to infinite values" can given different answers.

A better intuition is that a limit always lets you approximate something "to arbitrary accuracy" in a "sufficient range of closeness".

If the limit of a function exists at a point, you can approximate the function to arbitrary accuracy sufficiently close to where the limit is being taken.

If the derivative of a function exists at a point, you can approximate the function's rate of change near the that point when you are sufficiently close to that point.

If the limit of a sequence exists, you can approximate the limit of the sequence with terms of the sequence, when the terms of the sequence are sufficiently large.

If the limit of a series exists, you can approximate the infinite sum of the series with finite partial sums the contain a sufficiently large number of terms.

If a set has a limit point, you can approximate the limit point with points in the set to arbitrary accuracy.

So if [math]v^{2} = v_{0}^{2} + 2a (x - x_{0})[/math] where [math]a = \frac{F}{m}[/math] really means [math]v(x)^{2}=v_{0}^{2}+2 \frac{F(x)}{m} (x - x_{0})[/math] then [eqn] \frac{1}{2} mv(x)^{2} - \frac{1}{2} mv_{0}^{2} = F(x) (x - x_{0}) [/eqn] and [eqn] \frac{d}{dx}\ ( \frac{1}{2} mv(x)^{2} - \frac{1}{2} mv_{0}^{2} = F(x) (x - x_{0})) = mv(x)dv(x) - (x - x_{0})dF(x) = F(x)dx [/eqn]. Integrating both sides [eqn] \int_{v(x_{1})}^{v(x_{2})} mv(x) dv(x) - \int_{F(x_{1})}^{F(x_{2})} (x - x_{0}) dF(x) = \int_{x_{1}}^{x_{2}} F(x) dx [/eqn] and letting [math]F(x) = \frac{dG(x)}{dx}[/math] results in [eqn] \frac{1}{2} mv(x_{2})^{2} - \frac{1}{2} mv(x_{1})^{2} = (G(x_{2}) + (x - x_{0}) \frac{dG(x_{2})}{dx}) - (G(x_{1}) + (x - x_{0}) \frac{dG(x_{1})}{dx}) [/eqn]. So what I'm wondering is if this can be solved as a system of first order linear differential equations where [eqn]G(x_{1}) + (x - x_{0}) \frac{dG(x_{1})}{dx} = \frac{1}{2} mv(x_{1})^{2}[/eqn] and [eqn]G(x_{2}) + (x - x_{0}) \frac{dG(x_{2})}{dx} = \frac{1}{2} mv(x_{2})^{2}[/eqn] or if the [math]dG(x_{i})[/math] term is treated as a constant in [math] \frac{dG(x_{i})}{dx} [/math], making these terms effectively zero.

How good are edx and coursera?
Am I better of just self studying?

>>8816114
I thought coursera machine learning course some years ago was nice. Was good for big picture and intuition that can sometimes get lost when you are following a textbook.

File: 1490665714339.gif (239KB, 500x419px) Image search: [Google]

239KB, 500x419px

>Company C is going to make open-topped boxes out of 6 x 16-inch rectanges of cardboard by cutting squares out of the corners and folding up the sides. What is the maximum volume that can be made?
V = L*w*h
We can assume L = 16 - 2h
We can assume w = 6 - 2h
So if we input these two formulas into our volume equation,
V = (16 - 2h) (6 - 2h) h
Which simplifies down to,
V = 96h - 44h^2 + 4h^3
Fast-forward taking the V' (d/dx) and setting it to 0 gives us,
h = 1.333 and 6

>...

I know the height, but why did I have to assume,
[ L = 16 - 2h ],
BUT NOT
[ L = 16 - 4h ],
to get the correct answer?

Length is getting reduced by the height in 4 places via 4 squares. This leads me to believe L = 16 - 4h.
Can someone explain?

how do i find the variance of half a gaussian distribution

>>8815388
It just appeared on a question sheet at our university...

>>8815274
Bump, any help with the above?

>>8815705
If you think about it, you'll see that any noninvertible matrix is a zero divisor (two sided)

if the moon came from earth's collision with another large body, do we know what part of the earth was hit by the body?
like is there just a big chunk of asia missing somewhere?

>>8816355
It's tedious but you can't go wrong with the brainlet way of simply showing that the (i,j)th element is 0.
I suspect that there'll be a couple of multinomial identities to help you along the way, since that looks somewhat like a negative multinomial distribution.

can someone reccomend a time series book which looks at multiple resolutions?

File: brainlet.jpg (10KB, 363x43px) Image search: [Google]

10KB, 363x43px

How do I prove this true for all positive integers? I honestly have no idea.

>>8816738
Induction is the standard method of doing shit like this.

It obviously works for integers up to 1.

Assume that it works for an integer n. Then write out the series up to (n+1)^2 and use the fact that [math]1^2+2^2+...n^2+(n+1)^2 = \frac{n(n+1)(2n+1)}{6}+(n+1)^2[/math]

File: image.jpg (2MB, 4032x3024px) Image search: [Google]

2MB, 4032x3024px

Why is the denominator (n+1)! and not (n+1)?

How did the factorial get there? This is part of the professor's answer, so I'm assuming it's correct, as when I did it without the factorial I got the wrong answer.

>>8816738
It's a special case of Faulhaber's formula, which is proved in the wikipedia.

https://en.wikipedia.org/wiki/Faulhaber's_formula

>>8816742
What is the context of this?
These don't make much sense if you just write the one line you're stuck on.

File: image.jpg (1MB, 4032x3024px) Image search: [Google]

1MB, 4032x3024px

>>8816758
Power series expansions of ODE's.

Sorry in advance for terrible penmanship.

>>8816793
The factorial shouldn't be there. Are you sure it's not a_0 over (n+1)! instead of a_n?

The solution to this is just an exponential function, and looking at the coefficients of that should tell you than you are just dividing by (n+1).

>>8816807
I rechecked the answer, it's a_1/(a+1)!, so if the numerator is specified in such a manner, then the denominator becomes a factorial in this context?

I know it's an exponential from the ODE, but getting there is causing the confusion. Wouldn't the denominator in the sum need a factorial in order for the corresponding series to be represented as an exponential function?

>>8816742
>>8816807
The problem is that the ? operation is not defined for this question.

>>8816824
>it's a_1/(a+1)!
this makes more sense

>Wouldn't the denominator in the sum need a factorial in order for the corresponding series to be represented as an exponential function?
Well, it depends.

Writing out [math]a_{n+1} = \frac{a_n}{n+1}[/math] is how you get the coefficients to zero, but that's only a recursive formula. You can also continue another step to get [math]a_{n+1} = \frac{a_{n-1}}{(n+1)(n)}[/math], and again and again until you get down to a_1. This is how the factorial arises.

>>8816846
Okay, that makes a little more sense now. Thank you!

So I'm supposed to evaluate the residue of

cotan(pi*z) / z^3

I write the cotangent as cos/sin and write their respective McLaurin series so that I get (omitting costants)

(1 - z^2 + z^4 - z^6 + ...) / (z - z^3 + z^5 - z^7 + ...)

I can rewrite the sin expansion as

z * (1 - z^2 + z^4 - z^6 + ...)

Now the cotangent becomes

1/z * (1 - z^2 + ...) * (1 + z^2 - ...)

When I take into account the 1/z^3 then I end up with an expression with only even powers, which means the residue is zero, despite the professor claiming it's - pi/3.
But if instead of 1/z^3 I put 1/z^2 I get odd powers and the residue is exactly - pi/3.

So am I right or did I mess something up?

Is there any real difference between the writing style of a formal report and a scientific paper?
Writing a formal report for my physics experiment and the requested layout looks very much like that of a paper ( i.e seen in Nature etc)

How do you prove that the two field extensions
Q(i) : Q and Q(j) : Q are (or are not) isomorphic ?
I know that the degree of these two extensions is 2 but i don't know how to conclude

>>8816478
Also any invertible matrix can't be a zerodivisor

>>8817083
Well you either have to find an (field) isomorphism between the two or find some algebraic property that is found in one and not the other.
In your case, they are not isomorphic and I think the simplest way to proceed is to note that [math]\mathbb Q(j) = \mathbb Q(\sqrt{-3})[/math] since [math](2j+1)^2 = -3 [/math] and because the two extensions have the same degree. Then, prove that [math]\mathbb Q(i)[/math] doesn't contain a square root of -3, which is clear

Pure math, Actuarial math, Econ, or some sort of Engineering? I'm two years through uni and hate CS. I go to a pretty good school.

How do I get good at solving physics problems? First exam coming up in 3 weeks, and I need to be able not just to apply a formula, but actually reason using diagrams, unit vectors, integrals, all that jazz.

>>8817171
There's a secret knowledge about how to pass exams successfuly, but for you to attain it, you will have to work very hard.
*wink* *wink* motherfucker

>>8817119
i don't understand how the fact that Q(i) does not contain sqrt(-3) would prove that the two fields are not isomorph

Let [math]\alpha=9+2\sqrt{23}, u=24+5\sqrt{23}, m\in\mathbb{Z}[/math], and let [eqn] \begin{cases}
x =\pm\frac{1}{2}(\alpha u^m+\tilde{\alpha}\tilde{u}^m)
\\ y =\pm\frac{1}{2\sqrt{23}}(\alpha u^m-\tilde{\alpha}\tilde{u}^m)
\end{cases}
[/eqn]
Note that [math]x,y\in\mathbb{Z}[/math]. Show that [math]x[/math] and [math]y[/math] cannot be squares at the same time

>>8817296
Field homomorphisms preserve polynomials. This is key point in field theory.

Can a summation with infinite indexes still be able to converge?

>>8817502
[eqn]\sum_{k=1}^\infty \sum_{i_k=1}^\infty \frac{1}{i_k^2}\delta_{1i_k}=\frac{\pi^2}{6}[/eqn]

if V is a vector space over a field F, why is scalar multiplication the mapping [math]\odot\colon\mathbb{F}\times V\to V[/math] rather than [math]\odot\colon V\times \mathbb{F}\to V[/math]? or doesnt it matter

>>8817502
[eqn]\sum\limits_{i=1}^\infty\frac{1}{2^i}=1[/eqn]

>>8817619
I'm talking like
[math]\sum\limits_{a,b,c,d...=0}^\infty \dfrac{1}{2^{abcd...}}[/math]

>>8817600
usually scalar multiplication is shown as mapping (2,V) to 2V
(2 is the scalar, V the vector)

if you wanted, you could define it as mapping (V,2) to 2V

>>8817635
You could pbly make sense of such expression by introducing some strangue measure - but I dont think it has any meaningful sense of cenvergence in the classical sense.

Can a compact Fluorescent light bulb detect leaking microwaves from a mircowave oven?

Specs on bulb:

>Luminus 13W, Compact Fluorescent Lamp
>13W
>20V/60Hz
>210Ma
>860 Lumens
>6500K

Brainlet here. The notation is going to suck as I don't have any software.
and have to do it over 4chinz. Apologies for the eye strain ahead.

Here are the first 7 terms from an infinite sequence.
Where X0 = 1250.

1250, 1236, 1218, 1196, 1170, 1140, 1106, ....

14 is first subtracted, then an extra 4 every following term.

So, the first term a = 1250 and the common difference d = -14 - 4(n-1)

How the fuck do I find the closed form for this?

I have found a recurrence system that works.

X0 = 1250, Xn = Xn-1 - 14 - 4(n-1) (n=1, 2, 3, ...)

I can't find the closed form from this, however.
It should be given by Xn = d*n + (a-d) or by Xn = a+ (n-1)*d.

Using either of those gives -2(2n^2 - 3n-630), which is wrong, but very close to the actual closed form -2(n^2 + 4n - 630).

P-p-please help g-g-guys.
L-l-love you. Full homo. Just joking, no homo.

Hello. I've recently begun learning about Gauss's Law and I have a question pertaining to it.

You should never have an electric field inside a conductor (according to gauss law). With this in mind, let's say that a spherical conductor is hollow, and you have a charge in the middle of it (positive). The inner charge of the conductor is equal in magnitude but opposite in charge (you won’t get any electric field inside of the conductor). What if the charge in the conductor exceeds the counter charge capability of the conductor?

I come here for a simple problem request. Last week in number theory I was introduced to the groups and rings formed by Z/nZ plus some results like Lagrange's Theorem.

Does anyone have any simple problems that can be solved with only this? I tried to look for this over the internet and my first idea was to look for algebraic number theory but all I find seems to be way too advanced for what I'm doing but I want to practice doing proofs using these new tools.

>>8817935
x^p=x mod p for every prime p

My mom hates her new stove because of how far her designated stew pot sits from the burner. It takes her too long to make a stew. If I buy her a nice flat grate for a grill that will fit instead, how can I be sure it is safe to cook on indoors and won't kill her? As in, it's not coated with anything that will put off dangerous fumes when heated?

>>8818023
Correct me if I am wrong.

I know that if G is a finite group (Like Z/Zp) and x is an element of that group then x to the order of the group needs to equal 1. So

[math] x^{|\mathbb{Z} / \mathbb{Z}p|} = 1 [/math]

But, I think, the order of Z/Zp is just p - 1 so

[math] x^{p-1} = 1 [/math] so [math] x^{p-1}x = x [/math] so [math] x^{p} = x [/math]

>>8818068
> the order of Z/Zp is just p - 1 so
Why?

>>8818080
Wait, I think I am wrong on that one. What I actually mean is [math]( \mathbb{Z} / \mathbb{Z}p)^*[/math] which I can use instead because I don't need addition.

And then that group contains only 1,2,3,...,p-1 so the order is p-1

>>8816069
Can someone answer this?

File: images.jpg (8KB, 245x205px) Image search: [Google]

8KB, 245x205px

>>8817751
G-g-guys please help

Say I know the covariant components of a vector in cylindrical coordinates and want to find its contravariant components. I've read pretty much everywhere that for orthogonal coordinate systems (like cylindrical coordinates?) contravariant and covariant components are the same, but wouldn't then the matrix representation of the metric tensor be the identity matrix? (which is not the case for cylindrical coordinates).

If I explicitly compute the contravariant components I get the same answer as if I just had used the metric tensor to raise an index. Why aren't both components the same if the coordinate system is orthogonal?

>>8818237
[math] a_n = 1250 -14(n-1) - \frac{4(n-2)(n-1)}{2}[/math]

Sure, you could divide the 4 by the 2 but I am letting it that way so that you can puzzle over which identity I am using.

where do i get a textbook if i cant find it on libgen

or should i just cough up the $80 and wait for a hard copy

>>8818313

amazon, ebay, etc

>>8818313
I had some luck on sci-hub.cc with books from World Scientific. If this fails I'd just look for a cheap used copy on bookfinder.com

So in equations, you can just stick things next to each other if you want to multiply them, but when should you use the multiplication sign instead?

So here's the thing, I did an exam last friday on combinatronics.

There was this question along the lines of:
Suppose an equation x_1+ x_2+ x_3+ x_4+ x_5+ x_6=29, where x_1>=1, x_2>=2, x_3>=3, x_4>=4, x_5>=5, x_6>=6
How many possible solutions does this equation have?

In all honesty I didn't even know how to start it and just got as far as assuming we had a minimum sum of 21 under the restrictions, so it was a matter of partitioning the necessary 8 among six possible x_n.
I don't know if this is even close to being right but it's all my dumbass could do, as I was running outta time anyway.
Can someone shed some light on this?

>>8818394
well 1+2+3+4+5+6=21=29-8

so the problem boils down to how many ways can you put 8 identical "balls" into 6 "boxes"

>>8818419
edit: sorry i just saw you wrote that in your original post

to count this, imagine the 8 balls as stars *. we can put lines between the stars like this:

*|**|*|***||*

this corresponds to putting 1 ball in the first box, 2 in the second, and so on

there are 8+5=13 total positions, and each configuration corresponds to choosing 5 of these as the positions of the lines

>>8818394
forgot to quote
>>8818429

>>8818419
>>8818429
Yeah, that was pretty much my train of thought.
The thing is we had predetermined answers we could choose for each question, like questions in a column and the answers on another column. Can't really recall how it's called in burgertongue but you can picture what I'm talking about.
Anyway, none of the answers I had left at that point were below like 873 I think. The other three I had were higher, and even then every single answer, used or not, didn't go below the hundreds.
If the answer isn't more than that, then it was possibly a fuckup on the teach's part.

>>8818464
the answer is 13 choose 5=1287

>>8818471
Fuck my laifu.
I remember that answer being part of the ones I had left. I chose the 800 one on a whim just because I didn't have time to get to a solid result in the end.
I still would've had to demonstrate my work with the procedure, but you know, maybe pity points woulda been possible.

I tried just about every formula in a panic with the time running out except for actually using stars and stripes first.

Cheers anon, at least I got that over with instead of leaving it bothering me without knowing.

Why isn't writing things vertically to reduce the usage of parentheses more common? Why is division the only operation that is commonly written vertically?

>>8818464
>we had predetermined answers
I absolutely hated this shit when I was taking classes. Now makes grading easier. I'm part of the problem now.

>>8818501
Do you have an example?

That aside, vertical space seems much more valuable in English. So much so that I often see vectors written horizontally and the rest of the discussion has to deal with transposes.

why do we feel like peeing and pooping when we are scared? Imagine if we get attacked by someone and try to run, but keep leaking down there, it would probably make it harder to run away

What makes computer hardware so error free?

Any medfags here? Can drinking on an empty stomach really increase the chance of peptic ulcers?

>>8817935
Prove that any group of prime order p is cyclic (ie. isomorphic to Z/pZ).

Proce that a group G of order n is cyclic if and only if, for each divisor d of n, G has at most one subgroup of order d. (If you know what a field is :) Deduce that, given a field F, any finite subgroup of F* is cyclic.

Let g and h be two elements of a group G such that gh = hg. Assume g has order m and h has order n. What is the order of gh ? Deduce that a finite abelian group G has an element of order [math]\text{lcm}(\{order(g), g \in G\})[/math]. (Hint: use induction).
(requires more imagination:) Prove that, in general, the product of two elements of finite order may not have finite order.

What are the automorphisms of the group [math](\mathbb Z/n \mathbb Z, +)[/math] ?

How many group homomorphisms are there from [math]\mathbb Z/m\mathbb Z[/math] to [math]\mathbb Z/n\mathbb Z[/math] ?

I've been reading about the classification of simple finite groups and am wondering if there has been any similar effort to classify all objects of a certain type.

>>8812892
why don't soldiers just fight with lazer guns and plasma rifles? wouldn't it be cheaper than bullets?

>>8818812
https://en.wikipedia.org/wiki/Classification_theorem

>>8812892
Hello /wsr/ failed me so im here crawling to you masterminds.. i need some help with a physics question...

What is the maximum possible power output (i.e, at 100% efficiency) when 50x10^3 kgs-1 of water falls 50 m and then through a turbine at a hydroelectric dam (in MW)?

Can someone show me how they can calculate this????

File: penguin heat loss question.png (33KB, 792x210px) Image search: [Google]

33KB, 792x210px

Hello does anyone know how to solve this?? i got up to calculating heat transfer coefficient for the whole system but dont know where to go from there.

File: CDF.jpg (9KB, 426x79px) Image search: [Google]

9KB, 426x79px

Can this function be the joint CDF of X and Y?
I see no reason why it shouldn't be

>>8818842
>I see no reason why it shouldn't be
then it must be

>>8818847
But how is it explained
The only thing that comes to my mind is that max value is 1, minimum is 0
What should I look at

>>8818853
>What should I look at
the definition of a joint CDF

>>8818855
Shit this looks stupid but it was actually helpful
My book didn't include anything like that, but it was easily found on the internet
Thanks, kek

File: eq.png (20KB, 815x328px) Image search: [Google]

20KB, 815x328px

Which expression is the given expression equivalent to?

Якщo = if

>>8818944
>what have you tried so far

>>8818947
I have literally no idea what to do, nothing seems to fit.

>>8816069
I think you have many mistakes much higher. When you first take derivatives you should keep terms like [math]\frac{dv(x)}{dx}[/math] and [math]\frac{dF(x)}{dx}[/math]. If you are taking the derivative you should get [math]m v(x) \frac{dv(x)}{dx} = \frac{dF(x)}{dx} (x-x_0) - F(x) [/math]

>>8818958
all the possible answers are there already... just plug in simple values of alpha and see which match

>>8818969
I see what you are doing but you must be careful with your steps before getting to the end of the line with all the differentials. The short answer is I don't think the final is true because it isn't based on correct prior steps

File: miller-rabin.png (17KB, 634x84px) Image search: [Google]

17KB, 634x84px

Any number theorists here that could give me a hand with this?

>>8818978
>not giving any context or explanation of what the notation d even means
you guys really need to learn how to ask questions

Would it be possible to build a space telescope that was large and sensitive enough to directly observe solar planets, and if so how big would it have to be?

File: fast-exponentiation-algorithm.png (13KB, 412x111px) Image search: [Google]

13KB, 412x111px

>>8818982
>>8818978
My mistake.
The question is referring to 'd' as used in the fast exponentiation algorithm shown in pic

File: problemo.png (86KB, 1628x362px) Image search: [Google]

86KB, 1628x362px

>>8812892
Could someone give me some guidance with pic related? It is from Apostol's Analytic Number Theory book.

I have several questions:

1) Where even is the mobius function there? I don't even see the mobius function so why is that a variation of the mobius inversion formula?

2) How do I even tackle this? The book I am using proved the usual mobius inversion formula after defining dirichlet multplication and then using it. But now I am left completely dumbfounded because I can't use that same approach because I don't have a divisor sum, I have a divisor product. I need help with understanding this.

>>8818944
[math] \cos 2a = 2cos(a)^2 - 1 [/math]

>>8819029
>1) Where even is the mobius function there? I don't even see the mobius function so why is that a variation of the mobius inversion formula?
i'm just guessing but it might be a slight generalization, i.e. taking a(n) to be the mobius function works but so does any other function that satisfies those conditions

>>8819046
also because the dirichlet inverse of mobius is the identity, so b(n/d) disappears on the expression for f(n), which makes it looks like the classical mobius inversion where mobius is in one expression but no arithmetic functon in the other

>>8819051
You are right. Okay. Now how do I prove this?

What I kinda realized is that because exponents to multiplication is kinda like multiplication to addition, what I have here is dirichlet multiplication.

The left hand side looks a lot like g = f*a, if only the product was a sum, and f^a was f*a

And then I could do g*b = f*a*b
and because b is the inverse of a, f=g*b

But I am guessing. Is this true? How could I formalize this? I assume that if I want to go this route, I would have to prove that this product thing is equivalent to dirichlet multiplication and I am not sure about how to do that.

Plus, I'd prefer to do it another way because now I would be using things not taught in the book which is like cheating.

>>8819035
Why the fuck is this not on wikipedia? Fucking retarded bullshit. Can't even find the full table for angles that are divided by 30.

WELL AT LEAST THEY GOT 100000000000 TAYLOR'S BULLSHIT APPROXIMATIONS FFS

idk if this gets you far enough for a solution but as a hint, there's an operation that turns products into sums

>>8819064
learn to read brainlet
https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Double-angle.2C_triple-angle.2C_and_half-angle_formulae

>>8819065
>idk if this gets you far enough for a solution but as a hint, there's an operation that turns products into sums
meant for
>>8819060

>>8819067
Wait. You absolute madman. Are you telling me to take the log of the entire thing to get a divisor sum?

Fuck I should have thought of that. Will report back with progress and my fields medal

>>8819072
>Are you telling me to take the log of the entire thing to get a divisor sum?
yep, and that's why the conditions f(n)>1 and a(1)!=0 are there

File: image.jpg (2MB, 2448x2448px) Image search: [Google]

2MB, 2448x2448px

>>8819075
Ah. When it goes this smoothly it feels good.

It's funny how the log function disappears after the calc sequence but then it comes right back. This is actually the first exercise in the entire book that needs the log function like this.

File: 51HFpcDYCIL._AC_US160_[1].jpg (5KB, 160x160px) Image search: [Google]

5KB, 160x160px

What's the densest material that I can buy in the form of a sphere that isn't harmful to be held by a human (can't be radioactive or like how lead leads to lead poisoning, that sorta thing) and it isn't a ridiculously expensive precious metal like gold or platinum?

I just really want to own some small object that I can hold in the palm of my hand that feels really damn heavy, really for the novelty of such an experience.

File: Unbenannt.png (29KB, 847x679px) Image search: [Google]

29KB, 847x679px

how do they (the answer) get from 14*1/3 to 43/3

>>8819118
probably typo

>>8819118
>>8819119
has to do something with mixed number and exact form
but how the fuck can i calculate this we are only alowed to use casio-fx87De
and the casio multiplies the number before the fraction with the fraction

I want do drop CS and study sociology in university while studying computers and math by myself. Will i regret if i do that? Is it possible to learn stem independently?

>>8819132
>study sociology
Are you retarded?
How do you plan to get a job?

how do i find the x intercepts of f(x)=x^3-12x+2? i know you set f(x) to 0 and solve but i'm not sure what steps to take to factor it or if i should use quadratic formula

>>8819157
Use the cubic formula.

>>8819157
obviously not the quadratic formula since it's not a quadratic

the rational root test (https://en.wikipedia.org/wiki/Rational_root_theorem) tells you none of the roots are rational either, are you sure you wrote it down properly?

File: Capture.png (35KB, 462x252px) Image search: [Google]

35KB, 462x252px

>>8819167
yes, the teacher said to find the x and y intercepts for the functions on all the homework problems since we will have to do it on the test, but i'm not sure how to do it on some of these. hopefully he just spaced out and forgot it wouldn't work on some of these because i don't remember him showing us how to do it in class. i've never even heard of the cubic formula before

I am stuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuupiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiid.

That's said, I kicked my caffeine addiction and suffer the consequences like a man.
How long does it take until my brain gets rid of the additional adenosine receptors my addiction started?

>>8819127
Try working out 14 * 3 on paper. Hopefully it won't take too long.

>>8819433
We don't use 'stupid' anymore. The correct term is brainlet.

That aside, grats on kicking your addiction.

What kind of question is this, and what would you answer?

You've spent the last year as a customer of some unspecified company. You have great memories of services this company has provided and overrall you enjoy their service. There are, however, a few things you deeply dislike about the company. You've requested multiple times that they fix these issues, multiplie chances. Each time they reply that they will attempt to resolve these issues, but everytime they come up short of what you need. The frustration of these persistent issues has mounted to the point where you are considering leaving them. Lately the issues have been especially terrible and you decide enough is enough. You drop the company and trash talk the service to friends and family. You are enjoying supplying your own service and are somewhat pleased with being on the market. Meanwhile the old service is falling apart, it's desperately changing things, fixing its issues and replacing its poor management. In the companies turmoil it has prepared a highly sweetened deal. Given the growth the company experienced with you as a customer it's focused and determined to fix your specific issues with their service. They extend this deal to you and they promise to take better care of their customers. It's difficult for you as a customer who has been abused in the past to trust this sweet deal. Only the company can truly comprehend its own intentions, it's aware that it will be hard for you to become a loyal customer again. So here's the question. Do you return to the new and improved company and save it, give it one last chance? Or do you condemn it to fail and search for a new company?

>>8813919
twig

File: Ccjeb41.jpg (54KB, 800x600px) Image search: [Google]

54KB, 800x600px

Is every nontrivial ({0}) subring of an integral domain also an integral domain?

>>8819664
look at the definition and you tell me. "the product of two nonzero elements is always nonzero". does this hold valid for subrings?

File: IMG_0134.jpg (1015KB, 2592x1936px) Image search: [Google]

1015KB, 2592x1936px

where am I going wrong here? i think it's somewhere around the tan substitution but I can't see it

>>8819685
I'd imagine since every element in that subring is also in the greater ring. My book defines an integral domain as, in addition to this property, having an identity 1 that doesn't equal 0 (a ring where 1 = 0 must be the trivial subring {0}) and commutative. Any hangups you can encounter with those two properties? Methinks not.

>>8812892
In class today the professor said that in [math](\mathbb{Z} / 5\mathbb{Z})^\times [/math], 5 = 1

What does that even mean? I thought that in multiplicative groups you only considered classes with inverses. So in the case of the multiplicative group of 5, you only consider 1,2,3 and 4.

Why is now 5 here? Can someone explain what this means? The professor used this for an algebraic proof of Fermat's little theorem and by applying this he complete lost me. I thought that 5 is not invertible mod 5, therefore it isn't even an element of the multiplicative group.

Where am I wrong here?

File: 1487907463594.jpg (187KB, 1228x2048px) Image search: [Google]

187KB, 1228x2048px

Do Americans clap after lectures in uni?

>>8819799
your prof might have written 1=5 after taking an isomorphism (Z/5Z)^x to Z/4Z, but i'm just guessing

>>8819812
He didn't mention anything about isomorphisms.

>>8819821
what was the step in the proof that relied on 5=1?

>>8819826
5 is an example he gave after the fact.

In the proof he relied on p=1

The proof he did was the usual one:
Let a be the subgroup generated by a. Then the order of a divides the order of the multiplicative group mod p, which is p-1.

Let the order of a be n. Then n divides p-1. But by definition this means that there exists some k such that nk = p-1
but p=1, so nk=0. So:

a^(p-1) = a^nk = a^0 = 1

>>8819837
seems like a shoddy proof, where does p=1 come from? if p=1 then you can just immediately say a^(p-1)=a^0=1 and not have to even mention the order of a.

>>8819841
That's what I think. In his words, "in the multiplicative group, the class of p is the class of 1".

And then when I raised my hand to say that wasn't the class of p the class of 0, he answered that that interpretation only works in the additive group. In the multiplicative group p=1.

But then I checked the definition he gave me for multiplicative group, and the multiplicative group is a subset of the additive group. So how come changing to the multiplicative group modifies the structure of the members?

I am so fucking confused.

>>8819841
either the prof mis-spoke or sounds possibly confused, anyway a proper proof using these methods are here:
https://en.wikipedia.org/wiki/Proofs_of_Fermat%27s_little_theorem#Standard_proof

most importantly a^(p-1)=a^(nk)=(a^n)^k=1^k=1 without using the strange p=1

>>8818812
semisimple lie algebras

finitely generated abelian groups

>>8819109
couldn't you get a lead sphere with a plastic coat or something along those lines

>>8819865
Yeah. I read that as soon as I left class and it really makes me wonder why he'd incluse the detail of p=1

That completely threw me off.

>>8819810
Freshmen always clap after lectures.

>>8819732
Is your Jacobian from u -> w right?

>>8818272
Thanks man.
I'm not following how you've derived the value of d.

Are significant figures only counted from after the decimal point?
i.e.
1.2345 would be to 4 significant figures?

>>8820017
No, all nonzero digits are significant.

>>8820032
So 1.2345 would be to 5 significant figures? And 0.1234 would be to 4?

How do I figure out how many values in an equation I can turn into unknowns before destroying the uniqueness of the solution?

>>8819132
You will not only regret it, you will probably commit suicide, because it's a very stupid thing to do.

The purpose of going to college is to get a job, not to declare your personality to yourself and/or the world.

>>8820083
Are the equations linear? Post some examples of what you mean.

I have an IQ of 105, can I get a master degree if I work hard.

Would physics be possible?

Did we can write the intervals upside down ?
Exemple: [0,1] = [1, 0]

>>8820048
Yes.

>>8820120
I'm talking pretty much anything with values and an equals sign. To what degree can you replace those values with unknowns before the path back to the original equation is lost. I'm basically wondering how to turn things into sudoku.

>>8820185
No, unless the interval is a single point. the interval [a,b] is defined as {x:a<=x<=b}. so your first one is {x:0<=x<=1} but the second is the empty set as there is no x such that 1<=x<=0

File: modulation.jpg (36KB, 531x310px) Image search: [Google]

36KB, 531x310px

why are signals often modulated with higher frequency carrier wave? what is the problem with the signal frequency to be used for transmission?

What is the difference between a vertex graph coloring problem and an edge graph coloring problem? Like, what happens if you try to take an edge coloring problem and convert it into an equivalent vertex coloring problem?

>>8820235
ok, Thank you very much

Do multiple plus signs mean anything? Because it seems kind of a waste if there is no meaning assigned to something like 1++1, because it would be an easy extension to notation. Learning about arrow notation got me thinking this.

File: how.png (10KB, 722x200px) Image search: [Google]

10KB, 722x200px

If I am working with polar coordinates and I would like to have my measurements in multiples of pi (is that how you say it?) as in pi/2, 2pi/6 etc etc

How can I obtain the value like that? For example, if I take the inverse cosine of this quantity I get: 1.047 is there a way I can express this as I want it?

I know this makes me sound extremely dense but fuck just ignore it.

>>8820489
>1.047
pi/3

>>8820492

Or well yeah I could do that yes, but what of more elaborated results that don't necessarily ''fit''?

>>8820497
the standard values you should know are
cos(pi/2)=sin(0)=sqrt(0)/2
cos(pi/3)=sin(pi/6)=sqrt(1)/2
cos(pi/4)=sin(pi/4)=sqrt(2)/2
cos(pi/6)=sin(pi/3)=sqrt(3)/2
cos(0)=sin(pi/2)=sqrt(4)/2

most other values of cosine and sine won't be so easily represented

>>8820508
>>8820492

Alright thanks /b/ros will continue my crusade then

If f(x) is defined on an open interval (a,b) what is the max of the domain of f?

>>8820525
it doesn't have one

>>8820528
It doesn't have a domain?

>>8820532
doesn't have a max

File: quadratic-congruences.png (13KB, 697x70px) Image search: [Google]

13KB, 697x70px

To all the number theorists: any ideas/hints on how to approach this problem?

>>8820479
It's used in computer science as the increment operator
it doesn't mean anything in mathematics

>>8820535
chinese remainder theorem

>>8820553
Well that's a shame I guess.

Since addition -> multiplication -> exponentiation can be said to be a type of progression and they can be assigned the values of 1, 2, and 3, has anyone tried to create an operator along that progression that has a value that isn't a natural number?

Like imagine addition were denoted with a|b, multiplication with a||b, and exponentiation with a|||b. Could a half line work, or zero lines, or even negative lines?

>>8820579
a|b and a||b already have meanings

it sounds like you're just trying to make up notation for the sake of it instead of something actually useful

>>8820600
It was just an example. I could also say the operator is [math]\overset{n}{+}[/math](where 1 for n is add, 2 is multiply, etc.) to be more clear but I didn't think about using latex until just now.

The question is whether or not thinking of the operator as something with a function defined by a number like this could open any possibilities beyond just scaling it up.

File: 1489001974274.jpg (245KB, 947x1205px) Image search: [Google]

245KB, 947x1205px

Any small sources / papers / chapters of books or anything really that would delve a little bit more on conics for a beginner?

The book of calculus I was reading doesn't tell me much other than a few equestions and how they are defined... I guess I dont know what I am looking for?

I tried to understand them but I just dont get much.

>>8820579
Sounds quite a bit like Knuth up-arrow notation. These sort of operators seem to be known as hyperoperators

File: fuggin hell.png (20KB, 577x464px) Image search: [Google]

20KB, 577x464px

any suggestions how to solve this? could i somehow use voltage division to make it fast?

>>8820683
Better with the Latex working :

I'm working on the Görtz and Wedhorn right now and I'm trying to understand the automorphisms of [math]P = \mathbb{P}_k^n[/math]

They say that since the pull-back of [math]\mathcal{O}_P(1)[/math] must be [math]\mathcal{O}_P(1)[/math], we get a map [math]Aut(P) \rightarrow \Gamma(P,\mathcal{O}_P(1))/Aut_k(\mathcal{O}_P(1))[/math]

I don't understand why we have to take the quotient by [math]Aut_k(\mathcal{O}_P(1))[/math]. Does someone know where this comes from ?

File: Untitled.png (16KB, 490x289px) Image search: [Google]

16KB, 490x289px

Okay, seriously, how is part B not right? I've went back and redone it like 3 times and I get the same answer. I even plugged it into the original equation and it all gives the correct result of 1. I did a problem just like it a minute ago, exactly the same way I'm doing this one, and it was correct.

I feel like I messed up some small part and it's making the whole thing incorrect.

>>8820727
The solutions must be in the interval, the last two are out of it.

>>8820727
>in the interval [0,2pi)

>>8820730
Oh, I'm an idiot.

File: circuit.png (35KB, 792x627px) Image search: [Google]

35KB, 792x627px

How in the absolute hell do you figure out equivalent resistance or total current of these kinds of circuits? I just need a good walkthrough on this one problem.

>>8820658
You'd see I already knew about that if you scrolled up, but you did give me the idea to google "fractional hyperoperation" which may have started the process of my head collapsing into a black hole.

>>8820755
Whoops. I missed that.

But damn, there is a tetration forum. Who would have thought.

File: miller-rabbin.png (39KB, 662x263px) Image search: [Google]

39KB, 662x263px

Any number theorists have any idea how to do this?

>>8820943
well what happens after you went through it for 8 steps?

>>8814595
someone else please correct me if i'm wrong, but if you were to graph g(x) it's just a linear function where x>0. and h(x) is a sin (sinuous?) function where x does have a value at 0, but the graph "jumps" so it is discontinuous at 0. i think there is a way to find where functions are discontinuous without graphing, but i forget.

for differentiability, functions are differentiable where they are continuous, but not where there are corners, cusps, or vertical tangent lines. again, there might be a way to figure this out without graphing, but idk.

>>8814595
>>8822059
i looked it up, functions are continuous when these conditions are met:
1. f(c) exists
2. limit as x approaches c of f(x) exists
3. limit as x approaches c for f(x) is equal to f(c)

that's how you can prove it

>>8819566
>What kind of question is this, and what would you answer?
answers depends on your goal

If the observable univese were the size of a cubic meter, how many grams of matter would it contain? How many grams of dark matter?

>>8822191
There is no such thing stop watching shitty documentaries.

>>8822199
Seems like reasonable means for trying to grasp large scales. Same as when someone says: if an atom was the size of the earth, how large would a proton be?

File: Capture.png (280KB, 618x395px) Image search: [Google]

280KB, 618x395px

>>8822215
>https://www.youtube.com/watch?v=NFTaiWInZ44

>>8822199
Fine, I just want to have an idea of how sparse things are.

>>8822215
please go away

>>8822224
Found a pretty good comparisson, if you shrink the observable universe to the size of earth, all the regular matter in it would weight less than a grain of sand or ~10mg. Does that sound right to you guys?

>>8814815
best field for you is where you excel

going for anything else because of something like employability is pointless and WILL fuck you over in the long term on way or another

>>8814722
>>8814968
not true - it's not fully understood yet and leptin only is a small (you can debate the use of the word small) part of it

>>8815238
very very very much depends on the teacher
i saw things man
quantum 3 - 5 LP - you would be happy to get like 35/100 points on the test (which is 100% of the grade)
quantum 3 - 5 LP - another teacher - i'm pretty sure my dog could have solved that test (also 100% of grade)

those 2 dudes were 1 semester apart. Sooo it's way too random to give a general clue about it.
Think about it this way: Any chemistry field (even analytical etc) can be made so fucking hard you will cry (at least at a test environment)

do people of every language say 'ow' when in pain?

>>8813766
Read "why chemical reactions happen" by Keeler and Wothers

>>8813919
arasmus

>>8822864
Sorry, I meant a ramus

>>8822848
Non, en français on dit "aïe" et "ouille"

>>8822059
Btw the function is described as sinusoidal

>>8822848
Yes, though people say a lot of things when in pain.

>>8817935
You can prove Wilson's theorem easily using just basic facts on rings of the form Z/nZ: a number p is prime if and only if (p-1)! is congruent to -1 mod p.

File: MGS equations.png (1MB, 1323x1017px) Image search: [Google]

1MB, 1323x1017px

Quality might not be high enough

but are these actual equations or just gibberish?

If I've already taken two semesters of Calculus, should I go back over a textbook like Apostol or just keep rolling?

>>8819929
where do you find a lead sphere that has been embalmed with plastic?

How can I show that a nonidentity dilation with a center P commutes with a rotation of line l if and only if p is on l?

>>8823332
Also I'm sure one of you fags has the solution manual to george e martins transformation geometry textbook

>>8822920
laplace(?) transform, fourier transform, power series expansion

that's a weird form of the fourier transform i have only seen once in an physics book from the 80s

>>8823457
Motherfucking Kojima man...

>>8823306
Why don't you just use an acrylic coating?

Incidentally, as someone who worked his vacations away during his teenage years picking up lead shooting arcade BBs barehanded with no incident- so long as you don't touch your mouth, nose, eyes, and ears and wash your hands thoroughly, I don't see any means of lead poisoning. If you don't believe anecdotes, maybe you can believe OSHA:

>Lead (except for certain organic lead compounds not covered by the standard, such as tetraethyl lead) is not absorbed through your skin.

https://www.osha.gov/pls/oshaweb/owadisp.show_document?p_table=STANDARDS&p_id=10031

This seems like something that barely-just barely- belongs in SQG:

The UH BTI, under the review of DHS employees, is ready to award original and rigorous proposals regarding border security, immigration, and/or trade.

Would any of you with science, engineering, and/or technological backgrounds think to apply through your universities or other institution?

>>>/pol/120866251

File: MGS equations 3.png (2MB, 2649x2033px) Image search: [Google]

2MB, 2649x2033px

>>8822920
>>8823457
That's about the best it's going to get

File: Ripped Texture.png (176KB, 660x435px) Image search: [Google]

176KB, 660x435px

>>8823518
Ripped the texture

>>8823518
Hmm.
- Laplace transform
- Something looks like dirac delta. Maybe sampling using Laplace transform
- Laplace transform of the Laplace transform? Inside the integral it looks like a displacement. Not sure.

- Fourier transform
- Cosine Transform
- Sine Transform

- Power series transform. Something like the z-transform?

PROBABILITY

first:

=tex A = \frac{N!}{((n_1)! (n_2)! (n_3)! (n_4)! ... (n_k)!} , \text{where } n_1 + n_2 + n_3 + ... + n_k = N

convince me that A is indeed an integer.

second:

the above equation come from a probability book, its a theorem called Partitions Rule (which btw is not found anywhere in the goddamn net)

but the argument is that A is the number of ways to partition N elements into k sets. I dont understand it.