/sci/ - Science & Math

How does one measure atmospheric carbon as of 14 million years ago?

>>11186301
by looking at what kind of creatures lived 14 MYO
by looking at the gasses trapped in rock that is 14 MYO

Paste: https://pastebin.com/mxivnaiX
Unanswered questions from the previous thread:

Maths questions:
>>11183466
>>11184057

Physics questions:
Exceptionally none. Great job judyposter, yukariposter, furryposter and anons.

Chemistry questions:
>>11180835
>>11184331

Psychology questions:
>>11177211

Biology questions:
>>11174397
>>11183909

Geology questions:
>>11186295

/diy/ questions:
>>11182789
>>11182933 [also biology]

Stupid questions:
>>11174377
>>11175495
>>11175988
>>11176116
>>11177569
>>11180177
>>11182319
>>11184002
>>11186246 and >>11186259

/g/ questions:
>>11179604

Who the fuck knows questions:
>>11177879

>>11186330
>geology
Geography, actually, my bad.

>>11184057
You have that [math]a \cong a + b ~ (mod ~ b)[/math] by definition, so you're essentially using the transitivity of congruences to chain up adding b until you find a positive representative of the equivalence class.

Any good recs for books that take a rigorous, mathematically involved/advanced approach to statistical mechanics and thermophysics? I have Stowe's book on Thermo, Minlos' lecture notes and Ruelle but I was wondering if there was anything else that might be better.

>>11186375
I have this one, can't really say for the material since I suck balls at measure theory, so I'm not able to make it far into the book. It is quite old though (1949), so maybe your resources are better.

>>11184331
I'm shooting from the hip here but I'll double-check once I get home; don't you reverse the polarities of the cathode and anode when you perform electrolysis?

>>11186389
This looks promising, and seems to address what I was concerned about from a preliminary glimpse into the subject, so thank you.

>>11186407
Your welcome, your own references seem promising to me, so thanks also.
I've always felt that thermo and stat mech had the shakiest math background when presented by physicists, so I've been interested in seeing the rigorous presentation by mathematicians.

How realistic is to run a synthetic biology lab at home work a middle class income and make it profitable?

Whats the best introductory Linear Algebra textbook that someone with only high school level mathematics can work through successfully?

What's the best set of textbooks to get an introductory level of knowledge for chemistry?
I have no intention of ever doing them myself, but what little research I've done into cooking/processing things like LSD looks super fun I even enjoy just reading the papers and articles published about them but I dont understand half of what's in them
Also what's the best way to dispose of things like LSD and Mescalin, burn them?

>>11186423
Depends on how good you are at hiding from the cops.

>>11186330
>judyposter
>furryposter
one and the same, hun.

>>11186777
I mean, pretty much anything. Linear algebra is a neat subject because you really don't need any kind of background to jump in. It's better to know about how the solution spaces of ODEs and how conitnuous functions relate to lin alg, but not necessary.
Just jump in!

It's kinda obscure, but I really like "Lectures on Linear Algebra" by I.M. Gel'fand. Can't find a pdf anywhere, but it is very short and to the point. The problem with it is there are no problem sets. I first learned lin alg in a text my professor wrote, so that's not anywhere online.

I've just barely skimmed this, but this looks like a great intro if you want something free. https://www.math.ucdavis.edu/~linear/linear.pdf
The benefit of this text is it has cute pictures.

>>11186962
correction: there are examples scattered throughout gel'fand

>>11186962
>>11186978
Thanks for the rec anon, it's shockingly cheap so I might order it.

>>11186389
I can vouch for this book, Gamov is quite reputable.
>>11186375
In addition to what anon has already suggested, I also recommend Simon & Read's series on methods of mathematical physics. It delves mainly into foundations of QM and QFT in the later volumes but most of the background in Vol. 1, such as ergodic and representation theory, do see major applications in stat mech.
Besides, there's an exact mapping between [math]d[/math]-dimensional QFTs and [math](d+1)[/math]-dimensional stat mech systems.

>>11187020
>Read's
Reed's*

would i be better at maths if i liked anime

>>11174397
Isn't it simply a case of more water means more residues get washed down?

>>11174377
Just by having higher IQ would make it superior. Like, duh.

>>11176116
She was popular because she was an actually decently written, if kinda Mary-Sue-ish, stronk female character. Also people want to fuck the rabbit.

If I have a Python program that models the behavior of a double-pendulum, how can I numerically solve the Lyapunov exponent for it? Brainlet here, this is my first dip into chaotic dynamics.

Is it possible to have wood at really high temperatures but it not combusting? Also, is there liquid or gaseous wood?

>>11187345
>Is it possible to have wood at really high temperatures but it not combusting
Yes. This is how charcoal and coke is made. You heat green wood to very high temperatures in the absence of O2 to pyrolyse the cellulose. Basically the shit you don't want goes away and the stuff that burns really well remains.
>Also, is there liquid or gaseous wood?
no. wood is not a pure substance, it doesn't make sense for it to have distinct phases. just like there is no liquid air.

If I won't know that I'm dead when I'm dead does that mean that I won't die from my perspective?

>>11187362
Hate to say it, but your life still has an end from your perspective. Get used to it.

>>11187356
huh, actually there is liquid air. my point stands.

>>11186301
Drilling into ice sheets that 14 million ya

What's a good test for impact on a human skull? Someone bet me I couldn't split a skull with an axe and obviously I don't want to disprove him using someone's actual skull, what would be a good analog?

>>11186390
>>11184331
Not sure if you're still here but in a -spontaneous- redox process the substance with the highest standard reduction potential becomes reduced at the cathode. In electrolysis you provide provide the energy to flip any given process around. In your example, [math] \text{Cl}_2 + 2e^- \rightarrow 2 \text{Cl}^-[/math] spontaneously reduced at the cathode. But you reverse this process in electrolysis, forcing the stronger reductor to become the reductee and hence the chlorine reaction is at the anode.

Sorry if I made a mistake somewhere, it's been a while since I've worked with this stuff.

I often lose 1 of 3 items that I move around with, that being my wallet, keys, and phone (which I have no idea where it might be). I often lose concentration and can't recall certain thoughts after thinking them or actions that I have done recently.

Do I have early Alzheimer's, sci?

>>11187555
No, do you keep much in your wallet? Where do you live? Can we hang out?

I have another hypothetical particle question:

You have a particle that leaves behind a "trail" of sorts. This particle also leaves a "mark" on anything else it interacts with, even through indirect interaction. Unlike normal particles, this particle decides what it interacts with "first" based on how close to the origin it touches the "trail", as opposed to how early it touches the particle in time. However, the particle will refuse to interact with anything that carries its "mark", thus preventing any paradoxes. This means that, if you fire the particle then close a gate behind it, it will hit the gate even after it should have passed by the opening of the gate(unless the gate got "marked").

Does this still commit a lot of big no-nos in physics? I probably need to reword some of this.

>>11187757
My question is how is it even a particle if it is the trail that does the interacting and not the particle itself. Sounds like a silly game of semantics.

>>11186289
Really stupid question, I'm sorry but I haven't done math in a long time.
I'm currently trying to self-study math and I'm going through the Book Of Proof. There is an exercise here to prove that:

"If a,b,c∈Z then c⋅gcd(a,b)≤gcd(ac,bc).

But aren't both sides always equal in that case? I don't see when the left side would be smaller than the right side?

>>11187910
[math]c \leq 0[/math].

>>11187959
If we restricted a, b, c to positive integers the equality always holds, right?

>>11187961

>>11187959
Thanks mate, didn't think about when c is less than 0.
But doesn't the equality always hold also when c is 0?

>>11187969
gcd(0, 0) is finicky and I thought I'd include the possibility for completeness.

>>11186289
Where do i learn de Rham cohomology. I have taken a grad alg top class

>>11187972
I'll make a short addendum on this.
If you go by the argument laid out here, https://math.stackexchange.com/questions/495119/what-is-gcd0-0 , then it's natural to consider gcd(0, 0) to be zero.
However, defining gcd in terms of that ordering forces you to specify that you're picking natural numbers, whereas "largest integer" automatically implies that.
>>11187984
The course should have a name like "Differential Topology", "Smooth manifolds", "manifolds", "advanced calculus" or "differential forms", but it depends a lot.

>>11187984
I like spivak's differential geometry volume I. chapters about differential forms, integration, and the last chapter named "an excursion to the realms of algebraic topology"
if you want to go as deep as it gets, then bott tu.

In Latex, I want to organise a bibliography in two different sections, like this

>Fundamentals
>>[list of articles]

>Applications
>>[list of articles]

I've got a .bob with articles for each sections, but when I try to include the .bib for "fundamentals", it also includes the references for "applications".
How can I solve this?

>>11188161
Nevermind, now it seems that the second .bib doesn't even exist according to overleaf.

>>11188161
>>11188173
disregard this entire post, I found a fix.
biblatex is much more versatile than regular bibtex

sorry

Why doesn't my life feel normal again after I lived in a hotel for two months?
I moved back into my house two weeks ago and I still feel lousy and stressed.

>>11188256
Why did you move out for two months? Do you have a family back at home? Maybe your wife is cheating on you.

>This equation [x^2 + y^2 = 3z^2] simply states a relation between these elements in the ring Z. As such, the same relation must also hold in any quotient ring as well. In particular, this relation must hold in Z/nZ for any integer n.

Why does the quotient ring maintain the relation (a formal explanation would be appreciated)?

>>11188507
We have the quotient map [math]f_n: \mathbb{Z} \rightarrow \mathbb{Z_n}[/math], which is a ring homomorphism.
Then [math]f(x^2+y^2-3z^2)=f(x^2)+f(y^2)-f(3z^2)=f(x)^2+f(y)^2-3f(z)^2=f(0)=0[/math].
By the definition of the quotient map, [math]f(x) \cong x ~ (mod ~ n)[/math].

What sort of mental math is needed in college? How far can I go in life with just a calculator?

>>11183605
asking again from last thread

>>11188601
FUCK NEVERMIND I FORGOT TO DIVICE THE MASS FLOW TERM BY 2 FUCKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK
FOR 5 FUCKING DAYS AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

>>11188627
>>11188601
You okay baby? You know that Hin=Hout1 +Hout2 since the chamber is adiabatic. The mass balance is obvious.

>>11188657
it wasn't that simple in the slighest
I was well aware that the change in enthalpy is 0 because its a steady state operation, that had nothing to do with it

>>11188657
>>11188673
but still thank you for being the only person to reply last thread

is there a difference between a limit that doesn't exist and one that goes to infinity?

>>11188789
sin(x)

>>11188792
I get confused by answers like this:
https://socratic.org/questions/how-do-you-show-the-limit-does-not-exist-lim-x-4-x-4-x-2-8x-16

it's like people use the two things interchangeably sometimes

>>11187020
Thank you Yukari-fag I was hoping you would reply.

yukari-fag is a legend at this point

>>11188565
None.
Very, very far.
>>11188601
My bad for not tallying it up, slipped past me.
>>11188679
Please don't identify people based on writing style, it's spooky. Very spooky.
>>11188798
They are interchangeable, since infinity isn't a real number.

>>11188854
>They are interchangeable, since infinity isn't a real number.
they're not fucking interchangeable. sin(x) doesn't have a limit for x -> inf, but it's not infinity. it just doesn't exist.

>>11187366
Is there also liquid or gaseous humans?

what does it formally mean for two elements ([math] a,b \in R [/math]) of an arbitrary ring to be coprime? that a isn't in the ideal generated by b and vice-versa? i see the word tossed around without a definition, probably cause it's meant to be a direct generalization of what being coprime means in [math] \mathbb{Z} [/math], but since they aren't numbers necessarily i'm not sure how that generalization is supposed to be understood exactly

There are databases for just about every single thing about chemistry, but is there one of videos of the most important reactions? So we can have some idea of what the process entails. YT videos tend to be the more amateur stuff without those nice fancy lab equipments.

>>11188854
>None.
>Very, very far.
I wouldn't say that. Depends a lot on the professor. You should be able to calculate by hand anything a scientific calculator can do, but not all problems might allow the time for it.

>>11189051
My bad, I was referring to the context in the previous post.
>>11189086
They generate coprime ideals.
Ideals are coprime if their sum is the whole ring.
Sauce: wikipedia. Alternative definitions may be used elsewhere.

Bonus definition (made up by anon on the spot): two elements are coprime if, whenever one is in a prime ideal, the other one isn't.

>>11188789
>>11188798
I know of at least one undergrad analysis textbook that defines what it means for a sequence [math](a_n)_{n\geq 0}[/math] to diverge to [math]+\infty[/math]: [math](\forall \varepsilon > 0)(\exists n_0\in \mathbb N): n_0\leq n \implies a_n > \varepsilon[/math]. (Respectively for [math]-\infty[/math].) If this is not a standard thing, it should be for the sake of pedagogical clarity.

>>11187910
yes they are equal, modulo issues about negative numbers and 0

you can see this by the fundamental theorem of arithmetic. by the theorem, there is a bijection bertween positive integers and finitely supported functions [math] primes\to Z_{\ge 0}[/math]. let [math] f_n [/math] denote the function corresponding to the integer n. Note that [math] f_{gcd(n,m)}=min(f_n,f_m) [/math] and [math] f_{nm}=f_n+f_m [/math] where the minimum and sum are defined pointwise. in particular, the purported equivalence translates to [math] f_c+min(f_a,f_b)=min(f_c+f_a,f_c+f_b) [/math] which is clearly true

>>11187910
yes they're equal
note that for any integer-valued functions on the same domain, we have

f+min(g,h)=min(f+g,f+h)

where min(g,h)(x)=min(g(x),h(x)) and similarly for the sum. by the fundamental theorem of arithmetic, we can uniquely identify each integer with a fucntion [math] primes\to Z_{\ge 0}[/math]. under this correspondence, gcd corresponds to pointwise minimum, and multiplication corresponds to pointwise addition, thus establishing the claim

>>11186777
Strang, unmatched for baby matrix algebra brain bleaching, if you want to plug and chug without knowing what you’re doing that is the book for that topic.

>>11186777
a better option is to use google and do as >>11186962 suggested, you can find dozens of complete lecture notes on intro lin alg and abstract lin alg usually with significantly more detailed and interpreted results for spoonfeeding.

>>11189240
thanks, the second definition makes up for a pretty simple way to understand it

should i even apply to a PhD if i only have one semester of """research""" experience, where basically i just rearranged some equations to make an equation for a professors future research project and wrote about what type of X component they should use.
or should I just go for a masters degree, get more experience, and then apply for a phd?
the universities im applying to will consider me for the MS if i dont get accepted to the PhD, but i feel like with my measly experience and not much else to write about except grades, that they will just laugh my application off

are the oceans giant vats of dinosaur urine?

>>11186289
I remember a chemical that makes you unmotivated. What is it?

I have been researching a few uncommon chemicals, and every once in a while, I'll find that one of them has a CAS number indicated in a supplier's site, but when I search for it, no other site has it, only that one. Are these sites trying to pull some funny shit, or I can't find other sources because the official CAS listing is behind some gay-ass paywall like the Wechsler IQ test's population samples and data and shit?

>>11189588
Oxygen?

>>11189420
I didn't even know you could apply for it without a MS first...

>>11186289
How does one go about, to understand ODEs? I just can't seem to get it... Has anyone got a good book or video about them?

>>11189659
in the US you dont necessarily need an MS to apply to phd programs

>>11186289
I don´t know if this belongs more to biz or here. But I wanna learn shit about regression, correlation analysis for business related stuff. And look for website data and try to see if I can find something. Are there any good ressources(books, whitepapers) you can recommend?

Where do I obtain cute youmu illustrations?

hello pls help.

>if a ⊂ b, then b^c ⊂ a^c

what is this?

>>11190390
nvm i figured it, ^c is a notation for complement of a set

Let [math]a\neq 0[/math], [math]a\in\mathbb{C}[/math]. If [math]a^{i}[/math] is real for one value, how do I show that it is real for all values? By definition [math]a^{i} = e^{i\log(a)} = e^{i(\ln|a| + i(\text{Arg}(a)+2\pi k)}[/math] for [math]k\in\mathbb{Z}[/math]. Tried chasing a contradiction but I just can't seem to get anywhere with it. Is there a simple observation that makes this trivial ?

>>11190483
>if [math]a^i[/math] is real for one value
What do you mean with that? Real for one value of a? If so, the principle of explosion does the job.
>>11190380
pixiv is the main source, but I got this one from safebooru.
>>11189669
>good book
>ODEs
There aren't any, only decent and half decent. The one with historical notes is nice.

>>11190547
>there aren't any
what about Arnold's book? Isn't it considered the standard for the subject? Lots of pretty pictures too!

>>11190547
>explosion
My bad, I'm clearly going insane.
Still have absolutely no idea what he meant.
>>11190550
Arnold is really weird.
But sure, go ahead, if that's what you have on hand.

>>11190577
>Arnold is weird
Elaborate

>>11190547
>What do you mean with that?
I also do not know what exactly this means. The question doesn't elaborate. I thought it meant that for a particular value [math]k_{r}[/math], [math]a^{i}[/math] is real. [math]a[/math] is just an arbitrary non-zero complex number.

>>11190589
Coverage is all over the place.
For example, try to ctrl+f "Laplace".
The book is really weird. I wouldn't tell you it's garbage and you should instead read whatever else I'm recommending, but I wouldn't call it good either.
All in all, learning ODEs is just really shitty.
>>11190599
1^i=e^(i log 1)=e^0=1, so if we take it as any a, the result instantly falls flat.
But say, e^i=i sen 1 + cos 1, which is an a such that a^i isn't real.
I think there's a mistake somewhere.

>>11190608
i'm going to send this fuck an e-mail and demand an answer then.

Why is my right side of the body not as flexible as the left one?

>>11190608
looked for the question on google and got this as a solution. just wanna kms fuck this course

>>11190622
i don't even understand the conclusion

>>11190622
>>11190629
Oh, those retards meant real for any branch of the logarithm.
Absolutely autistic.

>>11190634
i spent two hours on this anon. there's no justice in this world.

Which math and physics concepts should I learn in order to have a good understanding of basic electronics? My goal is to work repairing consuner electronics

>>11190679
get the art of electronics by horowitz. if you are in the US then physics 2 and calc 2 should be enough, maybe up to differential equations at most

There's a circle 1 mile across just a few miles north of the china lake naval air weapons station, near death valley CA. Anybody have any ideas what it could be?
35°49'40.8"N 117°37'41.9"W

>>11190706
>art of electronics
that might even be overkill if his goal is to just repair. I think something like Practical Electronics for Inventors by Scherz is more approachable and teaches enough. Either way after learning the basics actual practical experience will be much more important, so >>11190679 you might want to find some sort of club or experienced enthusiasts to mentor you

Is it bad to go to work if I'm coughing? Like do I spread viruses and my coworkers secretly hate me?

I'm stuck in this question from "A First Course in Cauculus" and i can't find anything about it online.
"A box with open top is to be made with a square base and a constant surface C. Determine the sides of the box if the volume is to be a maximum."
It's in an section in the book describing the critical points (maximum/minimum) of functions using derivatives, where their slopes at that point should be zero, so the solution must have something to do with that.
There's probably more ways to solve this but if anyone can solve it using that slope property it would be appreciated. Thanks in advance.

>>11190782
In my attempt (I'm still taking early classes in Cauculus please don't bully) I tried to isolating the sides (h·x), putting that in the volume function and taking the derivative of whatever's there.

x2+4·h·x=C | x·x·h=V

h·x=(C-x2)/(4)

x·(C-x2)/(4) = V

Then I got (C-3x2)/(4) as a derivative. It's a quadratic without a b coefficient, so its maximum lies at 0 and that doesn't make sense. I also thought that the constant C would disappear somewhere in the equations, but I really don't know.

>>11190785
the maximum of the derivative shouldn't be relevant to you, you are looking for the zeros

>>11190785
critical points happen precisely when [math]f^{\prime}=0[/math]. Once you have your equation that you have to optimize, just differentiate and set it to zero.

Is the equivalent reactance of pic related (1/XC - 1/XL)^-1 ?

>>11190895
You're right that had nothing to do with it

>>11190955
I tried taking the roots off that derivate and i got (±√3·C)/(4). I could try substituting C but I don't know where to go from there. Maybe i'm in the wrong lead.

>>11191149
what would you substitute for? C is a constant, and basically the only value that is predetermined in the first place so having it in your result is basically exactly what you want

>>11190958
[eqn] Z^{-1}=Z_R^{-1}+Z_L^{-1}+Z_C^{-1}=\frac{1}{R}+\frac{1}{sL}+sC [/eqn]
If you are dealing with a sinusoidal voltage sources (alternating current) then [math] s=j\omega [/math]. Take the reciprocal of [math] Z^{1} [/math] to get equivalent impedance.
[eqn] Z=\frac{sRL}{s^2RLC+sL+R}=\frac{j\omega RL}{R-\omega^2RLC+j\omega L} [/eqn]

>>11190717
I know for a fact that's a weapons range. I drive up that way about once a year to camp and there is pretty much always military aircraft in the air around Ridgecrest.
Fun fact: when you turn off the 395 northbound to the 190 east to head into Death Valley, and before you head through the pass into Panamint Springs, there is a turnoff on the right hand side that leads down a road called Darwin Road. At the end of that road, there is a near-ghost town that has maybe a few dozen weirdos living there. The "town" of Darwin overlooks that weapons range. I don't recommend going there, but it is a definite trip. They all kinda protest the existence of China Lake NAWS.

>>11191432
take the reciprocal of Z^(-1) to get eqiv. impedance, obviously

Can someone help me with this

>>11191647
Ah, I think I see the problem.
January has 31 days, anon. If you ever forget that again, just ask me.

why is this true, i can only make sense of -1,0 and 1

>>11191776
Choose any integer [math] n \in \mathbb{Z} [/math] and let [math] y = n^{5} , x= n^{3} [/math].

>>11191722
>>11191647
Seriously now, evaluate the deterministic term and ask me again.

>>11191776

whenever the third root of x^5 is an integer

>>11191776
(a^5, a^3)

>>11191786

>>11191791
I'm not sure what you mean by determinsitic term. I tried letting n = 59 earlier and end up with T = 50 + 4en. My next thought is to let En be either 0 or 1.
My textbook says nothing probability for random variables and my professor is horribly bad.

>>11191817
something something normal distribution centered around en=0.5

>>11191817
>T=50 + 4en
So [math]4 \epsilon _n > 10[/math] and [math] \epsilon _n >2.5[/math].
You should have a table somewhere with that number.

>>11191827
So for T = 60, I would need to find en = 2.5.
How would I know what the SD is for a mean of .5? Also, you got .5 because it's the mean of N(0,1) right?

>>11191840
don't listen to me. i dont know anything. listen to this guy >>11191836

>>11191836
So I'm not supposed to use a normal distribution?

>>11191840
No, he got .5 because it's sunday night and he's tired, since he's a human being.
Just find P( N(0, 1)>2.5) on some table somewhere.

>>11191846
no lol
>identically distributed

Sometimes in movies and shit when someone's bleeding out or otherwise very injured someone will yell at them to "Stay awake!", as if them falling unconscious would ensure or at least increase the chance of their death. Is there any truth to that or is it just for drama?

>>11186289
>RANGE BANNED FOR DISPARAGING THE DISNEY MASTERS OF 4CHANNEL!

>FUCK YOU GOOK MOOT!

>>11191863
Yeah, falling asleep with a head injury in general is not a idea.
>why
I dunno. I've just heard this before outside the context of movie. Also I watch Live PD and I heard them say that to a guy OD'ing.

>>11191863
>death
Wild guess here: if you sleep, you might fall into a coma.
I don't usually post guesses, but my guts are very insistent on this one.

Is there any research into mating systems (plants) in translocated vs natural sites? Not looking at ecosystem restoration where there is essentially a metapop structure.

Second:

Is it possible to create a Dirichlet distribution for gene frequencies and use it in a chi squared (Bayesian) ala https://www.researchgate.net/publication/301874755_A_Bayesian_nonparametric_chi-squared_goodness-of-fit_test

Asking for a, um, friend!

My friend used microsat data, for reference

in a polynomial if the initial term x^n has n being odd, then it has at least one real root. why?

>>11191974
Because at x>>0 or x<<0, the highest order term dominates. So f(x) for large x is always positive (assuming positive leading co.eff.) and f(x) for very negative x is always negative. By intermediate value theorem, there is a real root.

>>11191974
if n is odd then the limit when x goes to +inf is +inf and the limit when x goes to -inf is -inf (assuming it's a monic polynomial, if the coefficient is negative just flip the signs), thus there have to be values for [math] a,b \in \mathbb{R} [/math] such that f(a) is positive and f(b) is negative, and since polynomials are continuous then the intermediate value theorem (or bolzano's theorem too) guarantees that there's one value c such that f(c)=0, where [math] c \in (a,b) [/math]

alternatively you can use the fundamental theorem of algebra, and since complex roots always come in conjugate pairs, and there are n (odd) roots, then if all roots were non-real one of the complex roots could not have its conjugate as a root, which can't be true for polynomials with real exponents

>>11192028
>which can't be true for polynomials with real exponents
i'm a fucking idiot, should have been real coefficients instead

What determines if a food needs to be kept refrigerated to avoid spoilage? Why is jerky OK to leave at room temperature for months but a cooked steak will spoil in hours?

>>11192028
wow that's a great answer, thanks so much

How do you get a TI calculator to do the correct order of operations?

I want it to graph 5e^( -0.1|x| )(sinx) - 1

It's a problem where they are asking you how many critical numbers this derivative has. There are 10 roots on desmos, but I can't get my TI86 to graph it properly. It just does a slightly curved line.

Can someone help my brainlet ass out? If [math] z \in \mathbb{C}[/math] is an algebraic integer, and [math] w \in \mathbb{C} [/math] is such that [math] w^2 = z [/math], why is [math] w[/math] also an algebraic integer????

>>11192390
Add a fuckton of paranthesis, everywhere that there could be even the slightest hint of ambiguity
You could also try rearranging the operations so that the order becomes less ambiguous, like instead of that just writing -1+5*sin(x)*(e^(-0.1*|x|)), so there are no confusions like if the sin(x) is part of the exponent or just a factor of the larger product, etc

"Q(√7) = {a +√7b : a, b ∈ Q}
is the set of rational numbers together with the root of 7."
>Show that Q(√7) is a field.
should i just write that: "it's a field because the distributive law can be applied, where: a · (b + c) = a · b + a · c"?
i really don't know what i'm doing or should write

>>11192519
You need that, yes.
You also need to show the entire set satisfies the properties of an abelian additive group.
You also need to show the set without 0 satisfies the properties of an abelian multiplicative group.

Alright so my current thought is to sort of work the proof backwards from how the statement is presented. So, start with the big intersection of all the conjugates of [math]Aut_E(F)[/math]. This is, by definition, the largest subgroup of [math]Aut_K(F)[/math] that is contained in all the conjugates of [math]Aut_E(F)[/math]. Then, show that the fixed field of this subgroup is Galois over K. Then, since the intersection is the largest such subgroup, it must be the smallest such extension over K. If that's the best way to approach it, then I would say I'm stuck in figuring out exactly what that big intersection subgroup looks like. I think once I know that, I can probably figure out its fixed field.

Professor said to consider the theory of group actions so I'm guessing that's where the structure of the big intersection will come from but I also don't know how to apply that. I don't really know what the intersection of all conjugates of a subgroup looks like.

Otherwise, if I'm not on the right path, I definitely need help on where to approach this from.

>>11192537
how to show that? should i just write down the defections of them?

>>11192559
>defections
definition

>>11192559
No, you literally start from the top.

Find an additive identity. Then take two elements from the set like [math]a+b\sqrt{7}[/math] and [math]c+d\sqrt{7}[/math] and add them to make sure you get another element of the set. You can check commutativity at the same time. Then pick 3 elements and make sure you can associate them under addition. Then make sure each element has an additive inverse.

Then do the same with all non-zero elements of the set and with multiplication.

Then make sure the distributive property holds.

>>11192580
ok thanks

HOW DO I SHOW THAT FUCKING [math] \{a + b\omega : a,b \in \mathbb{Z}[/math] for [math] \omega = e^{2\pi i/3}[/math] is closed under multiplication?? I can't getit for the life of me damnit

>>11192903
Note that ω^2=-ω-1:
(a+bω)(c+dω)=(bd)ω^2+(ad+bc)ω+ac
=(bd)(-ω-1)+(ad+bc)ω+ac
=(ad+bc-bd)ω+(ac-bd)
ad+bc-bd, ac-bd ∈ a

>>11192401
z^n + a_n-1 z^n-1 +. ...+ a_0=0
w^(2n) + a_n-1 w^(2n-2) + ... + a_0=0
And yes you are a brainlet. Should just give up

>>11192968
> ad+bc-bd, ac-bd ∈ a
should have been.
... ∈ a
(dunno what happened to the a symbol).

what the fuck is it with this wave of elementary field theory fags? Are all of you guys going through the same course or is it just one guy spamming FT questions.

determine circular frequency of free undamped vibrations

m=40 kg
c=2 N/mm

>>11193036
>3 variables
>can't solve it

>>11186289
>>11186330
what is the sauce?

>>11192044
Jerky is cured meat. Dry and high salt content. I'm not sure what the deal with jam is tho. See also: fermented foods. The "good" bacteria outcompete the "bad" ones.

>>11193045

>>11191846
You need the probability that a random variable drawn from N(0,1) is > 2.5. No idea what this guy >>11191857 means, the 'identical' part of iid means they're all from the same distribution.

>>11193054
https://mobile.twitter.com/i/web/status/1196792701791793158
https://www.pixiv.net/en/artworks/77833412

>>11193036
Hint: for small displacements [math]\frac{\Delta L}{\Delta x}=2[/math] where L is the natural length of the springs.
From the free body diagram and applying Newton's second law,
[eqn]m\ddot{x}+2cx=0[/eqn]
therefore we have that x(t) is the sum of a sine and a cosine with
[eqn]\omega=\frac{\sqrt{8mc}}{2m}[/eqn]

Apply yourself!

>>11193036
Hint: for small displacements [math]\frac{\Delta L}{\Delta x}=2[/math] where L is the natural length of the springs.
From the free body diagram and applying Newton's second law,
[eqn]m\ddot{x}+2cx=0[/eqn]
therefore we have that x(t) is the sum of a sine and a cosine with
[eqn] \omega=\frac{\sqrt{8mc}}{2m} [/eqn]

Apply yourself!

>>11193049
?

>>11192555
Just use the fundamental theorem of Galois theory.

>>11186289
Going through a book on proofs and there in an exercise here asking to prove that if [math] k \in \mathbb{N} \land n=2^k - 1[/math] then every entry in row [math] n [/math] of pascal's triangle is odd.
I couldn't think of a proof myself, so I tried looking online for proofs and I only find people using induction (which is taught later in the book) or using some obscure properties of primes or of numbers in general that I just don't believe the author meant to be used in this stage of the book. What is described so far in the book (that I think might be relevant) is Direct Proofs, Contrapositive Proofs, Binomical Coefficients and Pascal Triangle.
Does anyone have an idea for a simpler proof than those I find online?

>Direct Proofs, Contrapositive Proofs, Binomical Coefficients and Pascal Triangle
It'd be more elementary (if not necessarily simpler) to work with the definition directly: the [math]j[/math]-th entry is [math] \prod_{i=1}^j \frac{2^k-i}{i}[/math] and to show that this product is odd, we argue that for every term, every power of 2 in the (prime) factorization of the numerator also appears in the denominator, and hence cancels out.
Explicitly: if [math]2^l | 2^k-i[/math] for some l, then [math]l<k[/math] and so [math]2^k-i = 2^l(2^{k-l}-x)[/math] for some x, i.e. [math]2^l | i[/math].

>>11193520
Thanks! That was indeed much simpler than what I've seen in other places

>>11193520
Great job posting what I was going to post.
I'll leave anon a hint (read at own peril):
For a number [math]n[/math], the number of even [math]a[/math] such that [math]a|n[/math] is [math]floor(\frac{a}{2})[/math].
For all the obvious reasons.

ESL brainlet here. Need to quickly refresh and learn a lot of maths stuff, while having forgotten a lot of high school maths, for an AI and Machine Learning college course without an official maths prerequisite, despite it being very much necessary.

Is this the right order to read the Manga Guides? Calculus -> Statistics -> Regression Analysis -> Linear Algebra.

if I have y''-3y'+2y=0, y=c1e^2x+c2e^x
can either of or both c1 and c2 be zero?

>>11193814
Have you tried substituting the solution when one (or both) of the coefficients is 0 in the ODE and seeing what happens?

>>11193814
yes
>>11193733
I'm not convinced manga meme math is the best way to go

>>11193733
Ideally you'll go into regression analysis knowing linear algebra, but the choice between stats or linear algebra first is yours.
>>11193846
I have a copy of the statistics one.
It's pretty good. Nice and intuitive, would recommend to high schoolers and freshmen.
Doesn't get into detail on the subject, tho, so he might want to complement things with some other text.

what is the eletron "doing" in it's energy level?

>>11193814
> y''-3y'+2y=0, y=c1e^2x+c2e^x
Note that c1=y'(0)-y(0), c2=2y(0)-y'(0) => y(0)=c1+c2, y'(0)=2c1+c2. Once you have the general form for y(x), you can evaluate it and its derivatives at x=0 to obtain a system of linear equations which relates the coefficients to the initial conditions.

In this case, either or both coefficients can be zero depending upon initial conditions. If y(0)=y'(0)=0 then you get c1=c2=0 => y(x)=0.

If 3 doesn't divide r, then I need to show that 3 doesn't divide r^2+s^2 for any s.

I'm thinking since 3 is prime and r^2+s^2 = (r+si)(r-si), then either 3 | r+si or 3 | r-si, but that can't be the case since 3 doesn't divide r.

Is this good enough?

>>11194118
>either 3|r+si or 3|r-si
Do you actually have that property of the Gaussian integers?
Anyhow, just do modular arithmetic like a normal person.

>>11194150
How would you prove it otherwise? Do you mean showing that r^2+s^2 will not be 0 in mod 3? And that's because r = 1 or 2 mod 3, and so r^2 = 1 mod 3, and s = 0 1 or 2 mod 3, and so s^2 = 0 or 1 mod 3.

>>11194170
Yes, and neither of those sums three.

pls explain

>>11194241
Nevermind, I think I get it. One of them has to be zero so the equation can be equal to zero. Is that it?

>>11194241
A*B=0 if and only if A=0 and B=0
c'mon, love

>>11194247
if A=0 **or** B=0
>>11194246
yes

>>11194247
>>11194248
thanks mate

what am i missing here

>>11194250
die CSteen

>>11187377
Oldest ice core is less than million year. Chances are sediment build up is where they probably get some of the info, others might is just extrapolation from there.

>>11194261
what cs course includes R

>>11194250
That there's no trick.

>>11194248
and is multiplication, or is addition

>>11194338
Yeah you're right, fair enough seemed like there was more to it

Why are complex numbers given a geometric representation of a 2D plane? Seems kind of arbitrary... does it flesh out more with some theories?

>>11194391
because complex numbers are 2 dimensional by definition
>why are 2D spaces representative of 2D planes

>>11194398
i is just an addition to algebraic numbers that solves sqrt(-1). I see nothing inherently 2D about that

>>11194408
you don't see anything inherently 2D about a 2D space? damn

>>11194408
complex numbers are of the form a+jb where a and b are real and j is the imaginary unit. it is trivial to show this is a 2D space.

why can't I use u-substitution for this integral:
x(lnx)^2, u=lnx ?

>>11186289
How much water lube do I need to sustain my bodily machine if it weighs 69kg?

Why do we need to make functions have the same denominator before summing or subtracting them?

>>11194597
Because when you're summing or subtracting fractions, you're implicitly using the distributive property ax + ay = a(x+y), where a is 1/(denominator).

>>11194484
think: what would you be integrating with respect to?

>>11194391
Imagine the number line as an actual line of numbers. Multiply a value by 1 and you can think of that as travelling 360 degrees on the number line. Multiply by -1 and you travel 180 degrees on the number line to the values negative. Multiply by i and you travel 90 degrees.

That's the way I was told to teach the kids and I think when you have the actual number line and visualisation in front of you it becomes pretty clear.

>>11194170
Modulo 3: 0^2≡0, 1^2≡1, 2^2≡1. So the only way that r^2+s^2≡0 is if r≡0 and s≡0, i.e. if r is divisible by 3. If r isn't divisible by 3 then r^2≡1 (mod 3) and r^2+s^2≡1 or ≡2.

>>11186289
I have a psychics question.
You know how the center of the earth generates incredible heat because of the crushing gravity?
I know trying to defeat entropy is such a jovial thing but I can't figure out how this effect falls under it. Gravity is just something that heavy objects generate, and the incredible heat generated is a form of energy.

I'm not working at any area of science, if you can't tell that yet.

>>11194953
>psychics
>
lol
the core isn't hot because of gravity

>>11194953
The Earth's core doesn't generate heat as a result of pressure. It *might* generate some heat due to the fission of heavy elements such as uranium, but we don't know for certain. It's entirely possible that the core is hot simply because the elements were created hot (by nuclear fusion) and space is a good insulator (being a vacuum) so the core hasn't gotten much colder in the mean time.

>>11194995
based on a quick search, apparently the temperature of the core is a remnant from when the earth formed, and also because of various forms of radioactive decay, but not necessarily fission

>>11186289
Why do we need proofs?? Why not just take all true statements as axioms??

>>11195031
Because then the challenge would be to ensure that all of our axioms are consistent with one another. To show they are consistent we need proofs.

>>11195031
how do you know it's ""true"" in the first place ?

>>11186289
Will humanity prevent ecological collapse without killing off 90% of the population?

>>11193871
Thanks, kind anon.

>>11195235
yes

>>11195241
But reports say no

>>11195267
k

>>11195267
k

How can I start making a nuclear bomb?

>>11195306
what?

What's an example that shows that continuous images of simply connected spaces need not be simply connected?

I was thinking f(x) = (cos(x), sin(x)) is a continuous function that maps from R (which is simply connected) to S1 (which is multiply connected).

Similarly, an example of something that shows that continuous images of multiply connected spaces need not be multiply connected,

I was thinking f(x,y) = x where f(0,0) is undefined, since it maps the punctured plane (multiply connected) to R (simply connected), but I'm unsure if this example really works.

Can someone verify these examples?

>>11195353
>f(x,y) = x where f(0,0) is undefined,
don't think that's continuous

>>11195306
>acquire uranium
>enrich it
>breed plutonium
>learn electronics, make normal explosives
>???????
>profit

>>11195306
get a bunch of uranium-235 or plutonium-238 and just put it in the same place, now you have a nuclear bomb, easy

>>11195353
>>11195354
A better example for the second case: f: R2 - {0} --> (0, infty) where f(x,y) = sqrt(x^2+y^2).

>>11195361
Best example coming in:
f(x, y)=(e^x, y), where (x, y) is in Cartesian coordinates, and the right side is polar.

1'st semester of computer science in germany, we have a subject called "diskrete modellierung" which translates to "discrete modelling" i guess, i can't find a english book on it, do you guys know any?

>>11195457
What topics are mentioned in the unit description in the handbook?

>>11195482
>Basics
The calculation of sets
propositional logic
Understanding evidence, leading evidence
>Toolbox: Graphs
Graphs and trees
Markov Chains and Google's Page Rank
>Toolbox: Regular and Context-Free Languages
Finite automatic machines
Context-free grammars and recursively defined structures
>Toolbox: Logic
First-level logic (predicate logic)

HOW the fuck do I learn to graph functions? I'm thinking something like
>|sgn-1|*(x-3)
things like that. What should I start with in the first place? Should I calculate a few points and draw the line or what is the right method?
This shit makes my head hurt

If I'm finding the proofs in my undergrad real analysis class too long and complicated, should I give up?

>>11195494
Yes, but you'll need to look for particular points of interest if you don't wanna waste your time or fuck up because you missed something big. e.g. if you have something like sgn(x-1) you always have to look at three points, any negative (so x-1<0 or x<1), when the argument is 0 (x=1) and when it's positive (x>1), since it's where the sgn function has jumps that could mess up your graph. Similar thing with absolute value functions. For these special cases you'll just need a little experience recognizing where/why you should focus.
For continuous functions you can do just fine with some random values, just use common sense to figure out how to match them. Like if the expression is e^2x, you aren't gonna sketch straight lines that match your points, nor are you gonna make it look like the function grows slowly when it goes off-bounds. Obviously the more points you calculate and draw the easier it gets, but you don't wanna waste to much time calculating everything of course

>>11195543
>If [...], should I give up?
No. Answer is always no.

>>11195353
>Similarly, an example of something that shows that continuous images of multiply connected spaces need not be multiply connected,
constant map

alright, I asked this a few days ago but got no proper answer, so I'll repeat the question and see what happens

let r and s be two skew lines. how can I find the equation of the line t that intersects r and s, and a point P ∉ rUs? I had an anon saying that there would be infinite lines to match this description, but after thinking for a while I realized that would only be the case if there wasn't P outside of r and s. in this case there should be a single line that fits the requirements, I just don't know how to go about finding it

and as a second stupid question, if you allow me:
>consider the Euclidian vectors AB = DC. ABCD (with the vertexes in this order) is a parallelogram
this is wrong, apparently. why? doesn't "with the vertexes in this order" imply that it can't be drawn in a Z shape?

>>11195650
vertices* I'm sorry, I'm not familiar with math names in English

>>11195492
Seems too diverse to be from any one book in particular but it's all fairly widely covered so you should be fine looking up anything you find you're stumbling on.

If you made a sword out of ice, would it actually part flesh if it were sharp enough? Or just cut slightly and bruise

Hello friends. How would I invert this (it's supposed to be an elementary problem), to get the pair <x1, x2> as a function of y, without knowing the answer a priori?

>>11195650
I'm not sure where your problem is in [math]\mathbb{R}^2[/math] every two lines cross each other at some point unless they're parallel to each other. With that in mind, t shouldn't be too hard to find.

>>11195866
oh, it is in R3. sorry, I know it's important info to mention lol

How do you find the intersection of the following hyperbola and circle?

xy=1
2x^2+2y^2=5

How do I expand a conditional probability with multiple arguments in both variables? For example, how would I expand [math]P(A,B\mid C,D)[/math]?

>>11195990
Substitute [math]y=\frac{1}{x}[/math] into the equation of your circle, and solve for [math]x[/math]. You could also use [math]x[/math] in terms of [math]y[/math] instead.

>>11195990
Just use newtons method.
>>11196014
He'll just get 2x^4-5x^2+2=0 which isn't much better to solve.

>>11196032
>which isn't much better to solve.
sure it is. use the quadratic formula.

>>11196035
>^4
>quadratic

>>11196014
>>11196032
It helped, could factor 2x^4-5x^2+2=0 into (2x^2-1)(x^2-2)=0

>>11196042
yes?
let z=x^2 then you get [math] 2z^2-5z+2=0 [/math] and you may solve for z. Or you could do what >>11196048 did.
Newton's method is overkill and I study engineering~

>>11196061
not him but i'm interested. what do you do afterwards? you still have x^2

>>11196073
take the positive and negative square roots of z to get x, duh

>>11194484
To go from integrating in terms of x to u you would substitute xdu=dx, getting x^2 *u^2 du which doesn't really help here.

>>11196011
what does "multiple arguments" mean ? intersection ?

>>11195650
>consider the Euclidian vectors AB = DC. ABCD (with the vertexes in this order) is a parallelogram
> this is wrong, apparently.
It's not apparent to me. It may be that they're excluding degenerate cases (lengths or angles which are zero) from the definition of a parallelogram. It's pretty straightforward to show that AB=DC=>AD=BC, i.e. if one pair of edges have equal-and-opposite vectors then so do the other pair.

Is it possible to take continuous measurements/observations of something. I know the answer is no but I'm not sure why. By observation i mean in the quantum sense of collapsing a wave function.
As a second question, when a wave function collapses does it collapses into a delta function or a gaussian with width determined by the precision of the measurement/observation?

>>11196101
Doesn't ab=dc mean that both lines are the same with same end points? Then abcd would be a line.

>>11196095
I'm guessing intersection for [math]A[/math] and [math]B[/math]. For [math]C[/math] and [math]D[/math], I saw something called naive Bayes that takes care of it.

>>11196101
by apparently I mean that in the correction it says it is wrong, but I don't know what's wrong about it. it's from a Analitic Geometric exercises, so AB and DC are vectors, which can have the same components and still cohexist as different vectors in the space, differently from line segments for example (in which case saying AB = DC would imply they're the same line exactly). but I don't know Latex so I didn't bother using the proper vector notation, I'm sorry.
as for you question, I think so too. I'm clueless as to why it would not shape a parallelogram

>>11196149
from an Analitic Geometry exercises list* jesus christ i need to work on my english

>>11196109
I considered that, but it says ABCD (vertices in this order)", and I don't think you can call the points of a straight line as vertices (I could be wrong though)

What's the easiest way to find the period of a function? like sin(x) I know it's 2pi, but what would be the procedure for others like |sinx|, sin^2 x ?

>>11186289
how to calculate mean effective value
pic related

>>11196185
> What's the easiest way to find the period of a function?

If ∀x·f(x+T)=f(x) then T is a period of f. It follows that ∀n∈a·∀x·f(x+nT)=f(x). The fundamental period of f is the smallest T for which the original equation holds, with any integer multiple also being a period. Proving that T is a period of f is usually straightforward; proving that it's the fundamental period (i.e. no lesser period exists) may be somewhat harder. If you can plot a graph over a period it's usually quite obvious whether that period is the fundamental period or a multiple.

> like sin(x) I know it's 2pi, but what would be the procedure for others like |sinx|, sin^2 x ?
If f(t) has period T then so does g(f(t)), but the latter may have a smaller fundamental period than the former. E.g. sin(x) has a fundamental period of 2π while sin^2(x) and |sin(x)| both have fundamental periods of π following from sin(x+π)=-sin(x) and both x->|x| and x->x^2 being even (symmetric) functions, effectively discarding the minus sign in the previous equation:
|sin(x+π)| = |-sin(x)| = |sin(x)|
sin^2(x+π) = (-sin(x))^2 = sin^2(x)
This proves that both have period π, but proving that no lesser period exists is harder. For a "methodical" approach, you could try finding the Fourier transform and showing that it is non-zero only for ξ=n/T.

>>11196185
>easiest way to find the period of a function
You usually have a geometric reason to think a function has some period. The sine, for example, is given as a function of the angle, but it's fundamentally a function from a point in the circle to the x coordinate, with the circle looping according to angle. If you don't have any geometry, check if you can write it in terms of other periodic functions.
And once you have some periodicity, you can divide it by primes and check if it accepts refinement.
Say, |sin x| has at least period 2pi since sin x has. Try sharpening that further by graphing it.

>>11195650
Call the lines a: x+yt and b: z+ws, where x, z are their displacement vectors and y, w are the direction vectors, with parameters t and s defined for all the reals

First of all, notice that if P is any point in either of the planes given by p1: x+yt+ws or p2: z+ws+yt (so the planes generated by the direction vectors of both lines that contain one of the lines), then it is impossible to find a line that connects P and both lines a and b. That is because if you connect P with any point of the line that is contained in the respective plane, the resulting line can't ever escape that plane, and that plane is parallel to the second line so there is no intersection

And actually, you can use these planes to find the line you are looking for. If P isn't in either plane, then project it into a one of the lines (say a), using the shortest distance between a line and point. That projection line you find (which I'll call C) intersects both planes: it intersects p1 at one (the closest) point of the line a and it intersects p2 cause both planes are parallel. Find the intersection of C and p2 and displace it. Since lines a and b aren't parallel, then in a plane (p2) they have to intersect, which means that by manipulating the parameter t (so C remains intersecting line a) you will eventually have to land in line b. And you do that by finding which values of s and t give you the intersection of C and p2 in the plain equation z+ws+yt, and setting t=0 which immediately places you in line b

To finish it just find the line that connects P and the intersection of line c and plane p2, and the resulting line will intersect a,b and P.

>>11195543
read a proper analysis textbook, spend time on math stackexchange and look at Terence Tao’s site for Analysis he has very good tips on how to handle basic analysis proofs. If you’re getting an atrocious grade and finish with damage to your GPA at the end of the quarter in spite of honest efforts to improve, yes you should drop the math degree or focus more on a different field of math.

>>11196485
holy fucking shit. anon you're so fucking right. thank you so much. I hope I get to be as clever and good at math as you someday. this is actually such an abstract solution that I'm not sure if I understood it completely and am still digesting it, but I think I got the gist of it. it didn't even occur me to form planes out of their direction vectors or projection, that's absolutely genius. again, thanks a lot! I'll try that right away

>>11195650
> let r and s be two skew lines. how can I find the equation of the line t that intersects r and s, and a point P ∉ rUs? I had an anon saying that there would be infinite lines to match this description, but after thinking for a while I realized that would only be the case if there wasn't P outside of r and s. in this case there should be a single line that fits the requirements, I just don't know how to go about finding it
This is specifically for the 3D case, right?

P and r define a plane. The plane will intersect s at exactly one point S (if r and s are skew, then s cannot be parallel to the plane containing P and r). The line through P and S will intersect r at exactly one point R. Thus R,P,S are colinear and the resulting line is uniquely defined.

If r and s are each defined by two distinct points on the line, r1/r2 and s1/s2, the normal to the plane containing r and P is N=(P-r2)×(P-r1) and the plane itself is {x : N·x=N·P}. If the intersection with s is S=s1+t(s2-s1), then substituting x=S gives:
N·S=N·P
=> N·(s1+t(s2-s1))=N·P
=> N·s1+N·(s2-s1).t = N·P
=> N·(s2-s1).t = N·P-N·s1
=> t = N·(P-s1)/N·(s2-s1)
=> S = s1+(N·(P-s1)/N·(s2-s1)).(s2-s1)
= (N·(s2-P).s1-N·(s1-P).s2)/N·(s2-s1)

Performing the same calculation with r and s swapped gives you R.

A linear algebra question

If we have the linear transformation [math]L: \mathbb{R}^3 \to \mathbb{R}^3[/math] with eigenvalues -1, 0 and 1 and corresponding eigenvectors [math]v_1,v_2,text{ and} v_3[/math] how can i find the image of L, i.e [math]Im(L)[/math]. I know it is a singular transformation since it has an eigenvalue of 0 so its kernel is generated by [math]v_2[/math] but I don't know if that helps.

>>11196608
That's good, just a few things to clear up then, since I worded them poorly:
>Since lines a and b aren't parallel, then in a plane (p2) they have to intersect
Strictly speaking it's not a and b that intersect here, since of course a is in a whole different plane (p1) that is parallel to p2, what I mean here is the projected line (projected through the point P) of line a that lies in p2, so kinda what you'd get if you translated line a from p1 to the other plane. In a plane any two different lines that aren't parallel have to intersect, so the rest follows as usual: just change the parameter t that lets you move around in the direction of line a.

>To finish it just find the line that connects P and the intersection of line c and plane p2
Saying "the intersection of line c and plane p2" is incorrect, maybe you already got what I meant but obviously after you perform the translation I had mentioned before, the new point is no longer the intersection of C and p2 so that was my bad. If anything you can call it the displaced intersection.

>>11196740
The image of L is merely the space that L spans. You said it is singular, that should give you a hint as to the dimension of image(L).

>>11196740
Linear maps are determined entirely by their behavior at the basis. The eigenvectors with different associated eigenvalues are all obviously linearly independent, since if they weren't then by applying the definition of eigenvalues you'd get the the image of one eigenvectors would have to images: one when it's scales by it's eigenvalue and the other when it's linear combination is scaled by the generators' eigenvalues

You have three linearly independent (eigen)vectors in a three-dimensional vector space, so they form a basis. And you also know how they transform because of the definition of eigenvectors.

>>11186289
quick ask: could someone show me how to use the Mohr's Circle?
just want to make sure I get it properly.

>>11196770
don’t reply if you don’t know how to think or speak clearly retard

>>11196770
>then by applying the definition of eigenvalues you'd get the the image of one eigenvectors would have to images: one when it's scales by it's eigenvalue
Holy fucking crap I don't know how that ended up being written so terribly without me noticing earlier
By applying the definition of eigenvalues you'd get that the definition of one eigenvectors could have two images (assuming they aren't linearly independent): one that is its image when you scale it times it's respective eigenvalue and the other when you scale the linear combination (in terms of the other eigenvectors) times the generators' respective eigenvalues

I took a general topology class and now I know separation axioms and delved deeper into stuff I learnt in real analysis but still didn't meet any holes counting and studying weird shapes that you people talk about. What class is that?

>>11196775
MOHR'S CIRCLE PROCEDURE (to find principle plane stresses)

1) Draw a coordinate system with [math] \tau [/math] being the vertical axis and [math] \sigma [/math] the horizontal

2) Place point [math] C=\Big(\frac{\sigma_x+\sigma_y}{2},\ 0\Big) [/math] on the coordinate system

3) Place points [math] A=\big(\sigma_x,-\tau_{xy} \big) [/math] and [math] B=\big(\sigma_y,\tau_{xy} \big) [/math] on the coordinate plane. You should have a straight line at this point. This is the diameter of Mohr's circle.

4) Draw circle.

5) The angle between [math]A[/math] and the positive [math]\sigma[/math] axis is TWICE the angle between [math]\sigma_x[/math] and [math]\sigma_1[/math]

6) The radius of the circle is [math]\tau_{max}[/math]

Or, you know, you could just use the rank 2 tensor transformation law ya dingus

[eqn] \sigma'=Q\sigma Q^T [/eqn] with Q being the rotation matrix.

Or, you could use this (can handle 3D stress) https://www.desmos.com/calculator/opc1o0cwfz

>>11196841
Forgot to mention that [math]\sigma_1[/math] is the larger value at which the circle intersects the [math]\sigma[/math] axis, and [math]\sigma_2[/math] is the smaller value.

>>11196791
algebraic topology

>>11196841
thanks, this is great.

>>11196759
>>11196770
Dope! thanks goyims

I had to swap out of my Remimi wallpaper because I needed to use my laptop for a presentation, does anyone have any good ones?
>>11196032
>just use Newton's method

>be computer scientist
>go into /sqt/
>see myriad problems to answer
>don't know how to solve them
>"just approximate it lol"
What even is the point of posting that?
>>11196197
Give q explicitly as a piecewise linear function and split up the integral according to those pieces.
>>11196740
A nontrivial subspace of [math]\mathbb{R}^3[/math] is either one, two or three-dimensional.
It's not three-dimensional, because [math]v_2 \neq Im(L)[/math], and it's not one-dimensional because there is no [math]\lambda[/math] such that [math]L(v_1)=- v_1= \lambda v_3 = L(\lambda v_3)[/math].
Thus, it's two-dimensional.
Note: this sort of trickery doesn't work in more than three dimensions, you'll need to do it properly.
>>11196791
>holes counting
Homotopy theory or algebraic topology, different names for the same subject.
>weird shapes
Low-dimensional and high-dimensional topology.

>>11197040
> [math]v_2 \neq Im(L)[/math]
[math]v_2 \notin Im(L)[/math]

>>11197040
>>11197063
There's also the highly abstract and trivial solution kiddos just can't handle:
[math]L(span(A))=span(L(A))[/math], for any linear map L.
I really like this one.

why are chalkboards still used? whiteboards seem better in every way?

>>11197296
chalk never fails to make a mark
chalk never fails to get wiped off a board
chalk is for the american, the one who loves freedom and his country
"""whiteboards""" are something else entirely

>>11197296
Chalkboards smell better.

>>11197301
even 2ky knows what's up

Anyone here proficient in deep learning?

I don't see where the tan in the denominator came from

>>11197330
in the very first line you are letting x=4*tan(t) so x^4=(4*tan(t))^4

>>11186289
Can someone please help me with a basic induction proof?

The problem goes like this:

Prove that:
[eqn]\forall n \in \mathbb{N} \\ 1^2+2^2+\dots+n^2 = \frac{1}{6}n(n+1)(2n+1)[/eqn]

I confirmed for the n = 1 case and then I assumed the problem statement is true for my induction hypothesis, so for my n+1 case I end up with the following expression:
[eqn]\displaystyle \sum_{i=1}^{n} (i+1)^2 = \frac{1}{6}(n+1)(n+2)(2n+3)[/eqn]

The left hand side evaluates to(by the induction hypothesis):
[eqn]\displaystyle \sum_{i=1}^{n} (i^2+2i+1) = \frac{1}{3}n^3 + \frac{3}{2}n^2 + \frac{13}{6}n[/eqn]

Whilst the right hand side evaluates to:
[eqn]\frac{1}{6}(n+1)(n+2)(2n+3) = \frac{1}{3}n^3 + \frac{3}{2}n^2 + \frac{13}{6}n + 1[/eqn]

Wtf is going on?

Imagine that we have the [math]X_1, X_2, X_3[/math] random variables that have the following properties: [math]E(X_i)=0[/math] and [math]E(X_iX_j)=min(i,j)[/math].

Also consider that we have [math]Y_1, Y_2, Y_3[/math] defined as:

[math]Y_1=X_1, Y_2=X_2-X_1, Y_3=X_3-X_2[/math]

If you do the math you will find that: [math]E(Y_i)=0[/math] and [math]E(Y_iY_j)=0[/math]. Meaning that they are two by two independent. We need to find [math]E(X_3^2|X_1,X_2)[/math] and we could do:

[math]E(X_3^2|X_1,X_2)=E([X_3-X_2+X_2]^2|X_1,X_2)=E([Y_3+X_2]^2|X_1,X_2)[/math]

[math]E(Y_3^2|X_1,X_2)+X_2^2=E(Y_3^2|X_1,X_2)+1[/math]


This is the problematic part, is it valid to do:

[math]E(Y_3^2|X_1,X_2)=E(Y_3^2|Y_1,Y_2)=E(Y_3^2)=0[/math] since they are independent.


I think this is a fallacy and the correct answer can only be found by computing [math]E(X_3^2|X1,X2)[/math], if this is impossible then we cannot have an answer.

I know this image is a joke, but hypothetically speaking, what would happen if someone attempted to hold their shit in for an entire month? Would they just release it all while sleeping?

>>11197542
Dont despair anon, your left hand side is done wrong you need to prove that.

[math]16n(n+1)(2n+1) + ([n+1]+1)^2=16(n+1)(n+2)(2n+3)[/math]

Since you are adding the n+1 case to the formula applied to the case n it should result in the same thing to applying the formula to the case n+1. If the left hand side proves equal to the right side then you completed the proof

>>11197551
jesus crhist why it did not evaluate the equation?
Here it is again:
[math]16n(n+1)(2n+1) + ([n+1]+1)^2=16(n+1)(n+2)(2n+3)[/math]

>>11197553
REEEEEEEEEEEE
[math]16n(n+1)(2n+1) + ([n+1]+1)^2=16(n+1)(n+2)(2n+3)[/math]

If this one does not work you are on your own

>>11197550
Fecal retention

It's not fun

>>11197554
Please someone tell me why my equation is not working. TEX preview says its fine

>>11197554
Why are you adding [math]((n+1)+1)^2[/math] to the left hand side instead of [math](n+1)^2[/math]?
And why is there a difference between adding that term and evaluating the sum as I did?

>>11197559
Tex in /sci/ is sometimes fucky, dont stress about it

>>11197338
ohhhhhhhhhhhhhhhhhhhhhhhh
thank u

>>11196983
>>11196992
>>11197568
yw~

>>11197559
put spaces between the brackets and your TeX like
[math] TeX goes here [/math*]
[eqn] TeX goes here [/eqn*]

>>11197566
Whoops, I made a mistake. It indeed should be [math](n+1)^2[math]

About your second question they are of course equal, we know that from prior knowledge that the formula is correct. The issue here is that you need to prove it and it would be very difficult to factorize that polynomial.

Now if you cannot prove it I would recommend using my method since you can actually do factorization.

Put it on wolfram alpha and you will see that your equation is correct

>>11197597
Yeah when I evaluate the sum I end up with what I stated in my first post, it goes like this:
[eqn]\displaystyle \sum_{i=1}^{n}(i^2+2i+1) = \\ \displaystyle \sum_{i=1}^{n} i^2 + \displaystyle \sum_{i=1}^{n} 2i + \displaystyle \sum_{i=1}^{n} 1 = \\ \frac{1}{6}n(n+1)(2n+1) +n(n+1) + n[/eqn]

That simplifies to what I stated in my first post, which is missing a + 1 that you get when you evaluate [math]\frac{1}{6}n(n+1)(n+2)(2n+3)[/math]

Ill try your method, but id also like to know why what I'm doing is not working.

Thanks for the help

>>11197040
>newton was a computer scientist

>>11197542
>>11197619
> The left hand side evaluates to(by the induction hypothesis):
> [math] \displaystyle \sum_{i=1}^{n} (i^2+2i+1) [/math]
The sum is [math] \sum_{i=1}^{n+1} i^2 [/math], which is equivalent to [math] \sum_{i=0}^{n} (i+1)^2 [/math] = [math] 1+\sum_{i=1}^n (i+1)^2 [/math]

You're supposed to extend the sequence (same initial element, final element incremented by one), but you shifted it (replacing i with i+1 effectively increments both the initial and final elements by one), discarding the initial element of the sequence.

>>11197801
He's saying newton's method as an algorithm is something a CS would quickly jump to, not that newton was a CS, hun

>>11197922
Shit yes, thats actually kind of obvious, now I feel dumb as shit kek.
Thanks for the help.

I need help
Can someone prove that (2020^k +1) cant be a square number?

>>11198375
If a is a square root, [math]a ~ (mod ~ 2020) \cong \pm 1 [/math].
So [math]a= 2020n \pm 1 [/math].
Now, you try the two alternatives and show neither works.

I know someone with a PHD in Pathobiology. How much math should I expect her to know? Serious question.

>>11195834
nobody?

>>11198375
yes, 2020=1 mod 3, so 2020^k + 1 is 2 mod 3 so it's not a square

>>11198452
doesn't that just mean it's not square modulo 3

>>11198461
A square is a square modulo 3. If it's not a square module 3, it's not a square.

what's the answer to [math]\displaystyle \int_{ \{ |z-i|=1 \}} \frac{1}{(z^{2}+1)^{3}}dz[/math] .

>>11198596
[math](z^2+1)=(z+i)(z-i)[/math]
And then you apply the residue theorem.
>>11198413
None.

>>11198610
>None.
Really?

>>11198610
so it's [math]2\pi i[/math]?

>>11197559
you need to put a space after the first tag and a space before the last tag

>>11198653
Should be [math]6 \pi i[/math] because of the third power.

>>11198677
Wait, my bad, been a while since I've studied this.
It just zeroes.

>>11198682
0?

How can it be that jannies are such faggots

>>11198694
Yeah. [math] \cint \frac{1}{z^n} [/math] with n>1 don't contribute to the residue because you can analytically give their integrals.
i.e. [math]\frac{d}{dz} z^{-1} = - z^{-2}[/math] and so on.
All of its poles have order above one, and it's meromorphic everywhere other than i and -i.
So the integral zeroes.

Dumb question here, so I'm trying to iterate some ODEs on the increase of partial density
[math]\rho_{(i,t)} = something[/math]
with i is a certain gaseous species in the system and t is timestep.
For every iteration of timestep, do I need to calibrate(?) the partial density instead of just using the ODEs? like
[math]X_{(a,t+1)}=\frac{\rho_{(ia,t+1)}} {\Sigma\rho_{(i,t+1)}}[/math]
with ia=dummy species a
[math]\rho_{(a,t+1)}=X_{(a,t+1)}.\rho_{(g,t+1)}[/math]
with g=all gaseous species (assume to be dry gas)
or just using the ODEs?

Can I study biology in college if I am a complete and utter brainlet with a good memory?

Xa(t)=ρa(t)/Σ(ρi(t)) so yes, Xa(t+dt)=ρa(t+dt)/Σ(ρi(t+dt)) with dt being a small time step.
I not sure I really understand what your question is l, exactly.

>>11198734
Xa(t)=ρa(t)/Σ(ρi(t)) so yes, Xa(t+dt)=ρa(t+dt)/Σ(ρi(t+dt)) with dt being a small time step.

I not sure I really understand what your question is, exactly.

>>11198736
Yes. You still need to work hard and be able to do some math.

>>11198734
Re-read it, and no Σρi=/=ρg

>>11197931
>mathematicians don't understand sarcasm

This feels like the dumbest question I've ever asked in my life.

Can I draw a shape with only straight lines and with 45 degree inner angles, that doesn't overlap with itself?

My current best is pic, but it has an overlap and I'd like to avoid that if possible. I feel like there has to be some easier solution but I'm a retard apparently.

>>11198872
Autists aren't known for their ability to recognize verbal subtleties.

>>11198892
Does either one of these work as a shape?
Otherwise, there's a formula out there that gives you the sum of the internal angles in a polygon with n sides (and thus, n vertices). You might want to check if there is some number of sides a polygon can have for all of it's internal angles sum to 45n, where n is the number of vertices.

>>11198461
Squares cannot be congruent to 2 modulo 3.
(3n+k)^2 = 9n^2+6kn+k^2
The 9n^2 and 6kn terms are ≡0 (mod 3), so (3n+k)^2≡k^2 (mod 3). More generally, the residue of any expression involving only addition and multiplication is unchanged by adding multiples of the modulus to any of the terms involved.
(am+x)+(bm+y) = (a+b)m+(x+y) ≡ x+y (mod m)
(am+x)(bm+y) = abm^2+(ay+bx)m+xy ≡ xy (mod m)

k can be 0, 1 or 2. 0^2=0, 1^2=1, 2^2=4≡1 (mod 3). Thus a square cannot be congruent to 2 modulo 3. Formally, 2 is a "quadratic nonresidue" modulo 3. Similar rules apply for other moduli; search on "quadratic residue" for more details.

>>11198909
Thanks, but those don't work. I need the shape to be closed so if you walked along the edge, you'd eventually end up back where you started.

I'll have a look at some tools that might help, not sure where to start though.

I was watching a video about a 1906 steam car, and it seemed pretty cool, albeit quirky and difficult to get working. How efficient and eco-friendly could we make steam vehicles with today's technology?

>>11198892
For a simple polygon, i.e. polygonal Jordan curve, (without hole and no self-intersection), you can't have that.
The reason is that for all simple polygons, the sum of all inner angles must be [math] \ge 180^o[/math].
I think you can write a proof based on these. I'm too lazy for it, sorry.

>>11198892
For a closed loop of line segments, the sum of the "turn" angles at the vertices must be a multiple of 360°. Each interior angle is 180° minus the turn angle. For a non-overlapping path, the sum of the turn angles must be either 360° or -360°.

A non-overlapping path with 45° interior angles would require 135° turn angles, and 360 isn't a multiple of 135. For an overlapping path the concept of "interior" angle gets a bit fuzzy, but apart from that it's straightforward to construct a path with an equal number of clockwise and counter-clockwise turns (e.g. figure-of-eight) for which the sum will always be zero.

FWIW, this is all related to winding numbers.

>>11198930
Depends what energy source is used to generate the steam. It about the same situation as an electric car refueling on a coal power grid, environmentally speaking.

>>11198947
>>11198948
Thanks. I feel like I've wasted a lot of time working on this, now...

I'll have to make do with the thing I originally posted, with one intersection. It's for a uni project and it's going to be a zig-zaggy path to walk on, but it's going to be really messy with an overlap, but I guess if there's no other option then it's also the best option.

What happens when someone proves string theory right?

>>11198892
>>11198947
there exists a theorem of hopf which says that any embedded closed curve has turning number 1 or -1 (the tangent vector completes a rotation exactly by 2pi or -2pi). for a piece-wise smooth curve, the computation of turning number involves integral of the curvature with respect to the arc length, however for a polygonal curve the curvature is always zero and the only thing that contributes is the "jump" of the angle along the corners. you can deduce from this whether it is possible or not (I too am lazy to write the proof).

>>11198959
What are you doing, and what problems are you having?
If you have trouble dealing with overlapping edges, you can make a new vertex at the intersection, and break the self-intersecting polygons into two (or more) smaller polygons.
That's what people do in computer graphics.

>>11198960
Physical theories cannot be proven right

>>11198892
No, it's not possible.
The sum of the angles of an n-gon is (n-2)*180°.
The sum of the angles of your hypothetical n-gon would be n*45°.

Let's equate the two:
(n-2)*180 = n*45
180n - 360 = 45n
135n = 360
n = 8/3

Of course an (8/3)-gon doesn't exist, so it's not possible.

could it be written as pic related?

also what does this mean?

>>11199249
It couldn't.
>>11199254
[math]V \times V = [(x, y) such that x, y \in V] [/math]

>>11199266
why since "e" is a sub-element of i,j but i,j are elements of v?

>>11199272
I don't get what you are saying, E is not a "sub-element" of i,j, first of all i and j aren't sets, and even if they were, E isn't an element (no such thing as a sub-element, if is either an element or not, and if it's a collection of elements then it's a subset instead) of the specified set.
(i,j) IS a set, but it's not a set where E is contained, it is instead a set that is usually formally defined as {{i,j},{i}}, but all you need to know is that it's an ordered set (ordered pair, to be precise). E isn't neither a subset nor an element of (i,j), instead E contains elements (i,j), although maybe not all of them for all we know, we just know that it contains some.
And while i,j are elements of V individually, the ordered pair (i,j) is an element of [math] V \times V [/math] instead, which by definition is the set of all ordered pairs (i,j) such that [math]i \in V, j \in V [/math]
In other words what you have is [math] E \subseteq V \times V [/math], or E is a subset of that cartesian product VxV

>>11198909
PEDO ALERT

>>11199355
>th-thanks

>>11197546
This on please :(

>>11198974
It's not really a computer graphics problem, more of a general thing.

I'm trying to make a path a person can walk on in a VR environment, where their turning is dulled by 25% in the game. So, they turn 180 degrees in real life, and only 135 degrees in the game. This way, in theory, I can have the person explore a rather large virtual area with only a small real world area. And that in itself is really easy, you can just have a bunch of 45 degree angles zigzagging across an infinite plane.

The problem comes when I try to have the person get back to where they started in a natural way. In addition, there'll be an extra VR tracker attached to a physical object for the person to interact with, and that needs to be in a place where they can interact with it at the point when they need it, but also aren't walking into it constantly (because with the zigzags, they walk back and forth on the same line - having the object there would mean they bump into it).

My plan is to have a bit of path that sticks out of the zigzags, which forces the player off their single line, into an area where the object exists. Then when they're done they get back on their line. But then they're going a different direction in VR and I want them to end up back where they started. And doing that is making my brain melt.

Best solution I have is pic, but it's wrong and messy. The bits with 90 degree turns are where they go off to touch the object, then come back on course. Only issue is I only need them to do that once, and any further times risk hitting the object more. We can avoid that by having the number of zigs and zags be different at places where they shouldn't hit the object, but... argh.

You see why my brain is melting.

Can anyone explain to me why the derivative of ln(cos(x)) is 1/cos(x) and not -sin(x)/cos(x). I'm probably being stupid here but I thought the derivative of ln(x) is x prime over x.

>>11200613
>what is the derivative of x wrt to x