/sci/ - Science & Math

If [math]I = \int f(x)\ dx[/math] is it true that [math]\ln(I) = \int \ln(f(x))\ dx[/math]?

>>15183223
No.

>>15183237
Why not?

>>15183251
yes if f(x) is smooth, but generally, no

Good Afternoon /Sci/entists!

I still have this problem.

>>15183020

I am going to ignore the problem and finish getting everything else typeset in hopes someone knows the answer. If now I guess I will read more things about latex and fix it myself.

I decided filling every margin with maids is probably an impossible task because I made over 9000 pages. Instead I will use the wide margins where I write and put maids and where I am just drawing data I will use normal margins and draw Maid Space, but no maids.

This reduces the maids needed per book dramatically, and I can always just search "huge_boobs maid" on safebooru.

>>15183208
I like your rake-box-triangle-pole.

Thank you /sci/entists for reading my post.

Supposing you have a limited time frame to study, which is better: doing hard problems right away after learning a subject or doing smaller, easier problems first and build up on difficulty?

>>15183208
that is the weirdest 2hu ive ever seen

What's the difference between the 6th edition and the 7th?

What's the difference between the international edition and the US/Canada one?

Any good books/resources for studying intro circuits?

>>15183208
Thinking about that quip about GR, matter tells spacetime how to curve, curved spacetime tells matter how to move - does spacetime itself curve at the speed of light? assuming that's a meaningful and not completely retarded question to ask.

>>15183711
What do you mean by "does spacetime itself curve at the speed of light" ? Spacetime doesn't move, it's the background for things to move in.

>>15183716
>Spacetime doesn't move
What's the difference between spacetime curving and spacetime moving? Or am I thinking about this wrong.

I mean somehow the information about matter/energy/whatever has to be communicated to the spacetime manifold thingamabob so it knows how to curve right? That information should travel at the speed of light?

I'm imagining spacetime like a body of water, and matter moving in spacetime is like a drop of water falling on to it. And the wave traveling through the water in response to the drop is like spacetime curving in response to the matter. That wave has a certain speed associated with it, shouldn't space time itself have a certain speed or something associated with it? Is that basically what gravitational waves are? But gravitational waves aren't space time. Just like the body of water isn't the wave itself...

I don't know, I barely started reading about GR just trying to get a reasonable intuition before going into details.

>>15183730
I guess the more accurate analogy would be something like - the body of water slightly deforming in response to the drop falling on to it should have some kind of speed associated with it. That's what I'm thinking of when I ask if spacetime moves at c in response to matter.

>>15183730
>>15183735
Gotcha. You are talking about how changes in the curvature propagate. And the answer to your question is yes, those changes travel at the speed of light. The recent measurements of gravitational waves confirmed this. So if the Sun suddenly vanished the Earth would carry on moving along its curved orbit around the Sun for 8 minutes before it noticed.

What is the internet gas made of?

>>15183802
Ask /co/, this is the science board.

>>15183743

Biologically speaking, how do I find math?

>>15183818
How cute. Utterly wrong, but cute nonetheless.

How come scientific explanations are so shit? Why is there almost no effort made to connect concepts to their foundations in human experience? Do people have any idea what the fuck they're talking about?

>>15184029
> How come scientific explanations are so shit?
Subjective. Give an example.
> Why is there almost no effort made to connect concepts to their foundations in human experience?
Human experience is often wrong. If physicists stuck to human experience there would be no quantum mechanics.
> Do people have any idea what the fuck they're talking about?
Usually.

do atoms actually exist or is it just a model we made up that sorta lines up with what we observe?

>>15184081
both. the existence of such basic "building blocks" for matter is not really up for discussion anymore and they have even been imaged with the help of very special and complex microscopes. but the way we understand and study them is still just a model that best replicates their behavior. a very accurate model so far, but a model nonetheless. granted, it is hard to do much better when we are talking about objects that are so small they can't even interact with light and that are made up of hadrons and fundamental particles with such bizarre properties.

scientifically speaking, how did Johnny beat the devil? the devil's fiddle interlude was way cooler

Let [math]G[/math] be a locally compact group (may assume it's [math]\sigma[/math]-compact or 2nd countable) with Haar measure [math]\mu[/math]. Suppose [math]\xi \in L^2 (G, \mu)[/math] is translation invariant, i.e. for every [math]g \in G[/math], the functions [math]t \mapsto \xi(g^{-1} t), t \mapsto \xi(t)[/math] are equal in the [math]L^2[/math]-sense. Is [math]\xi[/math] almost surely constant?

>>15184156
The devil cannot create.

>>15183802
>his superpower is being a smartphone
This character had potential and they wasted him. They could've had him born in like the early/mid 80s so his power of being a smartphone was actually pretty good, until smartphones were invented and became widespread.

They could have set the story in like 2007. He's in his prime as a hero and now suddenly everyone who spends a couple hundred bucks on a new device is his equal in power.

That would be an interesting story. In 2004 he's godlike because nobody else has this ability. In 2009 he's on par with anyone who went to an Apple Store. Showing how he adapts to his superpower effectively being obsoleted by the natural progression of technology would be interesting.

>>15183802
>What is the internet gas made of?
Memes.

How concerned should I be about a feces-related infection if I wiped too hard and my butthole is bleeding? Should I disinfect it or should I just leave it alone and wipe more gently next time?

>>15183261
>>15183020
I don't see crooked squares. Do you mean the fact that they are not properly aligned? If so, maybe the \phantom{} command can help.
use \text{} for text, that should properly parse spaces.
I also don't understand what is too fat and not tall enough.

>>15184029
i try my best, but you people are just so retarded sometimes.

Tips for making a bunch of flash cards quickly? I got some notes, but didn't bother making flash cards, now I'm wondering what's a quick way to do it? I heard the best way is
>each card should be independent
>frame as a quesiton, so you can have double sided cards that asks you the question AND what is this topic on (so something like "who sucks dicks?" and "who is OP?" would be a card)
Anything else I should do?

>>15183600
The Art of Electronics

>>15184325
You should use water next time you disgusting fuck.

How did Franscisco the Man beat the devil?

>>15184293
dude, did you HEAR his fiddle interlude?

>>15184348
Thank you for telling me. I decided the boxes should not be there in this drawing. They are just visual noise so that problem became moot.

\text{} worked nicely and I attached the results. By too fat I mean it is wider than it is tall and I want to make the drawing shaped more like a square.

>>15184405
You can try for example

\renewcommand{\arraystretch}{2}
<matrix>

which would double the space between the lines. I expect this will look quite janky, but it's worth a try.

Also, to only have it affect the current matrix you should surround it with \begingroup and \endgroup.

>>15184293
neither can johnny dipfuck, learning a skill isn't creating, it's just fucking around. i don't see why he didn't just switch their solos if he wanted johnny to win. the devil's is objectively better. just make satan's song brighter, and make that the catchy tune that everyone knows, and make johnny's darker and devilish and with the backup fucks. makes no sense.

>>15184156
it only sounded nice post-editing, to make it a more believable matchup (although they went too far). if you were there to hear it live you'd realise a fiddle of gold actually sounds fucking terrible when played

>>15184368
cloze cards are the quickest

>>15184369
Wait meant for >>15183701

johnny got the home cooking from the judges, it was rigged from the start

>>15183208
Tried my hand at doing this since the usual 2hu anon isn't here.

Unanswered questions:

Maths questions:
>>15178581
>>15181990

Physics questions:
>>15171159
>>15174813
>>15175078

Chemistry questions:
>>15173180

Biology questions:
>>15180451

Engineering questions:
>>15177835

Maid questions:
>>15183020

Stupid questions:
>>15171328
>>15171534
>>15176020
>>15176656
>>15176670
>>15177381
>>15179072
>>15179263
>>15179520
>>15179707
>>15179803
>>15179826
>>15182468

you people are so fucking high. i could repeatedly rub my balls on a taut shoelace and make a better solo than the devil.

>>15184687
do it then, let's hear your fiddle solo

>>15184243
[math]0 = \int_{\Omega} \int_{\Omega} \| \xi (g^{-1} h) - \xi (h) \|^2 d \mu (h) d \mu (g) = \int_{\Omega} \int_{\Omega} \| \xi (g^{-1} h) - \xi (h) \|^2 d \mu (g) d \mu (h)[/math] so it's a.e. constant.

Is it normal to have learned absolutely nothing from physics classes? I took the two required for my major and did well in them (a- in both) but ive learned absolutely nothing. Now I'm in my engineering classes and I'm struggling to comprehend some of the stuff that is being taught.

>>15183208
is max|a_i|, where i is the index, the same as ||A||_\inf?

>>15184041
>Subjective give an example.
Wrong. It was an objective statement, and I will not give an example.
>Human experience is often wrong. If physicists stuck to human experience there would be no quantum mechanics.
It's not a choice.
>Usually.
I doubt it.

Anons do you eat blood bananas?
https://www.youtube.com/watch?v=MoRmtQht8-E

Why are you guys referencing a Charlie Daniels band song?
https://www.youtube.com/watch?v=sh7BZf7D5Bw

>>15185028
a question about it was asked

kind of a dumb question but if you integrate voltage v(t), do you just end up with voltage again as units? (but its an average)

>>15184676
Quite late, but good job.

How do I find love, from a high energy nuclear physics point of view?

Dear Fourierbros, today I write you requesting help.
Consider an arbitrary Fourier series [math]\sum_{n\in\mathbb Z} c_n e^{inx}[/math] whose coefficients go to zero at ±∞.
Obviously this might not converge, but intuitively i feel like this should converge for almost all x.
Is this true? Are there counterexamples?

>>15185345
Stop being a beta cuck and study the alpha particle. Pic rel.

>>15185401
Apparently not.
https://math.stackexchange.com/questions/288765/convergence-power-series-in-boundary

>inb4 that just means that the complex sums need not converge a.e.
Either the real part doesn't converge a.e. or the complex part doesn't. Pick your poison.

If there is a box over a frictionless surface, and the surface starts moving on one direction, the box is going to remain in the same position, right?

If I have a vector [math] \mathbf{u} [/math], is it correct to say that
[eqn]

\int_{\mathbf{v_0}}^{\mathbf{v}}\frac{d\mathbf{u}}{dt}dt = \mathbf{v} - \mathbf{v_0}

[/eqn]
?

I mean, can I integrate it as if I was integrating a non vector variable?

>>15185631
yes. as long as the direction it moves is orthogonal to gravity (not toward or away from the box)

>>15185636
What do you mean by integrating a vector? When most people say that they are talking about line integrals but that is not what you are doing there.

>>15185684
I mean integrate it as if it was a regular variable

>>15185636
You can, as long as the limits also have the same dimension as the vector u

>>15185692
you can't integrate any value on its own. Typical values are integrated y(x) or y(t)&x(t). You need a stricter definition of u which varies over a domain, or at least is defined in terms of one.

>>15185684
this anon is correct.

at which point in spacetime do I observe myself having sex with a woman? perhaps there is no such point

I was reading through Taylor's derivation of the rocket equation, and he does not treat the velocity and the momentum as vector quantities. why is that? I mean, why can he do that?

>>15185771
Because the calculation is done from the frame of reference of the rocket and assumes the thrust is along a single axis.

>>15185791
so I get that it is because everything is happening along a single axis and in the frame of reference of the rocket, is that it?

>>15185814
yes

>>15185175
If you remember to divide by the time interval you are integrating over, yes.

>>15184848
Yes. I've graded 101 classes, and can confirm you and many of your classmates are retarded

>>15184676
>>15171159
>In quantum mechanics, is spin a continuous state as long as you keep observing it? So if you measure an Up spin on a particle, can you watch it spinning Up for a period of time?
The idealized answer (no interaction of the particle with the environment, imperfect measurements, etc) is that if you measure it as up the wavefunction "collapses" and it continues to remain up if you are able to measure it again.

>>15183208
Why do I suddenly get really bad at math after spending ~15 minutes doing it?

>>15183208
What STEM degree do I need to apply as a /sci/ janitor?

>>15184789
Neat. Thanks very much

Good Morning /Sci/entists!

>>15184417
Thank you for telling me. It worked, but I didn't don't like how it looks so I changed it to less than 2. Now it is taller and more readable, but without getting tall enough to get scaling problems.

>>15184676
Thank you for listing the Maid Question. It got solved by the anon I wrote to in the above text.

>new maid questions
I made a tool called Senko MaidHelper so that latex can be a display layer for my Maid Space experiments so books can get made faster and I can give people books when they talk about Maid Space. When I make an experiment the output is in latex and paste in a latex document and compile the document and a document gets made that draws Maid Spaces. Now all my counting experiments with Maid Space can go directly into a PDF and make it easier to see it and share research on 4chan.

>I have two problems
First is for some reason my margins are always on the right. I don't want it like this. I want them to alternate so that when it gets printed it looks nicer and margin is always on the outside edge of the page instead of just always on the right of the page.

Second is I need to get a way to write DRAFT in big letters across every page in transparent letters.

I am going to put a draft on here and I want it clearly marked as a draft. This can make it where /sci/entists can help me make science words get nicer and then I edit the book to make a final draft and remove the watermark and post it on 4chan at CC0 so anybody who wants it can have it and anyone who wants to print it can print it. I hope somebody prints a copy with hard cover and nice high gloss paper like in Wolfy's books and mail her a copy because I got influenced to draw a lot of images with a computer by Wolfy. If I didn't read her triangle book I would never do better in data representation that just writing it in a grid with numbers on the console.

Thank you /sci/entists for reading my post

when I reference a book, should I write
name of the book, author
or
author, name of the book
?

>>15186672
the name of the author always comes first in every standard citation style I'm aware of

>>15183208
This is the formula for integration using spherical co-ordinates. Suppose I wanted to derive the surface area of a sphere from this formula, for some fixed radius R. My approach has been to assume the upper and lower bounds inside of the red box would be R and R, and p^2 would be R^2 as the radius would be constant. However, integrating from R to R gives me 0 and the entire integral becomes 0.

My intuition is that since there is no change in p, the integral would not be there in the first place, and I would only be integrating with respect to the two angles, but cannot prove this.

>>15186804
You can't calculate the area using a volume integral.

> However, integrating from R to R gives me 0
Well ... yeah. [math]\int_a^a f(x) dx[/math] is always 0 because of the definition of definite integrals.

>>15186815
Right, but suppose I wanted to find the volume of this segment but the one of the lengths is an infintesmal as opposed to 0. Then in some sense surface area is a volume with an infinitely small thickness that is not 0. How would i get the volume integral to represent this.

>>15186834
An infinitesimal volume is still a volume. It will not "shrink" down to an area.

>>15186838
If that's true then you also can't take infinitely many areas and add them together to give a volume. That is, they are tiny volumes added together which we call "Areas", proving my point.

>>15186882
>then you also can't take infinitely many areas and add them together to give a volume
and you cannot. an integral is NOT a sum, and adding areas does NOT give you a volume, that's precisely why we needed to define a new operation that could do that instead. the core part of the definition of an integral is the factor dx, and in fact what you are doing when you "add" multiple areas together is multiplying those areas by a new factor dx which turns each of those areas to volumes of width dx. in other words, you turn them into volumes before "adding" them up, and THEN you get, unsurprisingly, a volume
as >>15186815 mentioned, you cannot calculate an area with a given interval. if you fix the bounds of the radius of the integral to be the same, all you are doing is asking for the volume of a sphere with equal inner and outer radius, i.e. an empty sphere

>>15186916
>you cannot calculate an area with a given interval
with a volume integral

>>15186804
Read chapters about change of coordinates and Jacobian, it will teach you better tools on how to prove it.

>>15183208
what happened to 2hu anon ;_;

Let's take the typical problem of a ball dropped in a tunnel that goes from one pole to another of the earth (assuming the earth as an sphere etc). If we took into account that the earth is also spinning at a constant velocity, will this change the result in some way?
I think it won't affect in any way since it looks like the angular velocity of the earth will point in the same direction as the position and velocity of the ball, so there won't be any coriolis effect, nor centrifugal acceleration. But I'm not completely sure desu.

>>15186804
if you want to find the surface area you'll need to use a surface integral

>>15186916
im pretty sure its just an infinite sum

>>15187049
>Let's take the typical problem of a ball dropped in a tunnel that goes from one pole to another of the earth (assuming the earth as an sphere etc). If we took into account that the earth is also spinning at a constant velocity, will this change the result in some way?
>I think it won't affect in any way since it looks like the angular velocity of the earth will point in the same direction as the position and velocity of the ball, so there won't be any coriolis effect, nor centrifugal acceleration. But I'm not completely sure desu.
was this all a trick to get us to expand that thumbnail

>>15187155
lmao I'm genuinely not completely sure, but I will take that as a yes. I usually put into doubt my capacity for solving exercises, I'm usually super retarded.

>>15187146
that's on me, what i intended to say is that it's not just a sum but i didn't put enough thought into the phrasing
an integral is a whole construction that requires a sum, but also other tools like products and limits which drastically change the scope of what a normal sum could do. >>15186804 is a good example of why it's not just a sum and what's the difference between both. as i mentioned adding areas will not give you a volume but an integral will, and the reason for that is that the values you are adding represent entirely different objects because the integral isn't just adding them up and spewing something, it represents an entire process

>>15186984
If only i knew where yukariposter went

[eqn]
\left(\int_{-1-x}^{\cos{x}} e^{x^2t^2}\ dt\right)' =\\ \int_{-1-x}^{\cos{x}} \frac{\partial}{\partial x} e^{x^2t^2}\ dt + (-\sin{x})\cdot \left(e^{x^2\cos^2{x}}\right) - (-1) \cdot \left(e^{x^2(-1-t)^2}\right) =\\
\int_{-1-x}^{\cos{x}} 2xt^2e^{x^2t^2}\ dt - \sin{x} \cdot \left(e^{x^2\cos^2{x}}\right) + e^{x^2(-1-t)^2}
[/eqn]

Solution says I made a mistake at the partial derivative. Apparently the factor t^2 is superfluous. But why? (Wolframalpha didn't give me an answer I understood, so ask here.)

What is the next "big" math course that comes after the standard STEM math curriculum in college? So far I've taken: calc1-3, linear algebra, differential equations, discrete math, and a stats/probability course.

>>15187049
Just googled a similar exercise in hyperphysics, and it says in reality the ball would be intermediately colliding with the wall of the hole, why? The only force is acting on it is gravity which is radial, there is no force acting on the theta versor (using polar coordinates).

>>15187245
correct me if I'm wrong, but I don't think you can simply put the derivative with respect to x inside the integral if the limits of integration depends on x

>>15187263
While the angular velocity is the same all the way down ([math]\frac{d\theta}{dt}[/math]), the radial velocity is not constant and is at its highest at the earth's surface.

>>15187335
i mean yeah, of course, what i'm saying is: shouldn't d(theta)/dt be 0?

>>15187362
No. Why would it be?

>>15187291
>https://en.wikipedia.org/wiki/Leibniz_integral_rule
Are you aware of this? Interestingly, you can actually do this. However, I must've made a mistake at the partial derivative with respect to x.

>>15187386
cause there is no force acting on theta?

>>15187155
The rotational affects on the ball from the earth aren't something to worry about as it would be inside a tube and thus has no effect on the outcome. Gravity and air flow as well as the physical properties of the ball are what would make a difference to this.

>>15187415
You think the Earth isn't spinning?

>>15187516
The science is settled.

>>15187516
if it spins around the axis that coincides with the tunnel then that I don't see why that spinning would cause any external force on the ball.

>>15187251
Not a math major but this is sort of the direction i'm going

Real analysis & Abstract algebra -> Topology -> Category Theory -> ?

>>15187592
He said at the poles, the earth is tilted so doesn't revolve around them. But what you said should be correct.

>>15183208
I've never seen this in high school algebra, what's the author trying to tell me on the part about fractions?

>>15187682
That looks like something ChatGPT would write.

>>15187682
I love it when someone uses such obscure words as "abstruse", but then opts for "divisor" in a context where "denominator" would be much more fitting.
Anyway as far as I can tell it's just saying that if there's equality where the denominators cannot be made equal, the numerators have to be 0 or else you have a contradiction.
Excuse me. A "crevasse".

>>15187682
For the number (a/b) to equal (a/c)
1. b must equal c
2. b and c cannot equal zero

>>15187682
the way the author has worded this specific section makes me irrationally mad. just from the first equation you can immediately show that it doesn't work if x=0, the rest isn't wrong i guess but it's just pointless fluff. also one does not "decree" that the only solution is x=5, this can be proven rather easily without having to define anything, only the extra condition is required
and if he wanted an example of something that was resolved by defining something new then he could have resorted to Rusell's paradox which is more famous, can be described without even having to use equations and is the main reason actual axioms were defined

>>15187706
>>15187724
Thanks anon(s). The author is David Foster Wallace

>>15187398
that's remarkable, I didn't knew about this. do you know some textbook that has the proof?

>>15186984
I've literally posted twice on the thread, I was just being a lazy sack of shit and someone else made the new thread before me,

>>15187786
>Analysis Band II, Ehrhard Behrends
It's a German textbook, however.

>>15186661
>I want them to alternate so that when it gets printed it looks nicer and margin is always on the outside edge of the page instead of just always on the right of the page.
This depends on your preamble, but how I see people doing it is with the geometry package, generally.

\usepackage[margin=5cm]{geometry}

If you want them to alternate so that your book's gutter is larger you can use the `bindingoffset' option, along with a `book' documentclass (with `twoside' parameter if that's not the default).

>Second is I need to get a way to write DRAFT in big letters across every page in transparent letters.
I think what you are looking for is

\usepackage[scale=5]{draftwatermark}

How could I prove the linear order ⟨Z,<⟩ is not equinumerous to ⟨Q,<⟩.
I know that Z is a subset to Q but I'm not sure where to go from there.

>>15188951
I do not understand the equation. Z and Q have the same cardinality so they are by definition equinumerous. And if you are looking at the cardinality of the relations as defined formally, then they are infinite subsets of ZxZ and QxQ respectively, which also have the same cardinality so both relations are again equinumerous.

>>15188951
There are no integers between 0 and 1 but there are rationals between any two distinct rationals.

>>15183208
Can someone please explain why these signs are flipped once the parentheses are removed? (circled in red)

>>15188993
because you're subtracting the quantity in the parenthesis.
so basically, adding -1 times everything in the parentheses. and this flips the signs when distributed.

>>15188970
A linear ordering in my class is defined as a binary relation on a set that satisfies:
1. The relation is Transitive.
2. If x,y are members of a set, then one of the following is true for the relation R: xRy, yRx or x=y.
>>15188972
I'm not sure how to use this fact to prove they aren't equinumerous, as >>15188970 stated they have the same cardinality.

>>15188998
thank you

How do I prove that if a and b are well formed formulas, a b is a tautology

>>15189029
a <-> b is a tautology*

>>15188848
Thank you for telling me. I will make use of this.

Do you know if it is possible to make Latex draw hands? I want to draw hands raising and lowering fingers to show you can count from 0 to 1023 on your hands in radix 2.

They don't have to be super nice hands or photorealistic or anything crazy like that. Just have to be able to raise and lower and finger.

If this is not possible I will still make this drawing it will just take longer because I will draw it with Java as a PNG and put the PNG in the book.

>>15183208
Would it be fair to argue that there is actually no answer to this question because any rule you come up with for how to approach it is arbitrary and that 20 / 5 (2*2) is totally abstract without any connection to reality and effectively numerical gibberish?

how do gnats just magically appear in my trash bin? It is a bin with a tight cover and I do not put ANY food waste other than eggshells in the bin, and even then I usually pit the eggshells inside covered paper coffee cups (that I rinse out before discarding to prevent coffee/tea smell)
this makes no sense to me

>>15190297
No. The issue is that it's using a) two different notations for multiplication and b) different precedence rules for them. Giving multiplication precedence over division is logical, but contrary to recent historical precedent (e.g. practically every computer programming language in existence gives multiplication and division equal precedence).

>>15191000
Abolish infix, teach postfix.

Isn't there a trick to the l'hôpital rule that says a certain type of polynomial will always give out a limit of 0, so you don't have to go through the derivatives and check?
I vaguely remember something along the lines of that and I'm wondering if I just made that up

>>15191101
I'm not quite sure what you mean by "a certain type of polynomial". You use l'hopital on a ratio of two functions, not one

>>15191127
I didn't mean it that way, my wording is just fucked because I vaguely remember it.
It's ratio of two polynomials.

>>15191127
>>15191134
or so I think, it might've been a polynomial and another function, but there was something that let you skip all calculations

>>15191135
The only trick I can think of that works kinda like that is if you're looking at something like [math]\lim_{n \rightarrow \infty}\frac{P(x)}{Q(x)}[/math] , you can divide both numerator and denominator by the largest power of x that appears in either P or Q. this causes everything to disappear except for 1 or 2 terms and you can just directly evaluate what's left

I have some nub questions for math anons.
I have to learn the math topics mentioned below. I've googled and found these books, but being a nub, I'd appreciate it if you could let me know if I've selected some midwit books. I'm learning for CS.

>Probability and Statistics
The Elements of Statistical Learning
>Linear Algebra
Intro to LA - Strang
>Calculus
Stewart's Calculus

My math skills: refreshed precalc on Khan A and learned up to differentiation.

Purpose: Don't laugh, but I want to learn enough math and programming so I can read ML papers. It's hard to get undergraduate research positions in Australia because we have 3-year degrees, and research is done in an honors year or grad school. I want to get this down in x<2years and attempt to publish something on my own.

I'm 23 (former neet) and I'm starting uni in a few weeks.

>>15191159
there's nothing wrong with midwit books. stewart is not a snobby big brain textbook, but probably hundreds of thousands of people have learned calculus from stewart. it's perfectly functional
I think just grabbing the most popular option and getting on with it is a better use of your time than book nerd autism trying to find the "best" one

>>15191168
>just grabbing the most popular option and getting on with it is a better use of your time than book nerd autism trying to find the "best" one
Seconding this.
However, in cases when the popular option has parts that you don't understand, it can be worthwhile to explore other options that explain that part "better". But this kind of evaluation is not something you should be doing upfront, because you have no "a priori" idea of how to evaluate the improvement that each option brings.

how do i build discipline to study? i only ever cram 1day before a test for a few hours because it hasn't failed me yet.

>>15191159
The Elements of Statistical Learning is not a book on probability and statistics, but on machine learning.

Is there a general formula for the discriminant of a polynomial equation depending on the largest coefficient of that polynomial?

>>15191159
>>15191823
Also, if you're a beginner maybe look at 'An introduction to Statistical learning', which is friendlier and by mostly the same people.

>>15191825
There's this
[math]\Delta(f) = (-1)^{\binom n 2} a_n^{2(n - 1)} \prod_{i \not= j} (x_i - x_j)[/math] where the [math]x_j[/math] are the roots of [math]f[/math].

>>15191747
There is no magic pattern of behaviour that will make you study, you build discipline for something by doing it.
If you want to get better study habits you should study more and earlier.

How do I generally prove a function is integrable on a given closed interval?

>>15191948
Riemann or Lebesgue (or something more exotic)?

>>15191951
Riemann

>>15191970
You would show that, for any [math]\varepsilon > 0[/math], you can find a partition of your interval with mesh less than some [math]\delta[/math] (that depends on [math]\varepsilon[/math]) such that the difference between the function's upper and lower riemann sums is less than [math]\varepsilon[/math].

how can I start ejaculating faster? like premature ejaculation levels?
>why?
I masturbate a lot and I want it to take less time of my day.
>if you cum faster you'll just masturbate more often and ultimately spend the same amount of time masturbating
that's fine. I either spend the same amount of time masturbating but with more orgasms (net positive) or I spend less time masturbating (my goal). I win no matter what.
any tips?

>>15192037
You forgot:
>Scientifically speaking,

>>15192043
my bad
scientifically speaking, how can I start ejaculating faster? like premature ejaculation levels?
>why?
I masturbate a lot and I want it to take less time of my day.
>if you cum faster you'll just masturbate more often and ultimately spend the same amount of time masturbating
that's fine. I either spend the same amount of time masturbating but with more orgasms (net positive) or I spend less time masturbating (my goal). I win no matter what.
any tips?

if two things are touching does that mean they are applying pressure on each other?

>>15191000
How is it logical for multiplication to have precedence over division, when addition and subtraction universally have equal precedence?

>>15191058
It will be funny when sums are written as [math]a_1 a_2 a_3 \ldots a_n +++\ldots + [/math] instead of [math]a_1 + a_2 + a_3 + \ldots +a_n[/math]

Not sure if this is a stupid question or not, but:

Does every ordered field embed into the field of real numbers? How is this shown or disproved?

How do capacitors work? Is the charge not stored in the metal?
https://www.youtube.com/watch?v=9ckpQW9sdUg

>>15192088
No, unless there is a force acting to push them together.

>>15192133
Not inside, no. A capacitor usually consists of two parallel plates with an electric field inbetween, and the charges are accumulated on the plate surfaces.

>>15192126
>Does every ordered field embed into the field of real numbers?
only if it's an archimedean field. a total order can be defined on the field of rational functions over [math]\mathbb{R}[/math] which is not archimedean, so that's an example of a field that does not embed into [math]\mathbb{R}[/math]
>How is this shown or disproved?
you can check for the archimedean property. since we know it's true in [math]\mathbb{R}[/math] (and its ordered subfields), then any ordered field where it doesn't hold can't possibly be embedded into it

however, [math]\mathbb{R}[/math] does contain fields where the archimedean property need not hold, but this would require you to use a different order from the one inherited by [math]\mathbb{R}[/math]. so in the end they are not truly embedded as ordered fields, only as a fields

>>15189620
There are a few `hands' in the bbding package, but they are neither complete nor very expressive.
Maybe there are some emojis that do what you want?

What's the time complexity of sum(0,n) n!/(n-i)! ? Is it O(n!)?

>>15192367
[math]\sum_{i=0}^n \frac{n!}{(n-i)!} = n!\sum_{i=0}^n \frac{1}{i!}[/math], so yes.

>>15192367
It's O(n^2)

I'm trying to figure out how the autor was capable of deduce that the two functions have the same derivative. Obviously is not the same function, but the derivative/rate of change is the same.

>>15183223
>>15183251
Why should this be true? Using the chain rule, the derivative of ln( I ) is f / I , there's no reason for this to equal ln(f) .

If two elements x,y of a commutative ring R are congruent modulo every prime ideal of R , then does x=y ?

(This is obviously true when R is an integral domain since 0 is prime , but I'm wondering about the non-domain case)

I don't understand what's happening here. I know it's a sum but what?
I tried searching up similar questions but I can't find examples that explain it

>>15192477
Probably the double angle tan formula is being used to equate the two expressions given for y

>>15192477
They are the same function. The trig identity is [math]\tan 2y= 2 \tan (y)/(1-\tan^2(y)[/math]

>>15192634
Lol just noticed whoever made the pic has a typo in the 2nd line, the tan formula is still correct though

>>15192545
no, if that were true then every ring would be reduced

>>15192656
Oh right. Can I ask, if R is reduced, then is it true that x=y if x and y are congruent mod every prime ideal?

>>15192545
This is the same as claiming that if x is in every prime ideal, then x is 0. Same as claiming that if x is in the intersection of every prime ideal, then x is zero. Same as claiming the intersection of every prime ideal is the zero ideal.
The intersection of every prime ideal is called the nilradical, and is equal to the ideal of all nilpotent elements. So your claim is true if and only if the ring has no nilpotent elements.

>>15192685
see >>15192683

>>15192715
>>15192685 already provides a solution for >>15192683 (it is true)

>>15192740
Oops right, if x = y mod p then x-y is in p

Good thing there is a stupid questions thread

>>15192167
oh so the electrons and stuff don't apply anything

>>15192791
It's the ferm- exclusion principle that stops them getting too close but at rest ("touching") that doesn't come into play and all the electromagnetic forces should be zero (unless you talking about magnets).

>>15183208
If I have a velocity vector and a drag vector, each component of the drag vector is always opposite of the corresponding component of the velocity vector, right?
So if my velocity is positive in the x direction and negative in the y and z, the drag will always be negative in the x and positive in the y and z, right?

I searched every thread and their latest five replies for "ozempic", "sema" for semaglutide, and "weight" for weight loss.

Question: if weight loss and weight control becomes as easy as "eat this pill" then won't the USA greatly benefit from this? Shouldn't we be practically giving this out for free to overweight folks? It makes economic and health sense, no?

I get that this isn't exactly a scientific question unless we sort of include medicine, economics and Sociology into this discussion.

Pros:
>lower food demand, therfore lower food prices: perhaps lower cost of living
>better health: lower rates of diabetes, CHF, arteriosclerosis, and much more
>healthier people who work or leisure more of the time
>overall a more productive society full of happier people
>lower class people become notably healthier, happier, and more productive

Cons:
>none??
>maybe expensive, but we can scale up and subsidize it

Have other people talked about this yet?

It's not like semaglutide and tirzepatide are anti-aging medicines like I would like to see made, but they're clearly capable of helping create a better USA and perhaps a better developed world.

>>15183208
Should we accept that textbook entries and general knowledge in science is still "true" until there's deeper investigation in, say, a PhD thesis?

How do I learn number sense?

>>15193150
while being overweight is a health issue in its own right, it's also emblematic of other health problems that aren't solved by just losing weight
>shit diet = bad cardiovascular health
>sedentary lifestyle = bad cardiovascular health
>alcohol intake = bad for basically everything (except driving)
I still think it would be better than not doing it btw, unless the medicines are found to completely fuck up your metabolism and produce long-lasting consequences of their own, which I think is very likely to be the case

>>15193208
You could go and find the references for everything you read and then go prove them yourself but that seems like a really inefficient use of time. If you don't trust what the textbooks already say why would you trust some random's thesis?

We know electrons flow - to +

But i don't know if the - pulls electrons from + or + pushes electrons to the -

Is electticity Real wheel drive or front wheel drive?

>>15193690
>if the - pulls electrons from + or + pushes electrons to the -
neither, you have them backwards
"push" and "pull" are meaningless. they just flow.

>>15183208
Let R be a commutative ring. I already know that [math]p \in R[/math] is a prime element iff the principal ideal [math](p)[/math] is a prime ideal, but what if I have an ideal generated by two elements, say [math]p, q \in R[/math]. If [math](p, q)[/math] is a prime ideal, can anything be said about the primeness of p or q? And what if [math](p, q)[/math] is maximal?

>>15193719
Then what makes DC and AC different?
If there is no dominant direction of current, why we have separeted AC, DC?

>>15193907
consider p=4 and q=6 in the ring [math]\mathbb{Z}[/math]

>>15192173
But why was he able to disassemble the leiden jar and tap it together without a discharge shouldn't any charge imbalance equalise around the conductive metal?

First, second, third, and fifth order groups are unique, but fourth a sixth order groups are not. Why would nature do this? This is such a weird pattern

>>15194095
4 and 6 aren't prime numbers.

>>15194143
noncomposite might be a better term to use than prime (see 1), but the point still stands
>>15194095
Any group of prime order is necessarily cyclic. A group of composite order, just as a base, can be represented either as a cyclic group in itself or as a direct product of cyclic groups of orders of its prime factors, so it cannot be unique.

>>15194143
So groups with prime number order are unique and those with non-prime number order aren't? Is there a general formula that tells us how many possible groups there are of a given order?

>>15194191
Don't know of a general one (it'd be a very difficult question to answer), but a bit of searching found this result for orders up to 3
https://web.math.ku.dk/~olsson/manus/three-group-numbers.pdf

can anyone explain where the stuff in red came from, Im lost

>>15194262
ah I think I see, I was misunderstanding something

Let there be a system of particles, in which angular momentum is not conserved. At some moment, there is a collision between two particles of this system. After the collision forces will still the same right? So angular momentum still not being conserved. But right after and right before the collision, will angular momentum be conserved? If the collision is inelastic, will this change the answer in any way?

I don't understand what helicity and chirality is. What physical property do these measure?

>>15194462
symmetry. If it can be superimposed with its mirror image, it's chiral.

>>15194476
*achiral
if it can't, then it's chiral

>>15193943
AC is just DC that changes a lot

>>15194462
Simply speaking chirality is an inherent property of a particle (left or right-handed) while helicity is a projection of the spin along the direction of motion (more correctly, the momentum). So is the spin perpendicular or parallel to the motion, or it is "titled".

>>15194188
>>15194217
Alright, I definitely need to study the theory more, thanks anons

>>15194486
How can a massless particle have its helicity equal to it's chirality if they are different physical quantities?

>>15194570
With a massless particle the left and right components of the chirality are always equal (essentially they are neither left or right handed) and always point along the direction of motion. What they mean is that each identical component of the chirality are also equal to the helicity.

>>15194630
Forgot to mention since they are massless and travel at the speed of light the spin is always the same independent of the observer which is why neither the chirality or the helicity change.

Good Afternoon /Sci/entists!

Somebody in /wsr/ tried to draw the smallest anime maid. I put her on a Maid Space. Does it look like a maid to you? How can I make it look nicer?

I am debating making the space between the squares smaller.

>>15192280
Thank you for telling me. That one doesn't have the right hands. I will keep looking.

Thank you /sci/entists for reading my post.

is there a flower four set venn diagram?, or is the lotus one the only four set one?

>>15194686
here is the lotus i meant

>>15193150
remember these words:
"their livelihood depends on your illbeing"

>>15194675
>Does it look like a maid to you?

If you can look at it and within a specified amount
of seconds determine it's a maid, then it's a maid.

But of course, the more "info" put into creating the
maid, the lower the seconds to determine it as such.

Just my rule of thumb without delving into info theory, I guess.

I want to get into mathematical logic and I have relatively little math background (I'm an EE student), how do I start? Any courses/books

I'm in a college algebra class and I've completely forgotten all the algebra I learned in high school.

I'm on Khan Academy learning but I need a way to survive the class now so I don't bomb my grade for the whole semester. Google isn't helping because when I plug problems in trying to figure out how to solve them everything is locked behind a fucking paywall.

WWYD in my situation? How do I survive this class until I'm back up to speed? Dropping the class and cheating are not options. Please help me I'm fucking desperate.

>>15195005
Can you post a sample problem? I'm curious

>>15195009
This is from my test review, for a test that's this Tuesday. I don't even know where to start with this. I don't know what I don't know.

>>15195016
The american educational system is a tragedy

>>15195016
'solution set' means the collection of all values of x that solve either equation.
So, it is up to you to find these values and then indicate where they are, presumably on a (number) line.

If you don't know what 'interval' or 'set' or 'graph' means then you did not study or google for even 5 minutes.
To study you can use pretty much any material on the subject, they'll all be the same. Unfortunately there is no alternative to just putting the work in and making exercises like these, but on the positive side this stuff is really easy _if you study for a little bit_.

>>15195029
Truly

>>15195016
... college?

>>15195016
You are a midwit, give up

FUCKING HELP ME SIMPLIFY THIS PLEASE

>>15195272
There's nothing to simplify.

>>15195289
WHAT THE FUCK

>>15195294
Unless there is some extra information about any of the terms or their derivatives you can only factor a few more terms but that doesn't really simplify anything.

>>15195315
what a pain, I definitely fucked up somewhere but I dont wanna do it again

>>15195364
> I definitely fucked up somewhere
Yeah I would say so.

>>15195384
It should be like the top but I ended up with whats on bottom
I'll save this for office hours after it gets marked incorrect... saturday is the day for dumb quitters like me! :D

>>15194686
There exists no 4-side-symmetric Venn diagram made of convex sets

>>15187625
You think the Earth's axial tilt means it doesn't rotate about its poles?

>>15194745
What part of information theory talks about maids? Original maid drawing is attached.

>>15195555
>>15194745
I'm not sure if maids are discussed there, but the
main thing is if one could see it's a maid on a maid
space, then it takes the shortest amounts of time
to recognize it.

Is there a name for a ring-like structure and the only requirement is that the operations are closed? I'm looking for something like a ring-like equivalent of a magma.

>>15195562
Do you think it looks nicer or gets more like a maid if I reduce the spaces?

An anon told me how here:
>>15171231

If that anon is reading this, thank you for telling me. I apologize for not thanking you in that thread, I didn't see it.

>>15195695
Here is an even smaller spaces one. I think I like this one the most. I will probably redo all the Maid Spaces to have this type of spacing so the book can get less pages.

>>15195609
Try semiring, not sure if this is exactly what you’re looking for though

>>15195721
Actually the main thing I was trying to duck was associativity and distributivity of multiplication so it is kind of important that there is an additive inverse. I didn't know if a structure lacking those would be farther away from a ringoid than a semiring is. I'm developing a query language that is simply a ring since it's just a set of things. But I'm trying to generalize it further so that I can use the same structure for elements that share more in common with groups than rings. So it's not a deal-breaker if no such name exists. But I'm just looking to pacify some naming autism as I write my program. It's more a /g/ related thing so I could share my code, but they wouldn't be able to help me name it over there and I've had no formal education in math past some differential equations courses in college as an engineer so I'm getting most of my information from wikipedia. Thanks for your help.

>>15195760
Associativity can be relaxed for eg a non associative algebra.
Distributivity I have no idea why you’d relax though. You may as well consider the “multiplication” on its own then, since there’s nothing relating it to the addition.

>>15195775
Oh I see. I was hoping to make something like a free ringoid or whatever an equivalent to my structure is. To build expressions over that structure before evaluating them. So that you could construct an expression for a data type that has equivalent operations even if they may not satisfy the requirements of a ring. Again, this isn't really a problem for my purposes since I can just say that my free ring expression type can be evaluated by a semiring. But I see now that there's not really any reason to try to call something ring-like if its operations aren't related at all. I was hoping to find a neat single structure that articulated something like this but there is no real harm in trying to be less mathy about it I suppose.

>>15195792
I see now that something like a near-semiring is actually pretty close. Because most use cases I'm looking for are left-distributive.

>>15195805
Ah non commutative and left distributive, then okay, it makes sense you’d have to go a little outside the box.

>>15195843
To add to this, left distributivity is indeed a condition relating the multiplication and addition; so you do need to consider these operations together instead of separately

>>15195845
Thanks for your help anon

Does anyone know what symmetry is associated with Perturbation theory?

>>15196223
That's a nonsensical question. Perturbation theory is a method to solve some equation. However it is possible that the problem it is trying to solve may have some symmetry(s) that could affect the solution.

>>15196240
My professor keeps asking people this question on a Viva exam without providing any context. Apparently he meant a hydrogen atom and the symmetry is spherical symmetry which is broken by perturbation which should be obvious but no one got it because the question was phrased poorly.

>>15196410
> give me the answer to a question I did not ask.
that's far worse than phrased poorly.

>>15183208
Good Morning /Sci/entists!

I am working on typesetting the book more. When I draw counting or uncounting I try to make all the rows the same length as the radix because it gets patterns that look nice. My problem is after 8 of them it gets put on a new row because width is too big.

How can I reduce the space between the Maid Spaces so they can get closer and draw more of them on the page to display the data nicer and make the page count get smaller?

Attached is how it looks now. A maid told me how to make the cells get closer and I think it looks nice.

I am probably changing from bmatrix to regular matrix too now, because bracket just feels like visual noise.

Thank you /sci/entists for reading my post.

Does Serge Lang's Algebra (the grad algebra book) actually have any major issues? While the majority on the internet seem to praise it, there are a few people who claim the book is near to unreadable due to errors.

>>15196625
I removed the bmatrix and changed it to matrix and I like how it looks more. Also eliminating the brackets in the radix 9 and 10 counts and putting them at 9 per row and 10 per row respectively, instead of being trapped at 8 per row made the book get shorter. Now it has all the drawings and is under 200 pages, but unfortunately takes an hour to compile now.

Maybe if I can make the space between the rows smaller? I like the idea that all the books get a bonus chapter at the end which is just like an interesting open question in Computational Maidposting. I want to add a part about the Smallest Maid problem and use the drawings /wsr/ anons give me, but I also want the book less than 300 pages, drawings included.

When it gets printed I don't want it to be heavy. I want it to be possible to walk around while reading it. It has to do this while containing all the drawings, all the writing, all the code, anime maids in the margins of the writing and all the drawings. Also supporting text like table of contents and probably make a glossary?

I want it to look nice so it can get passed around at science meetings and people can see what Maid Space is doing and see the picture and it isn't heavy so it is easy to take with you.

Book is a physical object which has physical use and I want mine to be physically nice to use so people are inclined to use it.

>>15190376
Simple lifeforms can materialize from nonliving matter, just read Aristotle

>>15195708
I do agree, especially in the thumbnail you can see it well here.

>>15195708
This looks nice imo

im a bit confused here
the laplace operator shouldnt produce a vector so what exactly am I supposed to be taking the dot product of?

>>15196934
https://en.wikipedia.org/wiki/Laplace_operator#Vector_Laplacian

>>15196891
>>15196920
Thank you both for telling me your opinion. Book is recompiling with all the bmatrixes replaced with matrix and all the spacing closer.

>questions
>notation with default values?
Is it okay for a notation to have defaults? The 0 and 1 to the left of the Maid Space just mean it is the zeroth Maid Space in a list of Maid Spaces one long. I think maybe decide if no numbers are supplied then assume that as a default?

>copy-paste button?
I want to make it where if you have a PDF of my book you can click a code example and it goes in your clipboard. That way I can just include full source of some Computer Programs as source and you can read it and compile it if you want. Also it now makes it where if you have my book you have everything to reproduce experiments from the book amd there is no dependency on GitHub or external media to distribute the code. How can I put text in a clipboard in a PDF with Latex?

I "applied" pascals triangle to the coefficients of taylor series of multiple variables , and the method works. But why?

>>15196958
thanks
I hate dot and cross product nigger voodoo so much

>>15196891
>>15196920
I got rid of the bracket and I think it looks nicer with no brackets, but it took the numbers out of the corners? They're both like in the middle now? How do I put them back in the corner? Why is matrix doing this but bmatrix didn't? This is getting typeset with tensor.

>>15196973
I think there is no issue with default values in notation. I don't think PDFs support that kind of automatic copying. I would just put the code in normal text (can be copy-pasted in the worst case) and then embed a file with the source :
https://tex.stackexchange.com/questions/434186/how-to-embed-plain-text-data-into-a-pdf-with-latex

>>15197027
I might change the notation more where these numbers are kept elsewhere and printed once. There is not a lot of value in printing (2,2) 10k times and it causes compilation to get slower. I could potentially eliminate the use of Tensor completely.

>>15197035
Thank you for showing me attach file package. Maybe I an use it to attach Maid Cards and people can use Kurumi MaidCard to extract it or maybe just attach java directly. Either directly increases the powers of the book.

>>15196958
>>15197016
this shit didnt fucking help anyway what the FUCK why are there NO derivations for the enstrophy equation ANYWHERE
Id never even heard of enstrophy until I got this assignment

>>15197138
Then I think you need to post the full equation.

>>15197204
i am at a loss

>>15191828
>>15191168
>>15191823
Thanks for the adv frens

>>15197251
Im missing the u[dot][grad]w term from the substantial derivative but I think that'll only make it more confusing

Find the solution set for -8<2x+5<7 and write it in interval notation.

I got (-13/2,7/2). What am I doing wrong here?

Yes I'm retarded and a midwit, go ahead and get it out of your system.

>>15197251
>>15197313
yeah this shit only got worse

>>15197328
How come you did the lower bound correctly but not the upper?

>>15197328
you forgot to subtract 5 from the upper bound

>>15197371
>>15197379
I assume lower bound is -8 and upper bound is 7?
So I subtract 5 from both sides.

So.. (-13/2,1) right?

>>15197413
yeah

If it's actually the trajectory of stationary action that Hamilton's principle predicts why do we call it least action? Are there any examples where action is maximised?

>>15197472
It's just a convention. When you write a Lagrangian you do so such that the action is (locally) minimized. You could also write a Lagrangian so that it was maximized instead and the solution to the Euler-Lagrange equation (and hence the physics) would remain unchanged.

>>15197500
So you're telling me that if the action was a function of x like x^3 +px+q, only the minima would be the only stationary value that exists and to make the Maxima count I'd have to rewrite the equation with p'=-p and q'=-q?

>>15197513
Yup. Multiplying the Lagranian by -1 is the simplest method invert a minima. Though any saddle points would be unchanged.

What do I have to study to solve this? It sounds basic but I am a neanderthal.

We have a set with three characters E = {0, 1, #}.
For combinations in length n how many times do we have a combination with the character # appearing exactly k times in it?

>>15198136
That would be (elementary) combinatorics, probably.
You need to choose k spots for the pounds, and the remaining n-k spots have 2 options each. That gives [math]\binom n k 2^{n-k} [/math].

>>15198172
Thanks

>>15197079
Book got smaller with spacing and margin changes. Went from over 300 pages to under 180 which is nice because it makes space for the code and also more drawings with small maids.

I still haven't figured out how to get the numbers to stay in the corners or get spaces between rows of Maid Space drawings to be smaller.

I have to fix this and maybe write a little big more and probably remove the 0 and 1 from the left side of everything. Maybe remove all the numbers and put them elsewhere so only write them once so the document compiles faster example drawing have less visual noise so you can see the squares more and not get distracted by seeing (2, 2) 10k times.

Is there a way to calculate arbitrary sine and cosine values by hand without having to use infinite series?

>>15198780
>without having to use infinite series?
why?
well, anyways, sin(x) is the only solution to x''=-x and x(0)=0, so I guess you can use finite differences (numerical ODE) to approximate sin(x).
Subdivide [0,pi] using intervals of size t=pi/n and replace x'' with the discrete version. Now you need to find a sequence a_n such that:
a_0=0, a_n=0
n^2(a_(n+2)- 2a_(n+1)+a_n)=-a_n

For a given n, this is just a linear system which you can solve with a computer.

>>15198780
Any calculation of sine or cosine for arbitrary values is always going to involve some notion of infinite sequences simply because we are dealing with irrational numbers. You don't have to use a Taylor series though. As far as I understand most calculators use something called the CORDIC algorithm involving an infinite sequence of rotations.

Download link for LTspice on the analog website is broken. Anywhere else I can grab a download?

>>15198780
What do you mean by "by hand"? Any algorithm a computer uses, a human can use. The human will just be a lot slower.

>>15198795
CORDIC isn't used on modern hardware. Polynomials are faster if you can perform a multiply in a clock cycle. Also, CORDIC isn't a good fit for floating-point (it requires a huge table to get correct results for angles which are small enough to round to zero if using fixed point but not small enough that sin(x)=x is correct).

>>15183251
Non-linear integration is a thing, but only under specific circumstances. In general. integrals are linear operators. Your first hint that this isn't true in general is passing the non-linear natural log under the linear integration operator.

How do I solve this?

What's the real argument for quantizing gravity? "The other forces were quantized" doesn't count. What's wrong with simply accepting that gravity is fundamentally different from the Standard Model because it curves spacetime itself? We shouldn't even be calling it a force in the first place.

>>15199392
Isn't this just an application of Fermat's last theorem?

>>15198526
I am probably going to have to get the brackets back on the matrix and change it to bmatrix. It looks nice with squares, but it looks awful with numbers.

Here are Maid Spaces with Normie Numbers instead of squares. It looks bad and is hard to read.

>question
I put a lot of bmatrixes next to eachother using \quad. How can I make the space between bmatrixes smaller both in rows and columns so I can put 10 on a line like here? >>15196850

>>15197016
>>15197016
>I hate dot and cross product nigger voodoo so much
Kill yourself you fucking racist poltard loser.

>>15199531
Instead of quad, there are other spacing commands you can try. For example,

\,
\;
\:
\! (negative spacing)
\qquad

and probably many more. Some combination of these should allow you to finetune.

For spacing between lines (vertical), it matters how your document is set up. Is it one big math envoronment (if so which one), or one per line?

>>15193502
>If you don't trust what the textbooks already say why would you trust some random's thesis?
Textbooks are usually criticised in pedagogy for being very myopic to complexity; some history of science textbooks are even seen as "mythological" by some detractors since they're usually based on certain attitudes of the Enlightenment. A thesis is usually more in depth compared to a textbook entry anyway.

>>15197016
take the geometric algebra pill
https://www.youtube.com/watch?v=60z_hpEAtD8

I'm doing some LCMS with ESI as my source

I was wondering if there is any rule of thumb about if i should expect to see a compound in ESI +ve or ESI -ve mode.

Is it as simple as Acids = negative / Basic = positive as I'm looking for protonation/deprotonation, or is it not that sample ?

(if you can't tell I'm not a chemist and have limited chemistry knowledge)

not sure which equation to use.

would V= IR sin (wt) work as long as i state that t= 1?

Why can I fall asleep with a song stuck in my head and wake up with it still stuck the next day?

>>15199741
>Is it as simple as Acids = negative / Basic = positive as I'm looking for protonation/deprotonation
should be. i think sodium salts are also a thing, so check for +22 (iirc) amu peaks
>(if you can't tell I'm not a chemist
then don't sweat the details, it's not your job. consult the lab manager if you're concerned.

>>15199779
Very bad sleep quality

>>15199778
V=5sin(2000πt+φ), I=V/R => I=(5/51)sin(2000πt+φ).

>>15199801

I've been getting a couple of compounds come through as sodium adducts maybe I wonder where the sodium actually comes from as I've been running pure compounds at the moment. I would have thought that the only adducts would be H+/H- with the molecular H20 and acid.

I'm wondering if something is coming through from the column ?


>then don't sweat the details, it's not your job. consult the lab manager if you're concerned.

I'm trying to get some skills in the ol' multi-omics. 99% of it would just be using data procesing pipelines, but i can't help feeling cripplingly impotent when i don't understand what's going on a lack the skills to trouble shoot.

Genomics seems to much easier to get into. Lack of resources for HPLC and Mass spec seems huge.

>>15200156
thanks

quick question, shouldnt it be 10 in front of the sin? or do we just use 5 since its +5 to -5 volts in a phase?

Hey anon's! I have one requirement. How can I learn and master the Feynman's integration technique as a dumbass?

is there such a thing as a vector with no components?

>>15200573
https://physics.stackexchange.com/questions/176200/why-taking-components-of-a-component-of-a-vector-is-invalid

I think a vector with no components is called a component of a vector.

I think...

>>15200587
Sorry, I mean a vector in the sense of the mathematical vector space. Not one from physics. I think I figured it out:

>the empty set it the basis vector of the null space
>the empty set there is a vector
>all set contain the empty set
>the set of vectors of all vector spaces therefore contain the empty set
>the empty set has no elements
>therefore a vector with no components exists

I don't know, if that's valid, however.

>>15200602
*is, *therefore, *sets

Let [math]V_{i}[/math] be vector spaces and let [math] I := \{1\} [/math] be a set of indices. What is

[math]\displaystyle \prod_{i \in I} V_{i}[/math].

This one puzzles me. I think it's

[math]\displaystyle V_{1}\ \times \emptyset = \emptyset[/math],

but I'm not sure. Can anyone confirm if I understood this correctly / explain what I got wrong?

>>15199392
What is the context here? one interpretation is that you are working on R^2 with the norm p, and sin_p(t) and cos_p(t) are just the angle parametrizations of the norm p-ball. In this case, the result follows just from Fermat's last theorem as >>15199514 says.

>>15183208
I have two stupid questions, if any are willing to answer them.
1. How many mph would one have to travel to reach Jupiter from Earth in one day?
2. Let's say there is ship that can withstand the friction. Would traveling at Mach 100 in Earth's atmosphere have any negative effects on the planet?
Thank you all for your time.

>>15200602
>the empty set it the basis vector of the null space
>the empty set there is a vector
this jump in logic is wrong. the empty set is the basis of the trivial vector space PRECISELY because there is no vector in it. if there was a vector in the empty set then the generated vector space would be of dimension 1

the answer to your question becomes easy when you formally define "component". i imagine the confusion comes from the fact that we usually just infer the definition from the context of a coordinate system. if i were to define, for example, the [math]\mathbb{R}[/math] vector space [math]P_{2}[x][/math] of all polynomials of degree =<2, then each vector is actually a polynomial so there are no "components" of a point in a euclidean space, but in the end we still work with 3 constants which are the coefficients of the the polynomial in each degree. i think we can both agree those would count as components too, and if we use that intuition then we can just say that the components of a vector are the n scalars in a field [math]K[/math] that allow us to write a vector of an n-th dimensional [math]K[/math]-vector space as its unique linear combination. if we use that as a definition then the answer becomes pretty clear, because the amount of components of a vector is equal to the dimension of the vector space that vector is in

so if you want a vector with no components, you just want to look at the zero dimension vector space, i.e [math]V=\{0\}[/math]. and remember that the vector in that space is not [math](0)[/math], which would be the zero vector in a 1 dimensional vector space and thus has one component, but just [math]0[/math]

>>15200707
it's not correct. the symbol [math]\prod_{i \in I}[/math] simply means that the operator will iteratively keep adding factors to the product until it runs out of indices, going through each index in I one by one. if your indexing set only has 1 element then it will run out of indices after writing only one set in the product and then nothing else gets added, which means no empty sets

in other words, [math]\prod_{i \in I} V_{i} = V_{1}[/math]

>>15200802
According to: https://earthsky.org/astronomy-essentials/why-jupiter-closest-after-before-opposition/

460 mil. miles / 24 hr. = 19.17 mil. mi/hr

why is it that
[eqn]
\int_{t_0}^{t}\mathrm{d}(x(s)) = x(t) - x(t_0)
[/eqn]
?
shouldn't it be [math] t - t_0 [/math]?

>>15200929
[eqn]
\int_{t_0}^t x(s)\mathrm ds = t - t_0
[/eqn]

Also
[eqn]
\mathrm dx(s) = x'(s)\mathrm dx
[/eqn]
Where x'(s) is the derivative of x(s).

>>15199538
Thank you for telling me. \! worked. Now those pages look like the attachment.

I think the math part is kaotheorems?

>>15200232
10V peak-to-peak = 5V peak

>>15200707
The product of an empty set is the multiplicative identity. If the multiplication operator doesn't have an identity, then the product of an empty set is undefined.

>>15201170
>>15201170
>>15201170
New Thread.