/sci/ - Science & Math

>>9380516
Do problems/equations like this actually show up in applied math?

>>9380651
That's not a problem or an equation, it's just a fraction.

>>9380653
Well that was a dumb question. Would a fraction ever show up in this form in any equation?

>>9380658

No. Looks more like a practise problem for
basic simplifying shit, not something that you would ever actually come across with.

https://www.youtube.com/watch?v=WUvTyaaNkzM

What does he mean by dr?

What's the best way to review math from x-years ago?

bro someone wanna tell me how the FUCK these circles represent the flow of the vector field?

i thought the flow is the path a point would follow. can someone help me intuit it a bit bettter

>>9380711

He explains it in the video. Multiple times. It usually represents an arbitrarily small width of some square. Like in his circle example at the beginning when he approximates the areas of the rings as squares, he denotes the width of each ring as dr. It's handy to have a constant width so you can only focus on the changing lengths of the squares.

Does the brain burn more calories if you are thinking hard about something?

how do i study everyday for more then an hour and not feel tired

why is the GRE so expensive? any way to get waivers like the SAT?

I'm self-studying Abstract Algebra (Topics in Algebra by Herstein) and when I read the chapters I feel like I'm understanding the material, but when I get to the problems I can usually only manage like a third of them. Should I put it down and get How to Prove It or something?

>>9380789
The flow is tangential to the circles and it takes 1 arbitrary unit of time to cross from one circle to the next.

>>9380516
nice one brother. too much fuckery on this board. I was going to make a QTDNTOT thread but saw this. hopefully all they brainlets placing garbage, time wasting threads all over the board will stop and post here. lets make this a regular thing. QTDNTOT sci edition soon. the board space will hopefully free up for more beneficial threads for the people on here. the mods should be ashamed.

>>9380651
As you do algebra before simplifying it.

>>9380904
>I'm self-studying Abstract Algebra (Topics in Algebra by Herstein) and when I read the chapters I feel like I'm understanding the material, but when I get to the problems I can usually only manage like a third of them

That's normal. Just keep working on the problems.

>Should I put it down and get How to Prove It or something

You don't know how to do proofs?

>>9380942
I understand how to do them, I'm just... bad at them it seems. I'm an EE so I didn't take a lot of proof-based math courses.

What's the intuition behind inference with gaussian processes? I wrote a program for it but I've got no idea where the formula for [math]\mu[/math] and [math]\Sigma[/math] come from.

>>9380947
That or I'm just underestimating how hard the problems are, since the ones I can solve I can usually do in my head.

>>9380947
getting good at proofs goes like this:
0. understanding what constitutes proof. things like implications, necessary and sufficient conditions, and logic are key.
1. understanding common proof techniques e.g. direct proof, proof by contradiction, induction, etc.
2. being familiar enough with common tricks and the material you're working with to employ them in a proof.

there is more of a learning curve because you are not being taught some method of computation which you can apply to different kinds of problems. you're constructing an argument.

>Zip-Line Into River. Work out the mathematics of the situation from the provided videos. First carefully watch all videos and approximate all relevant distances. Find the slope of the zip-line and the speed of the person using the zip-line. Note that the person will undergo projectile motion once he lets go of the rope. Find how far from the shore he landed (on either side). Videos can be found at: http://www.youtube.com/user/piano4life18
This meme problem is really confusing me , isn't the slope of the zip line the distance of the zip line over the time it tooks to glide on it how is that diffrent from the speed (besides the sign)
Anyone has an idea how i tackle this problem and what i should calculate

>>9380912
>tangential

Is there an official name for the space that is perceived to exist on the other side of a mirror? I'm doing a project involving mirrors and I've been referring to it as "Virtual Space" since the image you see in a flat mirror is called a virtual image. This diagram calls it "the mirror world" which just sounds silly. Is there actually a name for this?

Thak Scrotungus.

Context: Physics, Dimensions.
Hypothesis: Velocity equals Motion over Resonance plus Vibrancy.
Explanation: The speed at which an object can be taken from one dimension and brought into another is solely up to the decision-making of the individual taking it.

Question: Having factored in simple stuff like Uncertainty Principle and Planck Length; what other maths exist to assist if proving this can be done? I'm happy to come up with my own, but that kind of thing does go over well in the community. I'm not gonna go expressing stuff like this in public until I've got filmable evidence.

>>9381041
pls helb

>>9381041
Is this a homework problem? How are you supposed to approximate anything remotely close to accurate from those videos? Also video 3 is hilarious.

Let [math]A=\mathscr{P}(\mathbb{R})[/math] and let [math]f:\mathbb{R}\to A[/math] be defined as [math]f(x)=\{y\in \mathbb{R}|y^2<x\}[/math]. Is [math]f[/math] onto (a surjection)?

>>9381421
>Is f onto (a surjection)?
obviously not

If I have a multivariate continuous probability distribution, and want to know the distribution of one of the variables at a fixed value of the other variables, how would I go about that?

I have a wavefunction of three variables, and I want to fix one at its expectation value, then vary another through a number of given values, and at each given value find the probability distribution of the third variable. Is there a physical way of doing this? I thought it could be as simple as just setting the other two as constant and then treating it as a single variable wavefunction.

>>9381425
That's what I thought, but this person thinks otherwise.
http://www.inchmeal.io/htpi/ch-5/sec-5.2.html
I thought maybe I was missing something.

>>9381439
Which solution is it supposed to be?

>>9381444
Sorry, it's solution 6 part b.

>>9381445
I can't tell what that solution is supposed to be saying with {q in R}, but an easy way to tell it's not onto is that every set in the image is 'negative symmetric' in the sense that if y is in the image then -y is in the image. So any subset of the real numbers that contains a number N but does not contain its negative -N can not be in the image of f

>>9381448
>an easy way to tell it's not onto is that every set in the image is 'negative symmetric' in the sense that if y is in the image then -y is in the image
should be: an easy way to tell it's not onto is that every set S in the image is 'negative symmetric' in the sense that if y is in S then -y is in S

>>9381448
>>9381465
My reasoning was that [math]f[/math] is not onto because there are subsets of [math]\mathbb{R}[/math] that are not connected intervals that can't be derived from the formula for [math]f(x)[/math], which are all connected intervals.

>>9381473
>My reasoning was that f is not onto because there are subsets of R that are not connected intervals that can't be derived from the formula for f(x), which are all connected intervals.
That's fine too

>>9380947
Many you should practice with easier math courses like combinatorics or graph theory.

>>9380947
>proof-based math courses
That's the only kind.

>>9381421
>Is f onto (a surjection)?
No, it doesn't even matter how f is defined. There is no surjection [math]f : A \to \mathscr{P}(A)[/math] for any set [math]A[/math]. See https://en.wikipedia.org/wiki/Cantor%27s_theorem

>>9381496
But neither of those are math courses.

>>9381609
except they are

>>9381611
It's rather obvious that a vulgar peasant such as yourself wouldn't be able to see the truth.

>>9381617
I suppose to you symplectic geometry isn't math either..

>>9381640
This post is pure retardation.

>>9381239
Yeah, Im juts gonna guess the distances and angles, just a bit confused ofbwhat should i do

What's the best resource to learn the Wolfram Language?

I know some elementary programming (really basic stuff with C, Fortran and Assembly, but never used any of these outside school) and I often use Mathematica for simple calculations, but that's about it.

>>9380947
It's ok. Abstract Algebra is a great place to start getting used on proving stuff.

>>9381432
>If I have a multivariate continuous probability distribution, and want to know the distribution of one of the variables at a fixed value of the other variables, how would I go about that?
The other variables having a fixed value is a 0 probability event.
P(A|B) "is not defined" when B has zero probability.
Look at this though:
https://en.wikipedia.org/wiki/Conditional_probability#Measure-theoretic_definition

>>9380942
>but when I get to the problems
Just treat the theorems themselves as problems. Try proving as much as you can without looking at the proof given in the book.

>>9381762
meant for >>9380904

>>9381718
I haven't found a single best resource for it. There's things like the introduction Stephen Wolfram wrote (https://www.wolfram.com/language/elementary-introduction/2nd-ed/)) but it's rather basic.

What helped me the most is looking at semi-complex examples and taking them apart piece by piece to figure out how exactly they worked. There are some good candidates for this reverse engineering in the feature showcases for new versions of the language (e.g. https://www.wolfram.com/mathematica/new-in-11/)) and the "Neat Examples" sections of the documentation for various functions (e.g. https://reference.wolfram.com/language/ref/GradientOrientationFilter.html).).

>>9381432
https://en.wikipedia.org/wiki/Conditional_probability_distribution#Continuous_distributions

Brainlet here.
If a key has 50% chance of opening a chest that has a key in it and that key in the chest has 50% chance of opening the second chest. What is the chance of opening the second chest?
Also if a study says that 1 out of ten people is homosexual. What are the chances that a group of ten men has a gay man?

And say how you solved both. Thanks.

>>9381789
1/3 for the first question

Second question is poorly worded. Could either be 1 or 1 - 0.9^10

Not telling you why tho ;^)

>>9381804
why not?How do you even come to a response like that?
brainlet too

>>9381789
0.5 chance of opening the chest, so 0.5^2 of opening both chests.
0.1 chance of a faggot, so 0.1^10 chance of one of them a faggot

Hey /sci/
I feel like a total fucking retard.
Whenever I try to solve most math or math-based programming problems, my brain just shuts down.
Take for example something I was just working on:
Write a program to find the 1000th prime number.
I have no goddamn clue where to start when solving something like this! Can someone point me in a direction to increase my ability here?

>>9381846
First question map out the possibilities: either the first key doesn't open, either the first key opens and the second key doesn't open, either the first key opens and the second key opens. That's one valid scenario out of 3 scenarios, hence 1/3.

Second one, the probability that there's a faggot in the group is equal to 1 minus the probability that there are no faggots in the group. There probability of being a faggot is .1, therefore the probability of not being a faggot is .9, so that the probability of all 10 people not being fags is .9^10, giving the result 1 - .9^10

>>9381865
Implement the sieve of erasthothenes.

>>9381858
lol

>>9381870
Thanks for the answer, but what I am looking for is more like how do I figure these things out myself? More specifically instead of feeling completely lost when approaching a problem, how can I figure out what steps to take to begin to solve it?

>>9381878
Well I mean I kinda knew that algorithm from experience, I guess the question supposes that you know it too.

>>9381865
Break the problem down into manageable parts. You might start out with something like[eqn]
\texttt{i = 0;} \\
\texttt{n = 2;} \\
\texttt{while i < 1000:} \\
\ \ \texttt{if is_prime(n):} \\
\ \ \ \ \texttt{i++;} \\
\ \ \ \ \texttt{n++;} \\
\texttt{print(n);}
[/eqn]without actually knowing how to implement [math]\texttt{is_prime}[/math], but now you've broken the problem down from "how do I find the 1000th prime" to "how do I decide if a number is prime" which is a less difficult sub-problem of your original problem. Eventually you'll have accrued enough knowledge to know that there is a standard and more efficient algorithm for this like >>9381870 pointed out, but when you're starting out it's okay not to be focused on the absolute best solution if it means you can get started.

>>9381916
Oops, n++ should not be double-indented.

Let V be a finite dimensional normed vector space over the Complex numbers or the Real numbers.
Let e1, ... ,en be linearly independent elements of V with ||ei||=1 for all i.
Consider a linear combination v := c1 e1 + ... + cn en

Does |ci| <= ||v|| hold?

It does hold if the norm is induced from an inner product and e_i are orthonormal, but if the norm isn't induced from an inner product or e_i are not orthonormal?

>>9381432

You can express it is a conditional multivariate using Bayes'.

I was working through some problems on the Challenging problems in algebra book to kill some time. For this one, the solution given in the book for the challenge is 8, but I get 24 (1243,1342,2134,2431,3124,3421,4213,4312,12034,12430,13024,13420,21043,21340,24013,24310,31042,31240,34012,34210,42031,42130,43021,43120)
Did I not understand something or is the book wrong?

>>9382062
wait lemme get this straight, that's just a linear combination of unit vectors right?

What's a bibliography database used for? Is it supposed to contain only all the works you've ever read or also the pages you find interesting?

I'm setting mine up right now, using JabRef, but noticed that there doesn't seem to be a way for a BibTex-key to contain multiple page ranges. If I say:

pages = {5--49}, {90--118}, {200-202},

It'll delete the latter two ranges:

pages = {5--49},

Am I supposed to put interesting pages into the keywords or comments instead? But then I can't cite it. Might as well not use JabRef then.
How am I supposed to know 6 years later where that noteworthy quote or table is? Having to go through the entire book/paper/... again just to find what could be appended to pages = ... seems clumsy.
Am I supposed to have an one entry per citeworthy passage? But then the entire thing becomes huuuuge and filled with countless similar-looking entries.

>>9382062
consider an arbitrary [math]u[/math] of unit length and put [math]v = -u[/math] but rotated by an arbitrarily small angle so that [math]u[/math] and [math]v[/math] are linearly independent. does your conjecture hold for this set of vectors ?

>>9381858
>>9381804
What I meant was what are the chances of the group having a faggot not a person in the group being a faggot.
If it's 1 out of 10 then the chances of the group of 10 people having a faggot in it is 100% but that's inaccurate.
Excuse my Englishletry

So how do i calculate arc length and why is it 10*x?

>>9382376
pic related

>>9382376
rtheta

>solving a problem
>my brain literally starts to hurt
is this normal

Why do structures such as the Solar System and galaxies form in disks rather than a general sphere? Obviously a single orbit will be in a plane, but why do they all line up?

>>9382206
Yes.

>>9382257
Oh right, if it held, then it would be 1 = |1| <= ||1*u+1*v|| < 1
I am retarded.
Thanks!

>>9382411
I don't think so.

>>9382376
[math]
r(t):=10(\cos t, \sin t) \\
\frac{d r}{dt} = 10(-\sin t , \cos t) \\
\lVert \frac{d r}{dt} \rVert = 10 \\ \\

\text{Arc Length } = \int_{0}^{x} \lVert d r \rVert = \int_{0}^{x} \lVert \frac{d r}{dt} \rVert dt = \int_{0}^{x} 10 dt = 10x
[/math]

How do you simplify the [math]E_{period}
[/math] equation in pic related? I'm assuming j stands for [math] \sqrt{-1}[/math], but even then, I don't know how the expression simplifies to one.

>>9382813
t. engineer

>>9382813
e^(j x) always has absolute value 1 when x is real (it's on the unit circle), and in your case w_0 and t are real

>>9382829
I mean... You're not wrong.
I just have no idea how they got it

>>9382831
Okay. That makes sense.
For some reason, despite seeing the whole e^ipi thing many times over, I still can't wrap my head around complex exponentials...

>>9382513
This has to do with the way in which the solar system formed. In short, a large cloud of gas collapses spinning faster and faster as it does (think conservation of angular momentum) and centripetal forces warp it into a disk

>>9382194
reread, the actual question asks for 1234, 12034 is a seperate Challenge question (which you correct btw)

>>9382859
>le centripetal jew

I'm old and brainlet and trying to remember quantum mechanics I had a lecture series on from more than a decade ago. Please tell me if I am remembering this correctly.

If you have a quantum mechanical system then that system has a wave function.
If you want to calculate a physical quantity of that system then you need to apply the correct operator to that system, e.g. the momentum operator.
When you apply that operator, you will only get a deterministic value if the wavefunction is an eigenfunction of that operator, otherwise you will get a probability distribution of the possible values that physical quantity could take.
My questions:
1. is what I have said correct so far?
2. for a wave function to be valid, does it need to be an eigenfunction of the hermitian operators of physical observables? i.e. is it impossible to have a quantum system whose wave function is not an eigenfunction of say the momentum operator? Or the hamiltonian operator?
3. if the operators of physical quantities can be applied to valid wave functions that are not eigenfunctions of those operators, then how do you obtain the probability distribution of possible measurements of that physical quantity? Is it simply the result of applying the operator to the wave function or do you need to integrate over it and multiply it by its complex conjugate or something?

>>9382865
>thinking I give a shit about idiotic semantics arguments

If 2 hydrogen atoms are bonded together, what does that visually look like? Is it like 2 planets which both orbit 2 suns in a figure 8 pattern?

>>9380795
>It usually represents an arbitrarily small width of some square.

physicist kys

>>9381114
Those names are as good as any.

>>9383026
no, it's quantum mechanical shit bruh

>>9383095
Really? How do you know if you mind be asking?

Also I believe that an OH molecule is able to exist for more than 10 minutes: just 1 oxygen bonded with 1 hydrogen. I might be wrong.

Time dilation. Time perception remains the same for two different observers moving at different speeds right right? . Entertain this absurd scenario involving two people: somehow we're able to live stream footage, say through Skype, ( let's also assume the delay is a negligible) of Person A on earth in a room and Person B on a ship . Person B is moving at the speed of light. Person A experiences less time right? Would they be able to perceive each others different age rates? Let's also assume they've got nothing to do but watch each other till either one dies. How's that for a stupid question..

what are some good biostatistics books?

>>9382813
|z|^2 is short hand for z* times z where z* is the complex conjugate.

(e^ix)* (e^ix) = (cos(x) - isin(x))(cos(x) + isin(x)) = cos^2(x) + sin^2(x) = 1

>>9383230
Thanks man!!
After I got the answer initially, I re-convinced myself that e^(ix) = i(sin x) + cos x, and then it hit me what taking the "absolute value" of an imaginary number was and then felt like a moron.

Oh well. Better now than later, I guess

>>9383169
>Person B is moving at the speed of light
this is impossible in a way you can't just hand wave away, lets assume you mean just a significant fraction of c, enough to cause noticeable time dilation. You have to consider the fact that it takes time for the video stream information to travel from one person to another, and this again this isn't something that you can ignore, the limit on the speed of information is a very fundamentally important one and is one way to explain that that Person A does indeed perceive Person B to age slower while Person B perceives Person A to age slower (from either one's perspective the other is the one with a velocity near c)

>>9382869
>1.
No. Sounds like what people would gather from skimming Griffith. Go read an actual QM book like Townsend, Sakurai or Landau-Lifshitz.
>2.
Eigenfunctions are representation of eigenstates of observables on [math]L^2[/math]. Eigenstates exist for any diagonalizable operator you want, since Hilbert spaces have [math]\mathbb{C}[/math]-linear representations. Now Hermitian operators have the nice property that if the Hilbert space is separable, then the eigenstates of the Hermitian operator spans the Hilbert space. This means that your space of states can be characterized by eigenstates of the Hermitian operator, which is very useful as it tells you immediately what "sector" of the Hilbert space corresponds to what measurement.
>3.
As I've said before, the eigenstates of an observable spans the Hilbert space, hence any vector in it can be written as a linear combination of them. The probability distribution is just the squared sum of all the coefficients. Namely if [math]\{|\psi_n\rangle\}[/math] are the eigenstates of an observable [math]A[/math] acting on the Hilbert space [math]\mathcal{H}[/math] such that [math]\mathcal{H} = \operatorname{Span}_n\left(\{|\psi_n\rangle\}\right)[/math], then for any state [math]|\phi\rangle \in \mathcal{H}[/math] we can write it as [math]|\phi\rangle = \sum_n c_n |\psi_n\rangle[/math], then the probability distribution of the results of the measurements of [math]A[/math] on the state [math]|\phi\rangle[/math] is [math]\sum_n |c_n|^2[/math].
Of course all of this is true only for single-particle systems in a pure state. Mixed states are characterized by the density matrix [math]\rho[/math] which mixes different eigenstates of an observable in different factors [math]\mathcal{H}_i[/math] of the total Hilbert space [math]\mathcal{H} = \bigotimes_i \mathcal{H}_i[/math].

>>9383160
In general, you cannot ask about what things look like at this scale, things do not have rigid boundaries or a single well defined position in the same way we like to think of, they exist as probabilistic superpositions, the model of an electron orbiting the nucleus is inaccurate.

>>9383324
to be clear I mean the classical model of an electron orbiting a nucleus in the same way a planet orbits a star is inaccurate

>>9383320
>>>/r/taiwan/

can someone explain why wormholes work in theory

>>9383320
Patchy is... pretty?!?!

>>9383350
Thanks anon but were you listening at all?

>>9383353
see >>9383328

>>9383320
>>9383320
Thank you for taking the time to write a long answer.
what is wrong about what I wrote for 1?

I'm sorry I'm not sure I understand the rest of your answer.

Are you saying that when an operator for a physical observable, like say the angular momentum operator or the position operator or the hamiltonian operator is applied to a wave function that this will always be equal either to the wave function multiplied by an eigen value or a linear combination of wave functions ?

>>9382813
[math]sin^2(x)+cos^2(x) = 1[/math]

>>9383370
>If you have a quantum mechanical system then that system has a wave function.
No. It may have several different wavefunctions and in general will. Given a symplectic manifold [math](M,\omega)[/math] satisfying the second intergrality condition the "wavefunction" is defined as a section on the reduced Hilbert space of sections. There may exist different such sections for a given Hamiltonian [math]H \in C^\infty(M)[/math].
>If you want to calculate a physical quantity of that system then you need to apply the correct operator to that system, e.g. the momentum operator.
The correct term is "measure". If you wish to measure an observable quantity [math]\lambda_n[/math] with respect to some state you need to project it onto the invariant eigenspace [math]\operatorname{Span}\{|\psi_n\rangle\}[/math] where [math]A|\psi_n\rangle = \lambda_n|\psi_n\rangle[/math], and the probability is given by the coefficient of the projection, i.e. the eigenvalue of the projector [math]P= |\phi\rangle\langle \psi_n|[/math].
>When you apply that operator
To what?
>you will only get a deterministic value if the wavefunction is an eigenfunction of that operator,
No. You get another state. Only when you take the inner product do you get a c-number.
>otherwise you will get a probability distribution of the possible values that physical quantity could take.
No. You get a linear combination of all the probabilities of a certain state lying within some eigenstate.
>Are you saying that when an operator for a physical observable is applied to a wave function that this will always be equal either to the wave function multiplied by an eigen value or a linear combination of wave functions ?
The probability of a state [math]|\phi\rangle[/math] will give you a measurement of [math]\lambda_n[/math] is [math]\langle\psi_n|A |\phi\rangle = \sum_m c_m \langle \psi_n|A|\psi_m\rangle =
\sum_m c_m \lambda_m \delta_{nm} = \lambda_n c_n[/math].

Is there any real strategy for graphing multivariable functions? Like I have a general idea of things like planes, cylinders, spheres, hyperboloids, ellipsoids, paraboloids, stuff like that.

But is there any strategy for graphing something like [math]\frac{{x}^{\frac{3}{2}}\ln{y}}{{(3x\sin{y})}^{2}}[/math] on paper?

>>9383515
Plotting points?

>>9383515
Fix a certain x or y and graph the corresponding univariate function of y or x at the proper value of the fixed variable. Repeat a few times and then switch variables and repeat a few more times. You'll end up with a grid looking thing. Now just interpolate the surface and bam you're done.

>>9383515
Notice you can separate it into z=f(x,y)=g(x)h(y) so it's one function scaling/riding on the other.

>>9380516
I feel like a total tard, can't even prove a simple limit.
I need to prove by definition (the epsilon delta way) that the limit of x^(1/3) as x approaches 27 is 3.
Can somebody help me out?

>>9383814
What have you tried?

>>9383823
when I need to find a limit with polynomials or rational functions I usually just break them into simpler pieces until I can find an expression that reminds me of delta (i.e something that looks like |x-x0|). sometimes I put certain restrictions on delta in order to make terms simpler.
But I don't know man, I never did this sort of procedure on a third root and I'm not sure (algebraically) how to simplify it into an expression I can work with.

>>9382864
I meant the challenge question, sorry about that.
The book says the solution is still 8 reasoning like in the picture, but I think with that reasoning there would be 3!*2!+3!*2!=24 rearrangements and even checked those 24 numbers, so I think the book is wrong but I wanted to be sure.

>>9383814
[math]x < (\epsilon + 3)^3[/math] and [math](-\epsilon + 3)^3 < x[/math]

>>9383814
Define [math]y = x^{1/3}[/math] and keep in mind that [math]y^3-3^3 = (y-3)(y^2+3y+9)[/math].

>>9383899
could you please show the way? that's what I'm struggling with - I'm stuck on the algebra

>>9383814
|x^(1/3) - 3| < epsilon for a given epsilon. You want to show that there exists a delta for which 0 < |x - 27| < delta.

Will do it just for positives.

x^(1/3) - 3 < epsilon <=> x^(1/3) < epsilon + 3 <=> x < (epislon + 3)^3 <=> x < 27 * (epsilon/3 + 1)^3

let delta = 27 * (epsilon/3 + 1)^3 - 27. Then clearly delta is positive and x - 27 < delta. Do the same with negative epsilon to get the absolute value inequality. Tadaa.

I have some issue with reading a formula:

[math]c=(2n - 1)\pi/2l[/math] which then later shows up in [math]exp(-c^2\alpha t)[/math], with n being used in [math]\sum\limits_{n=1}^\infty[/math]

How do I interpret that 2l part? As it's written, it's …pi / 2 * l, but if I use it llike that, the exponent becomes just insanely large, with the sum never converging. So …pi / (2*l) seems like the logical way, but wouldn't that strictly be wrong?

What do?

>>9383987
>[math]\sum\limits_{n=1}^\infty[/math]
why does that nor work?

[math]\sum\limits_{n=1}^\infty[/math]

>>9383987
>[math]\sum\limits_{n=1}^\infty[/math]
Stupid inline tex…

>>9383987
There's a minus sign in the exponential ya doofus

>>9383994
Fuck. Yeah, already put this in my code, don't know how that stayd in the post, but the issue remains. Now it converges to 0, which in turn zeroes out my whole calculation, so that also can't be right.

>>9383997
Well obviously the exponential term will go to zero, however your sum will have a non zero value.

>>9382383
Its called a sector, look it up

>>9384011
Sum also goes to zero most of the times. the l can be something between 1 and a few 1000, so the exponential turm approaches 0 quite fast, which in turn fucks the rest of the term.
I'm pretty sure it has to be (2l), but the formula is in some old ass paper, and I'm wondering about the conventions of how to write such a formula.

>be me
jk
Okay, I have ~two months to study a bit of math before joining college for EE, it's alright to follow this guide (at least until the calculus part) to remember/relearn pretty much everything I need? Thanks.

>>9380915
Yes, beneficial threads such as whether or not it's scientifically proven that dicks on a girl is gay or not

>>9384017
Link to paper?

>>9384072
http://onlinelibrary.wiley.com/doi/10.1029/WR008i002p00487/full
some groundwater stuff.

Will it be easier if I learn physiology as quantitative physiology instead of regular memorize-everything physiology?

>>9383519
Genuinely an awful way to picture things. I watch my students do this every semester and then completely mis-interpolate.

>>9384057
>it's alright to follow this guide (at least until the calculus part) to remember/relearn pretty much everything I need?
No, that's a memelist.

>>9384871
What do you suggest?

>>9380516

Are white people the best?

What books/subjects do I need to know before diving into pic related?

>>9385003
Nothing.

please help i am brainlet.
I'm trying to do this integral
[eqn]\int^1_{-1} \frac{1-x^2}{(1-\beta x)^5}dx[/eqn]
which mathematica says is
[eqn]\frac{2(1+\beta^2)}{(\beta^2 - 1)^3}[/eqn]
However, integrating by parts with [math]u = 1-x^2[/math] and [math]v' = (1-\beta x)^{-5}[/math]
so that [math]u' = -2x[/math] and [math] v = (1-\beta x)^{-4}/4\beta [/math]
then
[eqn]\int^1_{-1} \frac{1-x^2}{(1-\beta x)^5}dx =
\left[ (1-x^2) \frac{1}{4\beta(1-\beta x)^4}\right]^1_{-1}
+ \frac{1}{2\beta} \int^1_{-1} \frac{x}{(1-\beta x)^4} dx
[/eqn]
since the integrand vanishes at the endpoints this is just
[eqn]\int^1_{-1} \frac{1-x^2}{(1-\beta x)^5}dx = \frac{1}{2\beta} \int^1_{-1} \frac{x}{(1-\beta x)^4} dx
[/eqn]
but mathematica says these things are not equal
literally what the fuck am I doing wrong?

>>9385115
nevermind I got it
just typed it into mathematica wrong.

>>9384943
no
white people are the worst
if you are white please do not have children

>>9385013
Sweet. Thanks.

>>9385146
str8 lollin at u nigga

>>9380651
>>9380653
>>9380658
>>9380662
https://en.wikipedia.org/wiki/Synchrotron_radiation#Formulation

>>9380516
what are some ways a nigger might go about finding the exact value of this asymptote

>>9385416
It's where the bottom thing goes to 0.
Alternatively, when tan(x^3-π^2) goes to infinity.
x^3-π^2 = π/2 (or - π/2, but that's not the one).

(π/2+π^2)^(1/3) which is about 2.25327265176

>>9385454
>(or - π/2, but that's not the one)
look at the graph again, it is

>>9385454
>It's where the bottom thing goes to 0.

oh yeah. that seems obvious now that you said that, which is the point of this thread so cheers

>>9380516
>come up with a clever name for this Neanderthal
The stinker

>>9380516
So let's say I'm factoring the binomial 3x^2-27
One way I solve it is factoring out 3 to get
3(x^2-9)
And then realizing I have a difference of perfect squares and expanding it to
3(x-3)(x+3)

The other way is through turning it into a trinomial and then using grouping.
3x^2+0x+27
3x^2+9x-9x-27
3x(x+3)-9(x+3)

Both get me the same answer, but is one method preferred over the other? If I were taking a course, would they expect the answer as
3(x-3)(x+3)
Or would they want the answer as
(3x-9)(x+3)?

What is the meaning of life?

>>9385635
42!

>>9385647
So 1405006117752879898543142606244511569936384000000000

>>9385618
The first one because it is more factored. Also you have to be 18 to post here.

>>9385126
Honest to god people say "just use mathematica" but my brainlet self ALWAYS types something wrong

>>9380516
/sqt/ <=> /mg>

how the fuck do i intuitively learn integrals

all I learned is some rules and u-substition -- 'methods'
my problem though is that
IT'S TRIVIAL
I wan't to have a deeper understanding of the integral more meaningful than
>it's just the area under the function bro
>it's the deriviative's opposite bro
>you can represent it as a reinmann sum
Because that sums up my understanding, and it looks so painfully plain

>>9385747
An integral is literally just that though, a continuous sum.

>>9385747
the fundamental theorem of calculus and the change of variables theorem is most of it. there's a characterization of integrable and bounded variation which is interesting too, and the riemann-stieltjes generalization

there are some interesting things you can learn about the riemann multiple integral and J-measurable functions, the lebesgue measure, etc etc, this would fall under measure theory

>>9385750
yeah and you can get entire sums with simple anti-derivative techniques

but I believe there is more to that,
by intuitive, i mean like I want to prove those techniques

>>9385771
thanks man, learned FTC recently, but measure theory is new.

I am trying to apply these integrals for physics.
thought I knew, but shit blewn me out the water.
professor is even hinting multi-var

>>9385400
is this next level math or something

>>9380516
How to write the M1, M2 etc?

>>9385668
I'm 20, just been reviewing maths from algebra and working my way back up to make sure I have a good foundation

>>9385824
let me rephrase this, what does the c) mean?
I've doing the a) and b).

>>9385747
>>it's just the area under the function bro
>>it's the deriviative's opposite bro
>>you can represent it as a reinmann sum
can you actually prove or properly define these things ?

>>9385953
yeah

>>9385953
It isn't difficult to formally prove, but if you want to understand it intuitively, try and think about the rate of the area under the function. as you traverse, you can think of it as adding small slices to the area, with the height being the value of the function, so you can see that the rate of change of the area is actually equal to the value of the function itself (derivative of integral is identity)

How hard would it be to do CE as a grad student if I have a BS in CS with a systems specialization?

>>9385938
list the walks you counted up in b

>>9385955
so what exactly is your problem ? you still don't know *why* it works the way it does ? or you find it unintuitive ? or you feel like there's something *deeper* going on ? because as long as you stick with just riemann integration, there isn't...

Could someone please tell me what does the i=1 represent? How do we know?

>>9386112
How old are you?

>>9386146
I don't think it matters. Please.

dont know if this belongs here
i have to send off my university application by the end of today. still a little unsure, anyone studied these things or have any insight: geography, physical geography, urban and regional planning, environmental management, and the wild card: classical studies
whatever it is im looking at going onto landscape architecture afterwards

>>9386163
It means the counting variable "i" starts at 1 and ends at n. The large sigma means that all terms that get counted up, need to be summed up with eachother.

is this solvable? if yes, how?

Can someone help me develop some intuition on how to interpret a quotient ring/group? Like what do the elements in a quotient ring/group represent, and how do I determine this?

>>9385472
oops

>>9386231
Thanks, Does the counting variable always starts at 1?

Does this make sense?

>>9385799
>yeah and you can get entire sums with simple anti-derivative techniques
>by intuitive, i mean like I want to prove those techniques
https://proofwiki.org/wiki/Fundamental_Theorem_of_Calculus

By the way, there's generalizations to that:
https://en.wikipedia.org/wiki/Stokes%27_theorem

>>9386112
It's just notation.
https://en.wikipedia.org/wiki/Summation#Capital-sigma_notation

>>9386238
[math] dX_s \text{ is } \frac{dX_s}{ds} ds[/math]
Then use linearity and solve.

>>9386266
No, it can be any number. It depends on where the summation starts.

>>9386288
Actually nvm. Mathematica says: "(no result found in terms of standard mathematical functions)"

>>9386274
looks gud, but that "sum 1/n = 3/2 + sum 1/(n+2)" is weird cause there is no start and end at the sum, and if both of them end at the same n it's actually false. i'd rather write it like pic

>>9386308
You're right. Thanks a lot!

>>9386308
whoops it should of course be k inside the sums in the first two lines

>>9386274
Yes, but you have to write out clearly that the sums at lines 6, 7, 8, 9 and 10 are finite, not series.
You are computing the partial sums s_k for (k=1,2,...) and then taking the limit.

For example line 6 makes no sense if you are talking about series. Right side would be Infinity minus Infinity.

Also, lines 7 and 8 should be written as sums, wtf are those commas.

>>9386163
it denotes which index the first summand has. In this case you have a_1 + a_2 + ... + a_n-1 + a_n because of the n on top of the sum sign, you stupid bitch. Now how old are you?

>>9386325
I see. It is indeed very messy and almost illegible. Thanks for the tips.

>>9386261
All quotient rings/groups arise from an equivalence relation which is compatible with the algebra structure. In this way, you can think of them as what happens to your group/ring when you assume some extra property.

For example, every group [math]G[/math] has a normal subgroup [math] [G,G] [/math] consisting of all commutators [math] [g,h]=ghg^{-1}h^{-1} [/math]. The quotient group [math]G/[G,G] [/math] is called the abelianization of [math]G[/math], because it's always abelian. The cosets of [math] [G,G] [/math] could alternatively be thought of as the equivalence classes induced by the relation [math]e \sim ghg^{-1}h^{-1} [/math] (or equivalently [math] gh \sim hg [/math]). This is the "extra property" we assume (i.e. that the quotient group is abelian).

Look up free groups and their quotient groups for the best examples of this idea.

>>9386261
You're just squashing a bunch of stuff to be zero. It makes the most sense in the context of polynomial rings, I think, where you can interpret it as adding the root of a polynomial to your ring.

>>9386163
It does if you are under 18 which you are.

>>9386261
if you like linear algebra, you can factor a vector space by a subspace. then cosets are then affine planes parallel to the subspace.

>>9386261
Consider G/N
You are considering N as e (identity) and you consider two elements a,b of G as equal if they are equal up to N (a=b*n).

For example, Z/4Z with addition.
You are considering 4Z (multiples of 4) as 0 and you consider two numbers a,b of Z as equal if they are equal up to a multiple of 4.

Another example: C/U (C: complex numbers, U: unit circle) with multiplication.
You are considering U (numbers of unit length) as 1 and you consider two number a,b of C as equal if they are equal up to multiplication by a unit length number. That's the same as considering that a,b are equal if they differ by a rotation; which is the same as considering that a,b are equal if they have the same length. So the cosets are {Circle of radius r; r in R}.

etc

>>9386471
damn, I wrote "consider" 9 times

>>9386471
Forgot to mention:
Define an operation on the cosets like this:
aN bN := multiply every element of the coset aN with every element of the coset bN = {an1 bn2 ; n1, n2 in N}

You say that "N is normal in G" (definition) whenever aN bN = abN for all a,b in G
And then you can prove that
N is normal in G if and only if a^(-1)na is in G for all a in G and n in N
and all the other equivalent definitions

>>9386493
Oh and
If N is normal in G, then G/N along with that operation is a group.
And if G/N along with that operation is a group, then N is normal.
(if and only if)

anybody knows why this reaction will not take place, but it does when ethylene oxide is used instead?

>>9386849
wrong fucking picture

>>9380871
adderal

For the notion of field of definition for a variety, I get the intuitive idea. In the formal definition that an $$L$$-variety $$X$$ is defined over the subfield $$K$$ if there is a $$K$$-variety $$X_K$$ such that $$X_K \times_K L \simeq X$$. My question is whether this isomorphism needs to be defined over $$L$$ (i.e. respects structure morphism)? For instance, it would be nice for an elliptic curve over $$\mathbb C$$ with j-invariant $$j$$ to be defined over $$Q(j)$$. This is true if we allow the isomorphism mentioned above to just be of abstract schemes, but I believe it isn't otherwise.

For the notion of field of definition for a variety, I get the intuitive idea. In the formal definition that an L-variety X is defined over the subfield K if there is a K-variety X_K such that [math]X_K \times_K L \simeq X[/math]. My question is whether this isomorphism needs to be defined over L (i.e. respects structure morphism)? For instance, it would be nice for an elliptic curve over [math]\mathbb C[/math] with j-invariant j to be defined over [math]\mathbb Q(j)[/math]. This is true if we allow the isomorphism mentioned above to just be of abstract schemes, but I believe it isn't otherwise.

>>9380516
ok so studying to increase iq scores is a thing but is this just maximing the gaming of a test like getting used to everything by drilling it a lot?
Doesn't this go against the spirit of the test? Are the results of someone who studied and grinded like crazy specifically for doing better in iq test questions really the same as the person who just got the result from taking it the first time with no prior exposure?

I am using R for basic statistics and I would like to know more about the following two claims I picked up:

- The linear model regression function lm() determines an intercept and a slope. The intercept is the same as the mean of the predictor, and is the same as a regression of the predictor to a vector of all 1's.

- Regression in N variables can be reduced to a regression N-1 variables, which means regression in N variables can be reduced to repeated regression in one variable.

Can someone point me in the right direction for these questions? Google brings up a lot of stuff but most of them are tutorials which avoid these questions.

i'm looking for a linear algebra book tries to give intuition for concepts and is full of illustrations. ideally it should cover matrices (determinants, systems of equations, etc.), vector spaces, linear transformations (their matrix representation / motivation for matrix multiplication) and bilinear forms. anything extra is fine too.
any ideas?
i'm looking at Linear Algebra: A Geometric Approah by Sernesi but from the amazon preview i can't tell if it's any good

>>9387143
>i'm looking for a linear algebra book tries to give intuition for concepts and is full of illustrations.

>>9387167
Unironically not a bad book.

How do earthworms move through soil? Their bodies are just so squishy and soil is tiny bits of rock

>>9385808
https://en.wikipedia.org/wiki/Retarded_potential

>>9385808
>>9388059
In fact https://en.wikipedia.org/wiki/Retardation
Under physics and engineering

Is climate change real?

Im a US citizen born and raised but want to do my MS in Europe as a sort of long study abroad/travel experience, would this hurt my chances to pursue a PhD in the US afterwards or would it not matter much? The university is still top 20 or top 10 in my field in the world so it is ranked highly.

>>9387043
This is one reason why IQ tests aren't perfect

Does Mars have an active core?

>>9388728
It doesn't appear to.

i can't do problems without, or with minimal numerical values
how do i fix this?

Is there any type of math that deals with using linear algebra techniques in the context of game theory? Like converting payoffs into tuples or vectors and performing operations on them to infer things about the game? Is there a name for that type of thing?

I have a linear map from R2 to R3 that is represented by this matrix:
1 3
2 6
3 9.
How can I find bases α and β for respectively R2 and R3 to transform this to a diagonal matrix with only ones or zeros on the diagonal?
I'm not necessarily looking for the solution, just how to approach this problem.

what is the topology of patchouli's ass

Is the heat death of the universe really the end?
Wouldn't all of the elements in the universe just decay into helium/hydrogen and then over fuckzillions of years succumb to gravity and make more stars, starting everything over again?

Assume this HYPOTHETICAL situation.

You have a coin that if flipped can results in one of the following outcomes: the first outcome is having a 6-sided dice land on the value "1", and the second outcome is having the dice land on any number but one. Assume that if the coin lands on heads, it will produce outcome one, and if it lands on tails it will produce outcome two, respectively.

When the coin flip is taken into consideration, is the probability of having the dice land on "one" .5, and is the probability of having the dice not land on "one" also .5?

>>9389391
Short answer: Yes.

Long answer: Yes, because the coin flip, a 50/50 chance, determines the dice roll.

>>9388217
>would this hurt my chances to pursue a PhD in the US afterwards
wouldnt it actually improve them
but I dont think europeans allow americans to do their master thesis in europe
it's not very common, not at all
you might experience a lot of hatred

>>9389260
[math]
α=:(α_1,α_2) \\
β=:(β_1,β_2,β_3) \\ \\

Τα_1=λ_1β_1 \\
Τα_2=λ_2β_2 \\


[/math]

This is cellular respiration: glucose + oxygen ---> carbon dioxide + water + energy. (Photosythesis is the left and right of that switched sides.)

Why does glucose and oxygen react? Isn't heat needed to break the bonds of the glucose and O2 molecules?

How do you counter racists who bring up things like
>Look at all the things white people have made! What have blacks made?
>Point out the Voltaire, Socrates, etc. of the negro. I'm waiting.
and so on? They've got a point, but I don't think it supports a claim of genetic superiority.

>>9389769
>How do you counter racists who bring up things like
You're assuming this can be countered.

Genuinely curious about this argument flat earthers use.
I'm a brainlet when it comes to astrophysics so this may have an obvious answer I'm not seeing

>>9389886

https://en.wikipedia.org/wiki/Sidereal_time

Even the ancients knew this

>>9389886
Baited and hooked.
The earth rotates about its axis AND revolves around the sun. Those are two separate motions. You can imagine a spinning ball and then having that spinning ball revolve around a center. The spinning stays because of inertia while the revolutions continue because of the central force of gravity.

>>9389883
I think prevailing science shows there is no link between race and intelligence.

>>9389886
Why do we feel nothing?

>>9389886
The answer is (as always) that the premise is wrong. It makes a little more than a full rotation every 24 hours.

>>9389889
Oh so our clocks already take that different into consideration?

Tell me if I'm taking this the wrong way. It takes about 24 hours for the 'meridian' to point directly back to the sun, not face it's original direction

>>9380516
pls help am brainlet

>>9389960

Correct. This difference adds up over the year to the shifting of the constellations with the seasons.

Our 24 hour day is set to the meridian finding the sun againsun, not the galactic reference frame.

What is an Alien Arithmetic Holomorphic Structure?

>>9389908
Because you are moving at the same time, it's like how you can walk inside of a train or even jump in it

>>9389908
https://en.wikipedia.org/wiki/Galilean_transformation

Protip: velocity is always measured respect a reference system. If you move at the same speed as the reference system, you will feel nothing.

That shit was fun when it was just a bunch of /b/ troll physics threads, flat earthers made it sad.

>>9389693
in the cells, there are lots of biochemical catalysators, and the oxidation is quite exothermic

I saw a post a while back that said math is not a universal language because it is based on human axioms. Even if that is true, wouldn't extraterrestrial beings still be able to grasp addition? In the sense that, if I one rock and I place another rock next to it. There are now 2 rocks. Even though the ET's might not understand the word "addition" wouldn't they still be able to comprehend that placing One object next to another object means there are now 2 objects. In that sense axioms do not matter because at this point it is a questions of semantics. Whether they call it addition, it is still adding one object to another to make 2 objects. Could someone help me out? Why would ET's not grasp simple edition?

why expansion of Universe is not considered as a fundamental (repelling) force?

>>9389769
> I don't think it supports a claim of genetic superiority.
It doesn't. Civilisation depends primarily on circumstance, and sub-Saharan Africa's geographical isolation is a significant factor in its exclusion. The orthodox history is particularly Euro-centric: between the fall of Rome to around 400 years ago, practically all of our scientific knowledge was "imported" from Asia.

>>9390178
The universe isn't expanding because of any extant force, but because of momentum imparted during the big bang.

>>9390115
I don't know how the species would build ships, decode transmissions, etc. without math.

>>9390272
Yes, that's my point. Basically he was arguing that because math as we know it was based on human axioms, math is not a universal language, because ET's wouldn't understand it. But only semantically. Any intelligent species would have to have some knowledge of mathematics.

will there be a cure for autism within the next 40-50 years?

>>9390292
No, you'll die a virgin.

>>9390296
that's a shame, i'd like to have children one day but i don't want them to have autism

>>9390297
Then stop being autistic.

Probably a shitty translation but anyway.

[math]f:R→R[/math]
[math]f[/math] is a monotonic function.
[math]0<f(x)<1, x∈R[/math]
[eqn]g(x)=f(x)/f^2(x)+1[/eqn]

Prove that [math]f[/math] and [math]g[/math] share the same monotonicity.

>>9390341
Suppose that f is increasing and prove that g is too. Then, suppose that f is decreasing and prove that g is too.

>>9390341
Does [math]f^2(x)[/math] here mean [math]f\circ f(x)[/math]?

>>9390347
No it's [math]f[/math] to the power of 2.

Also it's [math]g(x)=f(x)/[f^2(x)+1][/math]

>>9390346
Please elaborate

Is calling a linear transformation a function wrong? My linear algebra prof used the name function when talking about a transformation once and I've been thinking about it since.

>>9390351

Trying to do a instrument tuning, but need to solve a math first.
PS: You dont need to care, you can answer it with just math.

The questions.

I want the first 12 results of 1/x, where the result don't have repeating digits and when multiplied by 2 until it become a number between 1 and 2, it not equal to a previously valid number

> If 0<a<b, then:
> a<|x|<b <<->> a<x<b OR -a<x<-b
Guys, is the second part of this rule not wrong? Shouldn't the direction of the inequality be switched?

>>9390452
basically
w=z*(2^y), z=(1/x), 1<w<2, 0<x, -1<y, x is integer, y is integer, z is not repeating digits

>>9389979
A point [math] (x,y) [/math] is on the curve if and only if [math] ax^2+bx+c=y [/math] .
So [math] (x_1,y_1) , (x_2,y_2) , (x_3,y_3) [/math] are all on the curve if and only if all the equations bellow hold:
[math]
ax_1^2+bx_1+c=y_1 \\
ax_2^2+bx_2+c=y_2\\
ax_3^2+bx_3+c=y_3
[/math]
Which you can rewrite as
[math]
\begin{pmatrix}
x_1^2 & x_1 & 1 \\
x_2^2 & x_2 & 1 \\
x_3^2 & x_3 & 1 \\
\end{pmatrix}
\begin{pmatrix}
a\\
b\\
c
\end{pmatrix}
=
\begin{pmatrix}
y_1\\
y_2\\
y_3
\end{pmatrix}

[/math]

what is the motivation for orthogonal polynomials? i understand the definition, but why are they characterized as orthogonal? can they be used to construct some sort of basis?

>>9390456
Draw it.
x has distance from the origin ranging from a to b.
If x is positive, then a<x<b.
If x is negative, flip it to the positive side of the real line and you get a<-x<b which is the same as -a>x>-b.

>>9390503
Here's a use of them.

>>9390518

>>9390459
If x is an integer, then 1/x ends in repeating digits in every base (if the prime factors of x are also prime factors of the base, then the repeating digits will be zeroes). A number only has a non-repeating decimal expansion if it's irrational. And that's true for any base, not just decimal.

could someone who knows more about the subject give me a 3-4 sentence summary of how russells paradox affected the naive set theory? im doing an essay on it but i dont know much about everything related

>>9390518
>>9390520

that's neat. so that would be the most accurate 5th degree polynomial approximation of sin(x) along that interval, as measure by that norm?

i've never really thought about differences in accuracy of various polynomial approximations.

a polynomial regression would approach this solution given enough data points, right?

>>9390541
>a polynomial regression would approach this solution given enough data points, right?
You mean polynomial interpolation?
Not really. More points doesn't mean more accuracy. But it is true if the points are the "right" ones.
https://en.wikipedia.org/wiki/Polynomial_interpolation#Convergence_properties

>>9390518
>>9390520
Nice. I saw that inequality in my linear algebra course but we never used it like that. Good stuff.

>>9390503
Another use of orthogonal polynomials is in Gaussian Quadrature (Legendre Polynomials)

>>9390559

i mean polynomial regression. if you take random samples from -pi to pi then it seems like the polynomial regression should approach the solution given in axler's text.

So I'm going through Serge Langs Basic Mathematics as a review before I go to college.

I've never done a proofs before because shitty school, the first problem set asks you to prove a bunch of addition statements using commutative and associative properties, did I do this right?

>>9390646
So I'm going through Serge Langs Basic Mathematics as a review before I go to college.

I've never done a proofs before because shitty school, the first problem set asks you to prove a bunch of addition statements using commutative and associative properties, did I do this right?

So I'm going through Serge Langs Basic Mathematics as a review before I go to college.

I've never done a proofs before because shitty school, the first problem set asks you to prove a bunch of addition statements using commutative and associative properties, did I do this right?

>>9390649
Lang is a meme.

>>9390357
>Is calling a linear transformation a function wrong?
No, but it's better to call it a linear transformation since it implies the preservation of the algebraic structure (function does not).

>>9390272
they could simply grow them

If you turned the entire planet into a rocket how fast could the final stage be?

>>9390649
Associativity is about moving parenthesis not dropping them completely.

>>9390649
It's not entirely correct.
(a-b)+(c-d) =
=a+((-b+c)-d) by associativity
=a+((c-b)-d) by commutativity
=(a+c)+(-b-d) by associativity
=(a+c)-(b+d) by distributivity

>>9390859
I was thinking this, but they don't introduce distributivity until the next chapter.

>>9390787
Isn't that the same thing?
Essentially we are just removing parenthesis and placing them somewhere else when we move them.

>>9390492
still I don't see whether a, b, c as a solution of the system i.e. [math] a^2 + a + 1 = y_1 [/math]

Anyone know of similar videos like this? about evolution of life.
Preferrably videos without a bunch of scientists being interviewed. just a whole movie/video about origins of life.

thanks in advance guis

>>9391213

ffs, forgot the the video.

https://www.youtube.com/watch?v=StqZI9pMq0U

Am I supposed to try to prove things I come across in 'low level' calculus and mathematics or just study up on the actual proofs and figure out how they work? I'm never sure if these are proofs that I should be just researching to understand right now or if they're considered elementary enough that I should be practicing my proof making skills on them. I'm talking stuff like product/quotient rule, the proof that d/dx e^x is e^x, etc. I love looking up the proofs and testing myself on them later, but I'm not sure if this is proper.

>>9391521
Try proving things about divisibility and other things with integers
easy math but real proofs

>>9391521
The rule is that you should always attempt a proof after you read the statement. Your success rate and the time you should devote to this will be low now, and should steadily increase over time.

>>9391165
I don't understand what you are saying.

>>9391165
you're making a mistake in your matrix multiplication. It's [math] ax_1^2+bx_1+c = y_1 [/math]

What's going to be the difference between going to a no name state university and a top 10 public university in my state? Specifically for a computer science/mathematics degree (don't know which subject to focus on in college). Could either go to UW Madison or the second best WI school, UW Eau Claire. Madison's about 8k more per year, but it's pretty highly ranked whereas I'm sure people outside of WI haven't heard of Eau Claire or La Crosse.

I hear that it doesn't matter where you go to university in terms of finding a job, but if it does I'd see no reason not to attend the known, highly regarded university of Madison.

>>9380950
>gaussian processes
refers to the underlying probability distribution you assume you data follow. In particular, gaussian (normal) distribution with mean mu and covariance matrix Sigma

>>9380950
also
https://en.wikipedia.org/wiki/Gaussian_process#Gaussian_process_prediction,_or_kriging

>>9391616
After your first 3-5 years in the workforce, nobody will care where you went unless they're a fellow alum or its an Ivy. For getting that first job, you need a school that's well-connected to the industry you want to work in. The top tier public schools are really good at this, especially if you want to work outside of your state after graduation.

Question for med students: how much of your premed studies actually comes in useful? Here most people do a science degree to get into postgrad med but it's not required. Taking a look at some of the premed stuff and it seems barely relevant aside from a few basic math and biology concepts.

>>9391616
Merry Christmas fellow cheesehead! Madison of course, no contest. The other schools are for people who didn’t get into Madison, or who need to stay local. Yes, the longer you are out of college the less it matters, but your opportunities will be broader at Madison.

>>9392120
Opportunities such as taking grad courses, getting involved with research, attending talks and seminars, etc.

On the other hand if you just want to take it easy, do the standard undergrad sequence, then it probably doesn’t matter so much, and you’re more likely to be near the top of your class at the small school.

What is the Spivak of General Physics?

Linear Algebra:

Is C a subspace of R (over R)?

>>9392840
Oh goddammit. I mean is R a subspace of C (over R)

>>9392840
yes
it follows form the fact that R is a vector space over itself

[math]\lim_{x\to-1}[x+\surd (x+1)]/x(x+1)[/math]

does it equal infinity? or did I fuck up

>>9392870
>does it equal infinity?
No, since being "equal to infinity" isn't even well-defined.

>>9392877
jesus fuck is it that hard to answer a simple question

>>9392882
Your question has no meaningful answer since the question itself isn't meaningful.

>>9392886
holy fuck what does the limit I posted earlier equals to?

>>9392870
Why don't you explain why you think it's infinity?

>>9392894
>what does the limit I posted earlier equals to?
It doesn't.

>>9392898
Just plug it into wolfram alpha. This requires no brain, just calculation.

>>9392901
>Just plug it into wolfram alpha. This requires no brain, just calculation.
If wolfram says it's infinity then why are you asking if you fucked up?

>>9392904
I'm not that dude... I actually misquoted you. Sorry.

Lets imagine i have a bar like a lifting bar with weights in each side but not on the top of each side, just like a normal lifting bar, and then i have another bar but this is longer than the one before(this means the weights are now further away from the pulling point) if i pull the first and then the second with the exact same weight and pulling from the middle for example which one of them will need less force?

>>9392898
I end up with:

[math]\lim_{x\to-1}1/[x+1+\surd (x+1)][/math]

which should be 1 to an number tending to become zero, which should equal infinity

>inb4 all math "genuises" shit on me for telling that an limit equals infinity while I should say that the limit can't be calculated or some shit

just be done with it, that's the way my country's shitty educational system has defined it to be, writing your bs on an exam paper will result in loosing the whole thing.

>>9392911
>my country's shitty educational system
Where are you from?
You don't need to learn it wrong just because your country is shit. Write whatever they want on the test, but study right.

>>9392914
Found an example where it shows a limit being equal to infinity. The book is 20+ years old, maybe that's why.

Still, what's it equal to? I need to be done with this shit.

>>9392921
You're right.

>>9392921
>>9392939
Actually, the limit does not exist, you just forgot to say that it was coming from the right of -1. If so, then it diverges.

>>9392940
It's coming from the right of -1, you're right, sorry I've been solving math for the past 3 hours and I'm getting tired.

What does diverges mean? I can't think of something equal in my language.

>>9392944
>>9392944
>What does diverges mean? I can't think of something equal in my language.
It goes to +-infinity or it doesn't converge to a value. What I meant is pic related (that is, it goes to infinity).

>>9392946
nice, it's correct then. thanks anon.

>>9393042
[math]\sum_{n=0}^\infty -1^n[/math]
doesn't go to infinity but it diverges…

>>9390670
Not >>9390649
but what do you suggest?
Paul notes?

>>9393052
Suggest for what?

>>9380516
What is the risk of changing the orbits of planets to throw them out of the solar system or into the sun or other planets by nudging them with constant flybys of space ships used for colonization, travel, trade ect in the future?

>>9380900
Ask your university's financial aid office. There are no fee waivers, but fee reductions.

>>9393099
[math]\rightarrow0[/math]

>>9393110
https://youtu.be/YAnxt1YPWbk?t=352

"...conservation of energy, what energy our craft gains the planet must lose. When the voyagers used Jupiter to increase their speed to get to Saturn, Jupiter's orbit around the Sun slowed but only by about one foot per trillion years"

So, if we become a species that travels regularly and constantly through the solar system using bodies of mass to get from place to place, wouldn't that constant use of energy change orbits slowly but surely, and change them for the worse?

>>9380516
which releases more endorphins in the brain, exercising or sunlight? are there any studies where they have measured the exact amount released for different activities?

Someone explain this differential equation bullshit? How does he get that step?

>>9393474
>Someone explain this differential equation bullshit? How does he get that step?
Look at the green text beside it

>>9393479
I don't understand that part either.

>>9393484
>I don't understand that part either.
https://en.wikipedia.org/wiki/Integration_by_substitution

>>9393491
Thanks.

>>9393453
>In endurance exercise performed at a steady-state between lactate production and elimination, blood beta-endorphin levels do not increase until exercise duration exceeds approximately 1 hour [1]

>The researchers administered either a placebo or 5, 15, or 25 mg of naltrexone, a central and peripheral opioid receptor blocker
>The subjects were then asked to lie for 10 minutes on each of two tanning beds, one a true UV bed, the other rigged not to deliver UV light. Afterwards, the subjects, who were blind to the test conditions, were asked to describe which session made them feel best.
>With the placebo and the 5-mg naltrexone dose, the frequent tanners showed a clear preference for the UV bed—and more strongly so than the infrequent tanners. [2]
so tanning seems to clearly beat out light jogging or other endurance exercise, unless you exercise for > 1hr. which i never do. tanning releases endorphins within 10 min endurance exercise takes > 1 hr.

quite interesting, good to know as a lot of times to exercise i go on walks or light jogs. probably releasing almost no endorphins at all. if any it comes from the sun i get while outside. will be harder to compare anaerobic high intensity exercise though

1. https://www.ncbi.nlm.nih.gov/pubmed/1553453
2. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1513309/

>>9393553
I'd like to know the results for near and far infrared instead of UV.

>>9381114
reflection?