/sci/ - Science & Math

I'm a brainlet, can someone explain to me what the fuck is happening here? I assume [math]c=\frac{a}{a+b}[/math] came from [math]a-\left(a+b\right)x[/math] but what about [math]\left(1-x\right)^{b-1}[/math] and [math]x^{a-1}[/math]?

>>9308014
it's probably just a technicality of the definition of critical point

the derivative f'(x) is defined on the open interval (0,1) (you can't take the left limit to 0 or the right limit to 1), so 0 and 1 might not be considered critical points

so if
(1-x)^(b-1)x^(a-1)(a-(a+b)x)=0 for x in (0,1) then (1-x) and x aren't 0, so a-(a+b)x=0 gives you the c there

>>9308020
I'm still not sure I get it completely, but thanks man.

>>9308045
where did i lose you?

How many ways can I arrange three letters where repeats are allowed, but order doesn't matter.

For example I have 0,1,2

One option would be 0,0,1
0,1,2

but 0,2,1 would not be included in my list because it is a repeat of my second one above?

I got 10 so far? Is that all of them?

I have a simple function where the domain for X is restricted to integers. How do I plot that shit (with restricted domain for X) in Wolfram?

>>9308057
Here's the general solution. Learn it and you can do any of those problems in 2 minutes in the future
https://www.mathsisfun.com/combinatorics/combinations-permutations.html
https://www.mathsisfun.com/data/binomial-distribution.html

>>9308057
You can think the problem as having 3 buckets, each bucket representing a letter, and you put (three) stones in those buckets where the number of stones in a bucket is indicating how many of a certain letter you wanna pick.
https://en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)
The answer is [math] \binom{3+3-1}{3-1} = \binom{5}{2} = 10 [/math] .

>>9308268
http://reference.wolfram.com/language/ref/ListPlot.html

No idea how to do this. Any thoughts?

>>9308895

pathetic self-bump

>>9308895
>>9308909
Show that P(X > 0) is 1.

What do masters programs look for in people who have been in industry for a few years? What does a BS in engineering need to prove that they're competent for a MS in mathematics?

>>9308045
A brainlet explanation:
You have three terms, whose product equals to zero: (1-x)^(b-1), x^(a-1), and (a-a(a+b)x).
You know that one of them must be a zero, since the whole product is zero.

(1-x)^(b-1) can't be zero, since f(1) = 0.

x^(a-1) can't be zero, since f(0) = 0.

Therefore, (a - (a + b)x) must be the zero.

What's the clever way of solving this problem? I solved it using a fuck ton of trigonometry and algebra, but I'm retarded, so there has to be a better way.

>>9308918

P(X > s) = P(X > s | X > 0)

Is this how I prove that?

>>9308943
Sure you could do that. You could also let s = 0.

>>9308940
Surface of the sphere minus 6 caps, where the surface area of the cap can be found here:
https://en.wikipedia.org/wiki/Spherical_cap

>>9308895
It is really simple.
P(X<=0) = 1-P(X>0) = 1-P(X>0+t|X>t) = 1-P(X>t|X>t) = 1-1 = 0

>>9308972
Don't forget to add in the 6 disks.

Should I even start learning higher math when I'm bad at mental calculations?

>>9308994
Proofs don't require you to multiply 2 5-digit numbers in your head. You should be good.

>>9308994
All you need is logic and good abstract thinking.

>>9308922
>(1-x)^(b-1) can't be zero
Wrong.

>x^(a-1) can't be zero, since f(0) = 0.
Wrong.

>>9309001
>>9309007
So it's pointless as an adult to do basic multiplication and division with high numbers?

>>9309088
Wrong.

>>9309099
mentally?
yes
what are calculators for?

>>9309180
They're for weighing down papers

>>9309099
>So it's pointless as an adult to do basic multiplication and division with high numbers?
Yes, it is.
If you like it though, just do it. We all do pointless shit for fun.

solve this without a calculator.

>>9307840
How toxic is agricultural lime?
I live in the country and am surrounded by corn/beanfields. In an effort to get /fit/ I've started walking several miles per day on the dirt roads. The only problem is the farmers spread a bunch of lime a week or so ago. I looked up it's msds and read it's fairly nontoxic but the silica can cause lung problems. How long until I can safely resume walking them again? We've gotten a little moisture since they've spread it (maybe 1/4 inch all together). I eouldnt be as worried if it weren't so windy.

>>9309231
If you're that worried, why not just buy a cheap face mask?

Where can i download some free .dna or .prot files? i'm going to be working on SnapGene in a lab in a few weeks and i'd like some files to play around with to get a hang of this program before my training there

>>9307840
The teacher's answer is 14 choose 4 = 1001
but I can't seem to get that answer

Can anyone explain to me if I'm wrong, and if so, why?

>>9308994
>Should I even start learning higher math when I'm bad at mental calculations?
Doing calculations is irrelevant, that's what computers are for.
Nobody would spend his time calculating 123123123*231231231313-3233242 if a computer can do it in a billionth of that time.
I had classes were the professor did basic arithmetically mistakes and nobody cared.


>>9309099
Yes.

Is this a poisson process with lambda 4/3 or am I retarded

help

>>9309267
You write 25 as 1+1+...+1 (25 1's).
You put 5-1=4 bars in between so that they make 5 cells, each cell representing one of the x_i's.
Because you want at least 3 1's in each cell you just keep 5*3 1's aside and you put them after.
The problem reduces into having 25-3*5=10 1's and 4 bars and all you need is to choose the positions of the bars.

[math] \binom{(25-3 \cdot 5)+(5-1)}{5-1} = 1001 [/math]

>>9309267
>>9309493
Wait a minute. [math] \binom{14}{10} = \binom{14}{4} [/math] (you choose the positions of the 1's instead). You fucked up at the calculation.

>>9308940
The last post in the previous thread answered your question:
>>9309228

>>9309338
>Is this a poisson process with lambda 4/3 or am I retarded
The latter.
It says "the lifetime of a light bulb is exponentially distributed" and then it asks you questions about the lifetime of a lightbulb. It didn't ask what's the distribution of the number of dead lightbulbs after a certain time has passed.
T: the lifetime of a lightbulb (in years)
CDF of T is F(t):=1-e^( -1/4 x) [caveat: not sure if it is 1/4]
The answer to (a) is 1-F(2)
The answer to (b) is 1-F(1) because the exponential is memoryless. This obviously sounds retarded, but that's because T doesn't really follow an exponential distribution in practice.

>>9309541
Thanks for pointing that out to me.

If two vectors [math]\vec{a}[/math] and [math]\vec{b}[/math] are parallel, why does [math]||\vec{a}-\vec{b}||=\sqrt{a^2+b^2-2ab}[/math] and not simply [math]a-b[/math]?

>>9309681
>why does ||a⃗ −b⃗ ||=a2+b2−2ab
It doesn't. The thing on the right side of the equality is not defined (you can't square a vector).

>>9309685
Are you retarded? [math]\vec{a}^2=\vec{a}/cdot\vec{a}[/math], [math]||\vec{a}||=\sqrt{\vec{a}/cdot\vec{a}}[/math].

>>9309685
>>9309697
I meant [math]\vec{a} /cdot \vec{a}[/math].

>>9309697
>>9309702
Wtf? Fuck this gay ass site.

>>9309697
>Are you retarded? a⃗ 2=a⃗ /cdota⃗ , ||a⃗ ||=a⃗ /cdota⃗ −−−−−−√.
You can't square a vector, or divide vectors. Try rereading your textbook.

>>9309681
||a-b|| = sqrt((a-b)^2) = sqrt(a^2 + b2 - 2ab)

>>9309707
a2 = aa'

>>9309707
Kys.

>>9309681
Do you even understand what the things you write mean?

>>9309713
>||a-b|| = sqrt((a-b)^2) = sqrt(a^2 + b2 - 2ab)
You can't multiply vectors.

>>9309715
>Kys.
Nowhere on that page is a vector squared. Try rereading your textbook.

>>9309718
>You can't multiply vectors.
How about 1 by n matrices?

>>9309723
>How about 1 by n matrices?
What about them?

>>9309723
still can't

is there anything like factorials but for sums?

>>9309730
>is there anything like factorials but for sums?
https://en.wikipedia.org/wiki/Triangular_number

>>9309725
>>9309726
[1,1]^2 = [1,1][1,1]^T = 1*1 + 1*1 = 2. Huh, would you look at that.

>>9309735
>[1,1]^2 = [1,1][1,1]^T = 1*1 + 1*1 = 2. Huh, would you look at that.
You multiplied matrices, not vectors.

>>9309735
[1,1]^T is a n by 1 matrix, not 1 by n.

>>9309681
>>9309697
>>9309715
My dudes, I have realized my mistake. I apologize for my characteristically-4chan angst.

>If "A+B=C" and "B+A=D", what is "D-C"?
Am I retarded for not being about to figure this out?

>>9309783
>Am I retarded for not being about to figure this out?
Yes.

>>9309783
to be honest, yes

>>9309785
I don't get it, what's the answer here. It seems like an impossible question unless A and B have different values in the second equation.

>>9309796
D-C=B+A-(A+B)

>>9309798
That's not a real answer, though.
How are you suppose to figure what what the actual variables are?

>>9309783
>>9309796
[math]A+B=C \land B+A=D \longrightarrow D-C = (B+A) - (A+B) = B+A-A-B=0[/math].

>>9309783
>Am I retarded for not being about to figure this out?
Honestly? You should reconsider being a stripper.

>>9309804
Yeah, maybe. But I'm still fairly sure there's no actual numerical answer.

>>9309810
It's zero. Zero is a number.

>>9309812
Have different variables mean the same number doesn't make sense to me.

>>9309813
Having*

>>9309813
Different numbers can mean the same thing too:
1 + 2 = 3

>>9309813
What class could this possibly be for? Introduction to Pre-Remedial Babby Algebra?

>>9309823
I don't know, some friend I have just asked me over a text message. I doubt it's for a class.

>>9309205
56

>>9309830
>I'm asking for a friend hehe

Any help with 8.5.4c?

>>9309924
Use the method of characteristics.
[math] u_{tt} - c^2 u_{xx} = Q(x,t) [/math]
Therefore
[math] \frac{dx}{dt} = +/- c [/math]
and
[math] \xi = x + ct [/math]
[math] \eta = x - ct [/math]

Transforming the equation to the new coordinates,
[math] -4c^2 \frac{\partial^2 u}{\partial \eta \partial \xi} = Q(\xi,\eta) [\math]
Integrate along characteristic curves and enforce BCs

I study cs. I have this course that to pass you need to write an article of 10k words using latex. I can even "plagiarize" by translating articles from english . So my professor handed the topics to each student and I got to write about "Matrix logarithms". Where do I start ? I searched around the web and I don't know how I'm going to write 10k words about it. Is there any paper or part of a book that you have in mind and can recommend ?

>>9310146
there's no way that shit's getting graded, who's gonna read all that? Just put in random bullshit

What is the most intelligence species on earth after homo sapiens?

>>9310155
Homo Erectus

>>9310155
If there's a real neanderthal left in a cave somewhere probably them.

>>9310154

He proofreads a bit for possible google translate usage(some dumb dudes did it in the past). So far I'm thinking to get a chapter from a book + a paper.

>>9310163
I say structure it like this: paper, random bullshit, paper

>>9310161
>>9310162
Is, not was.

>>9310200
The world's a big place. I wouldn't be surprised if there's some left out in the bush.
Other options would be:
Octopus
Crows
Dolphins
Mushrooms

>>9309783
I’m a fucking pothead 18 year old with no scientific background who just lurks here because I find this board interesting and even I know you’re retarded.

>>9307840

>mfw row "15" (14) of Pascal's triangle, as expressed in base 10, contains 1001, 2002 and 3003 right next to each other like it ain't no thang and nobody's fucking with me

>>9309891
Not at all what I was implying. Might want to curb the autism so you can read social cues better.

>>9310229
It makes no sense to have different variables mean the same thing.

>>9310383
If there was no sense in it, then it would not have been asked. And if it wasn't asked, you would have never asked us and learned a lot!

>>9310497
Senseless things happen all the time.
Like you being born, for one.

What are Perfectoid Spaces?

>>9310595
>What are Perfectoid Spaces?
http://www.ams.org/notices/201409/rnoti-p1082.pdf

Can a head injury stop your heart?

I'm watching Death at a Funeral and a guy falls off a couch and smashes his head. A guy checks his pulse and concludes he's dead. I don't see how a hard hit to the head would stop the heart, was just wondering if it's possible or just a movie.

>>9310613
You do realize that your brain controls your heart, right?

>>9310613
The heart and lungs actually require the brain in order to function.

If you get hit in the head hard enough, your brain stem won't work and your heart will stop beating.

>>9310639
The brain doesn't vaguely control the heart though, a specific part controls the heart... and even with cardiac arrests, your heart doesn't just stop, it beats erratically. All I'm asking is can blunt force trauma from something like a fall cause the heart to stop. My thinking is injuries like that don't stop the heart, they cause brain damage rendering the person a vegetable. Accidents like car wrecks cause people to bleed out and have brain death due to lack of oxygen to the brain, but can a pure blow to the head stop the heart?

>>9310613
Your lower brain controls your vital organs (and your sense of smell)
You'd have to basically spear all the way through the head vertically or up from the bottom

Is the monopole moment of a charge distribution basically just the total charge?

Why does the entropy of a system that flows from hot to cold always increase?

>>9307840
Given two object of with mass m1 and m2, and speed v1 and v2, how do I determine the forces they extert on each other?

>>9310843
*velocity

>>9309493
>>9309497
Oooh, omg. Thanks! I'm retarded, lol.

I've been working on this for ages and have been unable to get a good result. any help would be appreciated, the answer is in the question but i can't figure out how to get to it

>>9311020
Q5, sorry i posted the uncropped image

>Start of bachelor
>Confidently did all sorts of algebraic manipulation, easily knew what to do and pulled it off successfully

>Postgraduate, starting on masters
>Now I double-check everything even though I turn out to be right most of the time. All confidence in my own mathematical intuition is lost, and I'll often forget absolute fundamentals like the definition of angular momentum

What the fuck happened? How do I go back? I didn't even do drugs during this period

>>9311143
stop giving a fuck

>>9311143
>the definition of angular momentum
Dude I forgot these shit too. Just read again, don't be ashamed.
I would double check my work only on exams or homework. Trust yourself nigga.
If you still have problems, double check only select/difficult problems

How would you digest this information?

I'm just dicking around, trying to figure out what kind of drone i could build and learning about all sorts of things in the process. I'm slightly struggling with visualizing data and understanding it's profile compared to other sets.

Considering i want to build a drone that has the longest flight times possible while still having a wide rage of thrust capability (""payload/carry capacity""), how would you display this set of information as such?

It took me awhile, but i think the orange propeller is shit, and that a 14x4.7 prop in 4s or 5s is best efficiency and thrust.

I still know nothing about what the RPM, etc.... values mean to an end user, but as somebody just hypothesizing about, how did i do?

Is there any alternative to MIT OCW? I mean with lectures and complete set of notes and problem sets
I don't liked the differential equations and linear algebra courses

>>9310146
http://eprints.ma.man.ac.uk/1852/1/covered/MIMS_ep2012_72.pdf
Or just google "numerical algorithms to estimate matrix logarithms" or something similiar.

>>9311180
http://coursera.org/
http://edx.org/

Do aliens exist? Is santa real?

>>9311197
>Do aliens exist?
probably

>>9311180
just audit your local community college classes

i have a matrix system that looks like this, where i know a...z
how do i go about finding what A looks like?

>>9311276
you might want to rethink your notation.
what exactly is x? is it a matrix? is it a scalar? is it the 24th component of your [a,b,...,y] vector?
what is z? is it included in your [a,b,...,y] vector? If not, A can't be a linear function in the case that z =/= 0

>>9311292
is this better?

>>9311304
[eqn]\begin{pmatrix}
x & & & & \\
& x & & & \\
& & \ddots & & \\
& & & x & -\gamma_s\\

\end{pmatrix}
\begin{pmatrix}
p_0(x)\\p_1(x)\\ \vdots \\ p_{s-1}(x) \\ p_s(x)
\end{pmatrix}
= x \begin{pmatrix}
p_0(x)\\p_1(x)\\ \vdots \\ p_{s-1}(x)
\end{pmatrix}- \begin{pmatrix}
0\\0\\ \vdots \\ \gamma_s p_{s}(x)
\end{pmatrix}

[/eqn]

>>9311276
Let e_i be the vector with 0's everywhere except the i-th position.
A e_i = the i-th column of A.

>>9311320
i'm assuming the [math]p_s(x)[/math] is a mistake?
also, how do you get the [math]\gamma_s[/math] in there (A)?

>>9311364
>'m assuming the ps(x) is a mistake?
nope. you need to have it in your vector, otherwise A*0 =/= 0, hence A isn't a linear map

>>9311364
>also, how do you get the [math] \gamma_s [/math] in there (A)?
3x4 example:
[eqn]
A=\begin{pmatrix}
x & 0 & 0 & 0 \\
0 & x & 0 & 0 \\
0 & 0 & x & \gamma_s
\end{pmatrix}
[/eqn]

>>9311368
well that's weird, >>9311304 is literally a screencap of my assignment, and it says the last element of [math]v[/math] is [math]p_{s-1}(x)[/math]

>>9311368
>>9311371
also, the vector by which you multiply A and x is the same

>>9311373
you seem to have troubles paraphrasing your assignment.
why don't you just post it?

>>9311377
i usually don't ask to be spoonfed, but oh well, this is pretty urgent and i have no clue what i'm doing this time
but i fully agree that my posts are just fuckup after fuckup

>>9307840
What is a computationally efficient way of showing that [math]S_n[/math] has more elements of even order than of odd order for [math]n \geq 4[/math]?

>>9311391
well that makes it more clear.
Basically for the first s-2 entries you just have a matrix with x on the diagonal.
For the (s-1) th column, you have
[eqn] \sum_{k =0}^{s-1} a_{k,s-1}p_k(x) = xp_{s-1}(x) -\gamma_s p_s(x) [/eqn]
That you got to solve for the [math]a_{k,s-1},~k=1,...,s-1 [/math]
The recurrence relation helps us with that.
Namely [math] xp_{s-1}(x) = \gamma_sp_s(x)+\gamma_{s-1}p_{s-2}(x) [/math]
So
[eqn] A= \begin{pmatrix}
x & & & &\\
0 & x & & &\\
\vdots & & \ddots & &\\
0 & & & x & \\
0 & 0 & \cdots & \gamma_{s-1} & 0\\
\end{pmatrix}
[/eqn]

>>9311422
the characteritstic polynomial is
[math] p(\lambda) = -\lambda(x-\lambda)^{s-1} [/math]
so the eigenvalues are 0 and x

>>9311417
The complement of A_n has half the elements of S_n Here, all elements must have even order (sgn is a morphism to Z_2). It remains to find a single element of even order in A_n.

>>9311422
>>9311427
alright, thanks for your time, i think i understood it

Doing materials chem grad work with liquid metal-elastomer composites.

Is there anyone familiar with AFM who has worked with a Digital Instruments Nanoscope II, III or IV? Trying to take nanoindentation measurements on soft sample surface and I'm at the end of my rope with this thing.

Anyone who has looked at the Nanoscope manual will know the thing is a fucking mess and hardly explains anything. My main issue is approaching the surface with live data collection as opposed to initiating a scan.

Can someone explain the difference between a motive and motivation, and their direct relation? I keep finding opposing explanations, in my book it says motivation is a process that affects the amount of effort we will put in to reach a goal which satisfies our motive. But it never says what the fuck is a motive, and from this I can't tell how motivation is related to a motive either. Btw. this is part of my ME curriculum. JUST

What's your favourite LaTeX editor?

>>9311662
Also it says that a person becomes frustrated when they can't decide which course of action to take to get to a goal and satisfy a motive.

"Conflict of motives" it says (oh okay, I'm choosing between two motives then), "where we have to decide between two different courses of action to satisfy a motive" (so wait a fucking second, are the motives conflicting or courses of action to satisfy the said motives), then further says "...we are equally attracted to two different goals" (SO AM I FUCKING CHOOSING BETWEEN TWO GOALS NOW??). I'm really confused. I know this is sci but you guys are smart enough to explain this.

>>9311671
If the courses of action are not conflicting then the end goals are per definition not conflicting.

>>9311692
Yeah but what if I've got the same goal that can satisfy a motive, but I've got two different courses of action I can take to reach the same end result? Or that doesn't work. Also, what IS a motive?

I understand that this is mostly conjecture, but what does the evolutionary "family tree" for homo sapiens look like?

As far as I can tell, it goes roughly

Sahelanthopus -> Australopithicines -> Homo Habilis -> Homo Erectus -> Homo Heidelburgensis -> Homo Sapiens + Homo Neanderthalensis + Denisovans

>>9311431
Elements of An are even permutations, that doesn't mean they have even order. For instance, all the 3-cycles are in An.

in my Dynamics course I'm so overwhelmed with the multitude of different paths and ways to achieve an answer, I can never link what my goal value is to how it relates mathematically to what I'm given.

I understand that's the entire point of engineering is figuring it out, but it just doesn't click with me. I hope I don't fail because I can't switch out at this point, I'm 4 years in and still have two more to go.

>>9311700
Well, you will obviously not have conflicting motives if you only have one motive. Even if you have conflicting courses of action.

My naive interpretation of your given definition is that 'motive' is essentially the same as 'goal'.
For example: if your motive is to pass your course, the a goal that satisfies that motivet is to pass the exam. Styding will then be the obvious course of action to reach that goal. Then you need 'motivation', or 'fuel' as i think of it, in order to put effort into studying. The motivation might be that you really really want to pass the course, or promise of some other desirable reward, or that you simply enjoy the process of studying.

What kind of math is this? This is from my Calculus I class, and my prof keeps dropping in questions like this that I don't think are calculus related. Is this what topology is like? Thanks

>>9311773
it's a very specific type of topology that is important for analysis/calculus

>>9311773
You could say it's real analysis. Which is the formal basis for calculus.

What exactly is a tensor? How is it different from a matrix?

>>9311797
matrices are special kinds of tensors
if you don't understand the wikipedia article on tensors, you probably don't need to know about them

>>9311773
It's Calculus. Real Analysis and Calculus are the same thing.

>>9311802
Stop withholding knowledge from me you elitist fuck.

>>9311819
https://en.wikipedia.org/wiki/Tensor

>>9310843
Are you referring to a collision between the objects?

If so, you can't determine the force, only the impulse (change in momentum = force*time product or, more accurately, integral of force wrt time). The actual force depends upon rigidity (collision between rigid objects results in a large force for a brief interval, more flexible objects will experience smaller forces for a longer interval).

To determine the impulse, you use conservation of momentum, either conservation of energy (elastic collision) or the coefficient of restitution (inelastic collision), and either the assumption that the forces are normal to the surface at the point of contact (frictionless surfaces) or the coefficient of friction.

>>9310696
The magnetic moment of a general charge distribution can be expanded into spherical harmonics, the first few orders are the monopole, dipole and quadrupole moments, etc. The monopole moment is the magnetic moment of the distribution if it were a single charge.

>>9311662
https://en.wikipedia.org/wiki/Motive_(algebraic_geometry)

>>9311711
pls answer

>>9311797
A tensor is a representation of a multilinear map in [math]\text{Hom}({\bf Vect},\otimes)[/math] on the category [math]{\bf Mat}[/math] of matrices. Let [math]F:({\bf Vect},\otimes) \rightarrow {\bf Mat}[/math] be a functor, then it is (or induces one, namely [math]F(f), f\in\text{Hom}({\bf Vect},\otimes)[/math]) a representation if it is covariant and right exact.

>>9307840
A computer network consists of six computers. Each computer is directly connected to at least one of the other computers. Show that there are at least two computers in the network that are directly connected to the same number of other computers.


Do i need a proof for this solution? Or can i just write an explanation?

this is my answer

There are six computers, each of which can be connected to between one and five other computers. If the first computer is connected to all five other computers, and each subsequent computer is connected to one less computer, that leaves the final computer without a unique number of connections.

In terms of the pigeonhole principle, the pigeons are the computers and the pigeonholes are the number of connections each computer has. In this case, we have 6 computers and only five unique connection numbers: {1 2 3 4 5} and thus one final computer is left out and must share a number of connections with another computer, or with more than one.

>>9311892
Fuck you.

>>9311806
>>9311778
>>9311776

What's the defining line, if any between topology and real analysis? The prof keeps namedropping topology "this is a concept/proof from topology". I understand math areas are all really closely tied together and it's hard to separate the two, but they seem almost like the same thing

>>9311950
Your explanation doesn't make sense to me.

Also, what do you think a proof is? "Show that" is the same thing as 'prove'.

>>9311984
"Topology is about counting holes."

>>9311986
the whole explanation doesnt make any sense at all?

>>9311984
the first real analysis class undergrads take is basically topology of metric spaces. in general real analysis and topology are very different fields though

>>9311992
Obligatory.

>>9312018
Ha!
And that pretty much exhausts my knowledge of topology.

Given some system of equations:
2x+3y=6
-3x = 12
14x+6y = 19

what would be the coefficient matrix and what would be the augmented matrix?
I don't know what they are when some equations have different numbers of unknowns.

>>9312047
https://en.wikipedia.org/wiki/Gaussian_elimination#Example_of_the_algorithm

>>9312047
Are you retarded? The coefficients are the numbers in front of the variables. The augmented matrix is the coefficient matrix + the column with the solutions. This is week 1 beginner LA stuff...

>>9312057
Perfect, thanks.

How is
3 − (2 + 2t) + 3(t) = 1 + t
when t's value is not known? How do you get 1+t from that?

>>9311992
"topology is useful in materials science, they use a lot of pliable materials"

this statement has been uttered in a top 30 US University

don't know shit about uni here
if i do genetics, do i need to get my masters before phd?
as far as i understand it the genetics path is bio bachelors > genetics masters > genetics phd
i liked the look of genetics because as i understand it's a stable well paying field, but i'm not looking forward to spending 8 years in uni, particularly considering im already 22

>>9312110
>How is
>3 − (2 + 2t) + 3(t) = 1 + t
>when t's value is not known?
3 − (2 + 2t) + 3(t) =
3 − 2 - 2t + 3t =
1 + t

>>9312110
You don't have to know [math]t [/math]. You can treat a variable just as a number using all the rules you know (because it is a number, just not one that you give a specific value to), so
[math]3 − (2 + 2t) + 3(t)=3-2-2t+3t=1+t [/math]

>>9312110
Are you joking or are you in elementary algebra 101?

>>9312131
why is it -2t and not +2t?

>>9312176
because distributive property
a(b+c) = ab + ac

>>9312185
Does that apply to if there's just a negative sign there as well then?
So -(a+b) = -a-b?

>>9312190
>Does that apply to if there's just a negative sign there as well then?
Yes since -(a+b) = -1(a+b)

>>9312190
Of course. Why wouldn't it?

-q = -1*q

is there a math symbol that means "all"?
not like sigma for sum, but something that means more like just "collection of all"

>>9312262
[math] \forall [/math]

>>9312018

>>9312267
I dont think that really fits
I just want to use something that means "this is the collection of all the things"

like "af" would maybe be "collection of all forces" and a would be the symbol. nothing's being done with the collection, I just wanted something to signify that the collection is all of the given thing.

and actually by collection I mean array. I just want short variable names and I want to use unicode stuff just to make it look cool, to be honest. I mean my problem is that I dont have a high resolution to work with so calling the array "forces" doesn't work because I have to write that a lot and it takes up a lot of screenspace. I want to call it af, but I don't know what symbol a should be, and I don't want it to just be a either, because that's not immediately obvious. the variable names should be immidiately obvious what they are.

how do you find the max of a function in a specific region?

for instance if i had f(x,y)=z and it's bounded by the functions y=g(x) and y=h(x), how would i determine the max of f(x,y) in that region?

>>9312376
>f(x,y)=z
?

>>9312380
z is a function of x and y

it's just one way to define a function

>>9312376
https://en.wikipedia.org/wiki/Lagrange_multiplier

>>9312447
wow i'm an idiot for not realizing i could use that for this
thanks

>>9312452
Did you mean restricted by the functions g and h?
In that case it's always Lagrange multiplyer (if the region is based on restrictions by other functions).

I want to prove that the cardinality of all analytic sets(in [math]\mathbb R[/math]) is equal to the cardinality of [math]\mathbb R[/math]. Is transfinite induction the way to go about this?

>>9312473
yeah i'm just not sure about how i'm supposed to handle this for the constraints with only one variable though, since we don't have z=g(x,y), we have y=g(x)

basically i'm talking about the "cylinder" that forms from g(x) and h(x)
g(x)=h(x) at two points, lets say x=a and x=b.
we're talking about the region f(x,y) from a<=x<=b and g(x)<=y<=h(x), so we're maximizing z (or f(x,y)) in this region.

so i'm not quite sure how to apply this lagrange multiplier here

Does i^(2/3) = -1?

>>9312542
No.

>>9312547
Why not?

>>9312553
>Why not?
Why would it?

>>9312542
i^(2/3)=(i^2)^(1/3)=(-1)^(1/3)

>>9312542
[math]i^{2/3}=e^{(2/3)ln(i)}[/math]
[math]ln(i)=i(\pi/2)(4n+1)[/math] where n is any integer.
we get [math]i^{2/3}=e^{i(\pi/3)(4n+1)}[/math]
we tend to take n=0 for the sake of simplicity (also called principal branch of the logarithm in case you care)

this just gets us [math]e^{i\pi/3}[/math] = cos(pi/3)+i*sin(pi/3)=1/2 + i*sqrt(3)/2

Here are two for limoncello recipes. Help me understand why the time increases.

1 soak peels of three lemons in 250ml alcohol for three days.

2 soak peels of 9 lemons in 750ml for 9 days.

Why should the time change. I feel it should not be change by the increase. The lemon/alcohol ratio does not change.

when measuring miles using a telescope, surveyors made an error of 6.5 feet per mile. if the total error was 55.25 feet, how many miles were measured?
a. 8.5
b. 48.75
c. 61.75
d. 359.25

>>9312702
A?

a salesperson works 3 days per week. she earns 1/3rd of her pay mon monday and 1/4th on tuesday. how much of her pay does she earn on wednesday?
a. 5/7
b 2/7
c 7/12
d 5/12

>>9312728
1-1/3-1/4?

>>9312728
What’s the point if these questions?

>>9312702
How old are you?

>>9312734
just pick the letter I'm math illiterate

>>9312735
it's a military test, there's like 3 more

>>9312737
18

>>9312728
How do you think this problem might be solved?

>>9312742
C

If you have an operator operating operationally on a separable function [math]\hat{\Omega}\Psi(x,y,z)[/math] such that [math]\Psi=f(x)g(y)h(z)[/math], does this mean that [math]\hat{\Omega}[/math] operates on all of the separable functions on just on one arbitrary function because of commutativity?

>>9312897
>or* just

>Be 25
>Spent my entire life bypassing math because I find it boring and it's not something I could just force memorize
>Never really managed to learn formulas or formal guidelines; I can usually just jury rig anything I need with basic logic.
>Fucked around with credits and classes and managed to avoid mathematics in college
>Graduate in business and computer science; no one has actually ever discovered or cared that I have literally at best a highschool freshman understanding of math
>I'm trying to apply to graduate school, and I'm worried they'll send me to calculus
>I don't want to live the rest of my life having no fucking clue how mathematics is done

Where do I start, /sci/? Brutally honest, I have no idea how to do long division; I simply break long division into sub equations. I have no idea how algebra is done, I just generally understand what outputs should equal what inputs and can work with it from there. I have no concept of the quadratic formula, or what a tangent is.

What is the best fundamental way to learn math from basic arithmetic to calculus? I'm looking to keep this an ongoing project over the next two years.

>>9312728
None. Wednesday is her day off.

>>9312482
My focus isn't DST but I think you might want to consider how many Borel sets are there and how many continuous functions are there?

>>9312920
You sound similar to a guy who can play music by ear but can't read music notation. You just have to hunker down and learn the common ways of writing and doing math, so you can understand the books and communicate with others about it. Learn standard math vocabulary and notation and methods, that's all.

>>9312920
Damn I thought I was fucked
Thanks anon

>>9312920
it's gonna be pretty fucking difficult since you won't have a teacher to guide you through this shit anymore, and since you've neglected it for so long you've likely lost whatever skills you learned in your most recent math class anyway

you're going to probably need to relearn algebra to some extent. i'd get the book Algebra by Gelfrand, then I'd get trigonometry also by Gelfrand (unless you end up not liking Gelfrands style, in that case there's many more trig/precalc books out there), then you'll need to learn calculus. if you're in comp sci and business you'll need some level of calculus, but it doesn't have to be 100% rigorous, as there's just no point for that. stewart's calculus 7th edition is pretty good and it's about as rigorous as you'll need. pretty sure this covers vector calculus as well, which is what you usually hear called multivariable calculus or calc III.
differential equations could be useful but it's unlikely.
if you plan on doing a lot more in compsci you'll want to learn linear algebra. almost any acclaimed book is fine (axlers linear algebra is what i learned from), but you should get a book on proofs (how to prove it by velleman is a good book on that) before doing linear algebra.

this isn't going to be something that you'll get done in just a few months, this might take you a full year or longer depending on how long you spend per day on it
that might sound intimidating but when you first crack open that book and work on the first few exercises and immediately blank, just know that's supposed to happen and that this won't be a chapter per day sort of thing. this will likely be a section per week and a half (on average) sort of thing, so don't freak out when you can't read it and immediately understand it

>>9312897
Well?

>>9313044
no one is going to reply because you need to reformulate that question, it's hard to understand what you're asking

>>9313068
If [math] \Psi = XY [/math] where [math]X[/math] and [math]Y[/math] are separable functions and [math] \hat{\Omega} [/math] is a linear operator, does [math] \hat{\Omega}\Psi = \hat{\Omega}X \hat{\Omega}Y[/math] or does [math] \hat{\Omega}\Psi = (\hat{\Omega}X)Y [/math]?

Is it possible to design a spacecraft that could land safely on the surface of different types of planets, or would you need to custom build one each time?

Wouldn't fitting in 4 AA batteries give you 12V?

>>9313106
4*1.5 is 6

>>9311754
When you get comfy with laws of physics.
Expessing something mathematicaly should be not be a problem.

>>9313072
it doesn't seem to hold.

for example if your operator is differentiation it might not work well.

>>9307840
is it possible to shock yourself with static electricity?

like not from touching metal but shocking yourself.

It happened to me a little while ago, I had my hands like a foot apart and it felt like I just got a static shock from one hand to the other.

>>9313072
No. Let the set of [math]\Psi:X \rightarrow \mathbb{C}[/math]'s form a Banach space [math]B(X)[/math] of functions on a compact set [math]X[/math], then the set of linear operators [math]\mathcal{B}(B(X)) = \operatorname{End}B(X)[/math] is an operator [math]\mathbb{C}[/math]-algebra which makes [math]B(X)[/math] into a left-[math]\mathbb{C}[/math] module. Given a tensor product structure on the Banach space [math]B(X)
= \mathcal{X}(X)\otimes \mathcal{Y}(X)[/math] the morphisms in [math]\operatorname{End}B(X) = \operatorname{Hom}(\mathcal{X}(X)\otimes \mathcal{Y}(X),B(X)) [/math] factors through this tensor product, meaning that the operator [math]\Omega \in \operatorname{End}B(X)[/math] factors into distinct operators [math]\Omega_{\mathcal{X}}\in \operatorname{Hom}(\mathcal{X}(X),B(X))[/math] and [math]\Omega_{\mathcal{Y}}\in \operatorname{Hom}(\mathcal{Y}(X),B(X))[/math] such that [math]\Omega = \Omega_{\mathcal{X}}\otimes\Omega_{\mathcal{Y}} [/math], but [math]\Omega_{\mathcal{X}}[/math] nor [math]\Omega_{\mathcal{Y}}[/math] will be equal to [math]\Omega[/math] unless [math]\Omega[/math] is the identity. In fact this can be proven from the universal property of tensor structures on monoidal categories.

[math]f:A\to \mathbb{R}[/math] is not uniformly continuous, then:

[eqn] \exists \hspace{0.1cm} \epsilon > 0 \hspace{0.1cm} \forall \hspace{0.1cm} \delta > 0 \hspace{0.1cm} \text{such that} \hspace{0.1cm} \forall \hspace{0.1cm} x,y \in A, |x-y|<\delta \implies |f(x)-f(y)| \geq \epsilon [/eqn]

Intuitively does this mean that when the distance between x and y is "small" the distance between f(x) and f(y) is "big"?

>>9313861
I don't think you negated that properly, see
https://math.stackexchange.com/a/205747/273960

>>9313861
https://en.wikipedia.org/wiki/Uniform_continuity#Visualization

>>9312951
Like that really is a bit of the dilemma. Should I bother learning how two digit multiplication is done even though I have perfectly good by passes for it and no one will ever care?
>>9312964
np
>>9312988
Thanks, I'll look into Algebra by Gelfrand.

>If you're in business you'll need calculus
Honestly, I have never once seen it employed and I work for a company that packages securities and manages investments. I sort of believe at this point that 90% of what people used to do has been offloaded to various programs we use.

>Compi Sci
Comp Sci definitely does require algebra, or at least abstract logical thinking, but I've found that if you can reasonably "toss around" the logic of a program you'll be fine.

>>9313920
Also, I found this guide, how shit is it?

>>9313927
>how shit is it?
Very, drop the memelist.

>>9313879
should be there exists x, y, yes?

>>9313932
>should be there exists x, y, yes?
yes

and so it doesn't mean that when the distance between x and y is "small" the distance between f(x) and f(y) is "big", but that *somewhere* where the distance between x and y is "small" the distance between f(x) and f(y) is "big"

Is it a common practice to use calculus or real analysis techniques on regression equations?

Like if you had a really strong regression with a low sum of squares, strong t-stat for all coefficients, etc., would it be acceptable to make inferences about the system that regression describes using more deterministic math? Is that something people do?

>>9313927
too much shit, most of the books are individually good tho

>>9313937
you fundamentally ignore that the methods you are using are also math. so yes, you can use math when you're doing math...

>>9313936
Ah, I see. Thanks.

>>9313931
>>9313938
Okay, so my plan at the moment is to read one foundational and one practical book at least.

So, I would read "LAWS OF TRUTH" or whatever, and Algebra by Gelfrand.

My goal is to get as many books in my reading simultaneously that don't depend on eachother or repeat eachother. Think 5 pages a day of 4 books.

>>9313970
4 books is too much. it's better to do 10 pages of 2 books.

I'd go with something like gelfand + one of the proof books. I don't know how useful a book on logic can be, but do try.

>>9313970
>>9313938
>>9313931
So, what is the best starting book for basic arithmetic or is that even necessary? Should I read "Basic Mathematics" by Lang?

>>9313977
>Should I read "Basic Mathematics" by Lang?
Lang is a meme

>>9313977
Algebra by Gelfand looks like a "basic math" book desu. it isn't necessary by any means, but it should be nice to go through it quikcly

>>9310146
Try "embeddable Markov Chains" .it uses matrix logarithms .

>>9313937
isn't that what we call finding a model?

>>9313976
>4 books is too much
I dunno, it's usually how I recommend reading things that might be extremely dry or requires lots of cross referencing. Seriously, it's much easier to convince yourself to read 5 pages of something you don't particularly care for than 10 pages.

Like right now I'm reading Starting Strength Meditations, Anna Karenina, and the Symposium. Pretty much doing 5 pages a day of various books will get you to read about 1-3 books a month.

>>9313979
Why tho

>>9314001
>Why tho
Read it and find out.

>>9313994
> I'm reading Starting Strength Meditations, Anna Karenina, and the Symposium
I'm obviously talking about real textbooks and not shit

>>9310813
Think about it conceptually. In order to reverse the process, it would require the amount of enthalpy transferred, plus some amount of extra enthalpy to achieve.

Example: I burn a piece of wood. It would require undoing every single H20 and C02 bond made from the reaction then using whatever process plants use to make woody polymers. That reversal is chemically hotter than burning the original piece of wood.

>>9314074
>>9310813
And by "It would require" I mean "the reveral would require"

>>9313920
let me rephrase that
if you're going into business calculus can be very useful at times. in comp sci calculus is way more useful, but only when you need it

also when i said linear algebra, realize that linear algebra isn't just your regular old algebra. you can't just "plug n chug" or "toss around the logic" for applications of spectral theorem, for instance.

>>9313927
meme tier shit made by contrarian undergrad math majors
you don't need to have this level of purity or rigor to do shit in business or comp sci

also shit like >>9313937 is an application of both calculus and linear algebra. worth noting that even if you know calculus and linear algebra you could be just like this guy and not know how to apply it. you learn how to apply this stuff after tons of experience, though (the ONLY other way would be courses designed to show applications)

>>9314048
>Not shit

No bully pls. Also, Starting Strength is actually super useful for doing vague physical work because it goes into mechanical depth for lifting things.

In statistics why is there a N-1 in the denominator of the sample variance as opposed to population variance which is only n?

>>9314215
It is so that the expected value of the Sample Variance (which is a random variable) is equal to the actual variance.
There's a deeper explanation about it involving "degrees of freedom". You can google it.

>>9307840
Trying to build a robot. What is a canned loop in wiring

>>9314215
Because it's an estimation, not the actual total population.

>>9314215
>>9314476
Oh wait I thought that by "population variance" you meant the variance of the distribution, my bad.
Anyway:
Let [math] X_i ; i=1,\ldots ,n [/math] be independent and identically distributed random variables.
[math] E(\sum\limits_{i=1}^{n}(X_i - \mu)^2) = n \sigma^2 [/math]
[math] E(\sum\limits_{i=1}^{n}(X_i - \bar{X})^2) = (n-1) \sigma^2 [/math]

See also this video:
https://www.youtube.com/watch?v=9Z72nf6N938

>>9312613
I would like an answer pls

>>9312613
Rule of three/Cross-multiplication.

>>9314572
If I’m cooking three times the pasta I don’t boil it three times as long

>Find a point D(x, y) such that the points A(−3, 1), B(4, 0), C(0, −3) and D are the corners
of a square. Justify your answer
I'm not sure how to solve this. The distance between A and C and C and B are 5, so point D will be 5 away from A and B, but how do I actually work out the x and y coordinates for point D?

>>9313861
Think of it this way: when a function is uniformly discontinuous on an interval, then in the [math]\epsilon[/math]-[math]\delta[/math] definition of continuity the [math]\epsilon[/math] does not depend on where you are in the interval, whereas just regular continuity allows this freedom.
For instance, the function [math]\frac{1}{x}[/math] is continuous but not uniformly continuous on [math](0,\infty)[/math] since the closer you get to [math]0[/math] the smaller you have to take your [math]\epsilon[/math].

>>9314215
An estimator [math] \hat{\theta} [/math] for a parameter [math] \theta [/math] is unbiased if and only if [math] E(\hat{\theta})=\theta [/math] . Or the expected value of the estimator is the parameter in question.

Say we mean to find the unbiased estimator for the variance of [math] X [/math] from a sample [math] X_1, X_2,...,X_n, [/math] iid. Then we'll use sum [math] \sum_{i=1}^{n} \frac{(X_i-\bar{X})^2}{n} [/math]

[math] E(\sum_{i=1}^{n} \frac{(X_i-\bar{X})^2}{n})=E(\sum_{i=1}^{n} \frac{X_i^2}{n}-\bar{X}^2)=E(\sum_{i=1}^{n} \frac{X_i^2}{n})-E(\bar{X}^2)=E(X^2)-(V(\bar{X})+E(\bar{X})^2)=E(X^2)-(\frac{V(X)}{n}+E(X)^2)=E(X^2)-E(X)^2-\frac{V(X)}{n}=V(X)-\frac{V(X)}{n}=\frac{n-1}{n}V(X) [/math]

So multiply by n/(n-1) to remove the bias.

>>9314828
the fact that it's a square gives you more information than only the distances. You have to use information about angles for example.

You can obtain a second equation by using perpendicularity between AD and BD for instance.

>>9312613
>>9314607
Pls Respond

>>9314910
I don't know the answer to your question. Have a (You), just so you know at least someone did

Anyone here familiar with computer architecture? I have a question and I'm not exactly sure how to go about solving it.

" Consider a hypothetical machine with a byte-addressable main memory of 2 Mbyte
and a block size of 32 bytes. Assume that a direct mapped cache consisting of 32
lines is used with this machine."

How many Bytes in total can be stored in the cache? What's the process involved in answering this?

Where can I find Boeing's major production facilities?

Someone can write this with the pretty math format /sci/ uses?
7.106 * 10^20 m^3
For those wondering, it's the volume of the Inner Van Aller Belt. I won't lie, I want it for a presentation and I'd do the formatting myself but I'm pretty stupid

>>9315443
https://www.codecogs.com/latex/eqneditor.php

>>9315447
Thanks mate.
Take some quality ratios for radiation in biological beings

>>9315447
Don't forget pic related.
Also there's a TeX preview option for replies on /sci/ next to the name and email field which I think a lot of people aren't aware of

>>9315455
ugh

Stuck with a detail of the proof of [math]f:\mathbb{R} \to \mathbb{R} [/math] by [math]f(x)=x^{2}[/math] not being uniform continuous. Starting out with the definition:

[eqn]\exists \hspace{0.1cm} \epsilon > 0 \hspace{0.1cm} \text{such that} \hspace{0.1cm} \hspace{0.1cm} \forall \hspace{0.1cm} \delta > 0 \hspace{0.1cm} \exists \hspace{0.1cm} x,y \in \mathbb{R}, |x-y|<\delta \implies |f(x)-f(y)| \geq \epsilon [/eqn]

the proof starts with: let [math]\epsilon = 1[/math] and write [math]x = y + \frac{\delta}{2}[/math]. Why do we know that such a substitution will make this work and what is the process for coming up with such a number? Surely it's not glorified guess work.

>>9315651
|x-y| < delta implies this substitution x=y+delta/2 in a way.
The 1/2 is chosen to fit the proof so it works for epsilon = 1 and it's something you choose after figuring out what |f(x) - f(x+a*delta)| is.

y = 2+2t
x+2y+3t=3
=
x+2y = 3-3t
=
x = 3-2y-3t
=
x = 3-2(2+2t)-3t
=
x = 3-4-4t-3t
=
x = -1-7t

Is that right?

>>9315657
>and it's something you choose after figuring out what |f(x) - f(x+a*delta)|
could you elaborate on this? what is 'a'?

>>9315666
a parameter between -1 and 1, because for |x-y| to be smaller than delta, y has to be in the open interval (x-delta,x+delta)

>>9315667
I understand that but then how does |f(x) - f(x+a*delta)| imply lead us to make the appropriate substitution?

>>9315674
the point was that there is not only one appropriate substitution.
The proof would probably work with delta/3 in the same way it works with delta/2. The only thing thats's important is that |x-y| < delta.
choosing y = x+delta/2 just leads to a particularly nice looking |f(x) - f(y)|

>>9315695
I see. I know that we are supposed to choose x and y, but I just don't follow how we chose 'x'. It does work, and as you said it works nicely, but I just don't know how you'd cook it up from scratch. To me it just looks like a good guess.

>>9315702
There is just no other way to choose y, other than in the open interval (x-delta,x+delta) without violating |x-y|<delta
Later on you choose x dependent on delta, so that the inequality holds (small delta -> large x)

>>9314910
for all we know it's bullshit.

take 3 jars of 250mL and get it over with in 3 days.

>>9309813
Let's call x the velocity of my car at a given time and y the number of girls you've had sex with at the same time. I'm writing on my computer so my car is at rest and you're a virgin, so both x and y equal zero.

What does a Green's function of the operator [math]\frac{d}{dx} +1[/math] look like, and how does one construct it?

>>9315791
Oops, [math]\frac{d^2}{dx^2} +1[/math]

>>9315651
>|x−y|<δ⟹|f(x)−f(y)|≥ϵ
That's just wrong.
[math] p \implies q \equiv \neg (p \land \neg q) \text{ ,therefore } \neg (p \implies q) \equiv p \land \neg q [/math]
this is not the same as what you wrote which is [math] \neg (p \land q) \equiv \neg p \lor \neg q [/math] .

For a reaction at 310 K, a catalyst lowers the activation energy by 30 kJ mol-1. By what factor is the reaction rate increased?

I have no idea how to even approach this question, I know nothing about the reaction or the activation energy, only have these 2 pieces of information

>>9315651
>Why do we know that such a substitution will make this work
You obviously have that x and y are less than δ apart (they are δ/2 apart)
And you also have
[math] | f(x) - f(y) | = | (y+\frac{\delta}{2})^2 - y^2| = | y^2 + 2 \frac{\delta}{2} y + \frac{\delta^2}{4} - y^2 | = | \delta y + \frac{\delta^2}{4} | = \delta |y+\frac{\delta}{4}| \stackrel{\text{when } y>0}{\geq} \delta y \stackrel{\text{when } y\geq \frac{1}{\delta}}{\geq} 1 [/math]

>and what is the process for coming up with such a number? Surely it's not glorified guess work.
It really is. And it is not the only way to do it.
The guy probably said let's have the distance be δ/2, cause why the fuck not.
After doing some simple algebra and imposing stuff on what y can be, he ended up with having [math] | f(x) - f(y) | \geq 1 [/math] whenever y is greater than 1/δ, and then he picked ε=1.

How do this? [math]\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}{\frac{x}{tan(x)}dx}[/math]
I can only get it into unintegratable functions but the solution has a closed form...

>>9315821
The answer is π log(2).
Are you allowed to use complex numbers?

>>9315829
Its not part of the course so I doubt the answer would use them, but i'll give it a go.

>>9315821
do

P A R A M E T E R

D I F F E R E N T I A T I O N

gg ez

>>9315833
Ok then.
First of all notice that the function is symmetric about the origin so you just have to compute the integral from 0 to π/2 and then double it.
How to compute the integral? Google is your friend. Type 'integral x \cot(x)' and you'll find it.
https://math.stackexchange.com/questions/698528/how-can-i-find-int-0-pi-2x-cot-x-dx

(always type it in latex and always use retarded american notation so that you will find the answers in math.stackexchange.com)

>>9315804
if I were to give an informed opinion, I would say it involves Boltzmann's constant.

[math]e^{\frac{- E}{k_B T}}[/math]

Does this ring a bell

>>9315791
>>9315792
Nvm, I got it!

Is there a name for when you are periodically extremely agressive (verbally) towards as many people as you can get to? It's bothering me and it's probably affecting me negatively.

Maybe once a day there will be a few hours where I'm in that state.

How's the research on artificial human tissues?

>>9315968
>Is there a name for when you are periodically extremely agressive (verbally) towards as many people as you can get to?
https://en.wikipedia.org/wiki/Menstrual_cycle

>>9307840
How do I cite a figure that I've edited for presentability with the Harvard referencing style?

>>9315816
Could you help me then with [math]f:(0,1]\to \mathbb{R}[/math] by [math]f(x) = \frac{1}{x^{2}}[/math]

We can let [math]\epsilon = 1[/math]

[math]|f(x)-f(y)|[/math] becomes [math]|\frac{y^{2}-x^{2}}{x^{2}y^{2}}|[/math]. [math]x = y + \frac{\delta}{2}[/math] is just as valid here to choose, yes?

We get We get [eqn]\frac{x\delta + \frac{\delta^{2}}{4}}{x^{2}(x+\frac{\delta}{2})^{2}}[/eqn]

which x could I use here?

>>9316107
should be [math]y = x + \frac{\delta}{2}[/math]. Of course [math]\frac{x\delta + \frac{\delta^{2}}{4}}{x^{2}(x+\frac{\delta}{2})^{2}} \geq 1 [/math]

>>9316107
For any delta, you can just let x go sufficiently close towards 0 to blow that expression up.
Try out x = delta^n for delta <1 and x = 1/delta^n for delta > 1

>>9316124
>should be y=x+δ/2
it doesn't matter

>>9316107
https://math.stackexchange.com/questions/1788104/prove-that-fx-frac1x-is-not-uniformly-continuous-on-0-1

>>9316130
thanks, I'll look at this
>>9316134
>Continuous Extension Theorem
>Cauchy continuity
gee, these would have been useful to know. we didn't cover those in class.

>>9316173
nu

one for the bump limit