/sci/ - Science & Math

~UNANSWERED~

Physics and Astronomy
>>11417272
>>11421369 (totally undefined)

Math
>>11414969
>>11415110
>>11417328
>>11418041 (subtle HW post)
>>11418107 (sounds like a regular cube)
>>11419218
>>11416947
>>11420292 (truncated sector?)

Biology and le epic virus
>>11420374
>>11420884
>>11418294 (never)

Chemistry
>>11423304 (heat transfer into something that is changing shape and chemically reacting is pretty complicated. I can't help you with the kinetics part)

Engineering
>>11416936
>>11419116 (mechatronics)
>>11423303 (industrial engineering is definitely not math heavy. barely even engineering, desu)

/g/
>>11421824

Stupid
>>11416906
>>11417604
>>11417648
>>11421665
>>11421936
>>11422276 (I'm here if you want to talk)
>>11423046 (grats~)

so, from what I can understand having only taken up to (and finished half of ) Ordinary Differential Equations so far...
It feels like the Calculus of Variations/Variational Calculus is a bit of a mathematical curiosity at best, among differential equations, which in the grand scheme of mathematics are already just a mathematical triviality.

I really, really, really, really like the concepts (from what I can understand) of variational calculus and what it offers for optimization. It blows my tits clean off. Are there any applications of it at all to electrical engineering given how niche it seems to be?

>>11423617
Variational calculus is how mathematicians actually solve optimization problems. You probably have seen that certain possibly non-linear PDEs can be expressed as the (strong) Euler-Lagrange (sEL) equations [math]L(\{J^k u\}_{0\leq k \leq m}) = 0[/math] for a functional [math]S[/math], as a point-wise version of the zero variation [math]\delta S = 0[/math] condition. Here [math]J^ku[/math] denotes the [math]k[/math]-jets of [math]u[/math], so [math]L[/math] requires [math]m[/math]-differentiability of [math]u[/math] to be a well-defined map.
However, functions [math]u[/math] for which [math]S[u][/math] is well-defined in general has much less regularity conditions on it than the strong EL. For instance, we only require [math]u\in H^1[/math] for [math]S = -\int dx |\nabla u|^2 < \infty[/math] while we need [math]u \in C^2[/math] for [math]\nabla^2 u[/math] to make sense, and [math]H^1[/math] is much [math]much[/math] larger than [math]C^2[/math]. This means that for generic [math]S[/math], optimization [math]\delta S=0[/math] may be achieved by functions for which you cannot even write down a strong-EL for. You cannot use techniques in PDEs, let along those you learn in an undergrad class, to solve these optimization problems. This is the basis and motivation for the theory of distributions.

>>11423631
I truly, finally feel like my engineering-oriented math classes are beginning to hinder me in my mathematical development and mathematical maturity. That which I feel truly motivated to learn as always feels forever just out of reach

>>11423508
Is the Wolfram a genetic hybrid of a wolf and a ram?

>>11423646
It is not just a mathematical curiosity. Plenty of physical systems are described by non-linear PDEs, such as KdV and the coupled oscillator. They also exhibit behaviours, such as shocks and caustics, that [math]cannot[/math] be described by their linearizations. Knowing how to solve them is what sets apart a plumber and an aerospace engineer.

I missed it in the tally. Here's a problem for anyone who knows about audio electronics.
>>11419722

Is there a fast way to find the third and fourth lowest bits of a binary number? E.g. for 54 = 0b110110 it would be 01.

Lowest two bits is easy, it's just the number modulo 4, but I'm having issues with the 3rd and 4th. Just taking it modulo 16 doesn't work.

Does anyone know the differences between being a research scientist at some federally funded lab like Lawrence Livermore or MIT Lincoln Labs, and being one in industry at a company like apple, microsoft, etc? i would assume the ones at a company make more $, but are the benefits worse or the jobs less stable?

Why does the lab part of all chemistry classes suck?

I took one chemistry class in high school. I completed 2 college level chemistry classes, and I'm currently in Chemistry 112. All four were with different teachers, and the lab portion of all of them was a bad experience. Yeah I occasionally observe some less-than-moderately-to-moderately interesting things happen, but most the time I just want to drink their shitty ethanol in their brown glass bottle (thereby getting drunk) and never have to do any more labs ever again. I swear, that shit is like my personal hell sometimes, it makes me or other people want to off themselves.

pic is capillary action of some gay ass chemicals in liquid form

>>11423930
Are you allowed to use bitshifts? If not, I guess you could subtract mod 4 and divide by 4.
B110110 mod 4 = B10
B110110 - B10 = B110100
B110100 / 4 = B1101
B1101 mod 4 = B01

>>11423508
Can anyone point me to a source for the formula given for this sequence?
https://oeis.org/A060461

I would be very grateful.

>>11424623
>Numbers k such that 6*k-1 and 6*k+1 are twin composites

>>11423930
For a given number n, take floor(mod16(n)/4). The floored division gets rid of the lowest two bits.

>>11424627
Yes? But I don't understand how the formula given follows from that.
a(n) = n + 6n/log n - O(n/log^2 n)

Where does that formula come from?

>>11423930
Try [math][(a ~ mod ~ 2^{n+1})-(a ~ mod ~ 2^n)]/2^n[/math]
Monkey-tier solution tho, bitshift is best.
>>11424631
You probably take a bunch of theorems like https://en.wikipedia.org/wiki/Prime_number_theorem and stack them on top of each other until the result comes out.

can someone explain what is happening in this substitution

how do I solve this for t < 0 ?
I am getting solutions y = tcos(2ln(t)) and tsin(2ln(t)) but the ln(t) shouldnt work out since t is less than zero

>>11424866
Just literally plug in x = u - 4 and distribute

>>11424868
Define [math]log(x)=log(-x)[/math] and check if it works.
>why should it
Muh branches and stuff.

>>11424891
>muh branches
Nevermind, I have a better argument.
[math]2 log (t) = log(t^2)[/math]

>>11424906
oh shit I didnt even notice thank you so much lol

tell me if I have this right:
when an object moves closer to the speed of light, it has more energy which is equivalent to having more mass, and more mass means more warping of space by the object due to gravity, so this is what causes length contraction

>>11424965
>when an object moves closer to the speed of light, it has more energy
Yes
>which is equivalent to having more mass
No
>more mass means more warping of space by the object due to gravity
Roughly yes
>so this is what causes length contraction
Not at all

Let me know if you want elaborations on any of that

>>11424982
I don't really understand what is causing the length contraction then
I understand the time dilation, because the overall speed of an object is always the speed of light, and as it moves through space faster, it moves through time slower. how this translates into changes in length I dunno.

>>11424701
Certainly that seems right, the connection to n/log(n) seems suggestive. But I can't figure out how exactly to go about it, and haven't been able to find any papers that do it either.

>>11425013
The fast-moving object's time is only slowed relative to an outside perspective. From the moving object's own perspective, its clocks are running at one second per second (reduntantly). So without length contraction, light in one frame would move faster (same distance in less time) than in the other frame.
Really, length contraction and time dilation are two sides of the same coin, due to the interrelation of time and space. Perceiving one or the other is just a matter of perspective, and depends on what you're trying to measure.

>>11425460
>without length contraction, light in one frame would move faster (same distance in less time) than in the other frame.
so the length that contracts isn't just the car on the road, but the road too

>>11425560
For someone on the road, the car contracts. For someone in the car, the road contracts.

>>11425565
yeah, so this is the reason for my confusion.
I thought it was just the car that contracted, because most of the descriptions I read say that an objects length contracts and don't mention the path too

>>11425575
It's all about which objects are at rest relative to a particular frame, and which are moving in that frame.
For the car frame, the car is stationary and the road is moving. For the road frame, the road is stationary and the car is moving.

mp3 files are discrete values and audio players on computers are able to play each bit, right?
so how does flac work and how is it processed/played? if they're considered lossless, i'm assuming it's one continuous wave instead of discrete values.

how do i convert garageband to mp?

How do i raise my iq? can i add white matter to my neck or chest or ass and let it innvervate?

can we use emotions to numerically solve differential equations thru meditation?

how do i cure raynauds disease?

how do i get 100 or 200 dollars really quick?

>>11425565
what about for the carr itself? or the air bumped by the car? or the phonon of air thats partially bumped and partially not?

>>11426028
>can we use emotions to numerically solve differential equations thru meditation?
I bet we could using electroencephalogram sensors

>After 1 week, the substrates were removed from the PMMA solution, and the freshly deposited wet polymer film was heated under vacuum at 130 ×bcC for 1 week to remove the residual solvent and ensure the equilibrium adsorption of PMMA onto the Cr surfaces via this annealing process
>heated under vacuum at 130 ×bcC for 1 week
>130 ×bcC
I have never encountered this before, can anyone shed some light on this?

Paper: https://pubs.acs.org/doi/abs/10.1021/la0157317

>>11426032
wait just realized the car is fast so its same as people

>>11426035
ooh. but meditation is coolar and tou dont have to carry aroud a thing.actally you could innervate your math brain with units of emotion. and you could visualize higher dimensions with emotion vectors, or color, or anything

Does [math]sin(\theta)[/math] really equal [math]cos(\theta+\frac{\pi}{2})[/math]?
I know they're equivalent in magnitude; but do they REALLLY equal each other? like can I substitute one for the other in literally any equation?

>11426070
I meant [math]cos(\theta-\frac{\pi}{2})[/math], my bad

>>11426070
>>11426072
yes. theyre the same function shifted in phase. so when u unshift the phase relative to parameter theta.. its the same;

they have the same value at every theta

>>11426070
also on the nature of equal. equal means equal. sin theta is just a series of numbers, one number for each theta. when a number equals another number it just does

and when a function equals another, it means, for each input N, each outN is the same

equal signs are the wholly holy unity, mathematically. artistically theyre not equal for different symbols are drawn (same w logical equicalence and varying statements). but perturbations in the system field are the same within any stable frame (stable is mostly just extant axioms and reflexive holding, the basis of logic afaik)

Show that if G is a finite group and a, x [math]\in[/math] G, then the order of [math]axa^{-1}] [/math] is equal to
the order of x.
This was a practice question for a midterm. I know what happens but I'm not really sure how I should be explaining it.

>>11426146
because the operators commute, your end result is x*identity. and the order of x is the order of x

>>11426146
x^n = e; x has order n.
(axä)^n = x^n
axäaxäaxä... = x^n
a(x^n)ä = x^n
a(e)ä = e
e = e

>>11426158
Why can we assume the operators commute?

>>11426166
thats for you to prove

So when there's a radical x (some variable) subtracted by something like e^x, we're supposed to multiply it by its conjugate to simplify it/get a cleaner equation right?
My issue is that I NEVER know when to multiple something by its conjugate, I then heard that you do it when there's a radical involved and I'm not sure if that's true or not so I'm just confirming it here.

>>11426146
Conjugation is an automorphism, and thus it preserves orders.
Specifically, if [math]f[/math] is an automorphism, we have [math]f(x^n) = f(x)^n[/math], and because it's bijective the right side is the identity if and only if the left is.

Is my information wrong, or is the greatest cost of using MRIs just having them in the "ready" state? As in, actually doing a scan doesn't take that much more power/cause that much more wearing on the machine.

>>11426214
>left side and right side
[math]f(x)^n[/math] is the identity if and only if [math]x^n[/math] is.

>>11426211
(y-sqrtx)(y+sqrtx)
y^2+x

if u dont want radical make it bye bye like easy

>>11426216
it is the jews

>>11426234
thanks love

>>11424021
bump

Do birds know that we cannot fly. I like to observe birds in my yard but they take off way before I get even a little close.

>>11426354
they probably know, i have talked to birds

>>11426354
They do, that's why they're alright coming so close. Birds know if someone gets too close to them, we can just fly away to safety.

>>11424965
sounds like you're learning Special Relativity at this point, so effects of mass on the geometry of spacetime never come in to play. in SR spacetime is always flat. Remember to keep track of your reference frames, and keep that spacetime interval invariant.

Can someone explain this to me? I genuinely don't understand it through the text, the topic is infinite sequences.

>>11426507
You have a sequence. A sequence can be thought of as a function f that assigns a number f(n)=a_n for any given natural number n. Now for the definition of convergence: Sequences converge to a value a' if and only if for any arbitrarily small number ε, you can find some corresponding number (usually quite large) N with the property that if you pick any n' greater than N, then the difference between f(n') and a' is less than the small number ε. Basically, the sequence gets bounded by ε past N. I've just restated the definition in slightly different language, but hopefully it is more clear. If you still don't understand, then just stare at your book's or my definition for a long time till it clicks.

Why can we not deduce physical constants of nature from physical theories? Why can we only measure them through experiments? Isn't that kinda weird?

>>11426507
Given a value for epsilon (eps), imagine the open interval (L - eps, L + eps). Now imagine that the sequence {a_n} has some "point of no return" beyond which every element of the sequence is contained in the interval. Call this point of no return N, so that all elements of the sequence beyond a_N are contained in this epsilon interval.
{a_n} is said to converge to L if, no matter how small you squeeze the interval around L, there is a point of no return N beyond which the sequence is confined to the interval around L. The particular value of N will depend on how small the interval is, but for any interval size, there is guaranteed to be a finite N if the sequence converges.

>>11426564
Not really. The scientific method requires that you do some experiments.

>>11426564
We can't deduce the constants because the constants depend on what arbitrary units we use.

>>11426577
... so why can't we derive them in natural units either?

>>11426747
Because it is impossible to learn about physical reality without doing experiments.

>>11426564
>Why can we not deduce physical constants of nature from physical theories? Why can we only measure them through experiments?
You do realize that physical theories are developed from experiment, right? Your question makes no sense.

>>11426800
>You do realize that physical theories are developed from experiment, right?
I hate to break it to you anon, but special relativity was founded on postulates and then verified experimentally.

>>11426822
...and those postulates were motivated by experiment. Maxwell's equations have so much experimentation behind them.

>>11426214
Conjugation is an inner automorphism. Specifically you need to prove that [math]f:G\rightarrow\mathbb{C}[/math] mapping [math]g \mapsto |g|[/math] is a class function, which doesn't follow as trivially as your post suggests.
>>11426564
Sure we can. QED proved that the fine-structure constant [math]\alpha = \frac{1}{137}[/math].

Don't call me stupid, I know.

Let p be a prime congruent to 7 mod 9. If a is a cube modulo p, show that a^((p+2)/9) is a cube root of a.

>>11426747
Natural units are based on the constants, your reasoning seems to be circular

>>11426822
Like the other anon said, SR was completely inspired by Maxwell's equations, which were built by compiling heaps of experimental results

What again is the name for the theorem which states that something about parallel intersections? Iirc it was about the ratio staying equal
>>11423532
>>>11420292(You)(Cross-thread) (truncated sector?)
I see, thanks. So I guess there is no "proper" name for it?

>>11427012
If [math]EB[/math] and [math]BC[/math] are parallel, there's:
[math]AB[/math] is to [math]AE[/math] as [math]AC[/math] is to [math]AD[/math]
[math]AB[/math] is to [math]AE[/math] as [math]BC[/math] is to [math]ED[/math]
[math]AB[/math] is to [math]EB[/math] as [math]AC[/math] is to [math]DC[/math]

>>11427518
>[math]EB[/math] and [math]BC[/math]
[math]EB[/math] and [math]CD[/math]
The rest should be correct.

If f'(a)<0<f'(b) a<b and f is differentiable, prove that there's a c between a and b such that f'(c)=0

>>11423508
Isn't the additive identity linear map bijective? And therefore doesn't belong to either of these subsets of L(V,W)? What am I missing here

PS: L(V,W) is the set of linear maps from V to W.

>>11427012
>parallel intersections
Non-Euclidean geometry?
If it's pic you're referring to, probably similar triangles

>>11427012
Thales.
>>11427564
[math]f[/math] is differentiable and thus continuous. Consequently, by Weierstrass, [math]f[/math] attains a minima. The minima can't be [math]a[/math], because [math]f'(a)><0[/math], and it can't be [math]b[/math], because [math]f'(b)>0[/math], and thus it's in [math](a, b)[/math] and is necessarily a critical point.
>>11427572
>additive identity
What do you mean additive identity linear map?

>>11427693
>What do you mean additive identity linear map?
Thanks. That was enough to see where I was wrong. I was confusing the multiplicative identity with the additive identity, the latter is the zero map, which maps any vector in V to the zero vector.

>question
If Mary is 16 years old, which is 4 times as old as her brother, how old is Mary?
>answer
16 / 4 = 4 so Mary is 16; her brother is 4.
Mary will be twice as old as her brother when the age of her brother is equal to the number of years between their ages.
16 – 4 = 12 so Mary will be twice as old as her brother when her brother is 12.
12 + 12 = 24 so Mary will be 24.


can someone explain to me why "Mary will be twice as old as her brother when the age of her brother is equal to the number of years between their ages." is true? i see that it works out but how did he come up with that rule?

>>11427774
M is Mary's age, B is the brother's age.
M = B + (M-B). Mary's age is the brother's age plus the difference in their ages.
If the brother's age equals their difference in age, then B = (M-B). Substituting, we find M = B + B = 2B.

>>11426070
If you want to know why, think of the unit circle definition for sine and cosine. Sine is normally the vertical coordinate along the unit circle, but if you rotate the circle by pi/2, a quarter turn, you're now measuring the horizontal coordinate which was cosine. The only issue that comes up is that the signs might be off (if you rotate one way it's equal, if you rotate the other the sign is flipped and you get -cos(x - pi/2) ).

>>11427774
>if Mary is 16 years old
>how old is Mary
16 years old.

>>11427810
i still don't get why it works..
>>11427841
lmao i meant
"Mary is 16 years old. She is 4 times as old as her brother. How old will Mary be when she is twice as old as her brother?"

Hey /sqt/, why isn't the moon pulled closer to the earth despite there being a gravitational force?

>>11427693
That's it, thank you very much!
>>11427518
>>11427578
Thank you very much for your help too!

>>11427879
>i still don't get why it works..
The age gap between Mary and her brother never changes (it's always 12 years).
So what you have to figure out is when
Brother age * 2 = Mary's age
Since we know the difference is constant we can just rewrite Mary's age in her Brothers age
Brothers age * 2 = Brothers age + 12
Now subtract Brothers age from both sides and you will find out that he has to be 12.
(In other words if the 12 year gap has to be his age, in order for Mary to be twice his age, since Mary = Brother's age +12 = 12 + 12)


>I suck at explaining, I hope it's still understandable

>>11427925
>In other words the 12 year gap has

>>11427896
Unless I am mistaken, it's the same principle, which you use with satellites

>>11427925
oh i get it now, since the difference never changes the brothers age most be the same as the difference
thanks<3

>>11427956
You're welcome! :)

In my textbook, in the proof of the second derivative test for R^n functions it says that the function must be C^3, why C^2 isn't enough?

>>11423617
Maybe something like numerical analysis of PDEs

>>11427693
But Weierstrass ensures me that f will have it's maximum and minima in a compact. If a choose [a,b] as the compact it doesn't ensures me that it will have necessarily a minima in (a,b), It just tells me that it will reach both it's maxima AND minima in [a,b], right? So those maximum and minima could be in a and b (I know it will reach a local minima in c but I'm just too retard to prove it).

>>11428223
>So those maximum and minima could be in a and b
they couldn't

>>11428274
Why? That's the thing. Also it won't have it minima in a nor c, but it can have its maximum in a or b.

>>11428284
If the minima were in a or b, the definition of the derivative would give you that f'(a) >= 0 or f'(b)<=0, contrary to the assumption.

>>11428223
>maxima this maxima that
No one gives a shit about maxima. The proof solely uses minima, and it only works because we ask for a minima. You'd need both of those inequalities backwards for a maxima.
It can't have a minima in [math]a[/math] because there is some [math]\epsilon > 0[/math] such that [math]x \in (a, a+ \epsilon )[/math] implies that [math]\frac{f(x) - f(a)}{x-a} < 0[/math], and then [math]f(x)<f(a)[/math].

>>11428307
Thanks bro

I don't feel right not doing math even though I have free time, is there something wrong with me? I'm not trying to subtly flex or anything, but because of an exam (a week ago) that had me hyper stressed so I studied nonstop for a week and now that it's over, it just feels fucking weird. I don't know how to describe it, it's empty. A part of me just wants to do nothing but then I subtly feel the pressure of the next exam 5 weeks later even though we haven't even talked about the topic yet. So like, my question is, is this normal? I know this sounds really stupid...

>>11426036
Anyone?

Should I travel to the UK for a university interview if the university refuses to conduct the interview via skype? or is the air fare not worth it considering there's no guarantee you'll get in even if you do a good interview since the uni is very competitive. I'm deciding whether to turn down an offer or buy the plane tickets.

>>11428698
Another question, maybe somebody knwos: how likely is it to get an engineering job in Europe with a South American degree (provided I'm an Italian citizen) vs getting a job with an European degree (or the same but with England instead of Europe). I want to leave my shit third world country when I graduate. Is the extra cost of an international fee worth it if my main prority is landing a job in a civilized country?

Could you guys give me your subjective rating of the difficulty of this problem?
I don't need a solution, I'd just like you to tell me how difficult this problem seems to you and maybe at what level of education one should be to solve this problem
The problem follows as such:

In the triangle ABC, angle BAC is two times bigger than angle ABC. Show that the following equation is true:
BC^2 - AC^2 = AB * AC

>>11428754
not difficult at all. high school geometry.

>>11428808
are all the steps to solving it immediately obvious to you?
if not, how would you attempt to solve it?

>>11428754
I haven't actually solved it, but it's just cosine law and algebra, isn't it?
I'd classify it as hard because AB*AC is shit to work with geometrically, and you basically need to pull the proof out of a tophat.
The level of education is just high school.

>>11428840
well, there are a few ways to solve it but I don't think you can actually solve it using only cosine law and algebra, although one solution does include cosine law
you should try solving it!

>>11428072
someone?

>>11428847
>can't solve it with just cosine law and algebra
If you want me to be specific, cosine law, algebra and the formula for cos(2x).
You have BC^2 = something, AC^2=something, and then you take the difference.

>>11428910
I still don't think it's possible using just that

Is it /sci/ enough to ask why my brain doesn't work?

>>11423508
Question about power system fault analysis.

Were doing fault analysis and there's something that doesn't add up.

As I've know it until now, if you compute the admitance matrix of a system ([math]Y_{bus}[/math]) and the invert it, you get the impedance matrix ([math]Z_{bus} = Y_{bus}^{-1}[/math])

For this reason, each time I've had to find [math]Z_{bus}[/math] I simply constructed [math]Y_{bus}[/math] frok inspection of the network diagram and then inverted it and havent had any problems.

But now that we're doing asymmetric fault analysis you have to find [math]Z_{bus}[/math] for each sequence network, namely:
[eqn]Z_{bus}^{(0)} \\
Z_{bus}^{(1)} \\
Z_{bus}^{(2)}[/eqn]
This is because for example [math]Z_{kk}^{(0)}[/math] would give you the zero sequence thevenin impedance the bar [math]k[/math] "sees".
Now, if I take the sequence network for any of the sequences of a given network, build its [math]Y_{bus}[/math] by inspection and then invert it I get a matrix [math] completely [/math] different from what [math]Z_{bus}[/math] actually is, why is this the case?

ignore this, tex for another board
[eqn]\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...=\frac{\pi^2}{6}[/eqn]

Been posting symptoms so far, worried about coronavirus infection but now, my eyes burn up randomly and I have pain near the ear, behind too, neuralgia they called it, unsure.
Do I have it? what should i look out for about this disease?

>>11429376
Less than a fraction of a fraction of a percent of the population has coronavirus right now. If you really are worried, watch your temperature and blood oxygen levels (you can measure that with many smartphones.)

>>11429395
I'm looking for that, if I get a fever I'll call the special number for quarantine.
But then, what could it be?

>>11428754
the difference of squares equals a parallelogram... anyway, medium-hard and HS

>>11429265
Anyone pls? Im sure EEs post here

>>11429453
Patience, anon

Any working Electrical Engineer have time to answer a few basic questions about work environment etc? Like a mini-interview to see if I should join the major

>>11429554
[eqn]:([/eqn]

>>11429684
Im working part time as an automation/IoT engineer on a startup, mostly for curriculum purposes. Ask up anyway.

Can someone please help with this question, I know that my selection of (D) and that its greatest lower bound is 0, but I have no idea how to calculate the least upper bound so that I'd be able to input it in...

Can someone please help with this Sequence question. I know that my selection of (D) and it's greatest lower bound of (0) is correct, but how do I calculate it's greatest upper bound? Is there a formula? Can someone please show me, I've been stuck at this for an hour and it's messing me up so bad as even the online textbook questions didn't even go over it.

>>11429688
Just the basic questions:
1) What do you think takes to succeed in this field
2) What type of people you think would enjoy this type of job/field
3) What separates a bad EE from a good EE student
4) Skills that ought to be learned but is glossed over/not taught at all in classes

Can someone please help with this Sequence question. I know that my selection of (D) and it's greatest lower bound of (0) is correct, but how do I calculate it's least upper bound? Is there a formula? Can someone please show me, I've been stuck at this for an hour and it's messing me up so bad as even the online textbook questions didn't even go over it.
(Had to delete twice because of the wrong terminology, sorry).

>>11427012
Anharmonic ratio.
https://en.wikipedia.org/wiki/Cross-ratio
It's invariant under [math]PSL_n[/math]. It's probably much stronger than what you were looking for but w/e.

>>11429702
a_n = (28/n) * a_(n-1).
Do you see why this is true?
Think about what this means for a bit.

>>11429698
>What do you think it takes to succeed
Well I haven't "succeeded" yes as im still studying and shit but I'd say passion and patience mostly.

>What type of people would enjoy this field
If you enjoy the following things you'll enjoy studying and working on EE:
1) math
2) physics
3) working with things instead of with people
4) building shit
5) computers
6) circuits and electrical mechanisms
7) thinking critically about problems
8) working for many,many hours on a single problem/proyect/thing

>What separates a bad EE student from a good one
A bad EE student is one that is there just because he thinks he'll make money and because the degree is relatively prestigious.
A bad EE just wants to memorize shit and apply formulas and doesn't want to actually take a step back and think critically and actually understand all the concepts and things he is working with.
A good EE is the logical negation of a bad EE.

>Skills that ought to be learned but are not really taught at class
Management skills, norms and regulations and shit are really important, how to deal with a prick boss, how to deal with retarded clients that dont know what the fuck they want, etc.

EE is pretty cool, but make no mistake, its as demanding as its fascinating.

In my personal experience I turned out a bit to academical for EE tho, I really like EE but I just needed to go deeper so I ended up starting a math double major, if you feel this could be your case just start with physics/math from the very beginning.

>>11429711
I've been trying to wrap my head around the equation you typed for a while, just how did you get it? Also how do I find (n) for that equation since the question wants me somehow solve for it but I don't how I can solve for (n) from your equation.
Sorry I'm stupid...

What is real projective space? IS eye sight non euclidean? why do the pareallel lines converge? DO they really be parallel ? what is a metric? Why does the sight function be one way? How do we sniff consistencies between sets? can we rewrite numbers for a geometry?

>>11429722
Well to start with, 4^n * 7^n = 28^n.
Now, write down the first few terms of 28^n / n!, writing it as a series of multiplied numbers without computing the multiplications. How does each term compare with the last?
Once you understand where the formula comes from, think about what it tells you about when {a_n} increases and when it decreases.

>>11429719
>A bad EE student is one that is there just because he thinks he'll make money and because the degree is relatively prestigious.
Fuck.
To be fair I didn't know which part of Engineering I should get into and just picked EE because they had us pick major day 1 and now I'm finished with the general classes and actually have to choose for real.
Thank you kind anon. I have some additional questions but if you can't answer them or too personal then that's fine too, I really appreciate it nonetheless, thank you.
1) Why did you pick EE
2) How did you grow your network?
3) What’s your favorite part of your job? Least favorite?
4) What do you wish you'd known before you entered this field?
5) Can you suggest some ways a person could obtain the experience necessary to enter this field?
6) What's a typical day for your work life?
7) General advice?

>>11429730
Oooooh I see it, I had to pull terms out and have those terms that were pulled out to cancel each other out right? That's how you got to the (28/n) * a_(n-1)? That's really smart...

>>11429736
Ill answer some and not more cause in lazy kek

>Why EE
Always liked physics and electronics, I built a tesla coil when I was 14 and everything started there

>How did you grow your network
Idk, guess im naturally charismatic and people like me so I know a ton of people

>Favorite part of job
Researching shit and making control algorithms

>Least favorite
Annoying corporate shit and coding annoying stuff, also boss is a giant prick

>What youd wish your know before going in
Wish I had more discipline at the beginning

>General advice
Go into EE if you find it interesting and actually want to learn it, don't make your life from now on a grind for a degree

>>11429892
>t. advertising representation manager market research chair of EE

>>11429898
What is this even supposed to mean?

If [math] U(f,P)-L(f,P)< \epsilon [/math] (P a partition of f), prove that f is integrable.
I guess I will have to prove that inf{U(f,P)}=sup{L(f,P)}, but not really sure how.

>>11429911
i mean a hypothetical scenario in which EE as a collective were to hire their official chair of market research management for representation in advertising

>>11429949
Yes, that's what you have to prove. You have inf(U(f, P)) <= U(f, P) < L(f, P) + epsilon, don't you? What does that tell you?

>>11423508
Okay guys im a stupid fag, so pic related, if someone can explain this to me, so my answer is different than the one in the book, and I was wondering what "rule" is being used to move that x and the \[\sqrt x\] being sent to the numerator, and keep the 2 on the denominator?

>>11430023
thanks for the help anon, so from what I understand the "x" exponents 8 - 3 is why you have exponent of 5 in the numerator now. Okay I see, thanks anon.

>>11430033
Ya you just have to get used to the notation and stuff again. It's a good idea to look up your exponent rules in general, going to need them.
For this one think about x^8(x^(-3)) = x^(8-3) = x^5.

cant imagine what it is like to go to one of those top high schools in the US and then go to college. some of these niggas are doing research and taking diff eq+ in high school.

Someone with some organic chemistry experience:
If I, a programmer with limited lab experience, tried to do https://www.drugfuture.com/synth/syndata.aspx?ID=129674
- What are the odds I end up dead?
- Would there be an easy way to mitigate the risks?
- Are my intuitions correct that the main problem is impurity / contamination?
- Is there a straightforward way to test the results? Maybe spectroscopy?

>>11423508
I want to nakadashi that mammal.

>>11429265
Jesus bro someone pls senpai

>>11429723

Here you go.

>>11430142

Seems interesting.

how many qubits of data are in an atom, ie quarks, gluons, w, z bosons, and shit?

>>11430146
>interesting
Not really. Projective spaces can be identified with [math]S^n/\mathbb{Z}_2[/math] and inherits the positive curvature metric from [math]S^2[/math] in the usual manner. Putting the horizon at infinity, it's quite literally how Renaissance/Baroque painters model their paintings with projective geometry.
>>11430216
Each free spin-1/2 encodes one quit.

>>11430260
>[math]S^2[/math]
[math]S^n[/math]*
>quit
qubit*

scientifically, how do i stop being lazy as fuck and study consistently and just follow a routine?

>>11430260
Put this where it belongs. Don't be preaching to the choir.

>>11424183
Some causes:
* Not knowing exactly what to do
* Poor/non-concise instructions
* Having to write down all the procedures (even though the procedures are already given in digital or printed out form) instead of just writing your observations next to the printed out procedures: waste of time.
* Having to work in groups, sometimes as a result of time constraints and not enough equipment to distribute to everyone.
* Other people in the group taking it way too seriously.
* Other people in the group being dicks.
* You yourself are a dick or have poor social/interaction skills.
* Not having enough time to appreciate the experiments which you do.

But yeah, have fun fiddling around with your aqueous solution of pee pee poo poo, dumb ass poorly designed chemistry labs.

I am a sophomore and this is my first time taking linear algebra, my teacher is using a graduate textbook from 39 years ago (https://www.amazon.com/Linear-Algebra-Graduate-Texts-Mathematics/dp/0387901108/ref=sr_1_2?keywords=greub+linear+algebra&qid=1583050588&sr=8-2)) We just started and already I see strange notation (pic related), this is fine I can work through it. I am a math major and I want to learn linear algebra right, but this seems too advanced. This is my only class this semester, so I am prepared to work 8 hours a day. Should I stick it out or drop.

Any resources to quickly pick up game theory?

>>11426146
You can show directly that the order of [math]axa^{-1}[/math] divides the order of x as follows:
[eqn]
(axa^{-1})^n \\
= \overbrace{(axa^{-1})(axa^{-1})...(axa^{-1})}^n \\
= a\overbrace{(xa^{-1}a)(xa^{-1}a)...(xa^{-1}a)}^{n - 1}xa^{-1} \\
= a\overbrace{(xe)(xe)...(xe)}^{n - 1}xa^{-1} \\
= a\overbrace{xx...x}^{n - 1}xa^{-1} \\
= ax^{n - 1}xa^{-1} \\
= ax^na^{-1} \\
= aea^{-1} \\
= aa^{-1} \\
= e
[/eqn]
then after that you can work the other way and show that the order of [math]xax^{-1}[/math] divides n. Let m be the order of [math]xax^{-1}[/math].
[eqn]
x^m \\
= a^{-1}ax^ma^{-1}a \\
= a^{-1}a\overbrace{(xe)(xe)...(xe)}^ma^{-1}a \\
= a^{-1}a\overbrace{(xa^{-1}a)(xa^{-1}a)...(xa^{-1}a)}^ma^{-1}a \\
= a^{-1}\overbrace{(axa^{-1})(axa^{-1})...(axa^{-1})}^ma \\
= a^{-1}(axa^{-1})^ma \\
= a^{-1}ea \\
= a^{-1}a \\
= e
[/eqn]
m divides n and also n divides m so m = n. That is the order of [math]xax^{-1}[/math] is the same as the order of x.

Given the limited information in pic related, is it possible to calculate the angle of ABE?

My ultimate goal is to find the length of AE and I know how to do it, but I need the above mentioned angle to do so.

>>11430345
Stick it out.
>>11430475
You can most certainly calculate [math]ABE[/math] up to two possibilities, although they might be equal.
The issue is as follow:
>ABC is fully defined
>we have the length of AD=AF+FD
>there are two lines leaving from A with length AD
>the only thing we really know about BE is that it crosses AD at a point F such that AF = 1, and then FD has the appropriate measure by default

>>11428072
Just twice differentiable is enough.

>>11429984
I could also say that L(f,P)<=sup{L(f,P)}, so L(f,P)+epsilon<=sup{L(f,P)}+epsilon then inf{U(f,P)}<sup{L(f,P)}+epsilon then (I don't know if the following is true) inf{U(f,P)}<=sup{L(f,P)}. But I trivially know that L(f,P)<=U(f,P) therefore sup{L(f,P)}<=inf{U(f,P)}, and since both statements are true inf{U(f,P)} must be equal to sup{L(f,P)}, is that ok?

>>11430855
Jesus fucking Christ.
We have that [math]inf ~ U(f, P) - sup ~ L(f, P) \leq U(f, P) - L(f, P) < \epsilon[/math], by the literal definition of infima and suprema, and since it's for all [math]\epsilon[/math], we have [math]inf ~ U(f, P) - sup ~ L(f, P) = 0[/math].

>>11430871
Why what I sad is wrong? Also epsilon>0, so epsilon can't be 0.

>>11430892
It's not wrong, it just goes on for half an hour.
>epsilon>0
Irrelevant.

>>11430900
It's not long at all and it's way more correct than yours :^)

>>11430908
>actually convincing me to write the entire thing
By the hypothesis, for every [math]\epsilon >0[/math], there is a partition [math]P_0[/math] such that [math]inf ~ U(f, P) - sup ~ L(f, P) \leq U(f, P_0) - L(f, P_0) < \epsilon[/math], thus [math]inf ~ U(f, P) - sup ~ L(f, P) \leq 0[/math]. Since [math]U(f, P) \geq L(f, P)[/math], we have [math]inf ~ U(f, P) - sup ~ L(f, P) = 0[/math].

>>11430921
I did literally the same

>>11430855
Correct.
>>11430871
Garbage proof, would mark you off for it. Shows no understanding of the problem.
>>11430892
You were right. Also if something nonnegative is less than epsilon for all epsilon > 0, as long as that thing doesn't depend on epsilon, then that thing is zero.
>>11430921
Much better.
>>11430929
Yes, he did.

come someone help me with this problem plox? i think you have to set up an integral, and so far i have
[eqn]\frac{1}{2}m\int_{0}^{1}(vx)^2dx[/eqn]
but i dont think thats right

>>11431406
nvm its right im so good :)

I feel like this is is a science related question.
How do I feel less thirsty?
I've eliminated added sugar from my diet, so no more stuff like juice.
I've been drinking exclusively water and coffee recently, but now I just feel more dehydrated. Drinking more water doesn't really help and it also doesn't help that I've started loading creatine.

Is there any intuition behind this proof? Or is it just some arbitrary piece of logic
>map matrix operators into a polynomial
>create a linearly dependent set of vectors corresponding to v, Tv, T^2v, T^3v, etc
>since all complex polynomials have a root, the operator T has an eigenvalue for all complex vector spaces
theres a corresponding proof as well showing all real vector spaces have a 1 or 2 dimensional invariant subspace using the real polynomial decomposition

>Projective geometry is less restrictive than either Euclidean geometry or affine geometry. It is an intrinsically non-metrical geometry, meaning that facts are independent of any metric structure.
what does this mean?

>>11431933
caffeine makes u pee
maybe less salt
probably just dont drink cofee

>>11432252
It's nonsense.

>>11432274
its from wikipedia anon

>>11432275
Try reading nLab instead. You can definitely endow a metric on projective spaces

>>11432278
sadly i am not good at higher math formalism and arcane notation yet so it all looks like nosnense

testing something

123 132 11 16 9
312 212 = 14 16 14 BASIC<3,4,2>=<95,134,98>
321 231 12 10 11

vs

123 132 123
312 of 212 of 3,4,2 = 312 of 19,14,13 = 86,97,98
321 231 321

okay i fucked up the calculations but its close enough

so a matrix on itself, then operated is like a matrix on a matrix'd vector.. so something is preserved? how, well im unsure but i know its associative, and a vector multiplies like a matrix

so its reasonable to assume factoring a chain of operators works like a polynomial. Kool

>>11432252
Seconding the other anon who said it's nonsense.

>>11432332
what is a metric btw?

and can you help me with this>>11432228

>>11432343
A metric is a function which tells you how far two points are from each other.
A distance from a point to itself is null, the distance from a to b is the distance from b to a, and we also have the triangle inequality. The basic intuition for triangle is in terms of paths, i.e. "if I go from a to b, and then from b to c, I've travelled more than I would have by going straight from a to c.". This doesn't work long term because muh inner metrics, but by then you've grown used to it.
For the other part,
>expecting there to be an intuition behind the proof Axler came up with specifically because he hates determinants

>>11432351
is the triangle inequality supposed to hold for all spaces, or just euclidean? and isnt there specific things to tell you the "value" of length

also, so u think thats just a random piece of logic? it seems like such an interesting piece of proof though. are there any other proofs?

>>11432369
>is the triangle inequality supposed to hold for all spaces, or just euclidean?
It's one of the three axioms for a metric I mentioned in my post.
>and isnt there specific things to tell you the "value" of length
What do you mean? You have a set. There are many choices of metric you can put on it. Sometimes, a space comes with a metric (i.e. Euclidean space), sometimes you deeply study a space and place an appropriate metric on it.

>>11432377
does euclidean/parallelogram space just mean a linear metric? are all metrics formulated in terms of tensors?

>>11432420
>does euclidean space just mean a linear metric
Sort of? Euclidean space is usually the entire structure of the affine space with a metric induced by the inner product.
>are all metrics formulated in terms of tensors
Nah, only semi-Riemannian metrics.

>>11432440
Then again, semi-Riemannian metrics aren't really metrics.
Scratch the semi.

>>11432440
all this stuff is so cool to me, different types of space. but lets get back to projective space i guess. For RPS, as in eyesight, what function is being mapped to what function there? like i guess you would take R3, each point in it having a euclidean vector, and then you draw it on a 2 dimensional sheet. i dont know what question im trying to ask but what "math" is going on there? what things are held stable and waht functions occur etc. are the numbers of the vectors in r3 relabeled, or are they simply redrawn onto a space with different background labels ?

>>11423646
You in enginnering? I used to feel the same way even though my engineering classes had the most maths out of all other engineering carreers at my college. Thats why i changed to compsi and maths, after having strong foundations on maths you can understand and solve problems much more elegantly and concisely.

>>11432464
>compsi
do you feel like theres a sufficient amount of math in your CS courses? when I was in CS it was 120% codemonkeying, does it get better in higher level/graduate courses?

>>11427564
Fuck off with your useless onetrick shitty problems, faggot.

>>11430345
You'll get used to the notation, it will quickly feel like second nature and you'll read it like English. Give it some time though.
The best thing you can do in this class is keep up a regiment of reading the book and starting your problem sets early, and make use of office hours with your professor or TA consistently even if it's not a particular question about the homework but you're trying to build intuition for something. Everything in linear algebra comes with an intuition, it may just be hard to find at first.
I also highly recommend Gilbert Strang's MIT OCW lectures online or 3blue1brown's essence of linear algebra series on youtube as tools for when you get stuck on a concept. The former is great for getting it all concretely and the latter is great for getting a geometric, visual idea of what's happening.

Any advices on deeply learning about differential equations? Preferably ordinary, I've read several books on it but hadn't really had a guide or someone to direct me into classicals in this area. Is there a ODE bible, or some highly regarded book on this topic?

>>11432490
pauls online notes

>>11428467
that happened to me during school, school just fucks you up. as a neet i read math on my free time for comfies and put away the book when i get tired. that said, i do feel empty if i dont do math for a few days. life is filt with other stuff anon, find other beauties

>>11432475
I haven't taken any serious compsci classes yet but I do not personally feel like the level and amount of maths present at compsci classes is enough. Also there are a lot of retards studying it, to the point where a lot of them, if not most, struggle with basic linear algebra proofs. Having said that, I do have to say that I don't think a good compsci graduate (as in able to get a job/go on to research) needs a shitton of maths, or at least not every single course that mathematicians must take. Also i feel like its much more importar to do your own research and have your own projectd outside of school. As an example, the guy that got offered a senior position on his first job isn't particularly savvy on maths nor does he get super high grades, he created a programming language and that's what got him fame and reputation (which managed to get him a high paying job and possibly a lot of job and academia offers in the future after he graduates).
I personally really like applied maths tho and I consider people who dont know it to be less than human. Also fuck every pure math faggot with their circlejerking useless math.

>>11428467
I used to make sure every semester I was taking a math-heavy course. You'll go insane if you try to traverse the vague horseshit of normie topics without something concrete to ground you.
Math has right and wrong answers. Math is comforting in its simplicity.

>>11423508
Where does life begin? DNA? Viruses?

>>11428467
ive gotten pretty much straight A's this semester so far but I got a 75 on an online quiz yesterday because I was chatting with my buddy and browsing /c/ instead of focusing. grade messed with me so much that I had a dream last night where I got the lowest score in the class on my circuits exam. like >>11432512 said, school fucks you up, dont get too caught up in it

>>11428467
I do feel empty when I dont do maths I like. I always make a distinction between "college maths" which is, mostly, boring, mandatory,... and "personal maths" which is maths I like: fun, optional, interesting. I always try to relate college maths with personal maths but that I cannot always achieve that. When i dont I tend to feel empty and miserable (like I did with linear algebra, which I dont like not one fucking bit).

>>11432521
>I personally really like applied maths tho and I consider people who dont know it to be less than human. Also fuck every pure math faggot with their circlejerking useless math.
this might be based if you werent CS
one of my grievances with CS is that theres no value to it: its extremely in high demand and its very hireable, but on a more fundamental level, CS is very rarely used for things that are truly important
engineers build bridges and cars and airplanes and power plants and, yes, some stupid pointless shit, but on a much smaller scale than CS. if you had said you preferred pure math, then I would respect what you study, but to say that pure math is useless makes me think youre closer to all of the other retards in there looking for glorified coding certificates

>>11432546
As a follow up;
You do need to be organized and responsible tho, you cannot dwelve too much in interesting problems that wont make you score higher but you cant either just be a soulless theorem spewing machine that swallows definitions and propositions and vomits it out at the exam. You need to find a balance. I do imagine the thesis being comfy af

>>11432546
As a follow up;
You do need to be organized and responsible tho, you cannot dwelve too much in interesting problems that wont make you score higher but you cant either just be a soulless theorem spewing machine that swallows definitions and propositions and vomits it out at the exam. You need to find a balance. I do imagine writing the thesis being comfy af

>>11432546
i find linear algebra extremely interesting, what dont u like about it? Its so cool seeing the way you can mix space around based on single dimensional bases!

>>11432580
> Its so cool seeing the way you can mix space around based on single dimensional bases!
What do you mean?
I just find the definitions and theorems not that intuitive and pulled out of some rando's ass. I can appreciate the utility LA has on several topics but I just strongly dislike it. I don't really like the algebra part of maths at all. I loved my numerical calculus classes and I look forward to learning more about diff equations tho.
>>11432552
I was baiting a little bit, what I wish to base my thesis on is a bit relates to functional analysis which is pure math af but im just tired of seeing pure math undergrads blasting through courses without having clear goals and just learning maths for the sake of it. When i began maths i was set on specializing on differential equations and everything related to it (im gravitating towards dynamical systems atm) but I failed to see that same "clearity" of goals in my classmates. Also,
>CS is very rarely used for things that are truly important
it really depends on what you define as "important". Under the flexibility of the definition you give "important" you can say that pure maths is highly unimportant, to the point where its degree of nonimportance is similar to that of phylosophy and social """sciences""".
Also i dont get what you mean by
>engineers build bridges and cars and airplanes and power plants and, yes, some stupid pointless shit, but on a much smaller scale than CS
To wrap it up, im doing CS mostly because of the money ngl. Although I do think that CS and Applied Maths complement each other quite nicely. I do feel like some maths courses I take are way too pure maths oriented for my taste and I do like the practicality of some CS classes. Also academia is cancer, I wouldnt really like to put myself through that.

>>11432640
>Also i dont get what you mean by
i meant that if an engie said they preferred applied math, that would be cool because they use it to create impactful things to improve society
if a computer scientist said they like pure math, that would be cool because they use it to create the mathematical models and foundations that the engies use
but for a person studying computer scientist to say that they prefer applied math, that would imply that that person focuses mostly on what CS can _make_, in a practical, productive sense of the word, and CS doesnt _make_ anything important
>im doing CS mostly because of the money
i wish you the best

>>11432661
I believe you might misunderstood me, im not only studying CS, im also doing Maths. Kinda like a double major if you will. I reall like theoretical maths just not when it becomes circlejerking useless garbage.

>>11430323
That question belongs here perfectly fine, hun.

>>11432722
>im also doing Maths
maybe i dont understand you; what difference does you studying maths make to what i said?

>>11428711
Are you a fellow che boludo? Y encima tano?

>>11432853
I believe you have a strong bias against compsci and I cannot figure out why. I thought it mightve been the lack of rigor and theoretical mathematics in it but that doesnt seem to be it considering your last comment.

>>11432937
i respect the mathematical side of computer science
classically, ALL of computer science should be mathematics
however the vast majority of undergraduate CS is essentially codemonkey boot camp
picture two sides of the computer science coin:
one side is largely based on mathematical theory (what i personally think is more prestigious and worthwhile)
and the other is software engineering (the reason most people in CS degree programs are there for)
you say that youre doubling in math
thats cool
you might say that doubling in math puts one closer to the mathematics side of the CS coin
i might agree
however, when you said you think pure math is a waste of time and prefer applied math, that gave me the impression that, to you, CS is mostly about developing products and services, and you dont see the benefits of the theoretical side
which would put you closer to the far side of the coin
i hope i explained it well enough
this is all just my opinion, anyway
and yes, im pretty biased towards undergrad CS :^)

how much calc 2 should i refresh on to take a "prob&stats 1" that has it as a prereq? calc 2 was in 2017 so it's safe to say i dont remember shit.
what parts of calc 2 will a statistics course involve

>>11423508
>furry post
Annnddd that's when I leave this board forever. Friendly reminder before I depart that
1) There is no fucking god
2) Incels correct
3) Civilization doomed

>>11433047
>what parts of calc 2 will a statistics course involve
uh... integrals?... probably?...
thats pretty much the only thing in calc 2
oh, and power series
come to think of it, its probably what the prereq is for

>>11432901
Not that anon pero imaginate ser argento y no tener la ciudadanía italiana.

one definition of a semiring is that it has a 0 where 0 * x = x * 0 = 0, and that this has to be defined explicitly because of the absence of an additive inverse property, but I don't really get this connection. Why would the presence of an additive inverse imply a multiplicative 0? thanks

Why doesn't a symmetric group include both (a,b) and (b,a)? E.g. why doesn't S_3 contain both (1,2) and (2,1)?

>>11433328
They're the same element

>>11433329
How so?

>>11433334
By definition

>>11433335
Oh shit yeah that's true.

>>11432785
Okay honey chan.

Need a bit of help with a topology task:
Prove that the closure [math]\bar{A}[/math] of any connected set [math]A[/math] is connected.

I found an easy prove that for any [math]x \in \bar{A} \setminus A[/math], [math] A \cup \{x\} [/math] is also connected.
My question is if that's enough, or if that only proves you could add a finite number of points to A and have it still be connected.
It feels like that, because you're only adding a point at a time, but then again you could say do this for all [math]x \in \bar{A} \setminus A[/math].

is there a mathematical theorem that proves that God does/doesn't exist?

>>11432490
There's Arnold.
>>11433051
>wrong
>wrong
>wrong
>>11433230
In a ring, the additive identity is naturally a multiplicative zero. Specifically, [math]ab=a(b+0)=ab+a0[/math], and thus [math]a0=0[/math] by the cancellative property (note: we usually prove the cancellative property from the group axioms, and it requires the inverse), for any [math]a[/math].
>>11433578
Assume [math]\overline{A} = B \cup C[/math], where [math]B[/math] and [math]C[/math] are closed, disjoint sets. Then [math]A[/math] has to be contained entirely in a single one of them, we'll assume [math]B[/math]. Then [math]B[/math] is a closed set which contains [math]A[/math], and since the closure is the smallest closed set containing some set, we have [math]\overline{A} \subset B[/math].
I skipped some arguments about passage from the subspace topology to the global topology, which are left to the reader.
Alternatively, the reader can consider the definition of connectedness by maps into discrete spaces being constant and do a generic argument on nets.

>>11433655
Alright thanks, though I'm still curious about my original question, would proving that [math]A \cup \{x\}[/math] is connected for any [math]x \in \bar{A} \setminus A[/math] be enough?

>>11433687
It works for countable amounts of points, yes, because ascending chains of connected sets have connected unions (same argument as earlier, really, split it up into the two disjoints, every element of the chain is in one of them, voilá).
I really don't know if you can do some cardinal fuckery to generalize it, tho.

>>11433655
Also, now that I think about it:
>Then A has to be contained entirely in a single one of them
Is this really always the case? Consider a discrete topology for example.

I think I'm losing my big toe to diabetus
can barely feel it anymore
is it possible to reverse this shit?

Hi frens! So you know how popmath youtubers say that two spaces are homeomorphic if one can be continuously deformed into the other.
I've come across the example of the single twist mobius band and the triple twist mobius band. They are homeomorphic, but in the way that they're embedded you cannot deform one into the other without cutting.
1. What are some other examples of this phenomena?
2. How would you rigorously justify that IF you can twist and turn one shape into the other, they are homeomorphic. I've been reading an algebraic topology textbook and a lot of arguments like this are used in the book. Given how many counterintuitive examples there are in topology, why would we expect that our intuitive notions of being able to transform one space into the other would formally imply the topological notion of a homeomorphism. Also, how would you formalize those arguments if you had to?
Thanks friends.

>>11423508
G'day, I was wondering why I was able to use the formula for specific enthalpy to solve question c.? I believe you are only supposed to use it for 1kg of gas though the question doesn't specify the mass, is this a case where I'd rearrange another formula to find the mass that'd be 1kg or is it more based on an underlying assumption that I'm currently ignorant of?

Probably very stupid question, but to prove that [math]B=\{sin(nx), cos(nx)\}[/math] is orthogonal and complete in [math]L^2(0,\pi)[/math] is it enough to check that:
[math]\langle sin(nx),cos(nx) \rangle = 0[/math]
[math]\langle sin(nx),sin(nx) \rangle \neq 0[/math]
[math]\langle cos(nx),cos(nx) \rangle \neq 0[/math]

or should I also check:
[math]\langle sin(nx),cos(mx) \rangle = 0[/math]
[math]\langle sin(nx),sin(mx) \rangle = 0[/math]
[math]\langle cos(nx),cos(mx) \rangle = 0[/math]
?

>>11433986
*meant to say [math]L^2(0,2\pi)[/math]

>>11433655
So the zero product property hinges on the existence of an additive identity and an additive inverse. Hey thanks!

>>11433732
Nah. [math]B[/math] and [math]C[/math] are closed, and thus [math]B \cap A[/math] and [math]C \cap A[/math] are closed in [math]A[/math]'s subspace topology. Then, [math](B \cap A) \cup (C \cap A) = A[/math], and because [math]A[/math] is connected, one of them is null.
>>11433962
>What are some other examples of this phenomena?
Knot theory.
>How would you rigorously justify that IF you can twist and turn one shape into the other, they are homeomorphic.
Depends on what you mean twist and turn. If homotopy, it doesn't work. For example, the eight path and the circle path are homotopical in [math]\mathbb{R}^2[/math] (because [math]\mathbb{R}^2[/math] has trivial fundamental group), but they aren't homeomorphic.
If isotopy, it's tautological.
>>11433986
The second one.

>>11433979
>a
[math] A=\pi d^2/4\ ;\ \nu=RT/P_i [/math]
>b
[math] v_i=\dot{m}\nu/A\ ;\ \Delta ke=(v_f^2-v_i^2)/2 [/math]
>c
[math] \Delta h=c_p\Delta T [/math]
>d
[math] q=-(\Delta h+\Delta ke [/math]
>e
[math] \dot{Q}=\dot{m}q [/math]

Be careful with your units as always and don't mix joules with kilojoules. The approximation I used for specific enthalpy is totally independent of how much gas you have. The only assumption is that [math] \c_p [/math] is constant over temperature (sometimes this gives poor results). You don't need to do anything with finding mass.
>>11433926
post betus toe. probably not btw.
>>11433051
And nothing of value was lost. Sayonara, nigga!

>>11434042
Yeah you're right it's a very neat proof compared to what I would have come up with.
How do you just pull these things out your sleeve?
I mean I was immersed in topology (or at least trying to be) and my best was the wacky [math]x \in \bar{A} \setminus A[/math] thing.

>>11434111
I have very large sleeves.

>>11434103
>post betus toe. probably not btw.
it looks normal but I've been losing feeling in it for months now
I also feel some painful tingles in it sometimes, not sure how to explain it
I've noticed it feels better when I don't drink soda for about 2-3 days in a row

>>11434141
Sounds weird as fuck.
Maybe you're just not getting enough magnesium or something.
>>11434126
It was a serious question.
Like do you live and breathe problem sheets?
Were you just born with a giant brain?
Did you look it up somewhere?

How do I know if a set in R^n (n>1) is bounded? How do I prove it? Or alternatively, how do I know if a set is compact?

>>11434159
I do usually drink ~1.5-2l of coca cola a day though

>>11427896
Bump

>>11434159
>Did you look it up somewhere?
That was the implied joke with the sleeves thing.
Honestly, I'm not bored enough to google things and rewrite the answer instead of just linking it.
But I really can't tell you whether I'm coming up with the proof on the spot or recalling it.
>>11434162
>bounded
You bound it.
>compact
Heine-Borel.

>>11434162
To prove that it's bounded you have to find a ball B(c, r) = {x in R^n : |x - c| < r} such that your set is a subset of B(c, r)

>>11432997
I do see what you mean and I actually agree with some of it.
>however, when you said you think pure math is a waste of time and prefer applied math, that gave me the impression that, to you, CS is mostly about developing products and services, and you dont see the benefits of the theoretical side
which would put you closer to the far side of the coin
Well yes, nigger. If i wanted to study theoretical CS i would just do pure maths +postgraduate studies on it. I do see some value on actual getting your hands "dirty" by learning how to actually code. I do agree with you on that most cs undergrads are retarda who cant into math. However i believe, and particularly with compsci, the actual implementation of algorithms and getting the computer to do what you want is the whole point of it. Sure, you can just become a poor delusional faggot by going into academia but that just doesnt cut it for me. Specially when most of it, if not all, of reseaech papers on pure maths dont have any relevance outside of a tiny group of cieclejerking selfeighteous pompous academics fucks who cant into adulthood.

>>11433729
Doesn't any union of connected sets, all of which share at least one point, remain connected?

>>11423508
Wow! Historically, furries have been hated on 4chan. I'm pleased to see how loving and tolerant nu-4chan is.
I am so proud of this community.
Trans Pride!

>>11433962
Yeah, youtube popmath likes to say words but you have to be careful with it all. Homeomorphic != homotopic != isotopic. All different. Look into ambient homeomorphisms maybe, and then isotopy.

>>11433160
Imaginate ser un sucio tano del sur y seguro tener ascendencia judia y/o arabe.
Imaginate no ser un españolchad.

>>11434111
You get used to it.
Also every math students answers some version of that question in their topology course.

>>11426036
Anybody at all?

>>11434269
Ascendencia del norte de italia y vasca ftw

Is it difficult to get a short-term student loan deferment?

>>11434320
Could it just be a formatting error of degrees C?

>>11434379
Makes more sense than being some obscure unit. Thank you.

>>11434252
im not trying to be rude but i think this board may not be for you

>>11423508
how long does it take for a paper to be sent to peer review (not actually be reviewed, but only be sent to review)??

I don't understand how the force P is obtained in pic related. I know that (1/2)*18*1 is the area of the triangle, but where does the 1 come from? And then why does it multiply by 18 again?

Assuming I just want to know the density function [math]\rho[/math] of a fluid through time, are there any tranformations I can apply to the velocity vector field/force/etc to make calculations easier?

>>11434103
Thank-you so much, I see that assumption makes more sense.

>input: \pi^2
>output:
thank you microsoft word

Is it retarded to apply to grad school for chemical engineering if I am graduating with a bachelors in mathematics with a minor in chemistry?

>>11434950
No, you'll probably be fine, but you will have to study a lot of things that you never learned. Should be easy, though.

>>11430315
please help

>>11435022
meditate
develop a passion and genuine appreciation and respect for what you do

>>11434854
Dam has thickness [math] t=1\ \text{ft} [/math]. Water has weight [math] \gamma=62.4\ \text{lbs/ft}^3 [/math]. Height is [math] h=18\ \text{ft} [/math]. It is known that pressure is proportional to depth, specifically [math]
p=\gamma y [/math] The horizontal component of the hydrostatic force on the dam is then [eqn] P=\int p\ \text{d}A=\int_0^t\int_0^h\gamma y\ \text{d}y\text{d}z=\frac{1}{2}\gamma h^2t=\frac{1}{2}(62.4)(18)^2(1)=10\ 109\ \text{lbs} [/eqn]

Because pressure increases linearly, the center of pressure (i.e., the centroid of the pressure distribution) is [math] 2h/3=12\ \text{ft} [/math] deep.

>>11434167
>

>>11434264
Agreed. Trans rights are human rights~

>>11434264
>Historically, furries have been hated on 4chan.
4chan also use to think rage comics were funny
the fundamental idea is that 4chan has always been contrarian

>>11435116
>imperial units
>stopped reading

>>11435127
>4chan has always been contrarian
>traditional family values and christianity are rampant on /pol/
I don't want to live on this Earth anymore. probability of ayylmaos take me away to explore space n shit?

Still need some help with this question, if anyone could help.

Let p be a prime congruent to 7 mod 9. If a is a cube modulo p, show that a^((p+2)/9) is a cube root of a.

>>11434264
they still are hated, fuck off degenerate

Why is duty cycle of American split phase systems 50%? The negative part of the waveform also does work just in the opposite direction, so why is it considered an ‘off’ time?

This is not associative right? i.e. (ab)(cd) is not equal to (abc)(d)?

>>11435422
[math](ab)(cd)=((ab)c)d[/math] where we've used [math]x(yz)=(xy)z[/math] with [math]x = ab[/math], [math]y =c [/math] and [math]z = d[/math]. Because multiplication is left to right, we also have that [math](ab)c=abc[/math], which completes the proof.
If you're asking if that's equivalent to associativity, you'll need something like an identity element (in which case it's trivial, a=e) or a cancellative law (which I can't prove, but my guts tell me it might work).

>>11435459
I'm sorry, I forgot to attach the image.

>>11435466
[math](a*b)*c= \frac{ab}{4} * c = \frac{abc}{16} = a * \frac{bc}{4} = a* (b*c)[/math]

>>11435473
Ya, I checked that first, but it doesn't work for (ab)(cd) and (abc)(d). Or, that's what I'm asking anyway.
Or if that even matters.

Given a closed rectangle R=[a_1,b_1]x...x[a_n,b_n] in R^n how can I say that there is a partition P of R such that the n-volume of each subrectangle is less than ε/k where k is the number of subrectangles B such that B ∩ δR is non-empty (subrectangles that intersect the frontier of R) and ε is arbitrary. I know that I can do this (I can’t think a reason why this wouldn’t be possible) but I got no clue on how to prove it and I need it for another proof

>>11435478
Use a really big rectangle R'=[a_1+ delta, b_1 - delta]x...x[a_n + delta, b_n - delta] (which, you'll notice, has empty intersection with the boundary) to cover up "enough" of the volume (adjust the delta until it's small enough) and fill in the remainder with the obvious rectangles.

>>11435315
oh sweaty, my post was sarcastic

teehee~

>>11435478
>>11435512
Oh, my bad, each subrectangle needs to have small volume.
Just induct on dimension.

>>11434926
In fluid dynamics, the system is typically modeled by a Hamiltonian [math]H[\rho,v][/math] as a functional of the density and velocity. The strong Hamilton equations of which give you conservation of mass and a flow equation.
If [math]F[/math] achieves a compact internal symmetry group [math]G[/math], we may represent [math]\operatorname{Lie}G \rightarrow TM[/math] on the tangent space satisfying [math][\alpha_t,\iota_{\xi_g}] = 0[/math] for all [math]g \in \operatorname{Lie}G[/math]. Suppose we can represent [math]\operatorname{Lie}G[/math] completely, by Graham-Schmidt decomposing [math]v = \sum_g (\xi_g,v) \xi_g + v_\perp \equiv v_K + v_\perp[/math], you can show that the part along [math]v_K[/math] has zero Poisson bracket with [math]H[/math]; meaning that they're integrals of motion. Hence the flow equation involves only [math]v_\perp[/math].

ivy leagues or oxbridge for experimental amo physics?

>>11435476
Keep in mind where you're using real number multiplication and where you're using the operation they defined. It sounds like that's what's messing you up.

>>11435476
>>11436058
(abc)*(d) = (abc)(d)/4 = ((ab)(cd))/4 = (ab)*(cd)

>>11434502
>implying
Whatever you say, buddy

>>11423508
Can anyone either explain or refer me to a technical discussion on the formalism behind differential equations?

It shouldn't be first dv and then du where I pointed?

>>11436498
Irrelevant. See https://en.wikipedia.org/wiki/Fubini%27s_theorem

I managed to get the right answer using a different substitution, but why doesn't this work?

>>11436879
This seems right you probably have an equivalent expression, what's the "correct" answer?

>>11436306
Because we need enough regularity in [math]F[/math] to make statements about and characterize its level sets, which constitute solutions to the DE. Generally [math]F[/math] is a functional derivative [math]\delta_u \mathcal{F}[v][/math] of an energy functional [math]S[u] = \int dx \mathcal{F}[u(x)][/math] and to optimize [math]S[/math] by enforcing the stationarity condition [math]\delta S = \int \delta \mathcal{F} = 0[/math] we need [math]\mathcal{F}[/math] to be at least Frechet differentiable.

Can someone give me hints on how to do this?
I know that I would eventually have to put the expression into an equality.
What I'm thinking of is:
1) Split (-1/7)^n and (x-8)^n to their own sequences and do them individually.
2) (-1/7)^n would just be geometric series
3) (x-8)^n would be plugged into the an inequality.
Is my 'plan' correct? I don't actually know if it's allowed to do (1)

Can someone give me hints on how to do this?
I know that I would eventually have to put the expression into -1<r<1
What I'm thinking of is:
1) Split (-1/7)^n and (x-8)^n to their own series and do them individually.
2) (-1/7)^n would just be geometric series
3) (x-8) would be plugged into -1<r<1
Is my 'plan' correct? I don't actually know if it's allowed to do (1)

>>11435813
Do you have some formulas I can copy and paste?
>>11437160
Use [math]a^n b^n = (ab)^n[/math]

>>11437160
>2) (-1/7)^n would just be geometric series
(-1/7)^n=(-1)^n*(1/7)^n
include 1/7 in the x-8 term and see what happens
The -1^n is just alternating and it converges when the rest is converges monotonously

>>11437167
>>11437165
Thank you two so much!

Now I'm absolutely lost, I know I have to use the a/(1-r) to find the sum of the series.
I don't exactly know how to find the following:
(a) and (r).
Do I plug in the inequality (15 > x > 1) into r? How do I find (a) in something like this?

I'm looking at the online textbook solutions but they didn't go over this so I'm super lost...

Here I have two different, but equal, probability expressions.

On the left, I have an expression for calculating the probability that if an experiment is repeated until a particular outcome with probability 1/x is achieved, x repetitions or fewer will occur. E.g., for x = 2, the probability that if you flip a coin until you get heads, you'll have flipped it no more than twice.
On the right, I have an expression for calculating the probability that if an experiment is performed x times in parallel, and a particular outcome with probability 1/x is monitored, at least one instance of the experiment will produce that outcome. E.g., for x = 2, the probability that if you flip two coins, at least one of them will land heads.
I ran these expressions through Wolfram Alpha, and it was able to confirm they are equal. Specifically, both of them simplify to 1 - ((x - 1)/x)^x, which, when itself read as a probability expression, might be taken as the probability that it will NOT be the case that an outcome with probability 1/x will fail to occur x times in a row. Intuitively, this makes sense.

My question is this: Are the expressions still equal if you take the sums away? If so, how would you go about proving it?

>>11437202
Just take the sums away and run the new equation through your program then compare to your old set of results. I personally don't see a reason why it can't work. But I stopped maths ages ago so don't take my word. To prove it just show its still equal with the same integers you use in the equation with the sums. I guess you could try with prime numbers to see what happens.

>just poke your equation until it does stuff.

>>11437190
a is everything without n in its exponent, so 1
r is everything with n with the condition that r<1, otherwise it diverges
Again, ignoring (-1)^n because that doesnt change the solution
1/(1-(x-8)/7)=7/(15-x)

>>11437202
>>11437215
Wow, this really was an /sqt/ worthy question. Took another look at it, I missed a trivial approach.
To test if they're equal when you take the sums away:
>1) take the sums away
>(1/x)(1 - 1/x)^(N - 1) = (-1)^(N + 1)(1/x)^N(xCN)
>2) change (-1)^(N + 1) to (-1)^(N - 1), it's equivalent for integers anyway
>(1/x)(1 - 1/x)^(N - 1) = (-1)^(N - 1)(1/x)^N(xCN)
>3) divide both sides by 1/x
>(1 - 1/x)^(N - 1) = (-1)^(N - 1)(1/x)^(N - 1)(xCN)
>4) simplify
>(1 - 1/x)^(N - 1) = ((-1)(1/x))^(N - 1)(xCN)
>(1 - 1/x)^(N - 1) = (-1/x)^(N - 1)(xCN)
>5) divide both sides by (-1/x)^(N - 1)
>(1 - 1/x)^(N - 1)/(-1/x)^(N - 1) = (xCN)
>6) simplify
>((1 - 1/x)/(-1/x))^(N - 1) = (xCN)
>((1/x - 1)/(1/x))^(N - 1)
>(1 - x)^(N - 1) = (xCN)
>7) expand definition of xCN
>(1 - x)^(N - 1) = x!/(N!(x - N)!)
There's no obvious reason why (1 - x)^(N - 1) should be a closed form for x!/(N!(x - N)!), at least not to my own untrained eyes. So maybe the sum is necessary for the equation to be true. Indeed, their graphs do not seem comparable (pic related).

>>11437165
Let's consider anexample. Suppose we have a 2D flow and [math]G = U(1)[/math], then [math]\operatorname{Lie}G \cong\mathbb{R}[/math] defines a real tangent vector [math]\xi_\theta \propto \partial_\theta[/math] (away from[math]r=0[/math]!), meaning that the orthogonal composition [math]v = v_r + v_\theta[/math] has [math]v_\theta[/math] staying constant under the [math]U(1)[/math]-invariant flow. In fact, using [math]\frac{d}{dt} = \dot{r} \partial_r + \dot{\theta}\partial_\theta[/math] we can show that only radial motion occurs in both [math]v[/math] and [math]\rho[/math]. This kind of flow models sources and sinks.

I bought too high of a strength of Trichloroacetic acid for a wart removal. Do I need a specific type of water to dilute it or is bottled fine?

>>11430702
Now I think I get it, it's because you have to use Taylor's, then because of the remainder it must be n+1 times differentiable. How the fuck can I apply this theorem to a C^2 function then?

Does anybody have a source about the coordinate free derivation of the material derivative?
In particular why [math]u\cdot\nabla (\rho u) = \nabla(\rho u \otimes u)[/math]

can I accurately test myself for type 2 diabetes at home with one of those glucose strip machines? assuming I buy plenty of strips of course

>>11437526
>have to use Taylor's
Do you, though?

>>11429265
Dude, have you considered that matrix multiplication in non-commutative, i.e. from R1 * R2 * R3 * ... * Rn = R follows that Y = inv(R) = inv(R1 * R2 * ... * Rn) = inv(Rn) * ... * inv(R2) * inv(R1)?

>>11437573
That's how my professor prove it in our textbook. How would you prove it, then? I just googled some proofs in english and both of them use that theorem. One of them didn't specify if ti has to be C^3 or not, and the other one said that C^2 was enough, but the dumbass forgot about the remainder.