/sci/ - Science & Math

>>10730319
Oh I forgot. The "steps" are all the same duration, so T/6 in this case.

>>10730319
The standard deviation is equal to the standard deviation of the height of each step, so 6 terms. Because every time you half [math]\delta[/math]x, the number of terms double but the ratio cancels out & stays the same.

>>10730333
I'm sorry, I have no idea what you just said. I googled it and it seems that you can use "rms" and "standard deviation" interchangeably? So I guess what you're saying is calculate the RMS of every term individually, is that right?

>>10730319
You take the root of the mean of the squares

>>10730343
Yeah basically. You can verify that if you write it out as a riemann sum. Every multiple of 6 points has the same rms.

>>10730353
(((Uo/3)^2+(2Uo/3)^2+(Uo/3)^3)*(T/6))/T , is that it?

I'm a mega retard and also from a third world country whose education system is the weakest part of it, please help. I can't wrap my mind around basic concepts of thermodynamics, specifically entropy. Why does it never decrease, and what is the difference between heat transferring and work? I'm trying to self-learn, but are too dumb to do so. Pls help

>>10730360
Actually:
sqrt((((Uo/3)^2+(2Uo/3)^2+(Uo/3)^2)*T/6)/T)
which equals to U/3
But it honestly doesn't seem right at all, I must be making a mistake somewhere?

Is buccal or sublingual the faster route of administration?
I know they're both fast for the enternal route but which is the faster one?

>>10730407
That doesn't have the right number of terms. Per my example there should be 6 terms and then the denominator should be 6 but there are only 3 terms there.

>>10730418
Yes, but the positive and the negative part are the same. Can't I just multiply everything by 2 and divide by T/2, which would equal to the thing I wrote?

>>10730434
Yes, but since there are 6 terms the denominator should be 6. The fraction should be the average of the terms. If there are 6 terms you have to divide the sum by 6.

>>10730444
Well I wrote T/6, I divided it by 6 didn't I? Oh my god I'm so sorry, I feel like I'm retarded because I don't understand what you're saying.

>>10730319
square each value of the graph. find the area under each segment and add the areas. divide by T. then squareroot. ROOT of the MEAN of the SQUARE of the signal.

>>10730454
Hmm, Yes, the denominator was 6. I guess I don't understand why you multiplied the numerator and denominator by T though. It should just be the sum of 6 Y values divided by 6. There's no need to multiply or divide by T. If you remove the T, you see that there are only 3 terms in the numerator, so the average is wrong. The numerator should be (((Uo/3)^2+(2Uo/3)^2+(Uo/3)^2)*2)

>>10730462
>>10730473
Oh lord is this it?
[math]
\sqrt{\frac{{}2*((\frac{Uo}{3})^2*\frac{T}{6}+(\frac{2*Uo}{3})^2*\frac{T}{6}+(\frac{Uo}{3})^2*\frac{T}{6})}{T}}
[/math]

>>10730486
No, sorry, lol. There should only be 6 terms, not T terms. So this is the RMS: [math]\sqrt{\frac{2*((\frac{Uo}{3})^2)+(\frac{2Uo}{3})^2)+(\frac{Uo}{3})^2)}{6}}[/math].

>>10730513
Okay, now you're just fucking with me, that's the same thing. ;_;

Thank you so much tho, saved my sanity here!

>>10730486
Those are equivalent though. So yeah, that's it, even though I still don't know why you put T in there.

>>10730525
Because when you work with other signals you need to divide by T. The general formula is this:
https://ec.kemet.com/wp-content/uploads/2015/08/formula_Integral_RMS.png
Force of fucking habit I guess, almost went insane.

>>10730513
this is correct and the most efficient way to do it. The only faster approach would be to know the fourier series components a priori and take the sum of the squares of those instead, a la parseval's theorem. you'd have to be careful to apply the correct scaling factor there though, depending on the exact form of fourier series/transform you're using.

>>10730530
You should only divide by T when you do an integral. This isn't really an integral though so no need for it here. But if you include the T then it's in the same form as the integral, if that's what you need.

>>10730319
(Uo/3)*sqrt((4*(1^2)+2*(2^2))/6)
= (Uo/3)*sqrt((4*1+2*4)/6)
= (Uo/3)*sqrt((4+8)/6)
= (Uo/3)*sqrt(12/6)
= (Uo/3)*sqrt(2)

The integral of a piecewise-constant function is just the sum of the integrals over the intervals, each of which is just value*time.

If the intervals are integer multiples of a constant, that constant will be a factor of both numerator and denominator and thus will cancel. If the values are integer multiples of a constant, that constant will factor out: sqrt((k*x1^2)+(k*x2^2)+...) = sqrt(k^2*x1^2+k^2*x2^2+...) = sqrt(k^2*(x1^2+x2^2+...)) = k*sqrt(x1^2+x2^2+...).

If I have x=A*B*y, where A and B are nxn matrices, then
y=A^(-1)*B^(-1)*x, right?

What do hard and soft scattering mean in the context of particle physics?

>>10731354
no, B^(-1) A^(-1)

>>10731355
Ok, thanks, exactly what I wasn't sure about.

>>10731356
To expand my answer: to obtain y, you multiple on the left by A-inverse, getting A^(-1) x = A^(-1) A B y = B y, then you multiply on the left by B^(-1), getting B^(-1) A^(-1) x = B^(-1) B y = y.

>>10730361
Do you use a book or Wikipedia? Entropy can decrease. Heat is heat and work is work. What is your confusion?

>>10731372
Yeah, I just wasn't sure in what order should I multiply.

What does it mean to "get an approximation that is accurate to 4 decimal places"?
Should I round before checking the 4 decimals or not?

Let's say x = 0.6180339887498948482...
and the approximation is 0.61805555555555... , is it considered accurate to 4 decimals or not?

>>10730319
>root mean square
Square root of the mean of squared values

in regards to complex functions, what is this z*/z-star function? I've never seen anything like it

Does anyone here know about control system diagrams? I am trying to figure out how he managed to get 1+D/C in series with C and B in negative feedback, isn't there a node in between the sum node?

>>10731732
And btw this is the solution

>>10731726
Complex conjugation: change sign of the imaginary part

I probably made a mistake somewhere, because my answer doesn't seem to be equivalent, but the idea should be right.

>>10731826
>>10731732
Oops

>>10731826
>>10731829
Thanks, what I didn't get was the node from the right of C went to the left, so that B was in feedback with itself

Shouldn't it be B*C instead of B/C?

>>10731853
I think I got it, I hope(?)
Starting from >>10731732
I moved the node at the right of C to the left, then switched the two branches and moved C to the further left

I did some molly (ecstasy) back then in college. At the time I didn't feel anything and life just went on. 4 years later I feel like my memory is not the same when I was younger. Is it normal or did drugs fuck me up ?

>>10731942
Yeah, it should be B*C, i fucked up. Basically you get the signal, multiply it with C, then with B, then feed it back. So you can take the original signal, split it and do just that in a separate branch, so you can simplify.

If I study 8~12 hours everyday for 3 weeks will be sufficient to refresh algebra/precalc and learn calculus 1? What textbook should I use?

>>10731976
I don't know about ecstasy, but marijuana fuck with your mind and memory, mainly if u are underage. The good news is when u stop to use, It get back normal.

>>10731726
As has been said: a postfix asterisk indicates the conjugate. (a+bi)*=a-bi.

Note that the conjugate operation isn't an analytic function. It isn't complex-differentiable (holomorphic) as the limit depends upon the direction in which δz approaches zero, meaning that there isn't a defined limit. It can't be expressed as a Taylor series, as any complex polynomial is analytic.

Analytic functions are always conformal maps; in a small neighbourhood, the mapping is approximately a rotation and uniform scaling. In the same way that any smooth function looks like a straight line if you "zoom in" far enough. But conjugation is a non-uniform scaling: the real part is scaled by 1 but the imaginary part by -1, i.e. it's a reflection.

For a conformal map, x+yi=f(u+vi), you always have ∂x/∂u=∂y/∂v and ∂x/∂v=-∂y/∂u (Cauchy–Riemann equations).

can someone help a math brainlet here
i have f(x)=x^3+3x^2

how do i get where does it have an inflexion point and its value at that point? i assume its easy to get its value when you know where is the inflexion point how do i get to know that
can someone spoonfeed a retard please?

>>10732216
an inflection point can only happen when the second derivative is 0
so just find f'' and set it equal to 0

Please help me understand how first equation transforms into the second one
How does 1 appear?
So I'll presume because you can essentialy multiply numbers by one anywhere because that doesn't change anything
Itt's equal to 1*x+3/16*1*x=456
Since x now is a common multiplier I can put it before the brackets x(1+3/16*1)=456
Which becomes x(1+3/16)=456
Because 3/16*1=3/16
Is it right?

>>10732295
just different form
if you do the multiplication x*(1+3/16) then you will get x+(3/16)*x (the top one)

>>10732295
yes that's right

>>10732130
>Analytic functions are always conformal maps; in a small neighbourhood, the mapping is approximately a rotation and uniform scaling.
Confirmal maps also require the derivative to be non 0 throughout. Sometimes the term conformal is even used to refer to biholomorphisms. This really confused me on a complex anal exam recently.

>>10732295
You are correct, you can substitute anything with itself*1

I have a question about collaboration between universities, specifically about student exchange programs. What do universities get out of them?
I am from Colombia and my university (top 300) has student exchange programs with several American universities. Why would an American university want its students to come to Colombia? Many Colombians would benefit from going to the US. Speaking English more fluently would be useful and the US is a developed country, so living there for a while would be nice. But in the case of Americans, how does going to a university from a third world country benefit? Is our institution better than those American universities academically, or what is it that they would be getting out of the program?

Alright, this god damn question took me a whole day to solve, I know its quite convoluted and that there is probably a simpler solution, but have I done anything wrong here?

Also, my brainlet ass is done taking pure math courses. Gonna stick to stats lol

>>10731372
A bit of both. I'm confused about the second law of thermodynamics. From what I can gather it says that if a system and environment interact through spontaneous heat transferring over time, the "total" entropy would increase over time until reaching a maximum point. So I am not sure if I'm reading it wrong or not, but I'm not sure what the "total" is (i think its the environment+system?), but also, a heat transferring requires a loss of energy and an energy absorption, so wouldn't one of the two bodies' entropy decrease a result?

>>10732532
Colomban booty

What's the linguistic difference between using "type", "model", or "mark" (and other related words that I'm missing) in relation to designating designs? Ex: Type 18, Mark II, Model 1897

How do you determine the equation of an exponential function with just the intercept given? I tried guessing a point that appeared to on the grid but that's obviously wrong. Is there a trick I don't know?

>>10732079
If you take a remedial course at a community college you can demolish algebra in less time than that. I did it studying only 3 hours a night and working. If my dumbass can do it, you can too. Just buy whatever book they tell you to, its cheap yo

>>10732823
Come on, man, I am being serious

>>10732781
Yes, one of the two bodies’ entropy decreases, can you think of what would happen to the body with +ΔH?

>>10730319
Is nuclear energy really that dangerous as the world makes it out to be? There's been so much advancement in nuclear science that it should be a very safe source of energy now-a-day.
t. dummy who knows nothing about nuclear energy

>>10733033
Here fren

>>10732079
I learned Calc 1 in a week with Khan Academy. Play the videos at 2x though.

>>10732079
Whatever path you choose, 3blue1brown’s videos on calculus are really useful.

what are the chances i get into a phd if i only have one semester of research experience? gpa will be about 3.8, gre 168Q, 159V, 4.5W, and letters of rec should be alright. I am in electrical engineering + physics minor, and will apply to mostly lasers/photonics programs. Rochester, UCF, and Arizona optics programs are my goal but will also apply to some rank ~15-50 EE programs.
I-I should at least get into the MS programs right?

>>10733121
> There's been so much advancement in nuclear science that it should be a very safe source of energy now-a-day.
The issues with nuclear power aren't technical, but political. From a technical perspective, the risks can be managed. But that won't happen if it's cheaper to just bribe the regulators (or rather the politicians who hire and fire the regulators). Or if you can otherwise game the system. E.g. even if a) there are issues which would justify closing a plant, b) the regulators accept that, and c) the politicians accept that, the public might not be very happy about the resulting blackouts, energy-use restrictions or price hikes.

The thing is, we're really bad at assessing very small risks with very severe consequences. With more common risks (e.g. road safety), you get vast amounts of statistical data on which to base decisions. When it comes to nuclear accidents, if you have enough data points to be statistically useful you've already fucked up rather badly.

How good would a year or two of working on a university nuclear reactor in undergrad look on a resume?

>>10730319
Don't try to memorize the mathematics first. What's a simple way to characterize what the question is asking? The RMS is the DC voltage that would deliver the same amount of energy to a resistor over the same amount of time as this signal. Now use your math tools and Ohm's law, and keep the algebra as simple as possible. You need to remember Ohm's law and these most basic equations for power and electrical energy. They're tools in your toolbox, and if you don't remember your tools, you're lost.

P=V^2/R, E=V^2*t/R. Assume R=1 and t_total = 6 (these assumptions don't change the problem at all).

>energy delivered by RMS voltage to resistor over 6 intervals
E = 6*(V_rms)^2

>energy delivered by given signal
E = (Uo/3)^2+(2*Uo/3)^2+(Uo/3)^2+(-Uo/3)^2+(-2*Uo/3)^2+(-Uo/3)^2

Equate the two and solve for RMS voltage.

>>10733504
After looking again, this seemed like an EE question at first, and I was an EE student once. Of course, the RMS value of functions is a bona fide mathematical problem, but an analogous physical situation was always more intuitive and easier to memorize to me. You don't technically need Ohm's law and the power equation, but their definitions lead to the same abstracted mathematical result.

what do for letters of rec if i sat in the back of class and just got good grades but didnt really talk with professors much

>>10730319
Is the decision problem for determining whether a given problem is undecidable itself undecidable? My gut intuition tells me yes but I couldn't find the answer after a few minutes of searching.

>>10733106
It would have a positive delta S after the process, but I can't understand how that makes the total entropy increase, since the other body should have an entropy loss

I'm current doing research under Professor A. Professor B does somewhat similar research, and offered my a position. I told him I am currently working under Professor A, and am unsure if I can "double-dip". He then offered me a joint position between himself and Professor A.

What exactly is a joint research position? Do I work under both separately, or does Professor A work on Professor B's research and vice versa? I couldn't really find information about this online, surprisingly

Does the quadratic formula
ax^2 + bx + c = 0
only work with a, b, & c being only integers?

>>10735329
You mean like this?
https://www.wolframalpha.com/input/?i=2*x%5E2+%2B+3*x+%2B+5+%3D+y

>>10735331
yeah
i.e.
can I solve for x using the quadratic formula but a, b and c can be non integers?
x = (-b +- sqrt(b^2 - 4ac)) / 2a

>>10735329
No, it works over the entire field of complex numbers (so including all reals).

>>10735341
By non-integer's I assume that you mean number's that have decimals in them (1.2, 3.1234, -0.571, etc)? Then, yes it can work with those. As far as I'm aware the quadratic formula can work with pretty much any number type.

>>10735342
so even imaginary numbers, nice

Is philosophy a superset of maths?

>>10735360
Do you consider finding the 4th derivative of f(x) = cos(sin(1/log(x^120 + 27))) to be philosophy?

>>10735400
Yes, I must consider solving the question vs getting pussy. Solving the derivative is just a rote application of the fundamental theorem of calculus.

>>10733033
[math]y=2\left(\frac{1}{2}\right)^x-7[/math]

(Sorry if this looks weird, first time using this Tex thing & my first /sci/ post)

>>10735329
It’s not hard to derive the formula by completing the square. If you do that, you’ll see that at no stage do you need the assumption that a, b and c are integers

I am interested in CFD. Two questions:

1. If I'm interested in CFD, where do you recommend I start (I've been working on some stuff in Matlab so far)

2. If I am first doing a master's in ME with a focus on fluid/thermal stuff (CFD), then is it also worth it to get a second master's in computer science?

why do only rounded apertures produce musical tones?

>>10734394
help please

>>10730319
Okay guys I am a math brainlet, I am taking intermediate algebra in college, during the summer, its a online course, since I enrolled at the last minute. I currently have a 97% in the class, but I still feel like I don't know shit. I took a look at pre calculus classes, and instead of monday,wednesday,friday (american community college) they're M-F.

Part of me wants to retake intermediate algebra at a slower pace to get a more solid foundation, but another part of me feels like I am doubting myself too much.

I guess my question is, even if you got a good grade in a math class, did you ever re take it to get a more solid understanding, or said fuck it and just advanced?

I am going for software engineering degree, and I have to go to calc III.

Lads am I retarded and forgot how to do integration properly, but is this correct? The C_1 term should be divided by r, right?

>>10736026
"what?"
Where's the result of the integration?

If after the first = you mean the partial of something with respect to r, that should be [math]{r^2 \over 2} \cdot \tau_{rz}[/math]

>>10736026
>>10736047
(and by that [math]\tau_{rz}[/math] I mean just the brackets).
In other words, (assuming nothing in the part in brackets depends on r), the result is [math]{r^2 \over 2}{p_0 - p_L + \rho g_{zl} \over 2L } + C[/math]

Yeah I’m good on that part, I’m just questioning whether I missed something or the lecturer forgot to divide through the C_1 by r

>>10736063
Okay, then I agree of course.

I Just don't see the use, to be honest, in doing it that way. What is that about?

>>10735943
My advice is to review the material on your own. I feel that retaking a course is too much of a hassle, but moving on without doing anything is shooting yourself in the foot.

>>10734394
>>10735864
no help for you there bud, you're on your own

>>10731355
>What do hard and soft scattering mean in the context of particle physics?
Anyone

>>10736198
*Anyone?

>>10736198
Do you mean something like hard-sphere scattering?

>>10736207
Yeah I always thought hard and soft referred to momenta, soft being low and hard being high
But I'm reading P&S and they also talk about "hard" processes and I don't understand what is meant with that, e.g. "an example of a QCD hard-scattering process is deep inelastic electron scattering"

>>10736136
It's using the Navier-Stokes equations to derive velocity of fluid in pipe flow as a function of r (how far away the fluid is from the centre of the pipe)

I had an annoying cold for 2 weeks which didn't want to go away and then on monday I started feeling a bit feverish.
Then I got annoyed and ate a whole bunch of vegetables and fruits (didn't eat well the previous weeks)
Since then I feel perfectly healthy again.
Is this just a coincidence with me being biased towards expecting to get better or a placebo?
Or are vitamins and all that "healthy" stuff actually that effective?

If I go to the bathroom ~3 hours after my last meal, then I can't poop but all I have to do is get out of the bathroom, eat something and then I can. Crearly my body was ready to poop, why did it have to wait until I ingested something to do it?

Second question: Does knowledge "settles" in the brain? I remember being completely lost and not understanding shit when I first took number theory and haven't studied it ever since. However, right now I'm helping a friend with his number theory homework and everything seems easy as hell. How could this happen if I haven't studied anything related to the subject in almost a year?

Do I have to be able to solve 100% of the textbook questions?
I can solve about 90% of all the exercise problems in a textbook(math/physics). Is this good enough?

>>10732532
>>10733090
Studying abroad in itself is considered to be a valuable experience by students. You don't go abroad for the quality of the institution but for the experience in itself, to see life in a foreign country, culture, to live independently in a foreign place. Furthermore, Americans may be interested in improving their Spanish if they speak it.

>>10733472
Work experience is always good on a resume. Later in life however it will be more useful when you apply at a nuclear reactor than at a bank.

>>10734394
Just mail, you don't know if you don't ask.

>>10735243
Ask your professors?

>>10737005
No idea but I noticed that when I take a course the first time it can be very difficult however when I review the subjects months or years later it seems much easier.

>>10737082
Generally no, that's probably good enough. Though it depends on what problems you have trouble with.

Why can't waves have a definite position in space? What stops me from just picking the point in the middle of the wave as it's position?

Give me the brainlet explanation please.

Alright, hold onto your neurons because i'm about to ask a really dumb fucking question.
Why don't companies lighten the weight of cars by putting helium or something in tanks under the car so it'll weight less. Shouldn't that give it better mileage and long to break down from use? The only thing I can think of is would probably make traction shit.

>>10737315
Because a cubic metre of helium provides only about a kg of lift.
Considereing that a car weighs over 1000 kg, making it a kg lighter is negligible and a waste of space.

>>10737308
you dont get to pick the middle
its probabilistic

>>10737308
You play guitar or anything? Think about a chord. A chord is composed of multiple notes (each of which are composed of multiple frequencies), but if you strum a chord out you get a define location in time and indefinite tone. If instead you pluck an arpeggio, you get distinct notes spread across a more vague section of time. Is is the i tuition behind uncertainty. Btw, the image you posted captures it pretty well. Just stare at it a while.

When trying to find a variable in algebra, what does it mean getting 1=1 instead of a letter being equal to a number?

My mind has been occupied with how elementary geometry and other abstract concepts make sense in our universe. Specifically:
>How is an angle defined, given only that space is Euclidean (no usage of goniometric functions; these are derived from the Euclidean metric)?
>I've understood that rotational invariance of space requires a Euclidean metric? Is this true, are there counterexamples or, instead, what would instead be the most general metric that is preserved under rotation? Am I reasoning in circles because a rotation is defined precisely on Euclidean metric?
>What is the notion that gives meaning to the inner product in quantum mechanics? I've always found its property of conjugate symmetry "unnatural" and unnecessarily technical.

>>10737905
usually means you fucked up somewhere, it would be like getting x = x

I know how to factorize polynomials but I just work step by step and cannot see the bigger picture of what I'm doing.

Is there a useful guide to this? Every resource I find teaches you to recognize the patterns and memorize the formula, nothing more. Am I reading too much into it and that's all there is to factorizing?

>>10738035
I dont understand your question. You know how to factor polynomials but you dont know what the point of factorization is? The point is to find zeros.

>>10737905
It usually means that you assumed the result to be true and proved your particular strategy did not conclude in contradiction, but alas, you did not prove anything.

If I understand special relativity correctly, the perceived mass of something increases if its travelling near the speed of light relative to the observer. So - does the gravitational effect of something moving close to the speed of light increase as its mass increases?

For example, if a planet passes by the Earth at 50% the speed of light and causes a high tide, then another planet of the same rest mass passes by at 99.9999% the speed of light, does that second planet cause a much higher tide?

It's surprisingly difficult to find a straight answer to this through googling. It seems like the answer should be yes (after all, the mass is increasing), but I don't want to take it for granted.

how i can solve this shit?

>>10738469
mesh

>>10738469
One Diode at a time.

What's the heat capacity at constant pressure (C_p) of nitrous oxide? I tried looking it up, but my Google-fu has failed me. Thanks in advance.

>>10737905
Alternatively, it means your statement is true for all values of the variables.

How would someone equally distribute n points across the surface of a sphere? What about an oblate spheroid?

>>10738762
This is known was the Thomson problem; look it up.

>>10738436
I believe relativistic mass is a concept most physicists have stopped using. It's a way to preserve E=mc^2--namely by putting the Lorentz factor inside the mass. For purposes in SR, you cannot observe the difference but in GR mass has a new purpose (gravitation). I'd say therefore what you suggest isn't true (since the gravitational field must be the same from all inertial frames), but you probably want a second opinion on that.

What is the medium through which electromagnetic waves travel?

apostol, spivak.
which one is better for newb?

A car is riding down a slope of height h=20m without experiencing friction. At the very bottom it starts to go up a circularly shaped loop of height h' = 2R. Which maximum radius R is the loop allowed to have such that the car does not fall down at the top of the loop.

And why the fuck isn't it just m*g*2*R = 0.5 * m * v^2 with whatever velocity the car has after riding down the slope?

Yo so what exactly is beyond the observable universe? LIke if somehow I managed to get 100+ billion light years away from earth what does science say I'd see?

>>10739730
More universe. The end of the observable universe isn't the end of the actual universe.

>>10730319
How hard is doing an undergraduate math degree in the US? For reference, I'm starting at a school with a roughly top-25 math department; and for what it's worth, I got a 1580 on the SAT without studying.

>>10739736
Can we be certain it would follow the same laws as our observable universe?

Also how does that whole universe will eventually expand faster than the speed of light.

>>10739751
This is mostly curiosity for curiosity's sake but i wanted to know a thing.

Let's take the classic "sliding conducting bar in a magnetic field" problem, you have a U shaped circuit with its own resistance, a constant magnetic field and a bar moving at a certain velocity, this increases/decreases the area of the circuit thus changing the total magnetic flux and inducing a current through the circuit, nothing strange there.

If we add the inductance then no problem, we can say it's constant and calculating the current intensity is simple matter of applying the formula

[math]i(t)=\frac{v_0}{R}\left(1-e^{(-\frac{R}{L})t}\right)[/math]
Where [math]v_0=-\frac{d\phi(B)}{dt}=-B*a*v[/math] with [math]a[/math] being the width of the circuit.

The problem arises when i consider the inductance as varying with time, as the bar moves the circuit's area becomes larger, meaning a change in magnetic flux, however the inductance of the circuit is the flux divided by the current but the current is also affected by the inductance, at this point my math fails me and i find myself unable to find a solution to the problem. What happens in these cases? How does the system evolve in regards to current/impedance/voltage?

>>10738954
Thanks

>since the gravitational field must be the same from all inertial frames
Why?

>>10739737
It all depends on what courses you take. Ultimately, you can make it hard or easy for yourself, depending on how many pure or graduate modules you decide to take. I've heard that most students need to take Calc 1-3, DEs, discrete math and Linear algebra in their first 4 semesters or so. These are trivially easy, and you can get by with just practice (really depends on your teacher's exam I guess). If you decide to take more applied-oriented modules, they tend to be more computational and algorithmical, and hence easier, while, pure modules tend to be more theoretical and you prove results instead of compute things. These tend to be more difficult, especially as you get taught increasingly abstract things. Ultimately with enough work, you should be able to ace all of them unless you get an aids teacher (but I heard US has very inflated scores, so you'll get bumped up a bunch).

>>10739608
R=10m
Without friction, the car can obviously reach the height that it started from, which is 20m.
I don't know why you would calculate the velocity for this.

>>10739999
you are under no circumstances required to take more math than calc series a specialized probability course and some discrete usually with elementary lin alg thrown in. DE’s isn’t a degree requirement at even top tier CS programs like Stanford, they don’t have to take analysis at all, do not have to take difficult applied math like nonlinear dynamics or chaos theory, don’t have to do measure theory or topology. Very deceptive to suggest that a “proofs” class, some lin alg, baby calc and discrete is a lot of maths for an undergrad. Physics majors have considerably more mathematical training than most CS undergrads or graduate students ever will.

>>10730319
im only studying self-studying physics because i heard more advanced fields have a bunch of unformalized math. is there any point in acquiring physical intuition?

>>10740085
I was thinking of double-majoring in CS and math, does that make sufficiently rigorous theoretically?

>>10739954
Because the gravitational field is curved by mass, and mass is in fact the same in all inertial frames. I am not 100% sure, however; here is a Quora thread discussing it in more detail than I can bring: https://www.quora.com/Relativity-physics-Does-relativistic-mass-have-gravity

>>10740108
you make your own fucking schedule "kid", pick the classes you want.

>>10740108
Yes, very different from just a CS degree.

>>10740085
Are you literally braindead? why the hell are you speaking about CS? The poster was speaking about math undergrad

>>10739608
The kinetic energy at the bottom of the loop is equal to the gravitational potential energy at the top of the slope, which is mgh. Set the total energy at the bottom equal to the total energy at the top:

mgh = mg(2R) + (1/2)mv^2
gh = 2gR + (1/2)v^2

Set the centripetal force at the top of the loop equal to the force of gravity in order to minimize v (doing this means that the car just barely avoids losing contact with the loop, as there is no normal force):

mg = (mv^2)/R
g = (v^2)/R
v^2 = gR

Plug this into the first result:

gh = 2gR + (1/2)gR
gh = (5/2)gR
h = (5/2)R
R = (2/5)h

R = (2/5)(20m) = 8m

>>10740171
Why are you so angry?

Brainlet here. How is it possible for math to not be applicable in the real world?
People always say that applied math is what you study if you want to do things and pure math is if you are interested in only math. I have a hard time imagining that pure math is completely gone from any worldly connections and only lives in the world of math. It just seems absurd to me.

>>10740297
What about set theory? I have no idea how that would be applied to real-world problems

>>10740230
back to /r/math with you

>>10740330
S E E T H I N G

>>10740348
I heckin love doggos, don't you kind stranger?

>>10740326
It’s used all over the place computer science.

>>10740355
Upvoted!

>>10740326
https://en.m.wikipedia.org/wiki/Conflict-free_replicated_data_type

>>10740361
>>10740373
I don't see how this is set-theoretic. I'm thinking more about the infinite side anyway, stuff like large cardinal axioms.

>>10740297
While ultimately a lot of things can be used "in the real world", in the pure math world, these things tend to come after-the-fact, or inadvertently, or simply never. For example, consider the problem in pic related. It asks you to find whole number solutions to three quantities of fruits satisfying the equation in the pic. While this may seem at first glance like a distribution problem, that is, finding the "right" amount of food to give to each person or something of the like, there is no real-world scenario where such a relation might really come up, at least within the context of whole number solutions. There is no easy way to solve this problem, and the first solutions that might come up are in the hundreds of digits; quantities higher than there are atoms in the observable universe. How to solve such a problem (that is, finding all possible whole number solutions), is a typical problem of pure math. There is no reason as to why this might be helpful, or interesting, but solving it is in an of itself an interesting endeavour to some people. A typical solution might have to delve into the theory of elliptic curves, which is a classical pure math topic that has only recently (past 30 years or so) acquired a use through encryption problems, however, its development was completely independent to its application to the real world.

Is this correct?

>>10730319
I'd written this off as being some fancy 0 since my prof is kinda retarded on other stuff and I didn't get much of the notation in the relativistic transformation part (not that this specifically can't be on me), but today it came back with oscillations.
What is this O or 0 he added in these equations? I'm not sure what it means/represents or why it's there.
Thanks.

>>10740881
https://en.m.wikipedia.org/wiki/Big_O_notation

>>10740760
First off, rotate the damn picture before posting it. Secondly, if you're multiplying row vectors by square matrices, you multiply the row vector from the right. So if [math]A[/math] is a [math]2\times2[/math] matrix and [math]\mathbf{x}[/math] is a [math]1\times2[/math] row vector, you would multiply them as [math]\mathbf{x}A[/math], not as [math]A\mathbf{x}[/math].

>>10740760
>>10740911
Anyway, computation looks good, but stick to the standard rules of matrix multiplication next time.

>>10740911
>>10740914
thanks

Why is it that my uni spends 11 million a year on nigger athletics?

>>10740964
Marketing.

Trying to figure out some line segment collisions using Bezier parameterization and the formula taken from https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection#Given_two_points_on_each_line

[math]t = \frac{(x_{1} - x_{3})(y_{3} - y_{4}) - (y_{1} - y_{3})(x_{3} - x_{4})}{(x_{1} - x_{2})(y_{3} - y_{4}) - (y_{1} - y_{2})(x_{3} - x_{4})}[/math]

my 2 line segments are
[math]\mathit{L}_{1} = \left \{ (x_{1},y_{1}), (x_{2},y_{2}) \right \} = \left \{ (1,4), (2,2) \right \}[/math]
[math]\mathit{L}_{2} = \left \{ (x_{3},y_{3}), (x_{4},y_{4}) \right \} = \left \{ (3,2), (5,2) \right \}[/math]

So the two segments shouldn't intersect. However, the article says that there's an intersection if [math]t\in [0, 1][/math]. And I'm getting

[math]t = \frac{(1 - 3)(2 - 2) - (4 - 2)(3 - 5)}{(1 - 2)(2 - 2) - (4 - 2)(3 - 5)} = \frac{(-2)(0) - (2)(-2)}{(-1)(0) - (2)(-2)} = \frac{0 + 4}{0 + 4} = \frac{4}{4} = 1[/math].

Which suggest that they ARE intersecting.

Why this happen?

>>10740964
Because it makes money

>>10739885
You should view it as changing the differential equation describing the current. In particular, if you use L=F/i where F is flux and i is current, you've just made the differential equation nonlinear, which in most cases has no closed form solution. In that case, your exponential decay equation for current no longer applies.

>>10741374
The intersection of the infinitely long lines falls within the first segment if t in [0,1].
The intersection of the infinitely long lines falls within the second segment if u in [0,1].
So the segments only intersect if the intersection of the infinitely long lines falls both within the first and the second segment. So only if t in [0,1] and u in [0,1].
But in your case only t is in [0,1], but u isn't.

What should I review to prepare for undergrad Analysis? I've been reviewing Linear Algebra and Calc 1, and have been reading A Transition to Higher Level Maths as recommended by the wiki. I just suck at proofs, especially induction, so I'm a bit scared I'm gonna be totally fucked. Only reason I passed discrete was because of a curve and the prof being completely incompetent.

>>10741433
ah ok. Thank you. I thought either worked, didn't realise it had to be both

Hi /sci/, I'm studying engineering and have lots of free time the next months. I felt they teached too little ODE and also I have curiosity about the topic but the moment I started studying on my own felt that I don't understand matrix operation/linear algebra that well.

Now I'm reading strang again and doing a bunch of problems since it is the way they teached me in college (just do problems and problems until the day they feel natural). I plan to keep doing lots of problems to get a "feel" for matrix operations.

Any better or different approach to this would you suggest?

>>10741436
Why don't you, I don't know... read analysis?

If you're really that scared, perhaps try something a bit lighter, like Spivak's Calculus.

>>10741450
Do you just wanna become competent at computing matrix operations, or would you rather better learn the theory behind them? You say you want a feel for the operations, but if you don't have it already, its because you're not understanding matrices as attached to a linear map.

I would suggest a more 'theoretical' course, like perhaps, Shilov's or Axler's Linear algebra books.

>>10741460
kek, downloaded that linear done right, then read 2 pages and deleted the book.

>>10741545
>brainlet detected

Let me preface by saying I know only remedial math. Im going to learn trig because I need it, but currently clueless.

I need to find the degree of taper for the core of tapered endmills (in blue). The core is where the spiraling cutting teeth protrude from.
Using an optical comparator, I can find the outside taper of the teeth.

The spiral is not a factor at all, is there some trig to figure out the degree of taper for the blue by measuring the 3 red dimensions with calipers?
Would I need to measure it some other way?

how do i win?

>>10741836
if you haven't fucked up with your flags then there's a mine in the bottom right of the 2x3 rectangle and the rest are free tiles

>>10741836
Click top left and pray?

>>10740051
This is wrong, another anon provides the right answer:
>>10740220
Thanks. I just don't get one minor thing: naively I would just split the calculation into calculating the velocity at the bottom, then calculating how far upwards the car gets. Why is it necessary to use the second condition mg = (mv^2)/R at all in this problem? My (flawed) understanding tells me this should be approached exactly like the vertical throw of a stone with initial velocity v_0.

Obviously the equilibrium of force corrects the result from R=10m to R=8m, but I still have difficulties to understand why there is any discrepancy

>>10741850
The car is going to have horizontal velocity at the top of the loop. It needs enough horizontal velocity to follow the track rather than falling off in a parabolic arc.

The required kinetic energy is the same as for a ballistic trajectory whose minimum radius of curvature (which occurs at the peak) is equal to the radius of the loop.

>>10741642
> is there some trig to figure out the degree of taper for the blue by measuring the 3 red dimensions with calipers?
No. You don't know the angles. You need the distances of the points from the axis of rotation (and from each other). Measuring the distance to some other point (even if the distance of that point from the axis of rotation is known) wouldn't help without knowing the angle between the measurement and the radial direction.

>>10741995
>It needs enough horizontal velocity to follow the track rather than falling off in a parabolic arc
this very detail I have needed, thanks!

>>10741545
Why? What's wrong. Asking unironically

>>10741436
By the nature of doing proofs, you are always going to suck at them at first and you will get more comfortable with them over time and more suited to them. Discrete math proofs are almost always bullshit combinatorial fuckery that is pulled out of someone's ass. Don't worry about that.

>>10742254
You're talking to someone who's having trouble understanding matrix operations, clearly not even realizing that they are precisely those used in elimination for linear equations in early algebra. Don't humor him.

>>10741995
>The required kinetic energy is the same as for a ballistic trajectory whose minimum radius of curvature (which occurs at the peak) is equal to the radius of the loop.
Can you elaborate a bit on exactly why this is the case? It makes sense, but I'm not quite sure why.

im programming and i need to calculate the angle of a right sided triangle. the opposite side is 2 and the adjacent side is 15.

shouldnt my calculation be angle = tan(o/a)? im doing something wrong because the function keeps outputting 0

>>10742448
you want angle=inverse tangent(opposite/adjacent)
the function is probably called arctan or atan

>>10730319
Can anyone help a brainlet? Two questions I have.

Are there any books you recommend which will make me go from high/middle school maths to undergraduate level? I barely studied mathematics in my life but I got interrested lately and want to catch up.

Has anyone here had problems with frequently making dumb mistakes? I get the overal concept but I frequently make little dumb mistakes like let's say anwsering 4*3 as 16. I pretty much had this since childhood so I wouldn't know how to fix it. For some reason I can't count accurately and it makes maths a bit harder for me.

>>10742600
Read the sci wiki

>>10739542
bump

Is it better to do a masters and then phd, or just go for the full phd first? im not sure if i want to commit to a full phd, but if i did an MS first and then PhD, would it take longer total time, or do most places shorten PhD requirements for people with a masters? i would go to the same uni for both preferably

How important is it to understand the mechanics behind the formulas and different rules you're using? I'm currently taking calc 1. I'm doing well enough in the class, but whenever I read the book and try to understand why what I'm doing works, I just end up getting confused.

>>10742342
> Can you elaborate a bit on exactly why this is the case? It makes sense, but I'm not quite sure why.

First, I should probably clarify this:
>The required kinetic energy is the same as for a ballistic trajectory whose minimum radius of curvature (which occurs at the peak) is equal to the radius of the loop.
with: "and whose peak altitude is the same as the top of the loop".

Consider the point where the car is at the top of the loop. Its vertical velocity is zero, its horizontal velocity determines the trajectory it would take if the track wasn't there. If the horizontal velocity is low enough that the trajectory's radius of curvature is smaller than that of the loop, the absence of the track doesn't matter; it will follow a parabolic arc inside the loop. If the horizontal velocity would keep the trajectory outside the loop, the track prevents it from doing that, i.e. it remains in contact with the track.

So it's basically a question of whether the loop inscribes or circumscribes the peak of the parabola.

>>10742448
> im doing something wrong because the function keeps outputting 0

Are you dividing integers? In most programming languages, dividing two integers yields an integer result (typically truncating, i.e. rounding either toward zero or toward negative infinity), so 2/15=0. You'd need to convert one or both values to a real (floating-point) type to get a real result, e.g. angle=atan(2.0/15).

Is environmental engineering even a real thing?

>>10742297
>always going to suck at them
fixed

>>10743163
for you its not important trust me

>>10743262
Interesting! Thanks.

I am gathering data from a number of people (already listed). For time reasons, I can only gather data from a few. Is picking the first third of the list in alphabetical order a decent enough method of random sampling? (No repeated last names)

what is the job of an engineer like vs a scientist working in industry? i am doing EE right now but might switch to physics and go to grad school, most likely AMO

>>10743984
It's pretty hard to know how biased that would make the sample. For example it might bias your sample to a subset of races.

How does one prove that [math]H_1(G) \cong G/[G, G][/math] for a group [math]G[/math]?

How dangerous would the scales used to weigh the material for the Manhattan Project be to touch? Hypothetically? In 2019? Like, if you used equipment that had enriched uranium on it, but you didn't touch uranium itself, how much radiation would you be getting, and would you be safe?
Hypothetically?

>>10744676
>when you give most of the value of your labour to the bourgeoisie and can't afford bigger images than thumbnails

>>10744734
Okay, but seriously, how fucked am I if I handled equipment that held enriched uranium in the 1940s with my bare hands 3 times weekly for a year?

>>10744749
I'd already be making my funeral arrangements if I was you.

Is there any rigorous short calculus textbook which go straight and clear in the concepts? Every calculus book I'm looking for is over 1,000 pages.

>>10744858
>rigorous
eh... depending on what you mean by this "calculus made easy" by silvanus thomas is a great book. very short and has some good problems, but it's not rigorous in the sense of proofs. it's not an analysis book.

Is it possible for a complete lay person (with an a Bachelor) to get a PhD?
I'm thinking I could do something like write a 60 page report and show that to people in the field so they then see that I'm serious about researching the particular area

>>10742977
Any university with a phd program will have a master's program whose requirements you'll meet while completing the requirements for the phd. You can just ask for the master's around year 2 of the phd and get it for no extra effort.

>>10744858
It sounds like you probably want Lang's A First Course in Calculus, it is not really a very rigorous book, if you want rigor then Spivak, Courant and Fritz John, Apostol are the books to read but you are apparently in a rush! So, for you Lang will have to do.

in order to understand and make use things like:
a) fourier transforms, wavelet analysis
b) markov (incl. HMM), monte carlo
do I "simply" need to study calculus and linear algebra?

>>10744627
In what context? Algebraic topology? I mean, I don't know anything about group homology (although I've heard of cohomology). Well, if it's the first, the idea is that the fundamental group defines a canonical morphism into the first homology, and the kernel is precisely the commutator. If you tell me how you define a chain in this context perhaps I can think of something.

>>10745842
yeah pretty much
also
>xkcd

Does ranking or brand name of the university I get my PhD matter at all (for industry, academia, or govt lab) for getting a job after graduating, or is it more based on the specific program, or even the specific lab group or professors you work with?

Also does a masters make it easier or harder to get into a phd program? I have a 4.0 atm and plan to keep it and should have plenty of research experience so i think it should be an advantage right?

>>10746516
If you were what you claim, then you would know there are better people to ask these questions to than sci

>>10746525
im autistic and dont like asking professor things like that

>>10746195
This is all I have, and the exercise is to give a direct proof for >>10744627

>>10746516
>does school matter
In a field like Medicine or Law, sure. In a field like Engineering or Math, probably not. Engineering isn't glamorous or as much of as elitist tool.

Remember: becoming a Doctor is incredibly difficult. On the other hand, the jobs that require a Doctor outside of Medicine and Law is going to be a lot more experience and utility oriented. Mathematicians are kind of screwed, except they usually have some software experience. Finding someone with an MS in Applied Math or Statistics will be easier though and more practical because you don't need them that specific and they're cheaper.

Getting an MS then PhD isn't unheard of, and you can often find places that let you get both. Transferring is a huge issue though, most places might make you go through at least 1+ year of MS classes, even when you have the Masters. I say might because the amount of money they can make off a PhD is a lot, and many people won't make it, so it'd be attractive to get as many people in the programs as possible. Basically, staying at the same institution versus transferring is far more of a liability than getting an MS then PhD at a single institution. Master's often having their own project, such as a thesis paper, experiment, device, etc, so getting the MS could be extra unnecessary work on your way to a PhD, but doesn't let you fallback on an MS if you don't finish the PhD.

>>10739542
bump

>>10746249
>xkcd
yep!
thanks anyway

Can anyone explain why this method of finding the center of a circle works?
It looks like black magic to me, but I've checked it in AutoCAD and it does work

>>10737315
Helium is flammable, expensive and a bitch to seal in a tank.

>>10747632
>>10747632
The idea is this: you need two diameters to find the center. The easy way is to find two separate diamaters as in the first step of the picture. However, suppose instead you have two circles, each whose circumference goes through the radius of the other (they will necessarily have equal radii). Now remove your knowledge of their centers. Then if you find a diameter that goes through the center of one, you will then find the center of both.

In this case, the first diameter 'defines' the other circle, and the second lines is the diameter of the second circle, hence finding its center, and thus the center of the other.

>>10747746
What second diameter? You find out the radius with the second line you draw. I just cannot understand why it works. The first diameter is easy. But the second part comes out of the clear blue.

>>10747769
Yes, but the second line becomes the diameter of the second circle. So basically you exploit the same construction to create two diameters

>>10747791
Look at it again

>>10747803
...
I'm not saying the second line is a diameter of the first circle, but a diameter of the SECOND circle of equal radius. But the two circles are connected in the fact that once you find the center of one, you find the center of the other.

>>10747814
I know how it works but you've done nothing to explain or prove why it works. Why the second line become the diameter of the second circle?

How the fuck do I solve this

>>10747878
I was retarded and when I though on how to explain where I am stuck I solved it

If I know that ¬(p q), does that mean that p is true and q is false?

>>10748009
I meant ¬(p -> q), the site can't render the arrow.

>>10748009
>>10748012
yes

>>10748012
use [ math ] [ /math ] tags (no spaces) for [math]\mathbf{\LaTeX}[/math]

[math]\lnot(p \to q)[/math] is true if and only if p is true and q is false so they are equivalent.

https://web.stanford.edu/class/cs103/tools/truth-table-tool/

I've heard countless times loneliness is terrible for you is this true? and if so does it apply to people who feel lonely or people who don't socialize often? also does it still apply to introverts and people with autism?

why is it that in stochastic gradient descent for batch size n=1 (no batching), that

[math]var(Err) = \frac{1}{N} var(div)[/math]

where Err is standard error and div is the total divergence?

shot in the dark.. might anyone have a list of the readings for pic related?

the website http://deeplearning.cs.cmu.edu/ only has the supplemental readings

Spivak ch. 15 prob 11. How do I prove the first equation here?

>>10750182
this isn’t a hw board, you won’t become more competent if someone helps you

>>10750184
I'm a philosophy major, I'm self studying. Here's the answer in the book. Isn't the first equality here false?

>>10750193
No, look up the trigonometric identities with respect to the sum of angles.

>>10750238
I just realized I misinterpreted the parentheses. I didn't think cos(m - n)x meant cos((m - n)x).

Can you solve this solely by applying "sum of triangle's angles is 180"?
Is the answer 39?

>>10750832
well of course not
nothing is specifying the angle of this red line
it could have just as easily been in the position of this blue line for example

>>10751670
But it's not in the position of that blue line. It's in the position of the red line.

>>10751721
Are you trolling?

You asked if that angle could be determined from the given angles (51, 90, 90 and 90).
I just showed you that these angles do not determine the angle indicated by the question mark
So no, you can't determine what this angle is from the given angles.

Can't believe I have to spell this out for you.

If I try to make a field of size 6 defined as [math](\{\space (a,\space b):\space a\in\mathbb{Z}_2,\space b\in\mathbb{Z}_3\space\},\space \oplus,\space \otimes)[/math]
, where simply [math]\oplus:\space ((a, b),(c,d))\space\mapsto\space (a+_{\mathbb{Z}_2} b,\space c+_{\mathbb{Z}_3}d)[/math]
and [math]\otimes[/math] is defined analogously (with standard multiplication in Z2 and Z3)
Why isn't it a field? I'm aware that it would have a non-prime characteristic and I even know the proof of why that can't happen, but at the same time, if I try to see which axiom is violated, I can't see it.
>[math](\mathbb{F},\space \oplus)[/math] and [math](\mathbb{F}\setminus\{0\},\space\otimes)[/math] are Abelian groups
isn't that simply because it applies for Z2 and Z3? (with (0, 0) and (1, 1) as neutral elements)
>distributivity
can't see why that doesn't apply either

the answer to this will probably be fucking trivial (and that's also why I post it to /sqt/)

>>10752142
(1, 0) has no multiplicative inverse for example

>>10741836
Click the one above the three and the one to the left.

Have any advancements been made for graphene recently?

>>10752194
how did I not realize that?

Jannies pruned my thread, but dubs decides my research area for grad school. Must be in pic related and not crossed off

>>10752428
dubs decide for me something absolutely uninteresting
fuck off

>>10752428
nano and kys brainlet

>>10752428
quantum
>>10752439
tweaker

>>10752470
>tweaker
what?

>>10730319
2*sqrt(3)*Uo

I need to find structural materials that have high yield strength and low xray absorption. Any tips? I cannot seem to find specific resources investigating in this direction.

>>10752142
It's not hard to see that any finite field [math]\mathbb{F}[/math] must have prime power order. [math]\mathbb{F}[/math] necessarily has prime characteristic (why?), so it has a subfield isomorphic to [math]\mathbb{Z}_p[/math]. This means [math]\mathbb{F}[/math] is a vector space over [math]\mathbb{Z}_p[/math], and the result follows from linear algebra and a simple counting argument.

Would it be analogous to think of the Higgs field as a spider web that sort of absorbs and keeps vibrations stationary (ie give them mass)?

Electrical Engineering student here.
How important is it to have a 'good' calculator?
I've been using a TI-83 for the past 6-7 years.
Would getting a new one benefit me at all?

>>10753804
If you're getting along with just the 83, you're probably fine. Even the newer 84s can do a lot of cool things, but it's almost all nothing you can't do without one. If you enjoy math and aren't lazy, you'll probably be fine. Unless you really need to look at 3D graphs on a calculator.

>>10753804
Casio 9750 GII are so much easier to use. You can have the derivative at any point on a trace by just by just turning it on. You can mix and match equations, like having y= and then parametric iirc. TI can only do one a time.

One of the most convenient, you can just insert stuff anywhere as the default mode instead of overwriting.

I can't remember what else, but it's just so much easier to deal with. It's also cheaper if you have to replace, $50 vs more than twice for any comparable TI calculator.

>>10752271
The Moiré patterns from stacking graphene layers and rotating them seem to be the biggest thing so far. Can't say for sure though, as I'm just an observer and not an actual player in condensed matter.

So I am graduating this fall (dec 2019) and plan to apply to grad school as well which (if accepted) I would begin in Fall 2020. During the off time I have from January 2020 to August/September 2020 I will be working, but would preferably do an internship or two. Should this be fine or do most companies only hire interns that might still be in bachelors?
I hope to get a spring and summer internship, each at a different company for more experience, but my grad school focus (EE Lasers, optics) and preferred internships will be much different than my past internship of EE Hardware engineering, should this be a big deal or is an internship always good experience for a resume?

>>10752142
(1,0) has no inverse. If you multiply it by (a,b) you're gonna get (a,0) which doesn't look like it could be (1,1).

>>10743163
What degree are you trying to get?

>>10754979
I already posted that here >>10752194 and they acknowledged my post here >>10752420

>>10738695
No, you can get a true result from a false assumption.

Is there a name for this: A logical if-statement that, when proved, also proves its converse?

E.g.:

A operator B => B operator A

If you prove this, the converse is also true, by taking the order of parameters flipped

>>10755555
nice quints

commutativity

>>10752428
rolling optoelectronics and lasers

>>10752428
Q U A N T U M
O
P
T
I
C
S

I have a few questions. Firstly, does an implicit derivative guarantee that the equation from which it was derived is not a function? Second, let's assume that I did not know, and could not find out, the equation that a particular derivative belongs to, but I did know that it wasn't a function. Is there some method to find out how many outputs there are in that equation for a given input? I ask because I was practicing applying Euler's method of numerical approximation on a derivative that happened to be implicit, and I only successfully approximated one of the points at the given input, when I knew for a fact that there were two points to be approximated there (it was a horizontal parabola). Sorry if this is basic and stupid but I'm a little confused.

>>10756099
I just wanted to clarify that, while I was only able to find one approximate solution, if I hadn't known ahead of time that there were, in fact, two solutions, I never would have known that there were, in fact, two solutions. At best, I might have known that there were "more than one", but that doesn't necessarily mean "exactly two." There could have been a billion, for all I knew, if I didn't have the answer beforehand, and couldn't just integrate to have a look at the actual equation.

Sorry if I'm posting on wrong board, but /ck/ doesn't seem to have stupid question thread.

Does soda lose the carbonation over time? Let's say I pour a can of soda into a glass, will I still be able to feel the fizzy feeling after I left it alone for one hour?

>>10756165
define can, soda, glass, and fizzy

What was the name of that theory about how our planet is perfect for us so there must have been a god to make it that way? I want to say it's something like goldilocks but that was just about Earth's position in the solar system

>>10756165
There's a finite amount of CO2 in it, and each bubble that makes it to the surface takes away some of it.

you people need to learn to figure things out without help or you will literally never accomplish anything worthy of mention

>tfw need to get a 10 in a macroeconomics test not to have to do a recuperation test
>it's actually entirely possible, the subject is easy as shit and I've got it frontwards backwards
Lads, send your blessings so I don't do stupid shit.

What if we were to uplift squid/octopi? The largest hurdle is the need to at least quadruple their lifespan so they can learn and use that big brain of theirs

>>10738037
I think what anon >>10738035 is trying to ask is, is there a shortcut/shorter way to help to do it mentally.

What is research/RnD work like in an industry lab vs. government lab?

Any medfags here?
I went to the doctor today, and among other things, he prescribed me domperidone for nause I've been having.
I get home, read a little about it, and it says it'll give me bitch tits and will break my dick. https://en.wikipedia.org/wiki/Domperidone#Excess_prolactin_levels
Does this only happen at high doses or something of that type? I'm supposed to take 10 mg 3 times a day.

>>10730319
https://en.wikipedia.org/wiki/Root_mean_square

why didn't you just google for RMS?
it's all there in the fuckin article on wiki lol
why would you ask here

>>10732079
Yes, you can definitely do it.

>>10736479
All that healthy stuff are actually that effective.
Keep eating them.

>>10741545
Not surprised. You're a umb engineer after all.

>>10741450
>>10757599
Anyway, you should check out these videos
https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

>>10756673
What if I don't understand because there's a typo? Or the author worded it wrong so it is ambiguous?

SO(3)/SO(2) = S^2. I understand this, heuristically, namely that SO(3) is planar rotations about an arbitrary axis. By modding out the planar rotations, you are left with the axis, which assumes points on the sphere. However (and this is what I don't fully understand), the axis points to both one point and its antipode. Thus, we can only relate half of S^2 to SO(3)/SO(2) group elements. Is it so that you actually need the double covering of SO(3), rather than SO(3) itself, to get the full sphere? That is: Spin(3)/SO(2) = S^2?

>>10758429
>you are left with the axis
you are left with oriented axis. there two copies of SO(2) which leave the axis invariant - one which preserve the orientation of the plane and the other one that reverses it. To be left out with "just an axis", you would need to mod out O(n), and SO(3)/O(2) indeed is RP^2.

>>10758429
https://math.stackexchange.com/questions/1177583/quotient-spaces-so3-so2-and-so3-o2

>>10758477
I've seen O(2) and how it is basically SO(3) in addition to the negatives of the matrices (i.e. the mirror images, which are improper rotations). I don't under how the two copies of SO(2) manifest themselves in such a way that all rotations are still proper. Alternatively said: If I consider a rotation about an oriented axis, I can perform the same rotation (represented by the same matrix) about the oppositely oriented axis simply by taking the same angle but with opposite sign. Where in all this does my group group of rotations "double up", so that each may correspond to one point on the sphere?

>>10758485
I've seen this thread, and it's actually the reason I got so deep into it. The top comment claims that there is a unique rotational plane for each point on the sphere, but that's exactly my problem, since opposite points have the same planes.

>>10758515
I think you're thinking about this wrong. If you're picturing axes and rotation about axes, you're describing CONJUGATE SUBGROUPS to SO(2) in SO(3). There are many ways how to embed SO(2) into SO(3) and these are of course indexed by RP^2 - each SO(2) is uniquely given by an axis. But these are NOT the COSETS of the quotient SO(3)/SO(2), that's something different. I will give you more detailed answer if you want, just reply.

>>10757937
Use inference, find another book, make an effort to move past the obstacle for the sake of efficiency. Ask conceptual questions you can’t be expected to answer yourself without an enormous time investment and only if you really have a desire to engage with the people who help you. Time is not a freely available resource and you are wasting yours when you give up quickly.

>>10758559
Just to explain my background: I'm a physics student who just followed a course in group theory. All of the terminology is familiar although the concepts of cosets and conjugate subgroups in these specific contexts aren't very intuitive to me.

Just to sum up: SO(3) is indeed the set of rotations about every (unoriented) axis. These are /conjugate subgroups/, not /cosets (of the quotient group)/, which we are after. Would you care to explain the last part a bit more in detail? What are the cosets, why do we want them for the isomorphism, and how is this one-to-one relation realized?

So you have a random walk that stars from (0,0) and for every unit step it goes up by one with probability p and down by one with probability q=1-p. What's the expected definite integral up to a point?
Trivial is the case p=q where it is 0, but I don't have a clue as how to approach this problem.

>>10758605
You are absolutely retarded and have literally never pursued anything for over a month, except perhaps a videogame

>>10758636
So first we need to realize SO(2) as a subgroup of SO(3). Take it as rotations around the z-axis. Cosets are elements of SO(3)/SO(2) They are equivalence classes, [f] = [g] if and only if the transformations differ by an element of SO(2). More concretely if there exists a rotation around the z-axis R such that g = f o R. We are looking for a way to index these classes.

In this context it is best to picture R^3 as the z-axis and the orthogonal xy-plane, and to picture a transformation by what it does to these two subspaces. (Notice that we are using some axis to get an insight, but this is NOT the axis of the transformation - that's completely unrelated here). So from the above or from pic related, it's easy to see that two transformations are in the same coset iff they agree on the z-axis. And what it does to z-axis is uniquely determined by where it sends to red vector. It's clear that there is precisely S^2 such choices.

>>10758663
It's an affine transformation of the binomial distribution, for which the expected value is np and the variance is np(1-p).

Transforming the outcomes from {0,1} to {-1,1} gives an expected value of 2np-1 = np-n(1-p) = n(p-q) and variance of 2np(1-p) = 2npq.

>>10758786
So if a book is badly written you would take the time to bother someone else for an answer instead of just figuring it out for yourself?

>>10758885
if you honestly think that a person can always "figure out for himself" every single question, uncertainty and problem that arises from reading a math book, you also probably think that the highest form of math is calculus

>>10758867
I get the expected value/variance, but what about the area under the graph that is constructed by connecting the points passed?

>>10758921
Being combative for no reason at all and picking on retarded edge cases isn’t a good use of time.

>>10758955
do you consider shitposting on sci a good use of time ?

>>10758822
Thanks for all your help.
>So first we need to realize SO(2) as a subgroup of SO(3). Take it as rotations around the z-axis.
Just to get the hang of the terminology, we are embedding SO(2) into SO(3), right (so that we are still working with 3×3 matrices)? And as I understand it, the z-axis of our object is precisely chosen to agree with the axis of rotation of SO(2) (in the original configuration). The rest of your explanation is clear. But how about reasoning in the opposite direction: each point on a sphere can be seen as a rotation in 3D space, up to rotations about that point (vector). But opposite points seem to yield the same quotiented sets of rotations. I'm probably making the same mistake as before, I'll have to think about it a little longer.

It's been a while since I've done precalculus stuff, but as far as I remember square rooting and squaring are opposite functions, so the square of square rooting 3i is just 3i. am I wrong or is this guy wrong

>>10759019
It's a bit hard to see but that i is outside of the root

>>10759026
Are you serious?
I've been going over this dumb problem for like an hour wondering why I keep getting the wrong answer. fuck me

>>10759019
the i isn't under the root sign

>>10759019
check the radical again, that’s not the square root of 3i.

>>10758940
Let x[i] be the random steps, 1 or -1. Let y[i] be the sum of the first i steps: y[0]=0, y[i]=y[i-1]+x[i]. Let z[i] be the integral under the piecewise-linear curve through y[i]: z[0]=0, z[i]=z[i-1]+(y[i-1]+y[i])/2 => z[n]=(x[n]+3*x[n-1]+5*x[n-2]+...)/2
By linearity, E[A+B]=E[A]+E[B], so E[z[n]]=(E[x[n]]+3*E[x[n-1]]+5*E[x[n-2]]+...)/2
E[x[i]] is just p-(1-p)=2p-1, so E[z[n]]=(2p-1)(1+3+5+...) = (2p-1)*(i^2)/2.

If you consider the boundary case where x[i]=1 for all i, you just get the area under a straight line: the integral of x dx is x^2/2. If you set each x[i] to the mean step (which is just 2p-1), the integral is scaled by that factor.

>>10758822
that's pretty neat