/sci/ - Science & Math

What did y'all score on the SAT?

>>9692422
>ameridumb

>>9692422
the max possible score, without studying of course

>>9692414
Why is inductive reasoning valid?

>>9692440
>While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument may be probable, based upon the evidence given.
Come on anon, it's the second sentence in the wikipedia summary

>>9692445
This is nothing more than an argument by assertion

>>9692440
in the context of mathematics, certainly so.

>>9692422
0. I don't take murrimutt tests.

>>9692440
Because you literally show that something holds for any arbitrary step as long as the initial necessary steps hold. (In mathematics).

>>9692483
>>9692501
I'm talking less about mathematics and more in the sense of "What is the probability that the sun will rise tomorrow?"

>>9692513
that's a physical (ie mathematical) question tho.

>>9692513
This is the problem with statistics you see everything as a random variable when probably nothing is.

>>9692555
that's a feature of statistics, not a flaw.

Anyone have some good sources for me to grind through for infinite series and also summing up such series? I feel like I grasp most concepts but struggle on implementing them.

>>9692673
What do you mean? Because it removes bias?

>>9692682
you can treat anything you don't understand as a random variable, and then make reliable, repeatable predictions about large systems.

>bias
what bias? science doesn't have any concern with biases.

>>9692414
Lagrangian mechanics:
[math] \delta q(t_1) = \delta q(t_2) = 0[/math] is a common assumption.

I once asked why and what I got out of it was that it was because we know that the equations of motion q:t->q(t) exist. Is there some obvious condition we can use to know that such equations exist without knowing what they are?

Studying to be a programmer, is there any reason for me to learn above algebra? Does anybody here do math just for fun?

>>9692841
> Does anybody here do math just for fun?
yes
> is there any reason for me to learn above algebra?
do you ever wanna program a physics engine?
or render anything in 3d?

Is this the right place to ask for Matlab advice or would /g/ be a better fit? I'm trying to do something very basic (solve differential equation of something orbiting around the sun) but I need time scales of about 10k years. When I do it for 100 years the calculation takes 6 seconds, for 1000 years it goes up to 120 seconds and I haven't yet completed calculations for 10k years. Are there tricks to make it faster when I can't sacrifice more accuracy? Is Matlab better than Octave for this kind of stuff?

>sphere describing a simple harmonic motion inside a cylinder
>R is the radius of the cylinder
>r is the radius of the sphere
>R >> r and thus 1 << theta

I get that with 1 << theta I can assume sin(theta) = theta but what do the radiuses got to do with it? Pic of the problem.

>>9692856
>1 >> theta
Fixed.

>>9692856
It's not only because R >> r, it's also because you stay "na vizinhança do fundo". Try to make a drawing to scale if you don't get it, one with r = R/2 and one with r = R/10

>>9692871
Sorry mate but I still don't get it. I speak portuguese and I still don't know what the fuck "na vizinhança do fundo" is supposed to mean.

>>9692875
I don't speak portuguese either but I assume it means the ball never goes far from the bottom of the cylinder

>>9692849
>do you ever wanna program a physics engine?
>or render anything in 3d?

Sure, so I would take that as a yes.
I would be satisfied being a code monkey at the moment now however; better than being jobless.

>>9692841
Yes and yes
For further elaboration, read SICP

>>9692894
>>9692841
I do math for fun, double majored in math/cs in university.
Honestly any complex math should be coming from a library your company uses anyways. Or anything that isn't readily available and tested can be researched in google. But unless you're designing new algorithms or in top fields like AI/Big Data/3D/Sim stuff you can get away with basic calculus through your career.

>>9692900
i feel like an understanding of linear algebra is also crucial.

>>9692900
Ok thanks anon.

>>9692422
1460 because I'm not very good when it comes to reading/writing.

>>9692422
1460/1600

How do you find the distance between two parallel lines in space?

>>9693057
you have to use proj
Other than that I completely forget

>>9693057
you have y=mx+b and y=mx+c, so take some perpendicular line y=(-1/m)x+d and find its intersection with the two lines you started with, then calculate the distance of the line connecting those points

>>9692854
you might want to try out different ode solvers.
ode45 is the standard for matlab, but maybe ode23 or some other does a better job for your problem.
you can also play around with the RelTol and AbsTol options and see how it affects your accuracy

I'm FUCKING losing it guys.
I really want to get a phd in physics but I still want to be marketable enough to get a comfy job. Is it at all possible to specialize in a field that can make this likely? like I'm still really nu to physics and all that shit but I was thinking about focusing on solid state semiconductor physics and using that to get a good job at like intel or a place like that. If thats a retarded plan then can someone rec me some fields in physics that might get me a decent job? oh god oh fuck please I don't want to get stuck in academia all my life.

In the case of determining Se with Von Mises equivalent stress, would you set the loading factor to 1 even if there is torsion? The text book is rather vague on this since it doesnt use Von Mises for its example problems.

>>9692833
It's not just a common assumption, it's the what you need to assume to derive the E-L equations which are a necessary condition for solutions that extremise the the action, but not sufficient. That is, it could be that you get multiple solutions which aren't all extremiser (like an inflex point like x^3). The procedure is completely analogous to regular calculus which is that you find the derivative and set it to 0 and find the solutions, but for the proof of that you start assuming that an extremum exists. In here you say the same, assume that the curve exists, and then get to a condition it must meet that you can easily. The general procedure is then to say that if a particular curve is an extremum then you studu what happen when you change your curve a little, a variation of your curve. Because the integration domain is fixed, these new curves must be such that at the initial and end points they concide with the original curve because if not you lose an important restriction om the possible paths. Now why "physically" we justify this? Because experimentally it has been that way, but if you want to see it from a Newtonian perspective, in classical mechanics, if your potential energy doesn't depend of the velocity variable, then you can prove (for any sort of coordinate chart) that the your Lagrangian is a convex function (in the v variable)which is enought to conclude existence and uniqueness mathematically.

>>9693057
get an arbitrary point in one line and compute the intersection of the line going through that point and the parallel line. Take the derivative and find the minimum. Alternatively, find a line with guiding vector w that intersects both parallel lines, and normalise it by the distance between those two points (call this normalised distance w again). Suppose the paralells can be parametrised by some vector v in some direction. The magnitude of the cross product |v x w| gives you the area of the parallelogram spanned between the parallel lines and w, which is precisely d |v|, where d is the distance you want to find. But |v x w|=|v||w|sinT where T is the angle between w and v, and |w|sinT is precisely d, so that |v x w|= d |v| .

>>9692422
so according to this I have a GPA of 3.7 (didnt bother enough to achieve perfect grades)
Is this good? what amerifat uni could I get into?

>>9693057
How are the lines specified? Implicit or parametric equations?

For two parametric lines p(t)=a+t*c and q(t)=b+t*c, the distance between them is

sqrt((a-b)·(c×((a-b)×c)))/|c|

Note that (a-b)×c is the perpendicular to the plane containing the two lines, and c×((a-b)×c) is perpendicular both to the perpendicular (so it lies in the plane of the lines) and to the lines.

>>9692414
sinx = cosx-1
Please help I am trying to solve this 2 days now, no shitposting

What does it mean for a polynomial to be "over the complex numbers." Does it mean that the polynomial has complex coefficients?

>>9694204
>Does it mean that the polynomial has complex coefficients?
Yes.

>>9694205
So if I want to find a polynomial of least degree over the complex numbers with two complex roots, all I need to do is multiply the two factors that correspond to those roots?

>>9693892
Hint: Square both sides.
Hint 2: Solve a quadratic.
Hint 3: sin^2(x) + cos^2(x) = 1

>>9694221
>So if I want to find a polynomial of least degree over the complex numbers with two complex roots, all I need to do is multiply the two factors that correspond to those roots?
Yes.

if you take a formula that creates a 3d map along the complex plane such as x^2 graphed along the complex plane, what would be the term for a tangent that is actually not a line but rather a 2d plane that intersects as such a tangent would.

i'm about to go into calculus 1, but i was thinking about this problem.

>>9694234
Thanks man.

>>9694231
I did that but the answer is different it's
360K and 90+360K

>>9693892
>>9694369
Draw a picture.

Can someone help me write a partition function?

z = sum[g*exp(-e/kT)]

where g is the degeneracy of a particular energy level, e is the energy of one state, k is Boltzmann's constant, and T is temperature

So basically I am summing each state in the system with a given energy level?

What exactly does z even mean? I know it used to calculate probability and it's used to plug into the ensemble partition function (Z) in order to calculate state functions like U, H, F, G, S, and P.

In this chamber, a proton enters at speed V, and each chamber there magnetic field is a magnetic field that pushes the proton until it eventually leaves.
How does the speed at which it exits compare to when it enters?

Should they be the same?

>>9694369
The bottom line answer I get if you want to check your answer is [math]x = \pi n /2, \, n = 0, \pm 1, \pm 2, \dots [/math] (if you're not familiar with radians [math]\pi = 180^\circ[/math]). Keep trying if you can't get it immediately. I don't think you need to solve a quadratic, as long as you can think about where the zeros of sin and cos are. As the other anon said, it can help to draw a picture.

>>9694374
The degeneracy usually means different things depending on what you're looking at. If it's a large (or classical) object like a gas, it could mean how many objects at that energy exist. For example, in a mixture of chlorine and xenon, both could have the same energy, but then one would not distinguish the two in the sum. Therefore, you would put g=2 there.

If it's a quantum object it's a different story, depending on if its a boson or a fermion, but approximately the same thing.

>>9694392
Remember the Lorentz force law:
[eqn]\mathbf{F} = q (\mathbf{E} + \mathbf{v} \times \mathbf{B})[/eqn]
You should be able to work it out from the form of the law (in the absence of an electric field).

>>9694401
>πn/2
I always get π/2+πn (or πk)

>>9694401
>>9694422
I realised my answer isn't quite right. Should be [eqn]x =\lbrace 2n\pi, (2n+1/2)\pi \rbrace, \, n = 0, \pm 1, \pm 2, \dots[/eqn]

>>9694426
wait I am having a complete brainlet day that's wrong too

>>9692555

Phenomena simply have to behave "randomly enough" for statistical analysis to be valid to a high degree of precision (say, the degree of precision to which one can meaningfully distinguish between results).

>>9694436
>>9694422
I'm fairly sure it's [math] x = \lbrace 2\pi n, (2n - 1/2)\pi \rbrace [/math]

>>9694410
I had this written on my paper. So speed should be the same because the magnitude of the magnetic field being applied in each of the chambers are identical?

>>9694448
It's not about the magnitude of the magnetic field. It's about the direction the force is in. Since there's a cross product between B and v, the force should be perpendicular to the velocity. Does that help?

>>9694452
I understand that the velocity is perpendicular to the force from the right hand rule, but what does that say about the speed at which it enters and exits?

>>9693355
If you don't want A C A D E M I A to be the rest of your life why do you want a PhD? Just take an applied physics masters or a solid state physics one and apply for your meme companies.

Or embrace A C A D E M I A as the rest of your life, what you were meant to do in phyisics. I've already accepted i'm gonna be poor the rest of my life, but i love working in systems biology.

>>9692422
Without studying or cheating, I got somewhere in the ~85th percentile for math, which I consider more like the 95th percentile because I know how rampant cheating is.

Also I had only taken up to algebra, (no trig), so I feel pretty comfortable getting what I did despite it not being MIT or Harvard level. Of course, it won't matter for shit if I don't do anything with my life to prove to my shit university that cheating your way to a high GPA doesn't mean you're actually smart. Or that honor students aren't smarter than me when you give them curved grades, the best professors, and countless other benefits all based on their highschool GPA.

Most likely those honor students will go on to get good paying jobs and I'll never end up contributing to my field in any significant or noticeable way.

>>9693355
There are positions for PhD's (in chemistry and physics) to operate specific machines all day, for testing that things have the right properties, purity, whatever. They pay decently well and are comfy. They're far from academia if that's what you're looking for.

If my angular velocity is 1.92 radians/second,
the time it takes to come to a full revolution for a circle is 1.92t = 2pi, where t is the time it takes or should it be 360 degrees?

>>9694466
Consider Newton's 2nd law,
[eqn]
\mathbf{F} = m \frac{d\mathbf{v}}{dt} = \mathbf{v} \times \mathbf{B}.
[/eqn]
Now integrate over the path
[eqn]
\int \frac{d\mathbf{v}}{dt} \cdot d \mathbf{r} = \frac{1}{m} \int \left( \mathbf{v} \times \mathbf{B} \right) \cdot d \mathbf{r}.
[/eqn]
note that the left hand side may be expressed
[eqn]
\int \frac{d\mathbf{r}}{dt} \cdot d \mathbf{v} = \int \mathbf{v} \cdot d \mathbf{v} = \frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2,
[/eqn]
where [math]v = |\mathbf{v}|[/math]. You might recognise this as the kinetic energy. Now use chain rule on the right hand side
[eqn]
\frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2 = \int( \mathbf{v} \times \mathbf{B} )\cdot \frac{ d \mathbf{r}}{dt} dt = dt \int( \mathbf{v} \times \mathbf{B} )\cdot \mathbf{v} \, dt = 0,
[/eqn]
since [math]\frac{ d \mathbf{r}}{dt} = \mathbf{v} [/math].

>>9694525
wow

>>9694533
corrected mistake in the penultimate line
[eqn]
\frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2 = \int( \mathbf{v} \times \mathbf{B} )\cdot \frac{ d \mathbf{r}}{dt} dt = \int( \mathbf{v} \times \mathbf{B} )\cdot \mathbf{v} \, dt = 0
[/eqn]

>>9694525
Just take a step back and consider what you are asking.

>You have a circle.
>You can measure the position around the circle using degrees or radians.
>You can either say there are 360 degrees around a circle or that there are 2pi radians around a circle.
>You are told that the time it takes to travel around a circle is equal to 2pi radians over 1.92 radians.

So why would you ask if you should use 360 degrees rather than 2pi radians?

>>9692854
>Are there tricks to make it faster when I can't sacrifice more accuracy?
Yeah, use a better scheme.

>>9693355
>Money physics PhD

Solid State is the way. unless you go Plasma/MHD and worm your way onto Lockheed's meme reactor team.

>>9692414
What‘s the antiderivative of f(x)=1/x?

>>9694599
You can copy and paste that exact sentence into google and get an answer, brainlet.

>>9694599
you could just type that into wolfram alpha

>>9694599
http://wolframalpha.com/

>>9694599
https://www.wolframalpha.com/input/?i=What‘s+the+antiderivative+of+f(x)=1/x?

Prove the antiderivative of f(x)=1/x is ln(x) + C

>>9694599
Use the power rule: antiderivative of x^-1 = 0x^0

>>9694615
Proof by definition:
The antiderivative of 1/x is F(x) such that F'(x) = 1/x.
(ln(x) + C)' = 1/x
Therefore antiderivative of 1/x is ln(x) + C
QED

>>9694622
>Proof by definition

kill yourself

how can i prove for a real-valued function f that [math] \max f(x)=-\min -f(x) [/math]?

>>9694641
trivial

>>9694599
>>9694615
Do youre own homework. It's not like this shit is fucking hard, shit is so basic I bet you skipped the lecture on it.

>>9694648
can you answer the question?

Is this a Moore's machine? Is it even a deterministic FSM? Can this be described algebraically? It has no accept state, so would it be better described as a transition system? I dunno

>inb4 do you own homework

>>9694651
It's not homework you retard

>>9694656
I'm sorry anon it was pretty uncomradely of me to post that. I don't know how to prove it because I'm not a mathfag, but it just seems so obviously true.

>>9694651
If it's so easy, how come none of you can do it?

>>9694675
its ln(x)

>>9694708
See >>9694615

>>9694641
never mind it follows directly from the definition of max. idk why i didn't think to use that straight away

Hello, I am 18 and still in high school. I would like to teach myself physics by reading a lot. All the textbooks in the wiki are 200 bucks a pop, so should I just get an ereader and read them digitally?

>>9694761
http://gen.lib.rus.ec/

>>9692414
how to find a and b values? This is for complex numbers

>>9694797
quadratic formula

>>9694763
do people read the entire 1600 page textbook or bits and pieces of multiple textbooks?

>>9694797
two complex number [math] w,z [/math] are equal if and only if [math] \Re w=\Re z [/math] and [math] \Im w=\Im z [/math]. so you basically have two equations to solve

>>9692414
I fucked up a retards integral on my exam, got the answer but messed up when simplifying on the last line.
Now Ill get some bullshit like 95%, not even
bragging I want to kill myself. why am I such a brainlet.

>>9694761
http://www.feynmanlectures.caltech.edu/

>>9692422
1400/2100
t.i am not that smart
>>9692414
When does real math begin? Calculus is all done, and I'm almost done with ordinary differential equations. I get that calc is baby math on this board, so where do y'all say this starts to branch from baby math?

Should I go into chemistry or physics?

>>9694899
I'm currently doubled majoring in both, believe it or not. Both are math intensive; don't let retards convince you that chemistry is for mathlets. Physics is absolutely much more difficult however, but there's more job opportunities compared to chemistry. I personally think chemistry is more interesting in my opinion, but both are definitely interesting if you're smart enough to appreciate what's going on.

>>9694875
>so where do y'all say this starts to branch from baby math?
it doesn't.

>>9694875
>I get that calc is baby math on this board, so where do y'all say this starts to branch from baby math
algebraic topology

>>9694929
>algebraic topology
That's not even math.

>>9692414
I think this is the appropiate thread for this so lemme spill this out.
>Be EE undergrad fag
>Have calc class
>Professor is pure mathfag
>Discuss a demonstration after class
>"Anon you should double major in math or at least do a diplomate in analysis"
>"The diplomate can be done simoulstaneosly with your undergrad studies"
>"In fact, if youre willing, I can arrange a meeting with the math departaments ditector so that we can discuss the details of the diplomate and you can get to it"

Should I go for it? I seriously dont what to ve overwhelmed with EE + math diplomate studies.
The diplomate is basically a year of analysis.
I would start next semester.

>>9694948
why not? if you can handle the material and it won't be too much of a burden it can't hurt

Can some friendly soul please help with with Basic Stats?

How do I find the Z-score with the help of Alpha? t-score is so much easier, you just look at the alpha and df. What am I doing wrong? Please help me!

Question: Alpha=0,01, find Z-score. The correct answer should be -2,575.

>>9694963
Thats exactly the issue, idk if analysis on top everything I already must take would be too much.

>>9694948
would probs look very good on an application to grad school

>>9694948
Yes, but mostly just because if a professor picks you out you should definitely take him up on it.

>>9694988
>>9694986
You both make excellent points. Ill do it then

What exactly is entropy? I know it's Boltzmann's constant times the natural log of the multiplicity, and it has units of J/K, but what exactly does that give us? What is it measuring?

>>9695044
Classic answer would be disorder. In thermo it’s the lack of energy available to do work.

Always seemed like a very strange concept to me too desu.

>>9695065
Why would shuffling a deck of cards increase entropy? Shuffling the deck doesn't increase the number of ways of arranging the molecules, so why would the multiplicity increase?

FUCK FUCK FUCK

just realized i had a final at 6pm and it's 7:35pm !!!

just woke up from a nap so i dont really want to go out in public

WHAT DO I DO???

>>9695044
>I know it's Boltzmann's constant times the natural log of the multiplicity

Akshully:
S = U/T + KlogZ

>>9695108
some one pls reply!! im running out of time

this is a dumb question but if i have a capacitor that is rated at 20uF how many decimal places is that when i convert to a number that i can work with in physics problems. like .000002 or what? how many decimal places does the u mean?

>>9695127
http://www.endmemo.com/sconvert/fuf.php

Is 12 quarter units "as hard" as 12 semester units? I am trying to figure out of I should take more units or not now that I am switching from a semester to a quarter system school.

>>9695108
Better hope you can email your professor a decent enough bullshit excuse anon but you are likely fucked.

>>9695108
I sometimes get nightmares about this sort of thing happening.
Sorry anon. Hope it all works out in the end.

>>9695139
i'm on the bus right now and im 10 mins out from gettting to class. the bus keeps stopping for assholes crossing the street when theyre not supposed to

i dont even have any thing on me except my phone, no pencil even

the exam goes to 8 so im hoping i can show up at the last second and ask him to give me at least 10 mins to take the test

i didnt study either or even show up to class so he's not going to recognize me thankfully

>>9695147
What class is it anon? I am sorry but it isn't looking good.

>>9695146
>TFW had a nightmare about this literally last night
>TFW i'm not that anon
Thank god

>>9695108
Email the prof, said you are incredibly ill. Hope for the best.

>>9695149
calc 1

it sucks because im retaking the class for a better grade but i dont think its going to happen at this point

i didnt study because i already took the class but now i see why that was not very smart to do because i barely remember anything from last semester and im not sure what to write down if the prof even lets me take the exam

okay the bus is almost here so i may get there a bit before 8, ill let you guys know what happens

Need help with something,
I need the formula that gives that sequence.
27,25,21,15,10,6,3,1,.....

Some rules
1-The number after 1 will be less than 1
2-each number is smaller than the prevous
3-all numbers are higher than 0

>>9695164
>1-The number after 1 will be less than 1
>3-all numbers are higher than 0
What did he/she mean by this?

>>9695167
>what is a fraction

>>9695162
sigh

i walked into the class where the exam is supposed to be and there was no one here. then i started freaking out because i never checked the location of the final and just assumed it was in the same classroom as lecture is

but then i checked the final schedule online and realized the exam is next monday, so i freaked out over nothing

this has motivated me to study for calc 1 exam next week so i dont fuck up again

>>9695135
Maybe I can give you some input as I go to a thirdly? (Trimestral) Regime school.
The shorter the study period the easier it is to flunk the course.
Especifically: [eqn] \Phi = D \frac{A}{t} [/eqn] where [math] \Phi [/math] is the chance you have of passing the assignment with minimum marks.
[math] D [/math] is your difficulty constant, you can compute this number by taking your university's rank in your country and dividing it by the approval rate of the course youre trying to calculate difficulty for.
[math] A [/math] is the number of assignments in your course.
And [math] t [/math] is the time in months your regime lasts.
Note that [math] t [/math] is inversely proportional to [math] \Phi [/math] and [math] A [/math] is directly proportional to [math] \Phi [/math], this is in order with all current observations.
Feel free to improve upon my formula, but i think ill do its job.

i have a hard test in 3 days, should i play video-games before studying, after studying, or shouldn't i play them at all?

>>9695186
before studying. studying should be suplimented with lots of snack breaks and game breaks and naps for optimal exam performance

t.
phd doctorate in over 4 fields

>>9693325
>>9694566
Thank you both for your help, I already fiddled with reltol and abstol and I do not know what you mean by scheme, but it turns out pirtaing Matlab was the way to go (only 84s of calculations for 10k years of orbiting).

I'm taking Physics 2, Cal 3, Linear Algebra, and Statics in the Fall. Which of those should I dick around with over the summer to get a head start in?

>>9695197
statics is the hardest of those i'm pretty sure

calc 3 isn't that hard but it would help if you brushed up on vectors and polar coords. phys 2 is gonna be a bitch but theres not a whole lot you can do besides pepper your angus.

>>9695168
Then [math] f(n) = \begin{cases} \sum_{k=1}^8 a_i \prod_{i=1, i\neq k}^8 \frac{(n-i) } {(k-i)} & n \in [8] \\ 1/n & n>8 \end{cases}[/math]

>>9694875
topics that stop being baby math, but not quite pro math (and some canon intro books)
>commutative algebra (atiyah-macdonald)
>algebraic topology (hatcher)
>algebraic geometry (shafarevich)
>functional analysis (rudin, stein shakarchi)
>differential geometry (Lee)
>algebraic number theory (Stewart Tall)

As a reference, this is pre-K math:
>calculus (stewart)
>linear algebra (axler)

and the following is baby math
>Real analysis (Rudin, Tao)
>complex analysis (Ahlfors)
>algebra (Dummit Foote)
>intro diff geo (Do carmo)
>topology (munkres)

>>9696004
i think i mixed up the two last sections

>>9695197
Not linear algebra. It's the easiest of those by far.
Of the others it kinda depends on how well you take to each subject. If you thought the multivariable bit of calc 2 was hard then you should read calc 3.

What's the meaning of p = np, what is p, what is np, is this anywhere else (not math, nor cs) of importance?

>>9696013
P is the class of problems which have a polynomial-time solution. NP is the class of problems which have a polynomial-time solution on a non-deterministic machine. P=NP is whether the two classes contain the same problems (i.e. whether a polynomial-time solution exists for any problem in NP).

No, the question is directly relevant outside of theoretical computer science. Although if it turns out that P=NP, that means that certain "hard" problems actually have asymptotically-faster solutions than those currently known.

you guys know about the "system1" vs "system2" thinking theory ? I need an example of a case where people used system1, but system2 would be the better choice from the history/science/politics or whatever
my head is so full I cant find anything

need help with babby level statistics

I have 12 data points.
To these 12 points I fit a curve that is determined by 4 parameters.
To find these values I repeatedly draw them at random.
For each guess of the 4 parameters I calculate the difference by this hyopthetical curve and my observed data.
I square this difference and divide it by the square of the error in the observed data, and then calculate the sum of doing this for all twelve points.

The combination of parameters that minimize this sum is my best fit.

This is a chi-squared test correct?
What are degrees of freedom here?

Hi, could someone help me on finding the real part of that equation ? I guess you can't just take " [math]Aexp(ix)[/math] "

Lets say you have a slider that's 20 or 30 IQ points in length and you move it across the bell curve to compare two individuals at the opposing points of the slider. What is the difference in the difference? For example, to a person with an IQ of 100 someone who is 80 would appear to be somewhat mentally slow, but the difference between 100 and 130 isn't as great, and I'm guessing it wouldn't preclude the possibility of those two individuals being friends? Does a person with 130 appear to be mentally slow to someone who is 160? Or does the difference between individuals diminish as IQ increases? What about a 140 and a 170. Is the difference less significant at the high extremes?

>>9695178
lmao this exact same thing hapened to me. I took a nap and woke up, """realizing"" the exam was today, so i freaked and went on time. It wasnt that day lol. I studied and got a 8

>>9696102
>I guess you can't just take " Aexp(ix) "

Start there, then convert Aexp(ix) to trig functions using Euler's formula.

how do i solve? I need to graphic this
|z| < |z-1-i|
Prof didnt explain shit about this topic. I am in algebra 1.
I did this (plz no bully)
z < z-x-y
(cancel z)
y < -x
lol dont laugh plz give me the right way f doing this

>>9696143
Wait so the real part is only "Acos(x)" without any phase change ?

>>9696154
Almost.

Aiexp(ix) = (Ai)cos(x) + (Ai)isin(x) = (Ai)cos(x) - (A)sin(x)

Can you guys help me on this one? The context is deterministic finite automata,

>>9696172
I need to take the real part of that last equation, right ?

>>9696187
Take the two real terms. You should have Acos(x) - Asin(x) for your answer.

>>9696189
oooh yeah, thank you

>>9696178
You can model the levers with three bools, the possible states being decart. product.
when A: unless (!a || !d and a) goto !a,!d (preserving b).
...
Is this helpful?

What book is this from?

I have a problem:

>exam tomorrow morning
>don't want to study
>but want to do well

How do I meet my goal of doing well on the exam while also satisfying my desire to do nothing?

>>9696197
Introduction to Automata Theory, Languages, and Computations by John E. Hopcroft, Rajeev Motwani, Jeffrey D. Ullman.

btw, what exactly means the third bool? i don't quite get it

>>9696203
all the bools are the states of the lever, with right-ball-turning ( \ ) being true. You have 2 possible inputs. The states are 'err' and {(a,b,c) | a,b,c from (T,F)}

when 'A': unless (!a || !d and a) goto !a,!d (preserving b). // otherwise go to 'err'
(T,T,F) -> (F,F,F); (T,T,T) -> (F,F,T); otherwise -> err

The 'B' case is a bit harder since you need two conditions (not counting err).

>>9696218
If levers are such that you'd get to 'C', there is an error, no acceptance.

Do I really need a PHD in Population Genetics in order to get a job in it? So far I haven't been able to find anything that accepts a Masters for it.

>>9696218
*when 'A': unless (!a || !b and a) goto !a,!b (preserving c). // otherwise go to 'err'
x1 - a, x2 - b, x3 - c
Variable names were unclear.

>>9696200
You can study for the exam as much as you can, and remember to repay yourself by not doing anything later. You can do nothing when you die.

>>9696227
what would even the job be about? lol. Learn biology or statistics instead, right? Or ask what studied the people doing those jobs.

>>9696144
first draw |z|=|z-(1+i)|. This expression means "the distance from the origin is equal to the distance from the point 1+i". Basically, if you draw a point at 0 and at 1+i, then the above equation describes all the points that are equidistant from the two. Hence, it is a line that it the perpendicular bisector of the two aforementioned points. Now inserting the inequality, you get that you want the area under the line

>>9696246
>What is the job about
Genetics of a population anon. It's literally in the title.
>Learn biology or statistics instead
I choose to learn both.

>>9696248
Yeah, i found out after long minutes. The area is the one below (left, under) y = -x+1

>>9696249
Yes, bout I mean biology or statistics phd/masters will be enough i supose.

>>9696178
does this help

>>9696284
>s0 ///
>s1 \//
>s2 /\\
>s3 /\/
>s4 \\\
>s5 \\/
>s6 //\
>s7 \/\

>>9696289
You need to have finish (and start) states?

>>9696291
you're right, s0 is the starting state but i haven't marked the final states. I'm unsure of what they mean by it accepting when the marble exits through D

>>9696294
It means that all states but 'err' are 'accepting'. In the cases the balls would go to 'C' the state changes to err, which is not accepting. You don't out from err on any input, so the (D)FA rejects only if a ball goes 'C'.

+ Forget about the levers when you get to 'C', you don't go to those states but to 'err'

How in the world does proof highlighted in yellow work? How does he change the equals sign and how can he change a for |a| and b for |b| in the second line. I think I get it intuitively but as it seems the whole point of the prologue is to be rigorous (it's calculus by spivak btw). If you could tell me with very precise operations that would help too. Thanks

>>9696291
>>9696294
if i understand it correctly the final states should be the ones for which the last marble in the sequence exits at D, so just mark those as final

>>9696298
A: err -> err
B: err -> err
// * : err -> err, in general

>>9696299
a =< |a|
b =< |b|

>>9696300
A final state is an accepting state, because you an end on that and accept the input.

>>9696305
you don't have to end on it, though, do you? it's allowed to continue after accepting the input

>>9696178
there's a solution here slides 19-22

http://slideplayer.com/slide/4209905/

>>9696311
Yes, it's final in the sense that it's where the automaton should end.

>>9696302
what abut the change again in signs from line 2 to 3?. If a^2 = |a|^2 he shouldn't change signs again right?

>>9696320
>what abut the change again in signs from line 2 to 3?
What do you mean?

>>9696294
>>9696316
What I told you was: If a marble goes through C the game is lost
What it appears to mean: If the last marble was through C, it's not accepting, if it's D accepting

In the second case, you can't use 'err', because you need to preserve the state of the levers, so you have 4 bools.

>>9696325
he changes from a <= to an = sign even though the expression hasn't changed, I think. I can understand the change in signs (= to <=) from line 1 to 2 (like you mentioned a =< |a|), but not from line 2 to 3 (<= to =)

I got a decent grade when I was younger but I need a 7 or higher for what I want to do, the GCSEs are in 4 weeks and I have covered the foundation tier so now I am moving on the higher tier, is 4 weeks enough to get the grade I want?

9 = A**
8 = A*
7 = A
6 = B
5 = B/C
4 = C

>>9696334
Do one or the other, in the second case, A/R, are closely mirrored.

>>9696351
Well? Is 4 weeks enough study time for higher tier maths and for me to get a grade 7 or higher?

>>9696351
>>9696364
never mind guys, just found out

>>9696351
>A**

>>9696378
Funny dickhead.
>>9696382
Blame UK not me.

Go on then answer me pricks.

>>9696388
I don't know. Probably enough if you've been paying attention so far. Why don't you knuckle down and find out?

>>9696394
Bed time, just getting an opinion before bed.

Hey, I'm trying to prove the following but I'm kinda stuck:
Let [math]\pi , \tau \in S_n[/math], if [math]\pi \circ \tau = \tau \circ \pi [/math], then [math](\pi \circ \tau)^n = \pi ^n \circ \tau^n [/math] for all [math] n \in \mathbb{N}[/math].
I think that I need to show that [math] \pi \circ \tau = \tau \circ \pi[/math] if and only if [math]\pi , \tau[/math] are disjoint permutations but I don't think that it is enough to finish this exercise, I feel I should be using induction somewhere

>>9695197

Linear Algebra, it makes Statics easier since everything is a system of equations. Also get good at vector geometry.

>>9695197
what engineering? Mech? Electro?

>>9696412
nigga just write out (pi \circ tau)^n and use the relation

Am I fucked if I try to apply for grad school with only 1 semester of research? I am graduating for EE next spring, and want to apply for Optics/Photonics based grad schools (EE or Optics based, not ones that need physics GRE). I will have taken 4 senior/grad level courses by the time I apply and have a good gpa (3.9/4.0) and gre (98th %tile Q, 90th for V and W) scores. I started on the research part late as I didnt even think of grad school until I learned more about job opportunities of each degree, and I will probably not be able to get any this summer due to having to work for money and most are unpaid for me, but next fall and spring I will be working in an optics/laser lab with a very experience professor. Will this be enough for MS or PhD applications? Goal is PhD, but I am fine with attaining an MS before applying for PhD if it is the only option left.

If you point a laser light from above the ocean, to the deepest part of it, will it reach the bottom of the ocean? If no, why not?

>>9692422
2040
Only took it once

>>9696630
grad school is a meme unless you want to get stuck in a lab with a capped salary meanwhile BSc chads climb the corporate ladder

if for any given geometric progression: [eqn] \displaystyle \sum_{n = 1}^{\infty} ar^n = \frac{a}{1 - r} [/eqn] then why does this apply:
[eqn] \sum_{n = 1}^{\infty} 9\big ( \frac{1}{10} \big )^n = \frac{9\big(\frac{1}{10}\big)}{1 - \frac{1}{10}} [/eqn] why the fuck are you multiplying by the ratio on the top?

>>9696658
fuck for any given geometric series* where [math] r \in (-1,1) [/math}

When are people here going to buy enough $2 model rocket juice to send a camera outside of the atmosphere so /sci/ has it's own space probe to make sure NASA isn't lying to us and so we can explore things that they won't?

"But it won't go high enough?" The earth ain't flat, if it archs, we just make sure it keeps on pushing and it will leave the earth from the side instead.

>>9696670
you need equipment to transmit the photos to ground, and batteries for that aren't exactly lightweight, and it needs to fit and deploy without blowing up or killing itself. Then you gotta make sure that whatever staging for your engines isn't going to damage the payload. Then you need some way to keep the payload powered while in orbit,
In the end, hobbyist space exploration isn't something that is feasible without huge funds and people with experience in the field

>>9696632
Because the laser is not as bright as the sun and the sun doesn't reach the bottom.

>>9696670
>send a camera outside of the atmosphere
Not just any OTC camera will survive out of the atmosphere

>>9696685
Well the least we could do is calculate how many engines it would take to shoot a bowl of spaghetti into space. You figure it would probably take 12 A8-3 engines to get the bowl to raise 30 feet. We need to make that bowl fly 330000 roughly in addition to some silly string fireworks to light the engines at a certain rate rather than all at once. My equations lead to roughly 4000000 engines, costing roughly $1200000 in total. Considering how many redditors will probably spend $20 of their parents money on a patron to send a bowl of spaghetti into space we would need about 40000 donators to make this happen.

>>9696690
But the sun is far away and scattered everywhere. The laser is closer and a concentrated beam of light.

>>9692422
520

>>9696697
we have the technology.

>>9696701
Even lasers disperse as it is impossible to have perfectly parallel rays, scattering off of water and other particles may cause the laser to not reach as well

>>9696703
Sure, it's just expensive
Lack of funds :(

>>9692854
Don't use "for loops" or "linspace" or [x1:n:x2]

>>9696705
thx

>>9696708
->>9696698
Look at my redditors with parent's money thesis.

>>9696648
I am trying to get a comfy 40 hr/wk max lab job in industry so I don't care

If rain was made of Coca-Cola, what would a rainbow look like? Would there even be one?

>>9696734
The sun would reflect off of the sugars and make them painful to look at and probably blind people who stare at rainbows like they stare at the sun.

>>9696740
this can't be true.

>>9696698
>how many engines it would take to shoot a bowl of spaghetti into space.
so let's say your shitty non-aerodynamic payload is about 5 kilograms of dry mass, to achieve 9 km/s or about 32'000km/h you'd need ~500 kilograms of fuel with a specific impulse of 200 seconds. for 250 seconds it's ~200 kilograms, a total payload of around ~205kg reaching a total delta v of 32'000km/h in around 250 seconds with an average acceleration of ~3.75g
give or take a few drinks

>>9692422
2310 single sitting, 2360 superscore

>>9696743
sugar is a reflective substance in water and it doesn't' absorb light, so it would be somewhat more reflective, not to mention all the other shit in coke. Pic somewhat related, look at all the shiny shit in that pop!

>>9696749
we have plausibility!

>>9696759
770 reading 740 math 800 writing

>>9696630
anyone please help

>>9696760
>we have plausibility!
not quite
still, since the payload would be so light, solid fuel could be easily rigged up, and half a ton of it doesn't sound too unrealistic, and I assume the thrust range would not be way off either.

Could something like this actually work for an amateurish launch? No. Sure, you could probably reach a pretty high altitude with it, but in no real fucking way are you getting in LEO with a single stage rocket, no matter how little the payload. The thought experiment also loses itself in a way of aerodynamic losses, additional dry mass for the payload and some other minutiae that are the reason you won't go to space today.

Any biologist here?
Im and undergrad student who is studying biology, and we have this course where they are going to throw us into the wild for 1 day to make up an study about ecology, but i can't get an idea to what would be interesting to observe and study, given the time (no more than 6 hours) and lack of instruments (copybook and eyes). Because is ecology they tell us they want to see interactions between species, or types of distribution among them, but i have been thinking calculating diversity or species richness with an independent variable may be enough. Anyone would like to recommend me something to do?

>>9696764
>lowest score is in math while the highest is in writing
wtf bizarro world did you come from?

>>9696658
because it doesn't start at 0

>>9692414
If I show you to observe the meta pattern of primes will you steal it?

>>9697343
If you post it on math.stackexchange and sign your name at the bottom people will give you proper credit.

Pretty sure that's what that guy did who discovered the millennium prize problem. Except he didn't even sign his name on it, and he got tracked down by the government.

Does anyone know if this is a safe download

https://www.xoobooks.com/book/inorganic-chemistry-6th-edition/

Or what board should I ask?

>>9696658
That's not what the geometric series/progression says. It says that if [math]|r|<1 [/math] then

[eqn]\sum_{n=1}^\infty ar^{n-1} \longrightarrow \frac{a}{1-r}[/eqn]

not [math] ar^n[/math]

Why is the question often posed as: is light a wave or particle ? Aren't waves simply disturbances of matter ? So it would be impossible for a wave to exist without there being something there to disturb ? So shouldn't the question really be like why are these particles of light being disturbed in the same manner as waves ?

So hard to find explanation that isn't simplified or just DUDE WEED LMAO.

>>9697347
>Pretty sure that's what that guy did who discovered the millennium prize problem. Except he didn't even sign his name on it, and he got tracked down by the government.

Only the Poincaré conjecture has been solved and his solution was submitted as white papers to https://arxiv.org/ not stack exchange answers.

Why do stationary waves always start and end either with a node or an antinode? Can't they be in-between?

>>9697451
Because then it couldn't be a standing wave
It would interfere with itself in such way as to stop being standing and start shifting

I asked /diy/ for help on this but the method described was rather difficult and involved many electrical components and wiring, which I will consider but wondering if there are any more practical approaches

I have to build a prototype showing pic related accurately

A motor and sensor achieving 20 rad/s isn't that hard, but I need torque of 30 N*m in the opposite direction


Are there any other decent alternatives which could keep such consistency?

>>9697482
I don't know if this is practical or realistic, but take a wire and run a linearly increasing current from the base to the top. The top would be a battery to collect the energy, and the bottom would be the input.

The linearly changing current creates a curling magnetic field in the direction of M. If the weights are polarized (with a north and south pole at the sides), they should move in the direction you need them to.

>>9692414
You have 6 men who can dig 2500 gram per second.

With 24 men working at the same pace you should optimally finish digging in about 10-12 minutes.

So to keep this pace with additional workers we need to wet the dirt with a water for every worker more than 24.

every water you add will slow their pace by 4%.

So how many water will you have to add for them to keep the pace similar?

>>9697391
Yeah but you still wouldn't multiply the numerator by r.

>>9692422
I didn't

>>9692440
It's a way of thinking, that's how it's valid

And its accurate enough for most everyday tasks
But not accurate enough for science

>>9696013
The class P (standing for polynomial-time) is defined as:

[math] P = {L | for some polynomial time Turing Machine M, L = L(M)} [/math]

The class NP (standing for non-deterministic polynomial time) is defined as:

[math] NP = {L | for some polynomial time Non-deterministic Turing Machine M, L = L(M)} [/math]

It follows from the definition of P and NP that any problem which is in P is also in NP; this is because a polynomial-time DTM (deterministic TM) to solve the problem can be turned into a polynomial-time NDTM which simply ignores the guesses altogether. Thus [math] P \subseteq NP [/math]

It is widely believed, but not known, that [math] P \neq NP [/math]. The question is whether or not the two classes are equal is knows as the "P versus NP" problem, and is one of the most important unsolved problems in mathematics and computing.

>>9697567
your brainlet version of the geometric series [math]\sum_{n=1}^{\infty}ar^{n}[/math] behaves like this:

[eqn]\sum_{n=1}^{\infty}ar^{n} = \sum_{n=1}^{\infty}ar^{n-1} - a r^0 \longrightarrow \frac{a}{1-r} - a=\frac{ar}{1-r} [/eqn]

so yes you do multiple the numerator with r in this special case

Why is Latex not working...

[eqn] \sum_{n=1}^{\infty}ar^{n} [/eqn] behaves like this:
[eqn] \sum_{n=1}^{\infty}ar^{n} = \sum_{n=1}^{\infty}ar^{n-1} - a r^0 \longrightarrow \frac{a}{1-r} - a=\frac{ar}{1-r} [/eqn]
so yes you do multiple the numerator with r in this special case

Why is

Kinetic Energy
+
Potential Energy
=
Constant
?

How is it proven?

>>9697757
>How is it proven?
It isn't.
It is the conservation of Energy, the first law of thermodynamics.

>>9697757

Actually conservation of energy is only meaningful in a statistical context. Aside from this : by using noethers theorem you can show its the same as a system having a symmetry in time, and this you can show pretty easily

FUCK FUCK FUCK

ACCIDENTALLY WROTE

10^pH - 10^pKa = 10^(pH-pKa)

ON MY LAB REPORT

THE TA EVEN MARKED IT RIGHT

FUCK THIS SHIT IM OUT

>>9697757
Wait, I actually think I found out why.

Consider the integral
[math]
\int_{t_1}^{t_2} F \cdot d\gamma
[/math]
which is the work of a force F (coming from a conservative force field) on a path γ.

Viewing that force as a generic force (not just from a conservative field) we compute:
[math]
\int_{t_1}^{t_2} F \cdot d\gamma = \\
\int_{t_1}^{t_2} F(\gamma(t)) \cdot \dot{\gamma}(t) dt = \\
\int_{t_1}^{t_2} m \ddot{\gamma}(t) \cdot \dot{\gamma(t)} dt = \\
\frac{m}{2} \int_{t_1}^{t_2} \lVert \dot{\gamma}(t) \rVert ^2 dt = \\
\frac{m}{2} (\lVert \dot{\gamma}(t_2) \rVert ^2 -\lVert \dot{\gamma}(t_1) \rVert ^2)
[/math]
Assuming zero initial velocity we get
[math]
\frac{m}{2} \lVert \dot{\gamma}(t_2) \rVert ^2
[/math]

Now, viewing that force as coming from a conservative field we compute:
[math]
\int_{t_1}^{t_2} F \cdot d\gamma = \\
-\int_{t_1}^{t_2} \nabla U \cdot d\gamma = \\
-\int_{t_1}^{t_2} \nabla U(\gamma(t)) \cdot \dot{\gamma}(t) dt = \\
-\int_{t_1}^{t_2} \frac{d(U \circ \gamma)}{dt} dt = \\
U(\gamma(t_1))-U(\gamma(t_2) )
[/math]

Both of the above are equal to the original integral, therefore
[math]
\frac{m}{2} \lVert \dot{\gamma}(t_2) \rVert ^2 = U(\gamma(t_1))-U(\gamma(t_2) ) \implies \\
U(\gamma(t_1)) = U(\gamma(t_2) ) + \frac{m}{2} \lVert \dot{\gamma}(t_2) \rVert ^2
[/math]

>>9697798
my retard ta just looked at the final result, which was only correct because i got super lucky and my mistake ended up leading to the right answer anyway

>>9697805
Actually no need to assume zero initial velocity, just keep it and put it at the left hand side at the end.
And using t0 for t1 and t for t2 makes things more clear.

If there was a machine that you could plug yourself into to experience maximized pleasure, joy, euphoria etc. Until the day you die and it'd always feel novel to you but you would of course have to leave the world you know behind. Would you /sci/?

>>9697832
Of course?

>>9697832
Anyone who says no is lying.

>>9697832
No.

>>9697892
Why would I lie?

>>9697894
Ignorance, mostly.
Contrarianism could also be a factor.

>>9697832
no. did you miss that after school special when you were a kid?

>>9697898
>Ignorance
Then I wouldn't be lying.

>Contrarianism
I am sure the majority wouldn't do it.

>>9692414
I've got a final in 2 hours, how do I chill the fuck out? It's over the whole semester and i'm going back over all the old material and feel rusty as fuck. I pretty much just memorized things enough to pass the tests, but now I have to memorize everything at once.

>>9697906
>Then I wouldn't be lying.
So it's ignorance then. Thanks for clearing it up for me.

In a cyclotron, a charged particle spirals out of the center guided by a magnetic field and gaining kinetic energy from an electric field every half-cycle.

Why is the centripetal force only equal to the magnetic force? Why is it not equal to both the magnetic force and the electric force?

>>9696481
Mech.

>>9697926
A charged particle in a magnetic field will orbit around the direction of the field.

The electric field created by the particle can't do work on itself, so it doesn't contribute to the kinetic energy.

What is the Dirichlet generating function for the sequence 1, 1, 1, 1, 1, ... ?

>>9697939

I meant the electric field from the cyclotron's voltage input in the center gap.

>>9697945
Hint:
[eqn]\forall n\,\in\,\mathbf N^*,\,a_n\ =\ 1\ \Rightarrow\ \sum_{n\ =\ 1}^\infty\frac{a_n}{n^s}\ =\ \sum_{n\ =\ 1}^\infty\frac1{n^s}[/eqn]

>>9693408
most American universities, both large and small. For instance, Indiana University, Rutgers University, Florida State University. The list is very long with a GPA like that.

Using Biot-Savart Law, how do I find the angles for (ui/4piD)(costheta1-costheta2)?

I’ve divided the wires into 3 segments. I know that the first angle should be what comes first in the direction of the current, so my first angle would be 90degrees. But why is the second angle 135 and not 45?
For the 3rd segment, should my first angle be 45 and second angle be 135?
These angles make sense because I end up with a non-negative answer, but I don’t know why they should be 135 instead of 45

>>9697832
Not yet buddy

>>9697947
Oh ok. It has to do with the geometry. Since the e-field alternates, the average force on the particle is 0. (Being pushed as much as pulled)

It does get a kick from the e field every time it is exactly perpendicular, assuming the timing of the signal is correct. If the square wave phase is off by around pi, the particle will slow down. But it's a decent sized tolerance.

>>9698135
You have to remember the r vector in the bio savart. r^ = r - r'.

In other words, you have a vector from the origin to p and a vector from the origin to some dx along the current. If you use the angle you drew, you're measuring the opposite side, not the adjacent so the difference will be 180 - opposite.

>>9692414
How do I into Taylor series?

>>9698423
Which angle are you talking about?

The clouds started closing in and the sun was moving down, what the fuck was going on in th sky?

>>9698563
fuck, this was the pic I meant.

What’s the best way to learn the basics of linear algebra in a few months? I might need it at the end of a numerical analysis class but I have no serious background in it.

I cannot fucking wrap my head around Bessel functions and Legendre polynomials. plz help

>>9698568
Pick Sheldon Axler's book "Linear Algebra Done Right".

>>9698572
For spherical harmonics? It's just simple algebra/trig.

>>9698525
Just follow the formula.

any good youtube channels for discrete math, abstract algebra and real analysis?

>>9698614
What about error?

Stupid stats question.

I have a library of 10,000 elements.

I take a random sample of 3000.

Library elements can be sampled multiple times, both within a sample and between samples.

How many times do I need to sample the library to get 95% of the library elements?

I also want to make this general, so say I pull X% of my library in a given sample, how many samples are required to get Y% of total library elements?

>>9694946
>>9694929
>taking intro to differential forms
>pretty smooth going, lots of motivation/intuition from undergrad calc but no slouch in rigor

>nearing the end of the semester, professor decides to switch up the content from the usual "differential forms on differentiable manifolds" to studying forms on de Rham cohomology
>uses this to move us into general cohomology and homotopy theory
>this_isnt_what_i_signed_up_for.jpg

Admittedly it's pretty interesting and, since I'm not going to pursue any branch of mathematics like this in the future (my major is in the natural sciences, not mathematical), I'm glad to get a taste for this stuff. Still, it's going hella fast and is way different from anything I've ever studied in math. Shame I'll never use it after this course.

>>9698572
You're missing the point. Two dudes figured them out 200 years ago, so now you don't have to.

>>9698660
Not according to my teacher.
Although, to be fair, he's got to be like 8 million years old by now.

>>9694618
fuckin dick

>>9695178
youre a fucking brainlet anyway for your whole life situation leading up to here enjoy dropping out of college when you have to take actually difficult classes

>>9696658
write out the first terms u fucken brainlet

>>9696670
You can get something high enough to see the earth's curvature using just big ass balloons btw

>>9698627
nigga just double check ur work

is it possible for a sound to be heard in every corner of the world?

>>9692422
2

>>9692422
>taking SAT

>>9693408
American unis care more about what you did in school than your GPA. They're more likely to accept someone who took all AP classes and got a 2.9 GPA than someone who didn't take algebra until his junior year and got a 4.0

>>9694797
If a and b are real numbers then its easy. You just equate the real and imaginary portions then solve the simultaneous. But if "this is
for complex numbers" means a and b can also be imaginary then its a bit harder to solve. I dont want to try until you are more specific.

A^3-b^2 = 4
2a^2 *bi = 6 i

But then if a and b can be imaginary you have to minus RHS and then factorise then use null factor law.

>>9694661
Yeah, he's just asking very specific questions about a very easy level proof with no passion behind them at all because he's doing it for fun.

>>9692422
2170/2400

>>9698627
If the series converges, then the series is exactly equal to the function. The series will converge if f^(n)(0) (f^(n) being the nth derivative of f) grows more slowly than n! (which isn't a difficult requirement, given how fast n! grows).

The difference between a Taylor polynomial (a finite number of initial terms of the sequence) and the function is equal to the sum of the remaining terms; if the sequence converges, the sum is finite.

>>9696178

Why does this anon get a reply but I don't? Genuinely struggling with defining this...

>>9694659

>>9699195
there are functions with taylor series which converge but not to the original function

>>9692422
Way above average.
I cheated.

Im teaching myself edexcel a level further maths taking tests this time next year. Ill have 4 tests to prepare for and im lost when it comes to how to keep on top of this much work. Not in the sense of getting through it but crunching it down so i dont have to sift through 600+ pages of shit when im revising. So, stupid question time, how do i decide what is important and what isnt?

Is it possible to graduate undergrad maths without touching analysis in the final year? I'm very, very close to hanging myself

>>9699275
not in my eyes

If 2 + 2 = Fish. Then who eats it?

Nobody answered my question about the sun coming down through the clouds

>>9698563
>>9698566

>>9699275
>Is it possible to graduate undergrad maths without touching analysis in the final year?
Yes.

How do we get people to help space exploration with their own devices the same way they mine for crypto currency?